2020-07-10T00:13:12Z
https://researchspace.auckland.ac.nz/dspace-oai/request
oai:researchspace.auckland.ac.nz:2292/4965
2009-08-28T12:30:37Z
com_2292_122
col_2292_4963
2009-08-28T03:20:20Z
2009-08-28T03:20:20Z
2008-07
2008-07
http://hdl.handle.net/2292/4965
We extend the Gibbard-Satterthwaite theorem in the following way. We prove that an onto, non-dictatorial social choice rule which is employed to choose one of at least three alternatives is safely manipulable. This means that on occasion a voter will have an incentive to make a strategic vote and know that he will not be worse off regardless of how other voters with similar preference orders would vote, sincerely or not.
Is It Ever Safe to Vote Strategically?
Slinko, Arkadii
White, Shaun
We extend the Gibbard-Satterthwaite theorem in the following way. We prove that an onto, non-dictatorial social choice rule which is employed to choose one of at least three alternatives is safely manipulable. This means that on occasion a voter will have an incentive to make a strategic vote and know that he will not be worse off regardless of how other voters with similar preference orders would vote, sincerely or not.
Technical Report
Department of Mathematics - Research Reports-563 (2008)
1173-0889
http://hdl.handle.net/2292/4965
Research Reports - Department of Mathematics
https://researchspace.auckland.ac.nz/docs/uoa-docs/rights.htm
The author(s)
Department of Mathematics, The University of Auckland, New Zealand
http://www.math.auckland.ac.nz/Research/Reports/view.php?id=563
https://researchspace.auckland.ac.nz/bitstream/2292/4965/1/563.pdf
6d6ad529eecd998a9bc5b79b7f7c5983
https://researchspace.auckland.ac.nz/bitstream/2292/4965/2/563.pdf.txt
f98b75b7761c80138c9dec6e0b83dfba
oai:researchspace.auckland.ac.nz:2292/4966
2009-08-28T12:30:40Z
com_2292_122
col_2292_4963
2009-08-28T03:20:24Z
2009-08-28T03:20:24Z
2006-11
2006-11
http://hdl.handle.net/2292/4966
Some new results about linearly Lindelof spaces are given here. It is proved that if X is a space of countable spread and X=Y U Z, where Y and Z are meta-Lindelof spaces, then X is linearly Lindelof. Moreover, we give a positive answer to a problem raised by A.V. Arhangel'skii and R.Z. Buzyakova.
Some results on Linearly Lindelof spaces
Guo, Hongfeng
Jiang, Shouli
Some new results about linearly Lindelof spaces are given here. It is proved that if X is a space of countable spread and X=Y U Z, where Y and Z are meta-Lindelof spaces, then X is linearly Lindelof. Moreover, we give a positive answer to a problem raised by A.V. Arhangel'skii and R.Z. Buzyakova.
Technical Report
Department of Mathematics - Research Reports-553 (2006)
1173-0889
http://hdl.handle.net/2292/4966
Research Reports - Department of Mathematics
https://researchspace.auckland.ac.nz/docs/uoa-docs/rights.htm
The author(s)
Department of Mathematics, The University of Auckland, New Zealand
http://www.math.auckland.ac.nz/Research/Reports/view.php?id=553
https://researchspace.auckland.ac.nz/bitstream/2292/4966/1/553.pdf
a815a63d6409104d9228dd15128d5fea
https://researchspace.auckland.ac.nz/bitstream/2292/4966/2/553.pdf.txt
972d254aeda518fe1c86c531f4073160
oai:researchspace.auckland.ac.nz:2292/4967
2009-08-28T12:30:42Z
com_2292_122
col_2292_4963
2009-08-28T03:20:25Z
2009-08-28T03:20:25Z
2001-04
2001-04
http://hdl.handle.net/2292/4967
This paper concerns (redundant) representations in a Hilbert space $H$ of the form $$ f = sum_j c_jinpro{f,phi_j}phi_j, qquad forall fin H. $$ These are more general than those obtained from a tight frame, and we develop a general theory based on what are called signed frames. We are particularly interested in the cases where the scaling factors $c_j$ are unique and the geometric interpretation of negative $c_j$. This is related to results about the invertibility of certain Hadamard products of Gram matrices which are of independent interest, e.g., we show for almost every $v_1,ldots,v_ninCC^d$ $$ rank([inpro{v_i,v_j}^roverline{inpro{v_i,v_j}}^s]) = min{{r+d-1choose d-1}{s+d-1choose d-1},n}, qquad r,sge0. $$ Applications include the construction of tight frames of bivariate Jacobi polynomials on a triangle which preserve symmetries, and numerical results and conjectures about the class of tight frames in a finite dimensional space.
Signed frames and Hadamard products of Gram Matrices
Peng, Irine
Waldron, Shayne
This paper concerns (redundant) representations in a Hilbert space $H$ of the form $$ f = sum_j c_jinpro{f,phi_j}phi_j, qquad forall fin H. $$ These are more general than those obtained from a tight frame, and we develop a general theory based on what are called signed frames. We are particularly interested in the cases where the scaling factors $c_j$ are unique and the geometric interpretation of negative $c_j$. This is related to results about the invertibility of certain Hadamard products of Gram matrices which are of independent interest, e.g., we show for almost every $v_1,ldots,v_ninCC^d$ $$ rank([inpro{v_i,v_j}^roverline{inpro{v_i,v_j}}^s]) = min{{r+d-1choose d-1}{s+d-1choose d-1},n}, qquad r,sge0. $$ Applications include the construction of tight frames of bivariate Jacobi polynomials on a triangle which preserve symmetries, and numerical results and conjectures about the class of tight frames in a finite dimensional space.
Technical Report
Department of Mathematics - Research Reports-462 (2001)
1173-0889
http://hdl.handle.net/2292/4967
Research Reports - Department of Mathematics
https://researchspace.auckland.ac.nz/docs/uoa-docs/rights.htm
The author(s)
Department of Mathematics, The University of Auckland, New Zealand
http://www.math.auckland.ac.nz/Research/Reports/view.php?id=462
https://researchspace.auckland.ac.nz/bitstream/2292/4967/1/462.pdf
de305230850bbda270e97c96d0a93087
https://researchspace.auckland.ac.nz/bitstream/2292/4967/2/462.pdf.txt
a71b3d0517b3153ddfa270110c7b6c81
oai:researchspace.auckland.ac.nz:2292/4968
2009-08-28T12:30:43Z
com_2292_122
col_2292_4963
2009-08-28T03:20:27Z
2009-08-28T03:20:27Z
2001-04
2001-04
http://hdl.handle.net/2292/4968
In this paper we introduce the concept of F-consistency of a social choice function relative to the given class F of social choice functions. This refines the concept of consistency (self-selectivity), introduced by the first author, and allows to discover a number of classes F for which there exist F-consistent social choice functions which are neither dictatorial nor antidictatorial. Furthermore, under certain mild conditions on F all F-consistent social choice functions are described.
On consistent social choice functions
Koray, Semih
Slinko, Arkadii
In this paper we introduce the concept of F-consistency of a social choice function relative to the given class F of social choice functions. This refines the concept of consistency (self-selectivity), introduced by the first author, and allows to discover a number of classes F for which there exist F-consistent social choice functions which are neither dictatorial nor antidictatorial. Furthermore, under certain mild conditions on F all F-consistent social choice functions are described.
Technical Report
Department of Mathematics - Research Reports-461 (2001)
1173-0889
http://hdl.handle.net/2292/4968
Research Reports - Department of Mathematics
https://researchspace.auckland.ac.nz/docs/uoa-docs/rights.htm
The author(s)
Department of Mathematics, The University of Auckland, New Zealand
http://www.math.auckland.ac.nz/Research/Reports/view.php?id=461
https://researchspace.auckland.ac.nz/bitstream/2292/4968/1/461.ps
aa34f5a065285105d71e13b620f1c94b
https://researchspace.auckland.ac.nz/bitstream/2292/4968/2/461.pdf
2932103c6df2ade441da3fdf8185c9cc
https://researchspace.auckland.ac.nz/bitstream/2292/4968/3/461.pdf.txt
b2d57786036ca6728c3d54723d230f5f
oai:researchspace.auckland.ac.nz:2292/4969
2009-08-28T12:35:31Z
com_2292_122
col_2292_4963
2009-08-28T03:20:28Z
2009-08-28T03:20:28Z
2001
2001
http://hdl.handle.net/2292/4969
The purpose of a reservoir offset is to enable the application of calibration data ($mu(theta)$, emph{e.g.} shortciteNP{stuiver:98}) developed for one reservoir (primary reservoir) to CRA's from another (secondary reservoir). The usual approach has been to define the activity of the secondary reservoir as some form of constant offset (with error) from the primary reservoir (emph{e.g.} citeNP{stuiver93:_model_bc}). In this case CRA's from a secondary reservoir are not independent. However, the standard procedure for incorporating offset error into calibrated distributions assumes that the CRA's from secondary reservoirs are independent ({it e.g.} citeNP{stuiver93b}), accordingly the calibrated distributions are incorrect. In many cases this calculation error will be insignificant, however the calculation error will be significant in some situations and approaches such as sample based Bayesian inference need to be adopted if a non independent reservoir offset is applied.
Reservoir offset models for Radiocarbon calibration
Jones, Martin
Nicholls, Geoff
The purpose of a reservoir offset is to enable the application of calibration data ($mu(theta)$, emph{e.g.} shortciteNP{stuiver:98}) developed for one reservoir (primary reservoir) to CRA's from another (secondary reservoir). The usual approach has been to define the activity of the secondary reservoir as some form of constant offset (with error) from the primary reservoir (emph{e.g.} citeNP{stuiver93:_model_bc}). In this case CRA's from a secondary reservoir are not independent. However, the standard procedure for incorporating offset error into calibrated distributions assumes that the CRA's from secondary reservoirs are independent ({it e.g.} citeNP{stuiver93b}), accordingly the calibrated distributions are incorrect. In many cases this calculation error will be insignificant, however the calculation error will be significant in some situations and approaches such as sample based Bayesian inference need to be adopted if a non independent reservoir offset is applied.
Technical Report
Department of Mathematics - Research Reports-459 (2001)
1173-0889
http://hdl.handle.net/2292/4969
Research Reports - Department of Mathematics
https://researchspace.auckland.ac.nz/docs/uoa-docs/rights.htm
The author(s)
Department of Mathematics, The University of Auckland, New Zealand
http://www.math.auckland.ac.nz/Research/Reports/view.php?id=459
https://researchspace.auckland.ac.nz/bitstream/2292/4969/1/459.pdf
c0a8bbf93114c87409fa91f48848ed6e
https://researchspace.auckland.ac.nz/bitstream/2292/4969/2/459.pdf.txt
ee4d1b26cc386e92586e9ab585817b7b
oai:researchspace.auckland.ac.nz:2292/4970
2009-08-28T12:35:44Z
com_2292_122
col_2292_4963
2009-08-28T03:20:29Z
2009-08-28T03:20:29Z
2000-10
2000-10
http://hdl.handle.net/2292/4970
We show that, when the number of voters $n$ tends to infinity, all classical social choice rules are asymptotically strategy-proof with the proportion of manipulable profiles being of order $O(1/sqrt{n})$.
On Asymptotic Strategy-Proofness of Classical Social Choice Rules
Slinko, Arkadii
We show that, when the number of voters $n$ tends to infinity, all classical social choice rules are asymptotically strategy-proof with the proportion of manipulable profiles being of order $O(1/sqrt{n})$.
Technical Report
Department of Mathematics - Research Reports-458 (2000)
1173-0889
http://hdl.handle.net/2292/4970
Research Reports - Department of Mathematics
https://researchspace.auckland.ac.nz/docs/uoa-docs/rights.htm
The author(s)
Department of Mathematics, The University of Auckland, New Zealand
http://www.math.auckland.ac.nz/Research/Reports/view.php?id=458
https://researchspace.auckland.ac.nz/bitstream/2292/4970/1/458.pdf
795404ff436c176bbc7d05f6acf8a70c
https://researchspace.auckland.ac.nz/bitstream/2292/4970/2/458.pdf.txt
450ceb81b5dee13dddde933fdbdf0ba7
oai:researchspace.auckland.ac.nz:2292/4971
2009-08-28T12:35:44Z
com_2292_122
col_2292_4963
2009-08-28T03:20:30Z
2009-08-28T03:20:30Z
2000
2000
http://hdl.handle.net/2292/4971
In this note we check the interesting recent results of Gomez Portugal Aguilar {it et al} cite{aguilar00}. These authors fit a simple random walk with Gaussian increments to the radiocarbon calibration curve. They suggest that the posterior standard deviation of the calibration curve is smaller between years where observations were made than it is at those years. We find that in contrast to their result the posterior standard deviations of the calibration curve bow out slightly between observation points in our estimates, for a model of the kind they describe. In earlier work Christen~cite{christen94} conditions the random walk to visit the measured calibration values. Following cite{aguilar00}, we consider the unconditioned posterior distribution for calibration curves, and thereby improve slightly on the reconstructions of cite{christen94}.
Random-walk radiocarbon calibration
Nicholls, Geoff
Christen, J Andres
In this note we check the interesting recent results of Gomez Portugal Aguilar {it et al} cite{aguilar00}. These authors fit a simple random walk with Gaussian increments to the radiocarbon calibration curve. They suggest that the posterior standard deviation of the calibration curve is smaller between years where observations were made than it is at those years. We find that in contrast to their result the posterior standard deviations of the calibration curve bow out slightly between observation points in our estimates, for a model of the kind they describe. In earlier work Christen~cite{christen94} conditions the random walk to visit the measured calibration values. Following cite{aguilar00}, we consider the unconditioned posterior distribution for calibration curves, and thereby improve slightly on the reconstructions of cite{christen94}.
Technical Report
Department of Mathematics - Research Reports-457 (2000)
1173-0889
http://hdl.handle.net/2292/4971
Research Reports - Department of Mathematics
https://researchspace.auckland.ac.nz/docs/uoa-docs/rights.htm
The author(s)
Department of Mathematics, The University of Auckland, New Zealand
http://www.math.auckland.ac.nz/Research/Reports/view.php?id=457
https://researchspace.auckland.ac.nz/bitstream/2292/4971/1/457.pdf
6f1fc818fc7fb50903a8d7eabdca564a
https://researchspace.auckland.ac.nz/bitstream/2292/4971/2/457.pdf.txt
2fa4e64f4a2ff4c66bbaa7240389b949
oai:researchspace.auckland.ac.nz:2292/4972
2009-08-28T12:35:45Z
com_2292_122
col_2292_4963
2009-08-28T03:20:31Z
2009-08-28T03:20:31Z
2003-09
2003-09
http://hdl.handle.net/2292/4972
Bridge estimation, as described by Meng and Wong in 1996, is used to estimate the value taken by a probability density at a point in the state space. When the normalisation of the prior density is known, this value may be used to estimate a Bayes factor. It is shown that the multi-block Metropolis-Hastings estimators of citeN{chib01} are bridge sampling estimators. This identification leads to estimators for the quantity of interest which may be substantially more efficient. This report was submitted in July 2000. A revised version of this report was submitted in September 2003. The version below is the revised version. Print and electronic copies of the original version are available on request.
Bridge estimation of the probability density at a point
Mira, Antonietta
Nicholls, Geoff
Bridge estimation, as described by Meng and Wong in 1996, is used to estimate the value taken by a probability density at a point in the state space. When the normalisation of the prior density is known, this value may be used to estimate a Bayes factor. It is shown that the multi-block Metropolis-Hastings estimators of citeN{chib01} are bridge sampling estimators. This identification leads to estimators for the quantity of interest which may be substantially more efficient. This report was submitted in July 2000. A revised version of this report was submitted in September 2003. The version below is the revised version. Print and electronic copies of the original version are available on request.
Technical Report
Department of Mathematics - Research Reports-456 (2003)
1173-0889
http://hdl.handle.net/2292/4972
Research Reports - Department of Mathematics
https://researchspace.auckland.ac.nz/docs/uoa-docs/rights.htm
The author(s)
Department of Mathematics, The University of Auckland, New Zealand
http://www.math.auckland.ac.nz/Research/Reports/view.php?id=456
https://researchspace.auckland.ac.nz/bitstream/2292/4972/1/456.pdf
387b34015ad71c214a378e94a32af40c
https://researchspace.auckland.ac.nz/bitstream/2292/4972/2/456.pdf.txt
5677e86d27071a1b9916345d0f204520
oai:researchspace.auckland.ac.nz:2292/4973
2009-08-28T12:35:47Z
com_2292_122
col_2292_4963
2009-08-28T03:20:32Z
2009-08-28T03:20:32Z
2000
2000
http://hdl.handle.net/2292/4973
The Arak process is a solvable stochastic process which generates coloured patterns in the plane. Patterns are made up of a variable number of random non-intersecting polygons. We show that the distribution of Arak process states is the Gibbs distribution of its states in thermodynamic equilibrium in the grand canonical ensemble. The sequence of Gibbs distributions form a new model parameterised by temperature. We prove that there is a phase transition in this model, for some non-zero temperature. We illustrate this conclusion with simulation results. We measure the critical exponents of this off-lattice model and find they are consistent with those of the Ising model in two dimensions.
Spontaneous magnetisation in the plane
Nicholls, Geoff
The Arak process is a solvable stochastic process which generates coloured patterns in the plane. Patterns are made up of a variable number of random non-intersecting polygons. We show that the distribution of Arak process states is the Gibbs distribution of its states in thermodynamic equilibrium in the grand canonical ensemble. The sequence of Gibbs distributions form a new model parameterised by temperature. We prove that there is a phase transition in this model, for some non-zero temperature. We illustrate this conclusion with simulation results. We measure the critical exponents of this off-lattice model and find they are consistent with those of the Ising model in two dimensions.
Technical Report
Department of Mathematics - Research Reports-455 (2000)
1173-0889
http://hdl.handle.net/2292/4973
Research Reports - Department of Mathematics
https://researchspace.auckland.ac.nz/docs/uoa-docs/rights.htm
The author(s)
Department of Mathematics, The University of Auckland, New Zealand
http://www.math.auckland.ac.nz/Research/Reports/view.php?id=455
https://researchspace.auckland.ac.nz/bitstream/2292/4973/1/455.pdf
4f10901da89699ea8c7f23eb8820cb2a
https://researchspace.auckland.ac.nz/bitstream/2292/4973/2/455.pdf.txt
fd473f06617fd86871c4829b8258aa64
oai:researchspace.auckland.ac.nz:2292/4974
2009-08-28T12:35:48Z
com_2292_122
col_2292_4963
2009-08-28T03:20:33Z
2009-08-28T03:20:33Z
2000
2000
http://hdl.handle.net/2292/4974
In this note, we prove that every countably compact space with quasi--$S_1$--diagonal is compact. However, it is shown that it need not be metrizable.
A Result on $aleph_1$-Compact Spaces
Mohamad, A.M.
In this note, we prove that every countably compact space with quasi--$S_1$--diagonal is compact. However, it is shown that it need not be metrizable.
Technical Report
Department of Mathematics - Research Reports-454 (2000)
1173-0889
http://hdl.handle.net/2292/4974
Research Reports - Department of Mathematics
https://researchspace.auckland.ac.nz/docs/uoa-docs/rights.htm
The author(s)
Department of Mathematics, The University of Auckland, New Zealand
http://www.math.auckland.ac.nz/Research/Reports/view.php?id=454
https://researchspace.auckland.ac.nz/bitstream/2292/4974/1/454.pdf
c264124c06569a4e068b5cb9eeb31633
https://researchspace.auckland.ac.nz/bitstream/2292/4974/2/454.pdf.txt
1c704f52780b308bdd1a1baedb1f557e
oai:researchspace.auckland.ac.nz:2292/4975
2009-08-28T12:35:49Z
com_2292_122
col_2292_4963
2009-08-28T03:20:34Z
2009-08-28T03:20:34Z
2000
2000
http://hdl.handle.net/2292/4975
In this paper we show that a quasi--$G^*_{delta}$--diagonal plays a central role in metrizability. We prove that: if $X$ is a first--countable $GO$--space, then $X$ is metrizable if and only if $X$ is quasi--$sigma$--space; a $wtheta$--space is metrizable if and only if it is a quasi--Nagata space with a quasi--$G^*_{delta}(2)$--diagonal; a linearly ordered space $X$ with a quasi--$G^*_{delta}(2)$--diagonal is a $Theta$--space; a space $X$ is developable if and only if it is a $wtheta$, $beta$--space with a quasi--$G^*_{delta}(2)$--diagonal.
Some Results on Quasi--$sigma$ and $theta$ Spaces
Mohamad, A.M.
In this paper we show that a quasi--$G^*_{delta}$--diagonal plays a central role in metrizability. We prove that: if $X$ is a first--countable $GO$--space, then $X$ is metrizable if and only if $X$ is quasi--$sigma$--space; a $wtheta$--space is metrizable if and only if it is a quasi--Nagata space with a quasi--$G^*_{delta}(2)$--diagonal; a linearly ordered space $X$ with a quasi--$G^*_{delta}(2)$--diagonal is a $Theta$--space; a space $X$ is developable if and only if it is a $wtheta$, $beta$--space with a quasi--$G^*_{delta}(2)$--diagonal.
Technical Report
Department of Mathematics - Research Reports-453 (2000)
1173-0889
http://hdl.handle.net/2292/4975
Research Reports - Department of Mathematics
https://researchspace.auckland.ac.nz/docs/uoa-docs/rights.htm
The author(s)
Department of Mathematics, The University of Auckland, New Zealand
http://www.math.auckland.ac.nz/Research/Reports/view.php?id=453
https://researchspace.auckland.ac.nz/bitstream/2292/4975/1/453.pdf
5a06600e66ab1e4ab43a37a1d87b05ec
https://researchspace.auckland.ac.nz/bitstream/2292/4975/2/453.pdf.txt
b578ce73c0d4215b7ff4523924e2ca25
oai:researchspace.auckland.ac.nz:2292/4976
2009-08-28T12:35:49Z
com_2292_122
col_2292_4963
2009-08-28T03:20:35Z
2009-08-28T03:20:35Z
2000
2000
http://hdl.handle.net/2292/4976
This paper studies spaces with quasi--regular--$G_{delta}$--diagonal. It is shown that if $X$ is a normal space, then the following are equivalent: begin{enumerate} item $X$ admits a development satisfying the $3$--link property. item $X$ is a $wDelta$ with quasi--regular--$G_{delta}$--diagonal. item $X$ is a $wDelta$ with regular--$G_{delta}$--diagonal. item $X$ is $K$--semimetrizable via a semimetric satisfying $(AN)$. item There is a semimetric $d$ on $X$ such that: begin{enumerate} item [a.] if $langle x_n rangle$ and $langle y_n rangle$ are sequences both converging to the same point, then lim $d(x_n,y_n) = 0$, and item [b.] if $x$ and $y$ are distinct points of $X$ and $langle x_n rangle$ and $langle y_n rangle$ are sequences converging to $x$ and $y$, respectively, then there are integers $L$ and $M$ such that if $n > L$, then $d(x_n,y_n) > frac {1}{M}$. end {enumerate} end {enumerate}
On Spaces with Quasi-Regular-$G_{delta}$-Diagonals
Mohamad, A.M.
This paper studies spaces with quasi--regular--$G_{delta}$--diagonal. It is shown that if $X$ is a normal space, then the following are equivalent: begin{enumerate} item $X$ admits a development satisfying the $3$--link property. item $X$ is a $wDelta$ with quasi--regular--$G_{delta}$--diagonal. item $X$ is a $wDelta$ with regular--$G_{delta}$--diagonal. item $X$ is $K$--semimetrizable via a semimetric satisfying $(AN)$. item There is a semimetric $d$ on $X$ such that: begin{enumerate} item [a.] if $langle x_n rangle$ and $langle y_n rangle$ are sequences both converging to the same point, then lim $d(x_n,y_n) = 0$, and item [b.] if $x$ and $y$ are distinct points of $X$ and $langle x_n rangle$ and $langle y_n rangle$ are sequences converging to $x$ and $y$, respectively, then there are integers $L$ and $M$ such that if $n > L$, then $d(x_n,y_n) > frac {1}{M}$. end {enumerate} end {enumerate}
Technical Report
Department of Mathematics - Research Reports-452 (2000)
1173-0889
http://hdl.handle.net/2292/4976
Research Reports - Department of Mathematics
https://researchspace.auckland.ac.nz/docs/uoa-docs/rights.htm
The author(s)
Department of Mathematics, The University of Auckland, New Zealand
http://www.math.auckland.ac.nz/Research/Reports/view.php?id=452
https://researchspace.auckland.ac.nz/bitstream/2292/4976/1/452.pdf
ceb9d845381971b2eebb5e850a2bd9ba
https://researchspace.auckland.ac.nz/bitstream/2292/4976/2/452.pdf.txt
244f594adc0f693583fc15788f002e02
oai:researchspace.auckland.ac.nz:2292/4977
2009-08-28T12:35:51Z
com_2292_122
col_2292_4963
2009-08-28T03:20:36Z
2009-08-28T03:20:36Z
2006-08
2006-08
http://hdl.handle.net/2292/4977
We study holonomy algebras generated by an algebraic element of the Clifford algebra, or equivalently,the holonomy algebras of certain spin connections in flat space. We provide some series of examples in arbitrary dimensions and prove some general properties of the holonomy algebras under some mild conditions on the generating element. We show that the first non-standard situation to look at appears in dimension $8$ and concerns $4$-forms. In this case complete structure results are obtained when moreover assuming the $4$-form to be self-dual.
On algebraic torsion forms and their spin holonomy algebras
Bernhardt, Niels
Nagy, Paul-Andi
We study holonomy algebras generated by an algebraic element of the Clifford algebra, or equivalently,the holonomy algebras of certain spin connections in flat space. We provide some series of examples in arbitrary dimensions and prove some general properties of the holonomy algebras under some mild conditions on the generating element. We show that the first non-standard situation to look at appears in dimension $8$ and concerns $4$-forms. In this case complete structure results are obtained when moreover assuming the $4$-form to be self-dual.
Technical Report
Department of Mathematics - Research Reports-552 (2006)
1173-0889
http://hdl.handle.net/2292/4977
Research Reports - Department of Mathematics
https://researchspace.auckland.ac.nz/docs/uoa-docs/rights.htm
The author(s)
Department of Mathematics, The University of Auckland, New Zealand
http://www.math.auckland.ac.nz/Research/Reports/view.php?id=552
https://researchspace.auckland.ac.nz/bitstream/2292/4977/1/552.pdf
6aa65325feed383f9b6a635a388390e6
https://researchspace.auckland.ac.nz/bitstream/2292/4977/2/552.pdf.txt
1ea6fe0b7d8e4b717370c3c77518cce7
oai:researchspace.auckland.ac.nz:2292/4978
2009-08-28T12:35:51Z
com_2292_122
col_2292_4963
2009-08-28T03:20:37Z
2009-08-28T03:20:37Z
2000
2000
http://hdl.handle.net/2292/4978
In this paper, we study Moore and semi--stratifiable spaces. We give characterizations of developable and semi--stratifiable spaces. We prove that: a regular space $X$ is semi--stratifiable if and only if it is a $beta$, quasi--semi--stratifiable and the following are equivalent for a regular $wDelta$--space $X$: begin{enumerate} item[(a)] $X$ is a Moore space; item[(b)] $X$ is a hereditarily weakly $theta$--refinable space with a quasi--${G}_delta$--diagonal; item[(c)] $X$ is a quasi--${G}^{*}_delta$--diagonal; item[(d)] $X$ is a quasi--semi--stratifiable space; item[(e)] $X$ is a quasi--$alpha$--space. end{enumerate}
Characterizations of Moore and Semi-Stratifiable Spaces
Mohamad, A.M.
In this paper, we study Moore and semi--stratifiable spaces. We give characterizations of developable and semi--stratifiable spaces. We prove that: a regular space $X$ is semi--stratifiable if and only if it is a $beta$, quasi--semi--stratifiable and the following are equivalent for a regular $wDelta$--space $X$: begin{enumerate} item[(a)] $X$ is a Moore space; item[(b)] $X$ is a hereditarily weakly $theta$--refinable space with a quasi--${G}_delta$--diagonal; item[(c)] $X$ is a quasi--${G}^{*}_delta$--diagonal; item[(d)] $X$ is a quasi--semi--stratifiable space; item[(e)] $X$ is a quasi--$alpha$--space. end{enumerate}
Technical Report
Department of Mathematics - Research Reports-451 (2000)
1173-0889
http://hdl.handle.net/2292/4978
Research Reports - Department of Mathematics
https://researchspace.auckland.ac.nz/docs/uoa-docs/rights.htm
The author(s)
Department of Mathematics, The University of Auckland, New Zealand
http://www.math.auckland.ac.nz/Research/Reports/view.php?id=451
https://researchspace.auckland.ac.nz/bitstream/2292/4978/1/451.pdf
4713241d8c91e7f08b218c6c0b600ad4
https://researchspace.auckland.ac.nz/bitstream/2292/4978/2/451.pdf.txt
0c93121547d0268d00dbd7ef719fa9a9
oai:researchspace.auckland.ac.nz:2292/4979
2009-08-28T12:36:32Z
com_2292_122
col_2292_4963
2009-08-28T03:20:38Z
2009-08-28T03:20:38Z
2000
2000
http://hdl.handle.net/2292/4979
In this paper we investigate weak bases. We give a characterization of weakly developable spaces and metrization theorems. The metrization results are: a space $X$ is metrizable if and only if $X$ has a $CWBC$--map $g$ satisfying the following conditions: begin {enumerate} item $g$ is a pseudo--strongly--quasi--N--map; item for any $A subseteq X, overline {A} subseteq bigcup {g(n,x) : x in A }$; end {enumerate} a space $X$ is metrizable if and only if $X$ has a $CWBC$--map $g$ satisfying the following conditions: begin {enumerate} item if $x in g(n,y_n)$, $y_n in g(n,x_n)$, $x_n in g(n,y_n)$ and $y_n in g(n,x)$ for all $n in N$, then $x_n$ converges to $x$; item for any $A subseteq X, overline {A} subseteq bigcup {g(n,x) : x in A }$. end {enumerate}
Weak bases and Metrizability
Mohamad, A.M.
In this paper we investigate weak bases. We give a characterization of weakly developable spaces and metrization theorems. The metrization results are: a space $X$ is metrizable if and only if $X$ has a $CWBC$--map $g$ satisfying the following conditions: begin {enumerate} item $g$ is a pseudo--strongly--quasi--N--map; item for any $A subseteq X, overline {A} subseteq bigcup {g(n,x) : x in A }$; end {enumerate} a space $X$ is metrizable if and only if $X$ has a $CWBC$--map $g$ satisfying the following conditions: begin {enumerate} item if $x in g(n,y_n)$, $y_n in g(n,x_n)$, $x_n in g(n,y_n)$ and $y_n in g(n,x)$ for all $n in N$, then $x_n$ converges to $x$; item for any $A subseteq X, overline {A} subseteq bigcup {g(n,x) : x in A }$. end {enumerate}
Technical Report
Department of Mathematics - Research Reports-450 (2000)
1173-0889
http://hdl.handle.net/2292/4979
Research Reports - Department of Mathematics
https://researchspace.auckland.ac.nz/docs/uoa-docs/rights.htm
The author(s)
Department of Mathematics, The University of Auckland, New Zealand
http://www.math.auckland.ac.nz/Research/Reports/view.php?id=450
https://researchspace.auckland.ac.nz/bitstream/2292/4979/1/450.pdf
fe59c3d017f7389631426c6a69e07499
https://researchspace.auckland.ac.nz/bitstream/2292/4979/2/450.pdf.txt
37c62fe8586392038f048a3d07b9f34f
oai:researchspace.auckland.ac.nz:2292/4980
2009-08-28T12:36:34Z
com_2292_122
col_2292_4963
2009-08-28T03:20:39Z
2009-08-28T03:20:39Z
2000-06
2000-06
http://hdl.handle.net/2292/4980
We compare the efficiency, stability properties, overhead, round-off error propagation and storage requirements of fixed-stepsize high order Stormer and explicit Runge-Kutta Nystrom methods for N-body simulations of the solar system. The comparisons of the round-off error propagation and efficiency are made using realistic problems, one of which requires over 500 million integration steps. We find high order ERKN methods have better stability properties and smaller overhead than Stormer methods. Our numerical tests suggest ERKN methods are more efficient than Stormer methods for shorter simulations such as one that simulates ten million years of the jovian planets. However, the superior round-off error propagation of the Stormer method Comment: a) The Math Reviews classification above is for the 2000 MSC system, b) A pdf version of the file is available with the postscript and dvi versions
Comparisons of high order Stormer and explicit Runge-Kutta Nystrom methods for N-body simulations of the solar system
Sharp, P.W.
We compare the efficiency, stability properties, overhead, round-off error propagation and storage requirements of fixed-stepsize high order Stormer and explicit Runge-Kutta Nystrom methods for N-body simulations of the solar system. The comparisons of the round-off error propagation and efficiency are made using realistic problems, one of which requires over 500 million integration steps. We find high order ERKN methods have better stability properties and smaller overhead than Stormer methods. Our numerical tests suggest ERKN methods are more efficient than Stormer methods for shorter simulations such as one that simulates ten million years of the jovian planets. However, the superior round-off error propagation of the Stormer method Comment: a) The Math Reviews classification above is for the 2000 MSC system, b) A pdf version of the file is available with the postscript and dvi versions
Technical Report
Department of Mathematics - Research Reports-449 (2000)
1173-0889
http://hdl.handle.net/2292/4980
Research Reports - Department of Mathematics
https://researchspace.auckland.ac.nz/docs/uoa-docs/rights.htm
The author(s)
Department of Mathematics, The University of Auckland, New Zealand
http://www.math.auckland.ac.nz/Research/Reports/view.php?id=449
https://researchspace.auckland.ac.nz/bitstream/2292/4980/1/449.pdf
d576d9e4972680dc187998c08e66593c
https://researchspace.auckland.ac.nz/bitstream/2292/4980/2/449.pdf.txt
82149714809821a661e9dd53cf5004dc
oai:researchspace.auckland.ac.nz:2292/4981
2009-08-28T12:36:35Z
com_2292_122
col_2292_4963
2009-08-28T03:20:40Z
2009-08-28T03:20:40Z
2000
2000
http://hdl.handle.net/2292/4981
The analysis of acousto-optic scattering in a single-mode fiber in terms of the effective equation with perturbation caused by variation of the speed of light is done. Using an ansatz based on the Lorentz transform we reduce the corresponding equation to Mathieu equation with a non-canonical small (acousto-optic) parameter. In the lowest order of perturbation theory we calculate the positions and widths of spectral lacunae for the case when the elastic wave is infinite. This result is applied for the estimation of the reflection coefficient $R$ in the lacunae using methods suggested earlier by authors for investigation of periodic nanostructures. We calculate explicitly the reflection coefficient for scattering by a segment of elastic wave of length $L$ and derive the relation $|R_{max}|^2=hbox{rm tanh}^2,(pifrac{L}{c}Deltanu)$ for the maximal reflection coefficient ($c$ stands for the phase velocity of light and $Deltanu$ denotes the width of the reflection band in $Hz$).
Acousto-optic scattering in a single-mode optic fiber
Badanin, A.V.
Pavlov, B.
Pokrovski, A.A.
Prokhorov, L.V.
The analysis of acousto-optic scattering in a single-mode fiber in terms of the effective equation with perturbation caused by variation of the speed of light is done. Using an ansatz based on the Lorentz transform we reduce the corresponding equation to Mathieu equation with a non-canonical small (acousto-optic) parameter. In the lowest order of perturbation theory we calculate the positions and widths of spectral lacunae for the case when the elastic wave is infinite. This result is applied for the estimation of the reflection coefficient $R$ in the lacunae using methods suggested earlier by authors for investigation of periodic nanostructures. We calculate explicitly the reflection coefficient for scattering by a segment of elastic wave of length $L$ and derive the relation $|R_{max}|^2=hbox{rm tanh}^2,(pifrac{L}{c}Deltanu)$ for the maximal reflection coefficient ($c$ stands for the phase velocity of light and $Deltanu$ denotes the width of the reflection band in $Hz$).
Technical Report
Department of Mathematics - Research Reports-448 (2000)
1173-0889
http://hdl.handle.net/2292/4981
Research Reports - Department of Mathematics
https://researchspace.auckland.ac.nz/docs/uoa-docs/rights.htm
The author(s)
Department of Mathematics, The University of Auckland, New Zealand
http://www.math.auckland.ac.nz/Research/Reports/view.php?id=448
https://researchspace.auckland.ac.nz/bitstream/2292/4981/1/448.pdf
b83ace2c71cea78b34705e4be8aeea2d
https://researchspace.auckland.ac.nz/bitstream/2292/4981/2/448.pdf.txt
145b804477936b236fd0e452e74ae367
oai:researchspace.auckland.ac.nz:2292/4982
2009-08-28T12:36:35Z
com_2292_122
col_2292_4963
2009-08-28T03:20:41Z
2009-08-28T03:20:41Z
2000-05
2000-05
http://hdl.handle.net/2292/4982
N-body simulations in astronomy form a challenging set of initial value problems for numerical integrators. The challenge comes from the variety of problems and their size - one recent simulation required 300 million second order equations, another 90 thousand million integration steps. A number of integrators for specific types of simulations are available. We investigate what is required of an integrator intended to efficiently perform a wide range of N-body simulations.
Requirements of an N-body integrator for astronomy
Sharp, P.W.
N-body simulations in astronomy form a challenging set of initial value problems for numerical integrators. The challenge comes from the variety of problems and their size - one recent simulation required 300 million second order equations, another 90 thousand million integration steps. A number of integrators for specific types of simulations are available. We investigate what is required of an integrator intended to efficiently perform a wide range of N-body simulations.
Technical Report
Department of Mathematics - Research Reports-447 (2000)
1173-0889
http://hdl.handle.net/2292/4982
Research Reports - Department of Mathematics
https://researchspace.auckland.ac.nz/docs/uoa-docs/rights.htm
The author(s)
Department of Mathematics, The University of Auckland, New Zealand
http://www.math.auckland.ac.nz/Research/Reports/view.php?id=447
https://researchspace.auckland.ac.nz/bitstream/2292/4982/1/447.pdf
8efe76ea7353df284ffdc7b9e9cbc23e
https://researchspace.auckland.ac.nz/bitstream/2292/4982/2/447.pdf.txt
f5bcc1eb0887a3e5f8d9eca97eaee288
oai:researchspace.auckland.ac.nz:2292/4983
2009-08-28T12:36:36Z
com_2292_122
col_2292_4963
2009-08-28T03:20:41Z
2009-08-28T03:20:41Z
2000
2000
http://hdl.handle.net/2292/4983
For the Laplacean on a compact graph with edges of commensurate length and flux-conserved boundary conditions we provide a description of the spectrum in terms of the geometry of the graph.
A relation between the spectrum of the Laplacean and the geometry of a compact graph
Harmer, M.
For the Laplacean on a compact graph with edges of commensurate length and flux-conserved boundary conditions we provide a description of the spectrum in terms of the geometry of the graph.
Technical Report
Department of Mathematics - Research Reports-446 (2000)
1173-0889
http://hdl.handle.net/2292/4983
Research Reports - Department of Mathematics
https://researchspace.auckland.ac.nz/docs/uoa-docs/rights.htm
The author(s)
Department of Mathematics, The University of Auckland, New Zealand
http://www.math.auckland.ac.nz/Research/Reports/view.php?id=446
https://researchspace.auckland.ac.nz/bitstream/2292/4983/1/446.pdf
43b3ec35578845a4ed3e7ae48036025a
https://researchspace.auckland.ac.nz/bitstream/2292/4983/2/446.pdf.txt
3a0ac193361bb29fb5ee4a14c64d24fc
oai:researchspace.auckland.ac.nz:2292/4984
2009-08-28T12:36:37Z
com_2292_122
col_2292_4963
2009-08-28T03:20:42Z
2009-08-28T03:20:42Z
2000
2000
http://hdl.handle.net/2292/4984
We generalise the asymptotic formula for the scattering matrix in cite{BMPY} to the case of non-simple spectrum. This asymptotic formula is used to identify a simple family of switches and investigate the properties of a member of the family using numerical techniques.
Scattering on the annulus
Harmer, M.
We generalise the asymptotic formula for the scattering matrix in cite{BMPY} to the case of non-simple spectrum. This asymptotic formula is used to identify a simple family of switches and investigate the properties of a member of the family using numerical techniques.
Technical Report
Department of Mathematics - Research Reports-445 (2000)
1173-0889
http://hdl.handle.net/2292/4984
Research Reports - Department of Mathematics
https://researchspace.auckland.ac.nz/docs/uoa-docs/rights.htm
The author(s)
Department of Mathematics, The University of Auckland, New Zealand
http://www.math.auckland.ac.nz/Research/Reports/view.php?id=445
https://researchspace.auckland.ac.nz/bitstream/2292/4984/1/445.pdf
8e348b8e49890017009a9af5475ff6e4
https://researchspace.auckland.ac.nz/bitstream/2292/4984/2/445.pdf.txt
1281786feab6e9d2ef503472a1031117
oai:researchspace.auckland.ac.nz:2292/4985
2009-08-28T12:36:39Z
com_2292_122
col_2292_4963
2009-08-28T03:20:44Z
2009-08-28T03:20:44Z
2000
2000
http://hdl.handle.net/2292/4985
The theory of self-adjoint extensions is closely related to the theory of hermitian symplectic geometry cite{Pav,Kost:Sch,Nov3}. Here we develop this idea, showing that it may also be used to consider symmetric extensions of a symmetric operator. Furthermore we find an explicit parameterisation of the Lagrange Grassmannian in terms of the unitary matrices $U (n)$. This allows us to explicitly describe all self-adjoint boundary conditions for the Schr"{o}dinger operator on the graph in terms of a unitary matrix. We show that the asymptotics of the scattering matrix can be simply expressed in terms of this unitary matrix. \ Using the construction of the asymptotic hermitian symplectic space cite{Nov1,Nov3} we derive a formula for the scattering matrix of a graph in terms of the scattering matrices of its subgraphs. This also provides a characterisation of the discrete eigenvalues embedded in the continuous spectrum.
Hermitian symplectic geometry and the Schr"{o}dinger operator on the graph
Harmer, M.
The theory of self-adjoint extensions is closely related to the theory of hermitian symplectic geometry cite{Pav,Kost:Sch,Nov3}. Here we develop this idea, showing that it may also be used to consider symmetric extensions of a symmetric operator. Furthermore we find an explicit parameterisation of the Lagrange Grassmannian in terms of the unitary matrices $U (n)$. This allows us to explicitly describe all self-adjoint boundary conditions for the Schr"{o}dinger operator on the graph in terms of a unitary matrix. We show that the asymptotics of the scattering matrix can be simply expressed in terms of this unitary matrix. \ Using the construction of the asymptotic hermitian symplectic space cite{Nov1,Nov3} we derive a formula for the scattering matrix of a graph in terms of the scattering matrices of its subgraphs. This also provides a characterisation of the discrete eigenvalues embedded in the continuous spectrum.
Technical Report
Department of Mathematics - Research Reports-444 (2000)
1173-0889
http://hdl.handle.net/2292/4985
Research Reports - Department of Mathematics
https://researchspace.auckland.ac.nz/docs/uoa-docs/rights.htm
The author(s)
Department of Mathematics, The University of Auckland, New Zealand
http://www.math.auckland.ac.nz/Research/Reports/view.php?id=444
https://researchspace.auckland.ac.nz/bitstream/2292/4985/1/444.pdf
3775e2a2bcbe7f29286690599d65d82c
https://researchspace.auckland.ac.nz/bitstream/2292/4985/2/444.pdf.txt
9c84a629074ff9eb78a964737048e23a
oai:researchspace.auckland.ac.nz:2292/4986
2009-08-28T12:36:40Z
com_2292_122
col_2292_4963
2009-08-28T03:20:45Z
2009-08-28T03:20:45Z
2000
2000
http://hdl.handle.net/2292/4986
An {em open ribbon} is a square with one side called the {em seam}. A {em closed ribbon} is a cylinder with one boundary component called the {em seam}. We {em sew} an open (resp.~closed) ribbon onto a graph by identifying the seam with an open (resp.~closed) walk in the graph. A {em ribbon complex} is a graph with a finite number of ribbons sewn on. We investigate when a ribbon complex embeds in 3-dimensional Euclidean space. We give several characterizations of such {em spatial} complexes which lead to algorithms. We examine special cases where: 1) each edge of the graph is incident with at most three ribbons, and 2) every ribbon is closed together with a connectivity condition.
Sewing Ribbons on Graphs in Space
Archdeacon, Dan
Bonnington, Paul
Richter, Bruce
Siran, Jozef
An {em open ribbon} is a square with one side called the {em seam}. A {em closed ribbon} is a cylinder with one boundary component called the {em seam}. We {em sew} an open (resp.~closed) ribbon onto a graph by identifying the seam with an open (resp.~closed) walk in the graph. A {em ribbon complex} is a graph with a finite number of ribbons sewn on. We investigate when a ribbon complex embeds in 3-dimensional Euclidean space. We give several characterizations of such {em spatial} complexes which lead to algorithms. We examine special cases where: 1) each edge of the graph is incident with at most three ribbons, and 2) every ribbon is closed together with a connectivity condition.
Technical Report
Department of Mathematics - Research Reports-443 (2000)
1173-0889
http://hdl.handle.net/2292/4986
Research Reports - Department of Mathematics
https://researchspace.auckland.ac.nz/docs/uoa-docs/rights.htm
The author(s)
Department of Mathematics, The University of Auckland, New Zealand
http://www.math.auckland.ac.nz/Research/Reports/view.php?id=443
https://researchspace.auckland.ac.nz/bitstream/2292/4986/1/443.pdf
77ae936e3cef7d3a52e7240758ed9277
https://researchspace.auckland.ac.nz/bitstream/2292/4986/2/443.pdf.txt
8da58c3873cc9245d48f161061cc18a5
oai:researchspace.auckland.ac.nz:2292/4987
2009-08-28T12:36:40Z
com_2292_122
col_2292_4963
2009-08-28T03:20:46Z
2009-08-28T03:20:46Z
2000
2000
http://hdl.handle.net/2292/4987
In this paper, we study two types of topological games, ${cal G}(x)$-games and ${cal G}({cal F})$-games, and topological spaces defined by them, namely $cal G$-spaces and game-compact spaces. It is shown these games are associated with $kappa$-semi-stratifiabilty, which is the duality of quasi-metrizability. Finally, we apply these games and relevant properties to study multi-valued maps. Consequently, the Choquet-Dolecki theorem on multi-valued maps is deduced. Main results of Hansell et al in cite{Ha} are generalized.
Infinite Games Associated with Asymmetric Topology and Applications
Cao, Jiling
In this paper, we study two types of topological games, ${cal G}(x)$-games and ${cal G}({cal F})$-games, and topological spaces defined by them, namely $cal G$-spaces and game-compact spaces. It is shown these games are associated with $kappa$-semi-stratifiabilty, which is the duality of quasi-metrizability. Finally, we apply these games and relevant properties to study multi-valued maps. Consequently, the Choquet-Dolecki theorem on multi-valued maps is deduced. Main results of Hansell et al in cite{Ha} are generalized.
Technical Report
Department of Mathematics - Research Reports-442 (2000)
1173-0889
http://hdl.handle.net/2292/4987
Research Reports - Department of Mathematics
https://researchspace.auckland.ac.nz/docs/uoa-docs/rights.htm
The author(s)
Department of Mathematics, The University of Auckland, New Zealand
http://www.math.auckland.ac.nz/Research/Reports/view.php?id=442
https://researchspace.auckland.ac.nz/bitstream/2292/4987/1/442.pdf
53e4ed7cb2a6c2142e2c4937c56d1a66
https://researchspace.auckland.ac.nz/bitstream/2292/4987/2/442.pdf.txt
32792ee9a05f4a937c199f59067ee63e
oai:researchspace.auckland.ac.nz:2292/4988
2009-08-28T12:36:41Z
com_2292_122
col_2292_4963
2009-08-28T03:20:47Z
2009-08-28T03:20:47Z
2006-06
2006-06
http://hdl.handle.net/2292/4988
It is known that Dodgson's rule is computationally very demanding. Tideman (1987) suggested an approximation to it but did not investigate how often his approximation selects the Dodgson winner. We show that under the Impartial Culture assumption the probability that that the another approximation - we call it Dodgson Quick - for which thisconvergence of this probability to 1 is slow. We suggest convergence is exponentially fast. Also we show that Simpson and Dodgson rules are asymptotically different. We formulate, and heavily use in construction of examples, the generalization of McGarvey's theorem (1953) for weighted majority relations.
Approximability of Dodgson's rule
McCabe-Dansted, John C.
Pritchard, Geoffrey
Slinko, Arkadii
It is known that Dodgson's rule is computationally very demanding. Tideman (1987) suggested an approximation to it but did not investigate how often his approximation selects the Dodgson winner. We show that under the Impartial Culture assumption the probability that that the another approximation - we call it Dodgson Quick - for which thisconvergence of this probability to 1 is slow. We suggest convergence is exponentially fast. Also we show that Simpson and Dodgson rules are asymptotically different. We formulate, and heavily use in construction of examples, the generalization of McGarvey's theorem (1953) for weighted majority relations.
Technical Report
Department of Mathematics - Research Reports-551 (2006)
1173-0889
http://hdl.handle.net/2292/4988
Research Reports - Department of Mathematics
https://researchspace.auckland.ac.nz/docs/uoa-docs/rights.htm
The author(s)
Department of Mathematics, The University of Auckland, New Zealand
http://www.math.auckland.ac.nz/Research/Reports/view.php?id=551
https://researchspace.auckland.ac.nz/bitstream/2292/4988/1/551.pdf
8988f811ba192df7927aa30d71acdaac
https://researchspace.auckland.ac.nz/bitstream/2292/4988/2/551.pdf.txt
b42e1747632772cf853e644187fa106b
oai:researchspace.auckland.ac.nz:2292/4989
2009-08-28T12:38:53Z
com_2292_122
col_2292_4963
2009-08-28T03:20:48Z
2009-08-28T03:20:48Z
2000-03
2000-03
http://hdl.handle.net/2292/4989
Let $X$ and $Y$ be two compact Hausdorff spaces, and $E$ be a Banach lattice. We show that if there is a non-vanishing preserving Riesz isomorphism $Phi: C(X, E) to C(Y)$, then $X$ is homeomorphic to $Y$ and $E$ is Riesz isomorphic to $mathbb R$.
A Lattice-valued Banach-Stone Theorem
Cao, Jiling
Reilly, Ivan
Xiong, Hongyun
Let $X$ and $Y$ be two compact Hausdorff spaces, and $E$ be a Banach lattice. We show that if there is a non-vanishing preserving Riesz isomorphism $Phi: C(X, E) to C(Y)$, then $X$ is homeomorphic to $Y$ and $E$ is Riesz isomorphic to $mathbb R$.
Technical Report
Department of Mathematics - Research Reports-441 (2000)
1173-0889
http://hdl.handle.net/2292/4989
Research Reports - Department of Mathematics
https://researchspace.auckland.ac.nz/docs/uoa-docs/rights.htm
The author(s)
Department of Mathematics, The University of Auckland, New Zealand
http://www.math.auckland.ac.nz/Research/Reports/view.php?id=441
https://researchspace.auckland.ac.nz/bitstream/2292/4989/1/441.pdf
e5abf6b0c8aeca5e6160d1b83d1a6c75
https://researchspace.auckland.ac.nz/bitstream/2292/4989/2/441.pdf.txt
38102bb93f1e53037556fad34de15644
oai:researchspace.auckland.ac.nz:2292/4990
2009-08-28T12:38:54Z
com_2292_122
col_2292_4963
2009-08-28T03:20:48Z
2009-08-28T03:20:48Z
2000
2000
http://hdl.handle.net/2292/4990
In actual paper we develop the spectral analysis of Schr"odinger operators on lattice type graphs. For basic example of qubic periodic graph the problem is reduced to the spectral analysis of the regular differential operators on a fundamental star-like subgraph with a selfadjoint condition at the central node and quasiperiodic conditions at the boundary vertices. Using an explicite expression for resolvent of lattice-type operator we develop in the second sections the Lippmann- Schwinger techniques for the perturbed periodic operator and construct the corresponding scattering matrix. It serves as a base for the approximation of the multy-dimensional Schr"odinger operator by the onedimansional operator on graph : in the third section of the paper for given $N$-dimensional Schr"odinger operators with rapidly decreasing potential we construct a lattice-type operator on cubic graph embedded into ${bf R}^N$ and show that the original $N$-dimensional scattering problem can be approximated in proper sense by the corresponding scattering problem for the perturbed lattice operator.
Scattering on graphs and one-dimensional approximation of $N-$dimensional Schr"odinger operators
Melnikov, Y.
Pavlov, B.
In actual paper we develop the spectral analysis of Schr"odinger operators on lattice type graphs. For basic example of qubic periodic graph the problem is reduced to the spectral analysis of the regular differential operators on a fundamental star-like subgraph with a selfadjoint condition at the central node and quasiperiodic conditions at the boundary vertices. Using an explicite expression for resolvent of lattice-type operator we develop in the second sections the Lippmann- Schwinger techniques for the perturbed periodic operator and construct the corresponding scattering matrix. It serves as a base for the approximation of the multy-dimensional Schr"odinger operator by the onedimansional operator on graph : in the third section of the paper for given $N$-dimensional Schr"odinger operators with rapidly decreasing potential we construct a lattice-type operator on cubic graph embedded into ${bf R}^N$ and show that the original $N$-dimensional scattering problem can be approximated in proper sense by the corresponding scattering problem for the perturbed lattice operator.
Technical Report
Department of Mathematics - Research Reports-439 (2000)
1173-0889
http://hdl.handle.net/2292/4990
Research Reports - Department of Mathematics
https://researchspace.auckland.ac.nz/docs/uoa-docs/rights.htm
The author(s)
Department of Mathematics, The University of Auckland, New Zealand
http://www.math.auckland.ac.nz/Research/Reports/view.php?id=439
https://researchspace.auckland.ac.nz/bitstream/2292/4990/1/439.pdf
9d4e958b29ab1c4c78581f6d6ab41b8f
https://researchspace.auckland.ac.nz/bitstream/2292/4990/2/439.pdf.txt
326c3b2777685395d42225db9e1d792d
oai:researchspace.auckland.ac.nz:2292/4991
2009-08-28T12:38:54Z
com_2292_122
col_2292_4963
2009-08-28T03:20:50Z
2009-08-28T03:20:50Z
2000-03
2000-03
http://hdl.handle.net/2292/4991
{bf Abstract:} In this paper we prove that, for any subset $Deltasubset Z$, the probability, that a random $Delta_{ntimes n}$ matrix is singular, is of order $Oleft(1/sqrt{n}$
A Generalization of Komlos Theorem on Random Matrices
Slinko, Arkadii
{bf Abstract:} In this paper we prove that, for any subset $Deltasubset Z$, the probability, that a random $Delta_{ntimes n}$ matrix is singular, is of order $Oleft(1/sqrt{n}$
Technical Report
Department of Mathematics - Research Reports-438 (2000)
1173-0889
http://hdl.handle.net/2292/4991
Research Reports - Department of Mathematics
https://researchspace.auckland.ac.nz/docs/uoa-docs/rights.htm
The author(s)
Department of Mathematics, The University of Auckland, New Zealand
http://www.math.auckland.ac.nz/Research/Reports/view.php?id=438
https://researchspace.auckland.ac.nz/bitstream/2292/4991/1/438.pdf
e38be15fbd1fa9e575afdbdb4e399dec
https://researchspace.auckland.ac.nz/bitstream/2292/4991/2/438.pdf.txt
34fccbfa6837b30c8d8e8ef9eafe0935
oai:researchspace.auckland.ac.nz:2292/4992
2009-11-19T00:46:40Z
com_2292_122
col_2292_4963
2009-08-28T03:20:50Z
2009-08-28T03:20:50Z
1999-12
1999-12
http://hdl.handle.net/2292/4992
Numerically integrated ephemerides of the solar system and the Moon require very accurate integrations of systems of second order ordinary differential equations. We present a new family of 8-9 pairs and assess the performance of two new 8-9 pairs on the equations used to create the ephemeris DE102. Part of this work is the introduction of these equations as a test problem for integrators of initial value ordinary differential equations.
High order explicit Runge-Kutta pairs for ephemerides of the solar system and the Moon. (1999)
Sharp, P.W.
Numerically integrated ephemerides of the solar system and the Moon require very accurate integrations of systems of second order ordinary differential equations. We present a new family of 8-9 pairs and assess the performance of two new 8-9 pairs on the equations used to create the ephemeris DE102. Part of this work is the introduction of these equations as a test problem for integrators of initial value ordinary differential equations.
Technical Report
Department of Mathematics - Research Reports-437 (1999)
1173-0889
http://hdl.handle.net/2292/4992
Research Reports - Department of Mathematics
https://researchspace.auckland.ac.nz/docs/uoa-docs/rights.htm
The author(s)
Department of Mathematics, The University of Auckland, New Zealand
http://www.math.auckland.ac.nz/Research/Reports/view.php?id=437
https://researchspace.auckland.ac.nz/bitstream/2292/4992/1/437.pdf
b00b8216b1c72e7f471ad393aa03ad93
https://researchspace.auckland.ac.nz/bitstream/2292/4992/2/437.pdf.txt
c1fbb2388736a23a2db4085cbd653eb5
oai:researchspace.auckland.ac.nz:2292/4993
2009-08-28T12:38:56Z
com_2292_122
col_2292_4963
2009-08-28T03:20:51Z
2009-08-28T03:20:51Z
1999-12
1999-12
http://hdl.handle.net/2292/4993
Order five symplectic ERKN methods of five stages are known to exist. However, these methods do not have free parameters with which to minimise the error coefficients. By adding one derivative evaluation per step, to give either a six-stage non-FSAL family or a seven-stage FSAL family of methods, two free parameters become available for the minimisation. This raises the possibility of improving the efficiency of order five methods despite the extra cost of taking a step. We perform the minimisation of the two families to obtain an optimal method and then compare its performance with some published methods on the two-body problem for a range of eccentricities. These comparisons along with those based on the error coefficients show the new method is significantly more efficient than the five-stage methods. The numerical comparisons also suggest the new methods can be more efficient than some existing methods of other orders.
Order 5 symplectic explicit Runge-Kutta Nystrom methods
Chou, Lin-yi
Sharp, P.W.
Order five symplectic ERKN methods of five stages are known to exist. However, these methods do not have free parameters with which to minimise the error coefficients. By adding one derivative evaluation per step, to give either a six-stage non-FSAL family or a seven-stage FSAL family of methods, two free parameters become available for the minimisation. This raises the possibility of improving the efficiency of order five methods despite the extra cost of taking a step. We perform the minimisation of the two families to obtain an optimal method and then compare its performance with some published methods on the two-body problem for a range of eccentricities. These comparisons along with those based on the error coefficients show the new method is significantly more efficient than the five-stage methods. The numerical comparisons also suggest the new methods can be more efficient than some existing methods of other orders.
Technical Report
Department of Mathematics - Research Reports-436 (1999)
1173-0889
http://hdl.handle.net/2292/4993
Research Reports - Department of Mathematics
https://researchspace.auckland.ac.nz/docs/uoa-docs/rights.htm
The author(s)
Department of Mathematics, The University of Auckland, New Zealand
http://www.math.auckland.ac.nz/Research/Reports/view.php?id=436
https://researchspace.auckland.ac.nz/bitstream/2292/4993/1/436.pdf
fbe6384988da995c52327918a0f8ccad
https://researchspace.auckland.ac.nz/bitstream/2292/4993/2/436.pdf.txt
fd335309022096d6414c13170f131721
oai:researchspace.auckland.ac.nz:2292/4994
2009-08-28T12:38:57Z
com_2292_122
col_2292_4963
2009-08-28T03:20:52Z
2009-08-28T03:20:52Z
1999-11
1999-11
http://hdl.handle.net/2292/4994
The evolution operators, generators of which contain a numerical parameter forming a Markov process, are considered in connection with problems of financial mathematics. Under certain conditions the exact and explicit expressions for the values of the evolution operators averaged over trajectories of the process and for the corresponding variances are derived.Obtained results are applied for valuation of some financial products with account of floating interest rates.
Valuation of bonds and options under floating interest rate
Adamjan, V.
Pavlov, B.
The evolution operators, generators of which contain a numerical parameter forming a Markov process, are considered in connection with problems of financial mathematics. Under certain conditions the exact and explicit expressions for the values of the evolution operators averaged over trajectories of the process and for the corresponding variances are derived.Obtained results are applied for valuation of some financial products with account of floating interest rates.
Technical Report
Department of Mathematics - Research Reports-435 (1999)
1173-0889
http://hdl.handle.net/2292/4994
Research Reports - Department of Mathematics
https://researchspace.auckland.ac.nz/docs/uoa-docs/rights.htm
The author(s)
Department of Mathematics, The University of Auckland, New Zealand
http://www.math.auckland.ac.nz/Research/Reports/view.php?id=435
https://researchspace.auckland.ac.nz/bitstream/2292/4994/1/435.pdf
287d0ed3e5e2f7d5a92cf096f3d27eda
https://researchspace.auckland.ac.nz/bitstream/2292/4994/2/435.pdf.txt
0defec88488129861a60c5ceb79b13ec
oai:researchspace.auckland.ac.nz:2292/4995
2009-08-28T12:38:58Z
com_2292_122
col_2292_4963
2009-08-28T03:20:53Z
2009-08-28T03:20:53Z
1999-12
1999-12
http://hdl.handle.net/2292/4995
This study investigates factors affecting doctoral study in mathematics and mathematics education in New Zealand universities. In particular, it gives insight into the problems faced by students and provides comprehensive information for the mathematical community. A questionnaire to students gathered information including their financial support, initial motivation to pursue a doctorate, the level of satisfaction they were experiencing from their studies, their perceptions of the supervisory process, their experiences as research students, and their hopes for the future.
Experiences of Doctoral Students in Mathematics in New Zealand
Morton, Margaret
Thornley, Gillian
This study investigates factors affecting doctoral study in mathematics and mathematics education in New Zealand universities. In particular, it gives insight into the problems faced by students and provides comprehensive information for the mathematical community. A questionnaire to students gathered information including their financial support, initial motivation to pursue a doctorate, the level of satisfaction they were experiencing from their studies, their perceptions of the supervisory process, their experiences as research students, and their hopes for the future.
Technical Report
Department of Mathematics - Research Reports-434 (1999)
1173-0889
http://hdl.handle.net/2292/4995
Research Reports - Department of Mathematics
https://researchspace.auckland.ac.nz/docs/uoa-docs/rights.htm
The author(s)
Department of Mathematics, The University of Auckland, New Zealand
http://www.math.auckland.ac.nz/Research/Reports/view.php?id=434
https://researchspace.auckland.ac.nz/bitstream/2292/4995/1/434.pdf
c4f7b404d50d661d4763360e1b4a6291
https://researchspace.auckland.ac.nz/bitstream/2292/4995/2/434.pdf.txt
7eec6cf571a32c11c5046cd3ded119d9
oai:researchspace.auckland.ac.nz:2292/4996
2009-08-28T12:38:58Z
com_2292_122
col_2292_4963
2009-08-28T03:20:54Z
2009-08-28T03:20:54Z
1999-12
1999-12
http://hdl.handle.net/2292/4996
In this paper we investigate the social choice rule known as majoritarian compromise. We prove that it is asymptotically strategy-proof for $m be 3$ alternatives and that the ratio of the number of all manipulable profiles upon the total number of profiles is in the order of $O(1/sqrt{n})$.
The Majoritarian Compromise is Asymptotically Strategy-Proof
Slinko, Arkadii
In this paper we investigate the social choice rule known as majoritarian compromise. We prove that it is asymptotically strategy-proof for $m be 3$ alternatives and that the ratio of the number of all manipulable profiles upon the total number of profiles is in the order of $O(1/sqrt{n})$.
Technical Report
Department of Mathematics - Research Reports-433 (1999)
1173-0889
http://hdl.handle.net/2292/4996
Research Reports - Department of Mathematics
https://researchspace.auckland.ac.nz/docs/uoa-docs/rights.htm
The author(s)
Department of Mathematics, The University of Auckland, New Zealand
http://www.math.auckland.ac.nz/Research/Reports/view.php?id=433
https://researchspace.auckland.ac.nz/bitstream/2292/4996/1/433.pdf
4a3a1e36c8cf1881bd86f2d2889770cb
https://researchspace.auckland.ac.nz/bitstream/2292/4996/2/433.pdf.txt
e951fe317b3844d68e037e18e4ca4a96
oai:researchspace.auckland.ac.nz:2292/4997
2009-08-28T12:38:59Z
com_2292_122
col_2292_4963
2009-08-28T03:20:55Z
2009-08-28T03:20:55Z
1999-11
1999-11
http://hdl.handle.net/2292/4997
In this paper we prove that the plurality rule and the run-off procedure are asymptotically strategy-proof for any number of alternatives and that the ratio of the number of all manipulable profiles upon the total number of profiles in both cases is it the order of $O(1/sqrt{n})$.
Asymptotic Strategy Proofness of the Plurality and the Run-off Rules
Slinko, Arkadii
In this paper we prove that the plurality rule and the run-off procedure are asymptotically strategy-proof for any number of alternatives and that the ratio of the number of all manipulable profiles upon the total number of profiles in both cases is it the order of $O(1/sqrt{n})$.
Technical Report
Department of Mathematics - Research Reports-432 (1999)
1173-0889
http://hdl.handle.net/2292/4997
Research Reports - Department of Mathematics
https://researchspace.auckland.ac.nz/docs/uoa-docs/rights.htm
The author(s)
Department of Mathematics, The University of Auckland, New Zealand
http://www.math.auckland.ac.nz/Research/Reports/view.php?id=432
https://researchspace.auckland.ac.nz/bitstream/2292/4997/1/432.pdf
2890860d020e6e4c1882963044b5a355
https://researchspace.auckland.ac.nz/bitstream/2292/4997/2/432.pdf.txt
2dd32ca32a1190cc1667ba1b8dbda1dc
oai:researchspace.auckland.ac.nz:2292/4998
2009-08-28T12:39:00Z
com_2292_122
col_2292_4963
2009-08-28T03:20:56Z
2009-08-28T03:20:56Z
1999-10
1999-10
http://hdl.handle.net/2292/4998
There are many conditions equivalent to metrisability for a topological manifold which are not equivalent to metrisability for topological spaces in general. What are the weakest such? We show that a number of weak covering properties which are equivalent to metrisability for a manifold, for example metaLindel"{o}f, may be further weakened by considering only covers of cardinality the first uncountable ordinal. Extensions to higher cardinals are discussed,
Covering Properties and Metrisation of Manifolds*
Gauld, David
Vamanamurthy, M.K.
There are many conditions equivalent to metrisability for a topological manifold which are not equivalent to metrisability for topological spaces in general. What are the weakest such? We show that a number of weak covering properties which are equivalent to metrisability for a manifold, for example metaLindel"{o}f, may be further weakened by considering only covers of cardinality the first uncountable ordinal. Extensions to higher cardinals are discussed,
Technical Report
Department of Mathematics - Research Reports-431 (1999)
1173-0889
http://hdl.handle.net/2292/4998
Research Reports - Department of Mathematics
https://researchspace.auckland.ac.nz/docs/uoa-docs/rights.htm
The author(s)
Department of Mathematics, The University of Auckland, New Zealand
http://www.math.auckland.ac.nz/Research/Reports/view.php?id=431
https://researchspace.auckland.ac.nz/bitstream/2292/4998/1/431.pdf
782037476fb4d113df442be2d6221c4f
https://researchspace.auckland.ac.nz/bitstream/2292/4998/2/431.pdf.txt
eae4132b3613f127a266629c5534e6c3
oai:researchspace.auckland.ac.nz:2292/4999
2009-08-28T12:39:00Z
com_2292_122
col_2292_4963
2009-08-28T03:20:56Z
2009-08-28T03:20:56Z
2006-05
2006-05
http://hdl.handle.net/2292/4999
Several convexity properties are studied, with applications to power series, in particular to hypergeometric and related functions.
Generalized Convexity and Inequalities
Anderson, G.D.
Vamanamurthy, M.K.
Vuorinen, M.
Several convexity properties are studied, with applications to power series, in particular to hypergeometric and related functions.
Technical Report
Department of Mathematics - Research Reports-550 (2006)
1173-0889
http://hdl.handle.net/2292/4999
Research Reports - Department of Mathematics
https://researchspace.auckland.ac.nz/docs/uoa-docs/rights.htm
The author(s)
Department of Mathematics, The University of Auckland, New Zealand
http://www.math.auckland.ac.nz/Research/Reports/view.php?id=550
https://researchspace.auckland.ac.nz/bitstream/2292/4999/1/550.pdf
f5c4932a3c38b6dab3f3aa819038d4f0
https://researchspace.auckland.ac.nz/bitstream/2292/4999/2/550.pdf.txt
b1493a7171c74f236ec7acdc42ab533e
oai:researchspace.auckland.ac.nz:2292/5000
2009-08-28T12:39:01Z
com_2292_122
col_2292_4963
2009-08-28T03:20:58Z
2009-08-28T03:20:58Z
1999-10
1999-10
http://hdl.handle.net/2292/5000
The Bernstein operator $B_n$ reproduces the linear polynomials, which are therefore eigenfunctions corresponding to the eigenvalue $1$. We determine the rest of the eigenstructure of $B_n$. Its eigenvalues are $$lambda_k^{(n)}:={n!over(n-k)!}{1over n^k}, qquad k=0,1,ldots,n,$$ and the corresponding monic eigenfunctions $p_k^{(n)}$ are polynomials of degree $k$, % (with interlacing zeros) which have $k$ simple zeros in $[0,1]$. By using an explicit formula, it is shown that $p_k^{(n)}$ converges as $ntoinfty$ to a polynomial related to a Jacobi polynomial. Similarly, %for fixed $k$, the dual functionals to $p_k^{(n)}$ converge as $ntoinfty$ to measures that we identify. This diagonal form of the Bernstein operator and its limit, the identity (Weierstrass density theorem), is applied to a number of questions. These include the convergence of iterates of the Bernstein operator, and why Lagrange interpolation (at $n+1$ equally spaced points) fails to converge for all continuous functions whilst the Bernstein approximants do. We also give the eigenstructure of the Kantorovich operator. Previously, the only member of the Bernstein family for which the eigenfunctions were known explicitly was the Bernstein--Durrmeyer operator, which is self adjoint.
The eigenstructure of the Bernstein operator
Cooper, Shaun
Waldron, Shayne
The Bernstein operator $B_n$ reproduces the linear polynomials, which are therefore eigenfunctions corresponding to the eigenvalue $1$. We determine the rest of the eigenstructure of $B_n$. Its eigenvalues are $$lambda_k^{(n)}:={n!over(n-k)!}{1over n^k}, qquad k=0,1,ldots,n,$$ and the corresponding monic eigenfunctions $p_k^{(n)}$ are polynomials of degree $k$, % (with interlacing zeros) which have $k$ simple zeros in $[0,1]$. By using an explicit formula, it is shown that $p_k^{(n)}$ converges as $ntoinfty$ to a polynomial related to a Jacobi polynomial. Similarly, %for fixed $k$, the dual functionals to $p_k^{(n)}$ converge as $ntoinfty$ to measures that we identify. This diagonal form of the Bernstein operator and its limit, the identity (Weierstrass density theorem), is applied to a number of questions. These include the convergence of iterates of the Bernstein operator, and why Lagrange interpolation (at $n+1$ equally spaced points) fails to converge for all continuous functions whilst the Bernstein approximants do. We also give the eigenstructure of the Kantorovich operator. Previously, the only member of the Bernstein family for which the eigenfunctions were known explicitly was the Bernstein--Durrmeyer operator, which is self adjoint.
Technical Report
Department of Mathematics - Research Reports-430 (1999)
1173-0889
http://hdl.handle.net/2292/5000
Research Reports - Department of Mathematics
https://researchspace.auckland.ac.nz/docs/uoa-docs/rights.htm
The author(s)
Department of Mathematics, The University of Auckland, New Zealand
http://www.math.auckland.ac.nz/Research/Reports/view.php?id=430
https://researchspace.auckland.ac.nz/bitstream/2292/5000/1/430.pdf
02392e162629e63500c1b0e0d92684fe
https://researchspace.auckland.ac.nz/bitstream/2292/5000/2/430.pdf.txt
ab716449b24a52743d99b20b3182c2e9
oai:researchspace.auckland.ac.nz:2292/5001
2009-08-28T12:39:02Z
com_2292_122
col_2292_4963
2009-08-28T03:20:59Z
2009-08-28T03:20:59Z
1999-09
1999-09
http://hdl.handle.net/2292/5001
In this paper, we answer two questions of P. Fletcher and W. Lindgren. We prove that a space $X$ is $wDelta$ and has a quasi--$G^*_{delta}$--diagonal if and only if it is developable, a space $X$ is $beta$--space with a quasi--$G^{*}_{delta}$--diagonal if and only if it is semi--stratifiable, a space $X$ is $beta$, quasi--$gamma$--space and has a quasi--$G^*_{delta}$--diagonal if and only if $X$ is developable and a space $X$ is metrizable if and only if it is paracompact $beta$--space with a quasi--$G_{delta}$--diagonal.
Developable Spaces and Problems of Fletcher and Lindgren
Mohamad, A.M.
In this paper, we answer two questions of P. Fletcher and W. Lindgren. We prove that a space $X$ is $wDelta$ and has a quasi--$G^*_{delta}$--diagonal if and only if it is developable, a space $X$ is $beta$--space with a quasi--$G^{*}_{delta}$--diagonal if and only if it is semi--stratifiable, a space $X$ is $beta$, quasi--$gamma$--space and has a quasi--$G^*_{delta}$--diagonal if and only if $X$ is developable and a space $X$ is metrizable if and only if it is paracompact $beta$--space with a quasi--$G_{delta}$--diagonal.
Technical Report
Department of Mathematics - Research Reports-429 (1999)
1173-0889
http://hdl.handle.net/2292/5001
Research Reports - Department of Mathematics
https://researchspace.auckland.ac.nz/docs/uoa-docs/rights.htm
The author(s)
Department of Mathematics, The University of Auckland, New Zealand
http://www.math.auckland.ac.nz/Research/Reports/view.php?id=429
https://researchspace.auckland.ac.nz/bitstream/2292/5001/1/429.pdf
61d18b22bb82a6422175a8b90dc8060c
https://researchspace.auckland.ac.nz/bitstream/2292/5001/2/429.pdf.txt
edb0220319292dc033b99dacf1b43162
oai:researchspace.auckland.ac.nz:2292/5002
2009-08-28T12:39:03Z
com_2292_122
col_2292_4963
2009-08-28T03:20:59Z
2009-08-28T03:20:59Z
1999-09
1999-09
http://hdl.handle.net/2292/5002
This paper investigates metrization theory of manifolds. We show that diagonal properties play a central role in developing metrizability of manifolds.
Metrizability of Manifolds by Diagonal Properties
Gartside, P.M.
Mohamad, Abdul M.
This paper investigates metrization theory of manifolds. We show that diagonal properties play a central role in developing metrizability of manifolds.
Technical Report
Department of Mathematics - Research Reports-428 (1999)
1173-0889
http://hdl.handle.net/2292/5002
Research Reports - Department of Mathematics
https://researchspace.auckland.ac.nz/docs/uoa-docs/rights.htm
The author(s)
Department of Mathematics, The University of Auckland, New Zealand
http://www.math.auckland.ac.nz/Research/Reports/view.php?id=428
https://researchspace.auckland.ac.nz/bitstream/2292/5002/1/428.pdf
4d1323c6d328395d17db3160764f6ad9
https://researchspace.auckland.ac.nz/bitstream/2292/5002/2/428.pdf.txt
89fff1322142a8d21b52cd9405de3e45
oai:researchspace.auckland.ac.nz:2292/5003
2009-08-28T12:39:04Z
com_2292_122
col_2292_4963
2009-08-28T03:21:00Z
2009-08-28T03:21:00Z
1999-09
1999-09
http://hdl.handle.net/2292/5003
We show that all but $A_6$ non-abelian finite simple groups with no elements of order 6 are characterized by their element orders.
The Characterization of Finite Simple Groups with no Elements of Order Six by Their Element Orders
An, Jianbei
Shi, Wujie
We show that all but $A_6$ non-abelian finite simple groups with no elements of order 6 are characterized by their element orders.
Technical Report
Department of Mathematics - Research Reports-427 (1999)
1173-0889
http://hdl.handle.net/2292/5003
Research Reports - Department of Mathematics
https://researchspace.auckland.ac.nz/docs/uoa-docs/rights.htm
The author(s)
Department of Mathematics, The University of Auckland, New Zealand
http://www.math.auckland.ac.nz/Research/Reports/view.php?id=427
https://researchspace.auckland.ac.nz/bitstream/2292/5003/1/427.pdf
9782a124bcff8f544939ca11b22e33f7
https://researchspace.auckland.ac.nz/bitstream/2292/5003/2/427.pdf.txt
fb250413c9f4e2ea3776e64fdfe580d4
oai:researchspace.auckland.ac.nz:2292/5004
2009-08-28T12:39:05Z
com_2292_122
col_2292_4963
2009-08-28T03:21:01Z
2009-08-28T03:21:01Z
1999-09
1999-09
http://hdl.handle.net/2292/5004
This paper is part of a program to study the conjecture of E. C. Dade on counting characters in blocks for several finite groups. The invariant conjecture of Dade is proved for general linear and unitary groups when the characteristic of the modular representation is distinct from the defining characteristic of the groups.
Dade's Invariant Conjecture for General Linear and Unitary Groups in Non-defining Characteristics
An, Jianbei
This paper is part of a program to study the conjecture of E. C. Dade on counting characters in blocks for several finite groups. The invariant conjecture of Dade is proved for general linear and unitary groups when the characteristic of the modular representation is distinct from the defining characteristic of the groups.
Technical Report
Department of Mathematics - Research Reports-426 (1999)
1173-0889
http://hdl.handle.net/2292/5004
Research Reports - Department of Mathematics
https://researchspace.auckland.ac.nz/docs/uoa-docs/rights.htm
The author(s)
Department of Mathematics, The University of Auckland, New Zealand
http://www.math.auckland.ac.nz/Research/Reports/view.php?id=426
https://researchspace.auckland.ac.nz/bitstream/2292/5004/1/426.pdf
f8b8b73cdd73b15a3ec8fb62bd55d4a3
https://researchspace.auckland.ac.nz/bitstream/2292/5004/2/426.pdf.txt
e1151beff646d4a4bfb4916ef7f7f71d
oai:researchspace.auckland.ac.nz:2292/5005
2009-08-28T12:39:06Z
com_2292_122
col_2292_4963
2009-08-28T03:21:02Z
2009-08-28T03:21:02Z
1999-09
1999-09
http://hdl.handle.net/2292/5005
We generalize the p-local rank of a finite group, introduced by G. Robinson, to a p-block of a finite group and show that this has analagous properties.
The p-local Rank of a Block
An, Jianbei
Eaton, Charles W.
We generalize the p-local rank of a finite group, introduced by G. Robinson, to a p-block of a finite group and show that this has analagous properties.
Technical Report
Department of Mathematics - Research Reports-425 (1999)
1173-0889
http://hdl.handle.net/2292/5005
Research Reports - Department of Mathematics
https://researchspace.auckland.ac.nz/docs/uoa-docs/rights.htm
The author(s)
Department of Mathematics, The University of Auckland, New Zealand
http://www.math.auckland.ac.nz/Research/Reports/view.php?id=425
https://researchspace.auckland.ac.nz/bitstream/2292/5005/1/425.pdf
8bd717eb74a74ac75cf5e73a2a5f26bc
https://researchspace.auckland.ac.nz/bitstream/2292/5005/2/425.pdf.txt
50c183a8f673ead57f88db8a29178be2
oai:researchspace.auckland.ac.nz:2292/5006
2009-08-28T12:39:07Z
com_2292_122
col_2292_4963
2009-08-28T03:21:03Z
2009-08-28T03:21:03Z
1999-09
1999-09
http://hdl.handle.net/2292/5006
In this paper we show that two important generalized metric properties are generalizations of first countability. We give some conditions on these generalized metric properties which imply metrizability. We prove that, a space $X$ is metrizable if and only if $X$ is a strongly quasi-N-space, quasi$-gamma-$space; a quasi$-gamma$ space is metrizable if and only if it is a pseudo $wN-$ space or quasi$-$Nagata$-$space with quasi $G^*_gamma-$diagonal; a space $X$ is a metrizable space if and only if $X$ has a $CWBC-$map $g$ satisfying the following conditions: 1. $g$ is a pseudo-strongly-quasi-N-map; 2. for any $A subseteq X, overline{A} subseteq cup {g(n, x) : x in A}$.
Conditions Which Imply Metrizability in some Generalized Metric Spaces*
Mohamad, A.M.
In this paper we show that two important generalized metric properties are generalizations of first countability. We give some conditions on these generalized metric properties which imply metrizability. We prove that, a space $X$ is metrizable if and only if $X$ is a strongly quasi-N-space, quasi$-gamma-$space; a quasi$-gamma$ space is metrizable if and only if it is a pseudo $wN-$ space or quasi$-$Nagata$-$space with quasi $G^*_gamma-$diagonal; a space $X$ is a metrizable space if and only if $X$ has a $CWBC-$map $g$ satisfying the following conditions: 1. $g$ is a pseudo-strongly-quasi-N-map; 2. for any $A subseteq X, overline{A} subseteq cup {g(n, x) : x in A}$.
Technical Report
Department of Mathematics - Research Reports-424 (1999)
1173-0889
http://hdl.handle.net/2292/5006
Research Reports - Department of Mathematics
https://researchspace.auckland.ac.nz/docs/uoa-docs/rights.htm
The author(s)
Department of Mathematics, The University of Auckland, New Zealand
http://www.math.auckland.ac.nz/Research/Reports/view.php?id=424
https://researchspace.auckland.ac.nz/bitstream/2292/5006/1/424.pdf
4474aa6f686180136a76950ec9b463a5
https://researchspace.auckland.ac.nz/bitstream/2292/5006/2/424.pdf.txt
288598c79b4bcc929308a1f5bc0ca940
oai:researchspace.auckland.ac.nz:2292/5007
2009-08-28T12:39:07Z
com_2292_122
col_2292_4963
2009-08-28T03:21:04Z
2009-08-28T03:21:04Z
1999-09
1999-09
http://hdl.handle.net/2292/5007
In this paper we present the homeomorphism groups of manifolds, explaining why non-metrizable manifolds are better behaved, with regard to their homeomorphism groups, than metrizable manifolds. A proof that the natural topology on the homeomorphism group for a one dimensional metrizable manifold is the minimum group topology but the homeomorphism group does not admit a minimum group topology for a more than one dimensional metrizable manifold will be given. Likewise, examples demonstrating how badly behaved are the homeomorphism groups of continua, in comparison with homeomorphism groups of manifolds is also given.
Homeomorphism Groups of Manifolds*
Gartside, P.M.
Mohamad, A.M.
In this paper we present the homeomorphism groups of manifolds, explaining why non-metrizable manifolds are better behaved, with regard to their homeomorphism groups, than metrizable manifolds. A proof that the natural topology on the homeomorphism group for a one dimensional metrizable manifold is the minimum group topology but the homeomorphism group does not admit a minimum group topology for a more than one dimensional metrizable manifold will be given. Likewise, examples demonstrating how badly behaved are the homeomorphism groups of continua, in comparison with homeomorphism groups of manifolds is also given.
Technical Report
Department of Mathematics - Research Reports-423 (1999)
1173-0889
http://hdl.handle.net/2292/5007
Research Reports - Department of Mathematics
https://researchspace.auckland.ac.nz/docs/uoa-docs/rights.htm
The author(s)
Department of Mathematics, The University of Auckland, New Zealand
http://www.math.auckland.ac.nz/Research/Reports/view.php?id=423
https://researchspace.auckland.ac.nz/bitstream/2292/5007/1/423.pdf
812ee3878315a5fc0605ace2fb29d384
https://researchspace.auckland.ac.nz/bitstream/2292/5007/2/423.pdf.txt
ec5a857ce50d9594411ddd51269c9b15
oai:researchspace.auckland.ac.nz:2292/5008
2009-08-28T12:39:08Z
com_2292_122
col_2292_4963
2009-08-28T03:21:05Z
2009-08-28T03:21:05Z
1999-08
1999-08
http://hdl.handle.net/2292/5008
The definition for the domination graph of a tournament states that it has the same vertices as the tournament with an edge between two vertices if every other vertex is beaten by at least one of them. In this paper two new types of domination graphs are defined by using different relaxations of the adjacency definition. The first type is formed by reducing the number of vertices which must be dominated by a pair of vertices and the second by increasing the number of steps allowable for domination. Properties of these new types of domination graphs are presented with comparison between them where appropriate. In particular a full characterisation of each type is given for rotational tournements.
Domination Conditions for Tournaments
McKenna, Patricia
Morton, Margaret
Sneddon, Jamie
The definition for the domination graph of a tournament states that it has the same vertices as the tournament with an edge between two vertices if every other vertex is beaten by at least one of them. In this paper two new types of domination graphs are defined by using different relaxations of the adjacency definition. The first type is formed by reducing the number of vertices which must be dominated by a pair of vertices and the second by increasing the number of steps allowable for domination. Properties of these new types of domination graphs are presented with comparison between them where appropriate. In particular a full characterisation of each type is given for rotational tournements.
Technical Report
Department of Mathematics - Research Reports-422 (1999)
1173-0889
http://hdl.handle.net/2292/5008
Research Reports - Department of Mathematics
https://researchspace.auckland.ac.nz/docs/uoa-docs/rights.htm
The author(s)
Department of Mathematics, The University of Auckland, New Zealand
http://www.math.auckland.ac.nz/Research/Reports/view.php?id=422
https://researchspace.auckland.ac.nz/bitstream/2292/5008/1/422.pdf
f60c6c8f5be4503bca9edba1da5aa293
https://researchspace.auckland.ac.nz/bitstream/2292/5008/2/422.pdf.txt
dad1fa5e8696e4224f2d63756d794f8f
oai:researchspace.auckland.ac.nz:2292/5009
2009-08-28T12:39:09Z
com_2292_122
col_2292_4963
2009-08-28T03:21:06Z
2009-08-28T03:21:06Z
1999-06
1999-06
http://hdl.handle.net/2292/5009
This paper continues the study of preclosed sets and of generalized preclosed sets in a topological space. Our main objective is to establish results about the relationships between the various types of generalized closed sets. As a by-product, we are able to provide characterizations of certain known classes of topological spaces by using preclosed sets and their generalizations.
On Preclosed Sets and Their Generalizations
Cao, Jiling
Ganster, Maximilian
Konstadilaki, Chariklia
Reilly, Ivan
This paper continues the study of preclosed sets and of generalized preclosed sets in a topological space. Our main objective is to establish results about the relationships between the various types of generalized closed sets. As a by-product, we are able to provide characterizations of certain known classes of topological spaces by using preclosed sets and their generalizations.
Technical Report
Department of Mathematics - Research Reports-421 (1999)
1173-0889
http://hdl.handle.net/2292/5009
Research Reports - Department of Mathematics
https://researchspace.auckland.ac.nz/docs/uoa-docs/rights.htm
The author(s)
Department of Mathematics, The University of Auckland, New Zealand
http://www.math.auckland.ac.nz/Research/Reports/view.php?id=421
https://researchspace.auckland.ac.nz/bitstream/2292/5009/1/421.pdf
80fb8b6ef25350a1ca0d6f678ebf16a1
https://researchspace.auckland.ac.nz/bitstream/2292/5009/2/421.pdf.txt
e844c4beb2f87007408248af58341071
oai:researchspace.auckland.ac.nz:2292/5010
2009-08-28T12:39:10Z
com_2292_122
col_2292_4963
2009-08-28T03:21:07Z
2009-08-28T03:21:07Z
2006-05
2006-05
http://hdl.handle.net/2292/5010
We investigate harmonic forms of geometrically formal metrics, which are defined as those having the exterior product of any two harmonic forms still harmonic. We prove that a formal Sasakian metric can exist only on a real cohomology sphere and that holomorphic forms of a formal K"ahler metric are parallel w.r.t. the Levi-Civita connection. In the general Riemannian case a formal metric with maximal second Betti number is shown to be flat . Finally we prove that a six-dimensional manifold with $b_1 neq 1, b_2 ge 3$ and not having the cohomology algebra of $mathbb{T}^3 times S^3$ carries a symplectic structure as soon as it admits a formal metric.
Holomorphic forms of geometrically formal Kaehler manifolds
Grosjean, Jean-Francois
Nagy, Paul-Andi
We investigate harmonic forms of geometrically formal metrics, which are defined as those having the exterior product of any two harmonic forms still harmonic. We prove that a formal Sasakian metric can exist only on a real cohomology sphere and that holomorphic forms of a formal K"ahler metric are parallel w.r.t. the Levi-Civita connection. In the general Riemannian case a formal metric with maximal second Betti number is shown to be flat . Finally we prove that a six-dimensional manifold with $b_1 neq 1, b_2 ge 3$ and not having the cohomology algebra of $mathbb{T}^3 times S^3$ carries a symplectic structure as soon as it admits a formal metric.
Technical Report
Department of Mathematics - Research Reports-549 (2006)
1173-0889
http://hdl.handle.net/2292/5010
Research Reports - Department of Mathematics
https://researchspace.auckland.ac.nz/docs/uoa-docs/rights.htm
The author(s)
Department of Mathematics, The University of Auckland, New Zealand
http://www.math.auckland.ac.nz/Research/Reports/view.php?id=549
https://researchspace.auckland.ac.nz/bitstream/2292/5010/1/549.pdf
5a3fbd2a48f17d952779255abc258168
https://researchspace.auckland.ac.nz/bitstream/2292/5010/2/549.pdf.txt
77601d351ea52bc380c0eeedea9e3833
oai:researchspace.auckland.ac.nz:2292/5011
2009-08-28T12:39:11Z
com_2292_122
col_2292_4963
2009-08-28T03:21:08Z
2009-08-28T03:21:08Z
1999-08
1999-08
http://hdl.handle.net/2292/5011
Scattering problem for Neumann Laplacean with a continuous potential on a domain with a smooth boundary and few semiinfinite wires attached to it is studied. In resonance case when the Fermi level inthe wires coincides with some {it resonance} energy level in the domain the approximate formula for the transmission coefficient from one wire to another is derived: inthe case of weak interaction between the domain and the wires the transmission coefficient is proportional to the product of values of the corresponding resonance eigenfunction of inner problem at the points of contact.
Scattering on a Compact Domain with few Semiinfinite wires attached: resonance case
Mikhailova, A.
Pavlov, B.
Popov, I.
Rudakova, T.
Yafyasov, A.M.
Scattering problem for Neumann Laplacean with a continuous potential on a domain with a smooth boundary and few semiinfinite wires attached to it is studied. In resonance case when the Fermi level inthe wires coincides with some {it resonance} energy level in the domain the approximate formula for the transmission coefficient from one wire to another is derived: inthe case of weak interaction between the domain and the wires the transmission coefficient is proportional to the product of values of the corresponding resonance eigenfunction of inner problem at the points of contact.
Technical Report
Department of Mathematics - Research Reports-420 (1999)
1173-0889
http://hdl.handle.net/2292/5011
Research Reports - Department of Mathematics
https://researchspace.auckland.ac.nz/docs/uoa-docs/rights.htm
The author(s)
Department of Mathematics, The University of Auckland, New Zealand
http://www.math.auckland.ac.nz/Research/Reports/view.php?id=420
https://researchspace.auckland.ac.nz/bitstream/2292/5011/1/420.pdf
2fe4eae6a0d6d3e1ed30ec3553f36dbb
https://researchspace.auckland.ac.nz/bitstream/2292/5011/2/420.pdf.txt
e7bcce80996908063b7ce241bb87b46a
oai:researchspace.auckland.ac.nz:2292/5012
2009-08-28T12:39:12Z
com_2292_122
col_2292_4963
2009-08-28T03:21:09Z
2009-08-28T03:21:09Z
1999-06
1999-06
http://hdl.handle.net/2292/5012
Selfadjoint extensions of symmetric operators with infinite deficiency indices are discussed. In particular the operators describing the system of several quantum particles are investigated in detail and a few-body analog of Krein's formula for generalized resolvents is proven. The conditions for the semiboundedness of the simplest $M$-body quantum Hamiltonian with point interactionsin in the three-dimensional space are derived
FEW-BODY KREIN'S FORMULA
Kurasov, Pavel
Pavlov, B.
Selfadjoint extensions of symmetric operators with infinite deficiency indices are discussed. In particular the operators describing the system of several quantum particles are investigated in detail and a few-body analog of Krein's formula for generalized resolvents is proven. The conditions for the semiboundedness of the simplest $M$-body quantum Hamiltonian with point interactionsin in the three-dimensional space are derived
Technical Report
Department of Mathematics - Research Reports-418 (1999)
1173-0889
http://hdl.handle.net/2292/5012
Research Reports - Department of Mathematics
https://researchspace.auckland.ac.nz/docs/uoa-docs/rights.htm
The author(s)
Department of Mathematics, The University of Auckland, New Zealand
http://www.math.auckland.ac.nz/Research/Reports/view.php?id=418
https://researchspace.auckland.ac.nz/bitstream/2292/5012/1/418.pdf
d9c09b583907a66f66bfebc519b6e070
https://researchspace.auckland.ac.nz/bitstream/2292/5012/2/418.pdf.txt
ff08e085c4f6adacfd78c54f71bdda3b
oai:researchspace.auckland.ac.nz:2292/5013
2009-08-28T12:39:12Z
com_2292_122
col_2292_4963
2009-08-28T03:21:09Z
2009-08-28T03:21:09Z
1999
1999
http://hdl.handle.net/2292/5013
The spectrum of the perturbed shift operator $T: f(n)to al f(n+1)+a(n)f(n)$ in $l^2(Z)$ is considered for periodic $a(n)$ and fixed constant $al>0$. It is proven that the spectrum is continuous and fills a lemniscate. Some isospectral deformations of the sequence $a(n)$ are described. Similar facts for the perturbed shift in the spaces of sequences of some hypercomplex numbers is derived.
HILBERT THEOREM ON LEMNISCATE AND THE SPECTRUM OF THE PERTURBED SHIFT
Oleinik, V.L.
Pavlov, B.
The spectrum of the perturbed shift operator $T: f(n)to al f(n+1)+a(n)f(n)$ in $l^2(Z)$ is considered for periodic $a(n)$ and fixed constant $al>0$. It is proven that the spectrum is continuous and fills a lemniscate. Some isospectral deformations of the sequence $a(n)$ are described. Similar facts for the perturbed shift in the spaces of sequences of some hypercomplex numbers is derived.
Technical Report
Department of Mathematics - Research Reports-417 (1999)
1173-0889
http://hdl.handle.net/2292/5013
Research Reports - Department of Mathematics
https://researchspace.auckland.ac.nz/docs/uoa-docs/rights.htm
The author(s)
Department of Mathematics, The University of Auckland, New Zealand
http://www.math.auckland.ac.nz/Research/Reports/view.php?id=417
https://researchspace.auckland.ac.nz/bitstream/2292/5013/1/417.pdf
8dd42f0967abfc4e312de12277745595
https://researchspace.auckland.ac.nz/bitstream/2292/5013/2/417.pdf.txt
15cf326cf6982b528083473af89b34f3
oai:researchspace.auckland.ac.nz:2292/5014
2009-08-28T12:39:13Z
com_2292_122
col_2292_4963
2009-08-28T03:21:10Z
2009-08-28T03:21:10Z
1999-05
1999-05
http://hdl.handle.net/2292/5014
We consider the following objects: ${cal S}$ is a closed subspace of a Hilbert Space ${cal H}$, ${cal P}$ is the projection operator for ${cal S}$, and ${cal U}(t)$ is a strongly continuous group of unitary operators on ${cal H}$ with infinitesimal generator ${cal A}$. We let $U={cal U}(T)$, where $T>0$ is fixed. The questions that we ask are begin{itemize} item Under what conditions is $mathcal{P}Umathcal{P}$ a contraction? item Under what conditions can we steer $g in mathcal{S}$ to $hin mathcal{S}$ in the sense that we can find $fin mathcal{H}$ such that ${cal P}f=g$ and ${cal P}Uf=h$? end{itemize}
On the Interaction between a Group of Unitary Operators and a Projection
Taylor, S.W.
Littman, W.
We consider the following objects: ${cal S}$ is a closed subspace of a Hilbert Space ${cal H}$, ${cal P}$ is the projection operator for ${cal S}$, and ${cal U}(t)$ is a strongly continuous group of unitary operators on ${cal H}$ with infinitesimal generator ${cal A}$. We let $U={cal U}(T)$, where $T>0$ is fixed. The questions that we ask are begin{itemize} item Under what conditions is $mathcal{P}Umathcal{P}$ a contraction? item Under what conditions can we steer $g in mathcal{S}$ to $hin mathcal{S}$ in the sense that we can find $fin mathcal{H}$ such that ${cal P}f=g$ and ${cal P}Uf=h$? end{itemize}
Technical Report
Department of Mathematics - Research Reports-416 (1999)
1173-0889
http://hdl.handle.net/2292/5014
Research Reports - Department of Mathematics
https://researchspace.auckland.ac.nz/docs/uoa-docs/rights.htm
The author(s)
Department of Mathematics, The University of Auckland, New Zealand
http://www.math.auckland.ac.nz/Research/Reports/view.php?id=416
https://researchspace.auckland.ac.nz/bitstream/2292/5014/1/416.pdf
47bd1917d5204b3724667325f4bbf3cf
https://researchspace.auckland.ac.nz/bitstream/2292/5014/2/416.pdf.txt
80f62933d08f9e1c975c8b3b5242a7cf
oai:researchspace.auckland.ac.nz:2292/5015
2009-08-28T12:39:13Z
com_2292_122
col_2292_4963
2009-08-28T03:21:11Z
2009-08-28T03:21:11Z
1999-03
1999-03
http://hdl.handle.net/2292/5015
We study the boundary feedback stabilization for a one-dimensional wave equation with an interior point mass. We show that if the initial data belong to a certain invariant subspace of the semigroup of operators that generates the solution of the system, then the energy will decay like $C/$time. This improves a result of Hansen and Zuazua cite{hansen} who consider decay of solutions belonging to the domain of a power of the infinitesimal generator of the semigroup.
Boundary Feedback Stabilization of a Vibrating String with an Interior Point Mass
Taylor, S.W.
Littman, W.
We study the boundary feedback stabilization for a one-dimensional wave equation with an interior point mass. We show that if the initial data belong to a certain invariant subspace of the semigroup of operators that generates the solution of the system, then the energy will decay like $C/$time. This improves a result of Hansen and Zuazua cite{hansen} who consider decay of solutions belonging to the domain of a power of the infinitesimal generator of the semigroup.
Technical Report
Department of Mathematics - Research Reports-415 (1999)
1173-0889
http://hdl.handle.net/2292/5015
Research Reports - Department of Mathematics
https://researchspace.auckland.ac.nz/docs/uoa-docs/rights.htm
The author(s)
Department of Mathematics, The University of Auckland, New Zealand
http://www.math.auckland.ac.nz/Research/Reports/view.php?id=415
https://researchspace.auckland.ac.nz/bitstream/2292/5015/1/415.pdf
d271805306dc720f746e95be6856de1e
https://researchspace.auckland.ac.nz/bitstream/2292/5015/2/415.pdf.txt
720656779708a577a4ea33eaaa85ccd9
oai:researchspace.auckland.ac.nz:2292/5016
2009-08-28T12:39:15Z
com_2292_122
col_2292_4963
2009-08-28T03:21:12Z
2009-08-28T03:21:12Z
1999-03
1999-03
http://hdl.handle.net/2292/5016
Brachistochrones are constructed for repulsive central force, with logarithmic potential. Each pair of points is connected by infinitely many brachistochrones, on each of which the passage time is a local minimum, and the global minimum passage time is attained on one (or on infinitely many) of those curves. The bounded brachistochrones starting at a fixed point are separated from the unbounded brachistochrones by a Critical Brachistochrone.
Brachistochrones for Repulsive Logarithmic Potential
Tee, Garry J.
Brachistochrones are constructed for repulsive central force, with logarithmic potential. Each pair of points is connected by infinitely many brachistochrones, on each of which the passage time is a local minimum, and the global minimum passage time is attained on one (or on infinitely many) of those curves. The bounded brachistochrones starting at a fixed point are separated from the unbounded brachistochrones by a Critical Brachistochrone.
Technical Report
Department of Mathematics - Research Reports-414 (1999)
1173-0889
http://hdl.handle.net/2292/5016
Research Reports - Department of Mathematics
https://researchspace.auckland.ac.nz/docs/uoa-docs/rights.htm
The author(s)
Department of Mathematics, The University of Auckland, New Zealand
http://www.math.auckland.ac.nz/Research/Reports/view.php?id=414
https://researchspace.auckland.ac.nz/bitstream/2292/5016/1/414.pdf
ef8a40614ca5f45600863006914ed84a
https://researchspace.auckland.ac.nz/bitstream/2292/5016/2/414.pdf.txt
c399c593c4a87b9d120bb0b347f15b65
oai:researchspace.auckland.ac.nz:2292/5017
2009-08-28T12:39:17Z
com_2292_122
col_2292_4963
2009-08-28T03:21:13Z
2009-08-28T03:21:13Z
1999-03
1999-03
http://hdl.handle.net/2292/5017
The mathematical model of a simplest quasi-one-dimensional quantum network constructed of relatively narrow waveguides (the width of the waveguide is less than the de Broghlie wavelength of the electron in the material) is developed. This model allows to reduce the problem of calculating the current through the quantum network to the construction of scattered waves for some Schr"{o}dinger equation on the corresponding one-dimensional graph. We consider a graph consisting of a compact part and few semiinfinite rays attached to it via some boundary condition depending on a parameter $beta$ (analog of the inverse exponential hight $e^{-bH}$ of a potential barrier $H$ separating the rays from the compact part). This parameter regulates the connection between the rays and the compact part. Spectral properties of the Schr"{o}dinger operator on this graph are described with a special emphasis on the resonance case when the Fermi level in the rays coincides with one of eigenvalues of the nonperturbed Schr"{o}dinger operator on the ring. An explicit expression is obtained for the scattering matrix in the resonance case for weakening connection between the rays and the compact part.
About Scattering on the Ring
Bogevolnov, V.B.
Mikhailova, A.B.
Pavlov, B.
Yafyasov, A.M.
The mathematical model of a simplest quasi-one-dimensional quantum network constructed of relatively narrow waveguides (the width of the waveguide is less than the de Broghlie wavelength of the electron in the material) is developed. This model allows to reduce the problem of calculating the current through the quantum network to the construction of scattered waves for some Schr"{o}dinger equation on the corresponding one-dimensional graph. We consider a graph consisting of a compact part and few semiinfinite rays attached to it via some boundary condition depending on a parameter $beta$ (analog of the inverse exponential hight $e^{-bH}$ of a potential barrier $H$ separating the rays from the compact part). This parameter regulates the connection between the rays and the compact part. Spectral properties of the Schr"{o}dinger operator on this graph are described with a special emphasis on the resonance case when the Fermi level in the rays coincides with one of eigenvalues of the nonperturbed Schr"{o}dinger operator on the ring. An explicit expression is obtained for the scattering matrix in the resonance case for weakening connection between the rays and the compact part.
Technical Report
Department of Mathematics - Research Reports-413 (1999)
1173-0889
http://hdl.handle.net/2292/5017
Research Reports - Department of Mathematics
https://researchspace.auckland.ac.nz/docs/uoa-docs/rights.htm
The author(s)
Department of Mathematics, The University of Auckland, New Zealand
http://www.math.auckland.ac.nz/Research/Reports/view.php?id=413
https://researchspace.auckland.ac.nz/bitstream/2292/5017/1/413.pdf
3b0ec8cd9392d461d8cbc130870a8f68
https://researchspace.auckland.ac.nz/bitstream/2292/5017/2/413.pdf.txt
12469b355b5f8b1bb411590fef2c1961
oai:researchspace.auckland.ac.nz:2292/5018
2009-08-28T12:39:18Z
com_2292_122
col_2292_4963
2009-08-28T03:21:14Z
2009-08-28T03:21:14Z
1999-03
1999-03
http://hdl.handle.net/2292/5018
After showing that the topological notion of boundedly metacompact (first named finitistic) is equivalent to metrisability for a topological manifold we then study related notions. In particular we study the star order of covers of a space. This leads us to propose a definition of dimension which we call star covering dimension.
Boundedly Metacompact or Finitistic Spaces and the Star Order of Covers
Deo, Satya
Gauld, David
After showing that the topological notion of boundedly metacompact (first named finitistic) is equivalent to metrisability for a topological manifold we then study related notions. In particular we study the star order of covers of a space. This leads us to propose a definition of dimension which we call star covering dimension.
Technical Report
Department of Mathematics - Research Reports-412 (1999)
1173-0889
http://hdl.handle.net/2292/5018
Research Reports - Department of Mathematics
https://researchspace.auckland.ac.nz/docs/uoa-docs/rights.htm
The author(s)
Department of Mathematics, The University of Auckland, New Zealand
http://www.math.auckland.ac.nz/Research/Reports/view.php?id=412
https://researchspace.auckland.ac.nz/bitstream/2292/5018/1/412.pdf
ae0fc57e43fa175c329d25fbdc92f5bf
https://researchspace.auckland.ac.nz/bitstream/2292/5018/2/412.pdf.txt
dc86e30a2861087e60d3fdd8350bd9f5
oai:researchspace.auckland.ac.nz:2292/5019
2009-08-28T12:39:18Z
com_2292_122
col_2292_4963
2009-08-28T03:21:15Z
2009-08-28T03:21:15Z
1999-03
1999-03
http://hdl.handle.net/2292/5019
By blending techniques from Set Theory and Algebraic Topology we investigate the order of any homeomorphism of the $n$th power of the long ray or long line $L$ having finite order, finding all possible orders when $n=1, 2, 3$ or 4 in the first case and when $n=1$ or 2 in the second. We also show that all finite powers of $L$ are acyclic with respect to Alexander-Spanier cohomology.
The Torsion of the Group of Homeomorphisms of Powers of the Long Line
Deo, Satya
Gauld, David
By blending techniques from Set Theory and Algebraic Topology we investigate the order of any homeomorphism of the $n$th power of the long ray or long line $L$ having finite order, finding all possible orders when $n=1, 2, 3$ or 4 in the first case and when $n=1$ or 2 in the second. We also show that all finite powers of $L$ are acyclic with respect to Alexander-Spanier cohomology.
Technical Report
Department of Mathematics - Research Reports-411 (1999)
1173-0889
http://hdl.handle.net/2292/5019
Research Reports - Department of Mathematics
https://researchspace.auckland.ac.nz/docs/uoa-docs/rights.htm
The author(s)
Department of Mathematics, The University of Auckland, New Zealand
http://www.math.auckland.ac.nz/Research/Reports/view.php?id=411
https://researchspace.auckland.ac.nz/bitstream/2292/5019/1/411.pdf
755f983ad95c58ad8eed2daf977f175e
https://researchspace.auckland.ac.nz/bitstream/2292/5019/2/411.pdf.txt
39aab836188c3059344073e487eb212b
oai:researchspace.auckland.ac.nz:2292/5020
2009-08-28T12:39:19Z
com_2292_122
col_2292_4963
2009-08-28T03:21:16Z
2009-08-28T03:21:16Z
1999-01
1999-01
http://hdl.handle.net/2292/5020
Brachistochrones are constructed for attractive central force, with logarithmic potential. Each pair of points (except those with the centre between them) are connected by an unique brachistochrone.
Brachistochrones For Attractive Logarithmic Potential
Tee, Garry J.
Brachistochrones are constructed for attractive central force, with logarithmic potential. Each pair of points (except those with the centre between them) are connected by an unique brachistochrone.
Technical Report
Department of Mathematics - Research Reports-410 (1999)
1173-0889
http://hdl.handle.net/2292/5020
Research Reports - Department of Mathematics
https://researchspace.auckland.ac.nz/docs/uoa-docs/rights.htm
The author(s)
Department of Mathematics, The University of Auckland, New Zealand
http://www.math.auckland.ac.nz/Research/Reports/view.php?id=410
https://researchspace.auckland.ac.nz/bitstream/2292/5020/1/410.pdf
39abf29e99bdc810e1463605df3d4682
https://researchspace.auckland.ac.nz/bitstream/2292/5020/2/410.pdf.txt
d2f1108f5134946fb40a4966f088f9dc
oai:researchspace.auckland.ac.nz:2292/5021
2009-08-28T12:39:20Z
com_2292_122
col_2292_4963
2009-08-28T03:21:17Z
2009-08-28T03:21:17Z
2006-05
2006-05
http://hdl.handle.net/2292/5021
A two-dimensional junction is modelled by a quantum graph with a resonance hode. The boundary condition at the node is calculated from the frirst principles . In low temperators limit for simplest T-junction it coincides with the the boundary condition suggested by Datta. The free parameter contained in Datta's condition is interpreted in spectral terms of an intermediate Hamiltonian. The derived boundary condition is applicable for any junction of straight semi-infinite quantum wires attached to the quantum dot, if the junction is thin : the ratio r of the diameter of the quantum dot to the width of the wires is sufficintly large $r approx 4 - 10 $.
Boundary condition at the junction
Harmer, M.
Pavlov, B.
Yafyasov, A.
A two-dimensional junction is modelled by a quantum graph with a resonance hode. The boundary condition at the node is calculated from the frirst principles . In low temperators limit for simplest T-junction it coincides with the the boundary condition suggested by Datta. The free parameter contained in Datta's condition is interpreted in spectral terms of an intermediate Hamiltonian. The derived boundary condition is applicable for any junction of straight semi-infinite quantum wires attached to the quantum dot, if the junction is thin : the ratio r of the diameter of the quantum dot to the width of the wires is sufficintly large $r approx 4 - 10 $.
Technical Report
Department of Mathematics - Research Reports-548 (2006)
1173-0889
http://hdl.handle.net/2292/5021
Research Reports - Department of Mathematics
https://researchspace.auckland.ac.nz/docs/uoa-docs/rights.htm
The author(s)
Department of Mathematics, The University of Auckland, New Zealand
http://www.math.auckland.ac.nz/Research/Reports/view.php?id=548
https://researchspace.auckland.ac.nz/bitstream/2292/5021/1/548.pdf
876e32ebe386d978e022130acd180246
https://researchspace.auckland.ac.nz/bitstream/2292/5021/2/548.pdf.txt
c778d72087c01fb5a0db0d3091aec00a
oai:researchspace.auckland.ac.nz:2292/5022
2009-08-28T12:39:22Z
com_2292_122
col_2292_4963
2009-08-28T03:21:18Z
2009-08-28T03:21:18Z
1999-01
1999-01
http://hdl.handle.net/2292/5022
Brachistochrones for inverse square repulsion are expressed in terms of elliptic integrals, as for inverse square attraction. But, the set of brachistochrones is much more complicated than for inverse square attraction. Each pair of points is connected by infinitely many brachistochrones, on each of which the passage time is a local minimum, and the global minimum passage time is attained on one (or on infinitely many) of those curves. The bounded brachistochrones starting at a fixed point are separated from the unbounded brachistochrones by a Critical Brachistochrone, which is expressed in terms of elementary functions.
Brachistochrones for Repulsive Inverse Square Force
Tee, Garry J.
Brachistochrones for inverse square repulsion are expressed in terms of elliptic integrals, as for inverse square attraction. But, the set of brachistochrones is much more complicated than for inverse square attraction. Each pair of points is connected by infinitely many brachistochrones, on each of which the passage time is a local minimum, and the global minimum passage time is attained on one (or on infinitely many) of those curves. The bounded brachistochrones starting at a fixed point are separated from the unbounded brachistochrones by a Critical Brachistochrone, which is expressed in terms of elementary functions.
Technical Report
Department of Mathematics - Research Reports-409 (1999)
1173-0889
http://hdl.handle.net/2292/5022
Research Reports - Department of Mathematics
https://researchspace.auckland.ac.nz/docs/uoa-docs/rights.htm
The author(s)
Department of Mathematics, The University of Auckland, New Zealand
http://www.math.auckland.ac.nz/Research/Reports/view.php?id=409
https://researchspace.auckland.ac.nz/bitstream/2292/5022/1/409.pdf
9bd51e3965d5bb5c86b092c0d98fad36
https://researchspace.auckland.ac.nz/bitstream/2292/5022/2/409.pdf.txt
eea4d2e5fe3b8fcab82a978b804d4af1
oai:researchspace.auckland.ac.nz:2292/5023
2009-08-28T12:39:23Z
com_2292_122
col_2292_4963
2009-08-28T03:21:18Z
2009-08-28T03:21:18Z
1999-03
1999-03
http://hdl.handle.net/2292/5023
The Green's function for harmonic downward forcing of an infinite thin floating plate is derived. The Green's function models the response of a uniform sheet of fast ice when locally loaded at rates at which the ice may be taken to be elastic. A closed-form expression is given for the potential throughout the water and detailed expressions are given for the vertical displacement of the ice sheet. The displacement is graphed for various typical thickness of the ice sheet and for a range of frequencies of forcing.
Green's Function for Forcing of a Thin Floating Plate
Fox, Colin
Chung, Hyuck
The Green's function for harmonic downward forcing of an infinite thin floating plate is derived. The Green's function models the response of a uniform sheet of fast ice when locally loaded at rates at which the ice may be taken to be elastic. A closed-form expression is given for the potential throughout the water and detailed expressions are given for the vertical displacement of the ice sheet. The displacement is graphed for various typical thickness of the ice sheet and for a range of frequencies of forcing.
Technical Report
Department of Mathematics - Research Reports-408 (1999)
1173-0889
http://hdl.handle.net/2292/5023
Research Reports - Department of Mathematics
https://researchspace.auckland.ac.nz/docs/uoa-docs/rights.htm
The author(s)
Department of Mathematics, The University of Auckland, New Zealand
http://www.math.auckland.ac.nz/Research/Reports/view.php?id=408
https://researchspace.auckland.ac.nz/bitstream/2292/5023/1/408.pdf
2730338aa391c4015e5739bb10d3b4e0
https://researchspace.auckland.ac.nz/bitstream/2292/5023/2/408.pdf.txt
cba7f5f44d40293c4d9ef9d045c01adc
oai:researchspace.auckland.ac.nz:2292/5024
2009-08-28T12:39:25Z
com_2292_122
col_2292_4963
2009-08-28T03:21:19Z
2009-08-28T03:21:19Z
1999-02
1999-02
http://hdl.handle.net/2292/5024
A Bayesian method has been proposed for analysing radiocarbon dates. The method takes into account stratigraphic constraints on recovered calendar dates. We find that the non-informative priors in use in the literature apply a bias towards wider date ranges which is not in general supported by substantial prior knowledge. We recommend using a prior which has a uniform marginal date range. We show how such priors are derived from a model of the deposition and observation process. We apply the method to relatively large data sets, examining the effect that various priors have on the reconstructed dates.
Radiocarbon dating with temporal order constraints
Nicholls, Geoff
Jones, Martin
A Bayesian method has been proposed for analysing radiocarbon dates. The method takes into account stratigraphic constraints on recovered calendar dates. We find that the non-informative priors in use in the literature apply a bias towards wider date ranges which is not in general supported by substantial prior knowledge. We recommend using a prior which has a uniform marginal date range. We show how such priors are derived from a model of the deposition and observation process. We apply the method to relatively large data sets, examining the effect that various priors have on the reconstructed dates.
Technical Report
Department of Mathematics - Research Reports-407 (1999)
1173-0889
http://hdl.handle.net/2292/5024
Research Reports - Department of Mathematics
https://researchspace.auckland.ac.nz/docs/uoa-docs/rights.htm
The author(s)
Department of Mathematics, The University of Auckland, New Zealand
http://www.math.auckland.ac.nz/Research/Reports/view.php?id=407
https://researchspace.auckland.ac.nz/bitstream/2292/5024/1/407.pdf
7a1db8d8d30f9b7d5e54496555355d53
https://researchspace.auckland.ac.nz/bitstream/2292/5024/2/407.pdf.txt
7ec38834a0f19b99dcbdbda3de2a025b
oai:researchspace.auckland.ac.nz:2292/5025
2009-08-28T12:39:26Z
com_2292_122
col_2292_4963
2009-08-28T03:21:20Z
2009-08-28T03:21:20Z
1998-12
1998-12
http://hdl.handle.net/2292/5025
We consider a notion of embedding digraphs on orientable surfaces, applicable to digraphs in which the indegree equals the outdegree for every vertex, i.e., Eulerian digraphs. This idea has been considered before in the context of "compatible Euler tours" or "orthogonal A-trails" by Andsersen at al [1] and by Bouchet [4]. This prior work has mostly been limited to embeddings of Eulerian digraphs on predetermined surfaces, and to digraphs with underlying graphs of maximum degree at most 4. In this paper, a foundation is laid for the study of all Eulerian digraph embeddings. Results are proved which are analogous to those fundamental to the theory of undirected graph embeddings, such as Duke's Theorem [5], and an infinite family of digraphs which demonstrates that the genus range for an embeddable digraph can be any nonnegative integer is given. We show that it is possible to have genus range equal to one, with arbitrarily large minimum genus, unlike in the undirected case. The difference between the minimum genera of a digraph and its underlying graph is considered, as is the difference between the maximum genera. We say that a digraph is upper-embeddable if it can be embedded with 2 or 3 regions, and prove that every regular tournament is upper-embeddable.
Embedding Digraphs on Orientable Surfaces
Bonnington, Paul
Conder, Marston
McKenna, Patricia
Morton, Margaret
We consider a notion of embedding digraphs on orientable surfaces, applicable to digraphs in which the indegree equals the outdegree for every vertex, i.e., Eulerian digraphs. This idea has been considered before in the context of "compatible Euler tours" or "orthogonal A-trails" by Andsersen at al [1] and by Bouchet [4]. This prior work has mostly been limited to embeddings of Eulerian digraphs on predetermined surfaces, and to digraphs with underlying graphs of maximum degree at most 4. In this paper, a foundation is laid for the study of all Eulerian digraph embeddings. Results are proved which are analogous to those fundamental to the theory of undirected graph embeddings, such as Duke's Theorem [5], and an infinite family of digraphs which demonstrates that the genus range for an embeddable digraph can be any nonnegative integer is given. We show that it is possible to have genus range equal to one, with arbitrarily large minimum genus, unlike in the undirected case. The difference between the minimum genera of a digraph and its underlying graph is considered, as is the difference between the maximum genera. We say that a digraph is upper-embeddable if it can be embedded with 2 or 3 regions, and prove that every regular tournament is upper-embeddable.
Technical Report
Department of Mathematics - Research Reports-406 (1998)
1173-0889
http://hdl.handle.net/2292/5025
Research Reports - Department of Mathematics
https://researchspace.auckland.ac.nz/docs/uoa-docs/rights.htm
The author(s)
Department of Mathematics, The University of Auckland, New Zealand
http://www.math.auckland.ac.nz/Research/Reports/view.php?id=406
https://researchspace.auckland.ac.nz/bitstream/2292/5025/1/406.pdf
4ddb2578bdc48cf9d56e8152e7149311
https://researchspace.auckland.ac.nz/bitstream/2292/5025/2/406.pdf.txt
ecdf9b4d09e2b9c1c250ad10efce2d20
oai:researchspace.auckland.ac.nz:2292/5026
2009-08-28T12:39:28Z
com_2292_122
col_2292_4963
2009-08-28T03:21:21Z
2009-08-28T03:21:21Z
1998-11
1998-11
http://hdl.handle.net/2292/5026
Christiaan Huygens proved in 1659 that a particle sliding smoothly (under uniform gravity) on a cycloid with axis vertically down reaches the base in a period independent of the starting point. He built very accurate pendulum clocks with cycloidal pendulums. Mark Denny has constructed another curve purported to give descent to the base in a period independent of the starting point: but the cycloid is the only smooth plane curve with that property. Johann Bernoulli 1st proved in 1696 that, for any pair of fixed points, the brachistochrone (the curve of quickest descent) under uniform gravity is an arc of a cycloid. In 1976, Ian Stewart asked, what is the brachistochrone for central gravity under the inverse square law? The solution is found explicitly, in terms of elliptic integrals.
Isochrones and Brachistochrones
Tee, Garry J.
Christiaan Huygens proved in 1659 that a particle sliding smoothly (under uniform gravity) on a cycloid with axis vertically down reaches the base in a period independent of the starting point. He built very accurate pendulum clocks with cycloidal pendulums. Mark Denny has constructed another curve purported to give descent to the base in a period independent of the starting point: but the cycloid is the only smooth plane curve with that property. Johann Bernoulli 1st proved in 1696 that, for any pair of fixed points, the brachistochrone (the curve of quickest descent) under uniform gravity is an arc of a cycloid. In 1976, Ian Stewart asked, what is the brachistochrone for central gravity under the inverse square law? The solution is found explicitly, in terms of elliptic integrals.
Technical Report
Department of Mathematics - Research Reports-405 (1998)
1173-0889
http://hdl.handle.net/2292/5026
Research Reports - Department of Mathematics
https://researchspace.auckland.ac.nz/docs/uoa-docs/rights.htm
The author(s)
Department of Mathematics, The University of Auckland, New Zealand
http://www.math.auckland.ac.nz/Research/Reports/view.php?id=405
https://researchspace.auckland.ac.nz/bitstream/2292/5026/1/405.pdf
f5c1e89be8a6ee6ee08a62fb50d6a6a0
https://researchspace.auckland.ac.nz/bitstream/2292/5026/2/405.pdf.txt
921cbc795bfcd403f481b628f57a58d8
oai:researchspace.auckland.ac.nz:2292/5027
2009-08-28T12:39:29Z
com_2292_122
col_2292_4963
2009-08-28T03:21:22Z
2009-08-28T03:21:22Z
1998-09
1998-09
http://hdl.handle.net/2292/5027
The problem of description of those positive weights on the boundary $Gamma$ of a finitely connected domain $Omega$ for which the angle in a weighted $L_2$ space on $Gamma$ between the linear space ${cal R}(Omega)$ of all rational functions on $bar{bf {C}}$ with poles outside of $Clos Omega$ and the linear space ${cal R}(Omega)_-={bar{f}vert fin {cal R}(Omega)}$ of antianalytic rational functions, is a natural analog of the problem solved in a famous Helson-Szeg"o theorem. In this paper we solve more general problem and give a complete description (in terms of necessary and sufficient conditions) of those positive weights $w$ on $Gamma$ for which the sum of the closures in $L_2(Gamma, w)$ of the subspaces ${cal R}(Omega)$ and ${cal R}(Omega)_-$ is closed and their intersection is finite dimensional. The given description is similar to that one in the Helson-Sarason Theorem, i.e. the "modified" weight should satisfy the Muckenhoupt condition.
On the subspaces of analytic and antianalytic functions
Fedorov, Sergei
The problem of description of those positive weights on the boundary $Gamma$ of a finitely connected domain $Omega$ for which the angle in a weighted $L_2$ space on $Gamma$ between the linear space ${cal R}(Omega)$ of all rational functions on $bar{bf {C}}$ with poles outside of $Clos Omega$ and the linear space ${cal R}(Omega)_-={bar{f}vert fin {cal R}(Omega)}$ of antianalytic rational functions, is a natural analog of the problem solved in a famous Helson-Szeg"o theorem. In this paper we solve more general problem and give a complete description (in terms of necessary and sufficient conditions) of those positive weights $w$ on $Gamma$ for which the sum of the closures in $L_2(Gamma, w)$ of the subspaces ${cal R}(Omega)$ and ${cal R}(Omega)_-$ is closed and their intersection is finite dimensional. The given description is similar to that one in the Helson-Sarason Theorem, i.e. the "modified" weight should satisfy the Muckenhoupt condition.
Technical Report
Department of Mathematics - Research Reports-404 (1998)
1173-0889
http://hdl.handle.net/2292/5027
Research Reports - Department of Mathematics
https://researchspace.auckland.ac.nz/docs/uoa-docs/rights.htm
The author(s)
Department of Mathematics, The University of Auckland, New Zealand
http://www.math.auckland.ac.nz/Research/Reports/view.php?id=404
https://researchspace.auckland.ac.nz/bitstream/2292/5027/1/404.pdf
d366cd882c46d313ddd4674e89df98b0
https://researchspace.auckland.ac.nz/bitstream/2292/5027/2/404.pdf.txt
6e450d65b62436e8a7a9722d102fc1eb
oai:researchspace.auckland.ac.nz:2292/5028
2009-08-28T12:39:30Z
com_2292_122
col_2292_4963
2009-08-28T03:21:22Z
2009-08-28T03:21:22Z
1998
1998
http://hdl.handle.net/2292/5028
A graph is g-universal if it satisfies two conditions. First it must contain a subdivision of every proper planar graph of degree at most three as a subgraph. Second, the function g puts a restriction on the subdivision. In particular, for a planar graph H of degree at most three, a fixed vertex $w_0$ of H, and an arbitrary vertex w of H, the images of the vertices $w_0$ and w in the universal graph are no more than $g(d(w_0, w))$ apart. We show that a large class of planar graphs are $O(n^3)4-universal.
Planar Universal Graphs
Brand, Neal
Morton, Margaret
A graph is g-universal if it satisfies two conditions. First it must contain a subdivision of every proper planar graph of degree at most three as a subgraph. Second, the function g puts a restriction on the subdivision. In particular, for a planar graph H of degree at most three, a fixed vertex $w_0$ of H, and an arbitrary vertex w of H, the images of the vertices $w_0$ and w in the universal graph are no more than $g(d(w_0, w))$ apart. We show that a large class of planar graphs are $O(n^3)4-universal.
Technical Report
Department of Mathematics - Research Reports-403 (1998)
1173-0889
http://hdl.handle.net/2292/5028
Research Reports - Department of Mathematics
https://researchspace.auckland.ac.nz/docs/uoa-docs/rights.htm
The author(s)
Department of Mathematics, The University of Auckland, New Zealand
http://www.math.auckland.ac.nz/Research/Reports/view.php?id=403
https://researchspace.auckland.ac.nz/bitstream/2292/5028/1/403.pdf
de661f043c0d8e0feb2a5d1fe0e6d2c8
https://researchspace.auckland.ac.nz/bitstream/2292/5028/2/403.pdf.txt
8d44b82d171a69e03023243ef38a41a3
oai:researchspace.auckland.ac.nz:2292/5029
2009-08-28T12:39:31Z
com_2292_122
col_2292_4963
2009-08-28T03:21:24Z
2009-08-28T03:21:24Z
1998-08
1998-08
http://hdl.handle.net/2292/5029
We investigate computable isomorphism types of groups. Our main result states that for any $ninomegacup{omega}$ there exists a computably categorical nilpotent of class $2$ group $G$ which being expanded by a finite number of constants has exactly $n$ computable isomorphism types. This result is based on the similar result for computable nonassociative rings.
Computable Rings, Groups and Their Isomorphisms
Khoussainov, B.
Slinko, A.
We investigate computable isomorphism types of groups. Our main result states that for any $ninomegacup{omega}$ there exists a computably categorical nilpotent of class $2$ group $G$ which being expanded by a finite number of constants has exactly $n$ computable isomorphism types. This result is based on the similar result for computable nonassociative rings.
Technical Report
Department of Mathematics - Research Reports-402 (1998)
1173-0889
http://hdl.handle.net/2292/5029
Research Reports - Department of Mathematics
https://researchspace.auckland.ac.nz/docs/uoa-docs/rights.htm
The author(s)
Department of Mathematics, The University of Auckland, New Zealand
http://www.math.auckland.ac.nz/Research/Reports/view.php?id=402
https://researchspace.auckland.ac.nz/bitstream/2292/5029/1/402.pdf
440db32238d495c7ff33ea20fb95bdd8
https://researchspace.auckland.ac.nz/bitstream/2292/5029/2/402.pdf.txt
f12619889d25d180109029bcfd12c27d
oai:researchspace.auckland.ac.nz:2292/5030
2019-12-19T03:30:19Z
com_2292_122
col_2292_4963
2009-08-28T03:21:24Z
2009-08-28T03:21:24Z
1998-08
1998-08
http://hdl.handle.net/2292/5030
[no abstract available]
Dade's Conjecture for Steinberg Triality Groups $^3D_4(q)$ in Non-defining Characteristics
An, Jianbei
[no abstract available]
Technical Report
Department of Mathematics - Research Reports-401 (1998)
1173-0889
http://hdl.handle.net/2292/5030
Research Reports - Department of Mathematics
2041
16440
7362
7379
https://researchspace.auckland.ac.nz/docs/uoa-docs/rights.htm
The author(s)
Department of Mathematics, The University of Auckland, New Zealand
http://www.math.auckland.ac.nz/Research/Reports/view.php?id=401
https://researchspace.auckland.ac.nz/bitstream/2292/5030/1/401.pdf
5c8c382c698e4f62940ef6fdd034eed6
https://researchspace.auckland.ac.nz/bitstream/2292/5030/2/401.pdf.txt
cbe758027eb6d8145c7946349009f271
oai:researchspace.auckland.ac.nz:2292/5031
2009-08-28T12:39:33Z
com_2292_122
col_2292_4963
2009-08-28T03:21:25Z
2009-08-28T03:21:25Z
1998-06
1998-06
http://hdl.handle.net/2292/5031
In this paper it is shown that for all but finitely many positive integers $n$, there is a finite connected 7-arc-transitive quartic graph with the alternating group $A_n$ acting transitively on its 7-arcs, and another with the symmetric group $S_n$ acting transitively on its 7-arcs. The proof uses a construction involving permutation representations to obtain finite graphs with the desired property.
The infinitude of 7-arc-transitive graphs
Conder, Marston
Walker, C.
In this paper it is shown that for all but finitely many positive integers $n$, there is a finite connected 7-arc-transitive quartic graph with the alternating group $A_n$ acting transitively on its 7-arcs, and another with the symmetric group $S_n$ acting transitively on its 7-arcs. The proof uses a construction involving permutation representations to obtain finite graphs with the desired property.
Technical Report
Department of Mathematics - Research Reports-400 (1998)
1173-0889
http://hdl.handle.net/2292/5031
Research Reports - Department of Mathematics
https://researchspace.auckland.ac.nz/docs/uoa-docs/rights.htm
The author(s)
Department of Mathematics, The University of Auckland, New Zealand
http://www.math.auckland.ac.nz/Research/Reports/view.php?id=400
https://researchspace.auckland.ac.nz/bitstream/2292/5031/1/400.pdf
eb1878428c186f3a38e5114a93e6fee4
https://researchspace.auckland.ac.nz/bitstream/2292/5031/2/400.pdf.txt
3986823e268063da7555e1445bd7b612
oai:researchspace.auckland.ac.nz:2292/5032
2009-08-28T12:39:34Z
com_2292_122
col_2292_4963
2009-08-28T03:21:26Z
2009-08-28T03:21:26Z
2006-03
2006-03
http://hdl.handle.net/2292/5032
This paper presents a new model of voter behaviour under methods of proportional representation (PR). We assume that voters are concerned, first and foremost, with the distribution of power in the post-election parliament. We abstract away from rounding, and assume that a party securing k percent of the vote wins exactly k percent of the available seats. We show that, irrespective of which positional scoring rule is adopted, there will always exist circumstances where a voter would have an incentive to vote insincerely. We demonstrate that a voter's attitude toward uncertainty can influence his or her incentives to make an insincere vote. Finally, we show that the introduction of a threshold - a rule that a party must secure at least a certain percentage of the vote in order to reach parliament - creates new opportunities for strategic voting. We use the model to explain voter behaviour at the most recent New Zealand general election.
On the manipulability of proportional representation
Slinko, Arkadii
White, Shaun
This paper presents a new model of voter behaviour under methods of proportional representation (PR). We assume that voters are concerned, first and foremost, with the distribution of power in the post-election parliament. We abstract away from rounding, and assume that a party securing k percent of the vote wins exactly k percent of the available seats. We show that, irrespective of which positional scoring rule is adopted, there will always exist circumstances where a voter would have an incentive to vote insincerely. We demonstrate that a voter's attitude toward uncertainty can influence his or her incentives to make an insincere vote. Finally, we show that the introduction of a threshold - a rule that a party must secure at least a certain percentage of the vote in order to reach parliament - creates new opportunities for strategic voting. We use the model to explain voter behaviour at the most recent New Zealand general election.
Technical Report
Department of Mathematics - Research Reports-547 (2006)
1173-0889
http://hdl.handle.net/2292/5032
Research Reports - Department of Mathematics
https://researchspace.auckland.ac.nz/docs/uoa-docs/rights.htm
The author(s)
Department of Mathematics, The University of Auckland, New Zealand
http://www.math.auckland.ac.nz/Research/Reports/view.php?id=547
https://researchspace.auckland.ac.nz/bitstream/2292/5032/1/547.pdf
ab2615ca2591bd3e6758b5e04ad172fe
https://researchspace.auckland.ac.nz/bitstream/2292/5032/2/547.pdf.txt
6ed3fd56b4504cc4c9b198b21243161b
oai:researchspace.auckland.ac.nz:2292/5033
2009-08-28T12:39:36Z
com_2292_122
col_2292_4963
2009-08-28T03:21:27Z
2009-08-28T03:21:27Z
1998-05
1998-05
http://hdl.handle.net/2292/5033
We present here a novel numerical solution to the linear Boltzmann equation. The method is based on reducing the linear Boltzmann equation to a matrix partial differential equation rather than a partial integro-differential equation. A method for calculating the evolution using a complex generalised eigenfunction method is present for two simple example cases. The generalisation of this method follows straight forwardly.
A Novel Numerical Solution Method for the Linear Boltzmann Equation
Meylan, Michael H.
We present here a novel numerical solution to the linear Boltzmann equation. The method is based on reducing the linear Boltzmann equation to a matrix partial differential equation rather than a partial integro-differential equation. A method for calculating the evolution using a complex generalised eigenfunction method is present for two simple example cases. The generalisation of this method follows straight forwardly.
Technical Report
Department of Mathematics - Research Reports-399 (1998)
1173-0889
http://hdl.handle.net/2292/5033
Research Reports - Department of Mathematics
https://researchspace.auckland.ac.nz/docs/uoa-docs/rights.htm
The author(s)
Department of Mathematics, The University of Auckland, New Zealand
http://www.math.auckland.ac.nz/Research/Reports/view.php?id=399
https://researchspace.auckland.ac.nz/bitstream/2292/5033/1/399.pdf
82aed2a0c50d423a276dfb822a4cb8c2
https://researchspace.auckland.ac.nz/bitstream/2292/5033/2/399.pdf.txt
1669809ae4a25b44f6dac59830196931
oai:researchspace.auckland.ac.nz:2292/5034
2009-08-28T12:39:37Z
com_2292_122
col_2292_4963
2009-08-28T03:21:28Z
2009-08-28T03:21:28Z
1998-05
1998-05
http://hdl.handle.net/2292/5034
[no abstract available]
On one recent result on the intersection of weighted hardy spaces
Fedorov, Sergei
[no abstract available]
Technical Report
Department of Mathematics - Research Reports-398 (1998)
1173-0889
http://hdl.handle.net/2292/5034
Research Reports - Department of Mathematics
https://researchspace.auckland.ac.nz/docs/uoa-docs/rights.htm
The author(s)
Department of Mathematics, The University of Auckland, New Zealand
http://www.math.auckland.ac.nz/Research/Reports/view.php?id=398
https://researchspace.auckland.ac.nz/bitstream/2292/5034/1/398.pdf
c28811a16969e80407aa653114839840
https://researchspace.auckland.ac.nz/bitstream/2292/5034/2/398.pdf.txt
c40b734c9c90e7a7d3509c1a31913b0b
oai:researchspace.auckland.ac.nz:2292/5035
2009-08-28T12:39:37Z
com_2292_122
col_2292_4963
2009-08-28T03:21:29Z
2009-08-28T03:21:29Z
1998-04
1998-04
http://hdl.handle.net/2292/5035
and prove that the corresponding groups in each pair are isomorphic.
Certain cyclically presented groups are isomorphic
Johnson, D.L.
Kim, A.C.
O'Brien, E.A.
and prove that the corresponding groups in each pair are isomorphic.
Technical Report
Department of Mathematics - Research Reports-397 (1998)
1173-0889
http://hdl.handle.net/2292/5035
Research Reports - Department of Mathematics
https://researchspace.auckland.ac.nz/docs/uoa-docs/rights.htm
The author(s)
Department of Mathematics, The University of Auckland, New Zealand
http://www.math.auckland.ac.nz/Research/Reports/view.php?id=397
https://researchspace.auckland.ac.nz/bitstream/2292/5035/1/397.pdf
99a84867b9ee7dac4fdd4d2df1693f2a
https://researchspace.auckland.ac.nz/bitstream/2292/5035/2/397.pdf.txt
6bbd8415188e557108d63a87fc46cb6f
oai:researchspace.auckland.ac.nz:2292/5036
2009-08-28T12:39:38Z
com_2292_122
col_2292_4963
2009-08-28T03:21:29Z
2009-08-28T03:21:29Z
1998-04
1998-04
http://hdl.handle.net/2292/5036
[no abstract available]
On the Choquet-Dolecki Theorem
Cao, Jiling
Moors, Warren B.
Reilly, Ivan
[no abstract available]
Technical Report
Department of Mathematics - Research Reports-396 (1998)
1173-0889
http://hdl.handle.net/2292/5036
Research Reports - Department of Mathematics
https://researchspace.auckland.ac.nz/docs/uoa-docs/rights.htm
The author(s)
Department of Mathematics, The University of Auckland, New Zealand
http://www.math.auckland.ac.nz/Research/Reports/view.php?id=396
https://researchspace.auckland.ac.nz/bitstream/2292/5036/1/396.pdf
dd881f0107c9c2eb3cdc7750e4c4ab22
https://researchspace.auckland.ac.nz/bitstream/2292/5036/2/396.pdf.txt
94c6629af18a3f52ac09a6b64b84af80
oai:researchspace.auckland.ac.nz:2292/5037
2009-08-28T12:39:39Z
com_2292_122
col_2292_4963
2009-08-28T03:21:30Z
2009-08-28T03:21:30Z
1998-03
1998-03
http://hdl.handle.net/2292/5037
use it to classify the radical subgroups and chains of the Fischer simple group $Fi_{23}$. We verify the Alperin weight conjecture and the Dade final conjectures for this group.
The Alperin and Dade conjectures for the Fischer simple group $Fi_{23}$
An, Jianbei
O'Brien, E.A.
use it to classify the radical subgroups and chains of the Fischer simple group $Fi_{23}$. We verify the Alperin weight conjecture and the Dade final conjectures for this group.
Technical Report
Department of Mathematics - Research Reports-395 (1998)
1173-0889
http://hdl.handle.net/2292/5037
Research Reports - Department of Mathematics
https://researchspace.auckland.ac.nz/docs/uoa-docs/rights.htm
The author(s)
Department of Mathematics, The University of Auckland, New Zealand
http://www.math.auckland.ac.nz/Research/Reports/view.php?id=395
https://researchspace.auckland.ac.nz/bitstream/2292/5037/1/395.pdf
2568672a150650f109ea1e9e6cf91f98
https://researchspace.auckland.ac.nz/bitstream/2292/5037/2/395.pdf.txt
7963fcbce65bce06221890fffe72fefd
oai:researchspace.auckland.ac.nz:2292/5038
2009-08-28T12:39:41Z
com_2292_122
col_2292_4963
2009-08-28T03:21:31Z
2009-08-28T03:21:31Z
1998-04
1998-04
http://hdl.handle.net/2292/5038
from the Schwarz-Christoffel transformation of the upper half-plane onto a parallelogram and are naturally related to Gaussian hypergeometric functions. Certain combinations of these integrals also occur in analytic number theory in the study of Ramanujan's modular equations and approximations to $pi$. The authors study the monotoneity and convexity properties of these quantities and obtain sharp inequalities for them.
Generalized Elliptic Integrals and Modular Equations
Anderson, G.D.
Qiu, S.-L.
Vamanamurthy, M.K.
Vuorinen, M.
from the Schwarz-Christoffel transformation of the upper half-plane onto a parallelogram and are naturally related to Gaussian hypergeometric functions. Certain combinations of these integrals also occur in analytic number theory in the study of Ramanujan's modular equations and approximations to $pi$. The authors study the monotoneity and convexity properties of these quantities and obtain sharp inequalities for them.
Technical Report
Department of Mathematics - Research Reports-394 (1998)
1173-0889
http://hdl.handle.net/2292/5038
Research Reports - Department of Mathematics
https://researchspace.auckland.ac.nz/docs/uoa-docs/rights.htm
The author(s)
Department of Mathematics, The University of Auckland, New Zealand
http://www.math.auckland.ac.nz/Research/Reports/view.php?id=394
https://researchspace.auckland.ac.nz/bitstream/2292/5038/1/394.pdf
6bcf05d02d3fd4eb691e0282199bdaa6
https://researchspace.auckland.ac.nz/bitstream/2292/5038/2/394.pdf.txt
9fa6e77246688bf7d1b4c83c43582364
oai:researchspace.auckland.ac.nz:2292/5039
2009-08-28T12:39:42Z
com_2292_122
col_2292_4963
2009-08-28T03:21:32Z
2009-08-28T03:21:32Z
1998-03
1998-03
http://hdl.handle.net/2292/5039
[no abstract available]
1-factorizations of Cayley graphs on solvable groups
Alspach, Brian
Morton, Margaret
Qin, Yusheng
[no abstract available]
Technical Report
Department of Mathematics - Research Reports-393 (1998)
1173-0889
http://hdl.handle.net/2292/5039
Research Reports - Department of Mathematics
https://researchspace.auckland.ac.nz/docs/uoa-docs/rights.htm
The author(s)
Department of Mathematics, The University of Auckland, New Zealand
http://www.math.auckland.ac.nz/Research/Reports/view.php?id=393
https://researchspace.auckland.ac.nz/bitstream/2292/5039/1/393.pdf
0d43210f75fe5c592e2bfbb3a5bf30db
https://researchspace.auckland.ac.nz/bitstream/2292/5039/2/393.pdf.txt
e303e1d7a958e8f9e3fdbb27a894d2c7
oai:researchspace.auckland.ac.nz:2292/5040
2009-08-28T12:39:43Z
com_2292_122
col_2292_4963
2009-08-28T03:21:33Z
2009-08-28T03:21:33Z
1998-03
1998-03
http://hdl.handle.net/2292/5040
[no abstract available]
The Alperin and Dade Conjectures for the Conway Simple Group $Co_2$
An, Jianbei
O'Brien, E.A.
[no abstract available]
Technical Report
Department of Mathematics - Research Reports-392 (1998)
1173-0889
http://hdl.handle.net/2292/5040
Research Reports - Department of Mathematics
https://researchspace.auckland.ac.nz/docs/uoa-docs/rights.htm
The author(s)
Department of Mathematics, The University of Auckland, New Zealand
http://www.math.auckland.ac.nz/Research/Reports/view.php?id=392
https://researchspace.auckland.ac.nz/bitstream/2292/5040/1/392.pdf
4c931d2da6e06e62269dd0a2e59b1029
https://researchspace.auckland.ac.nz/bitstream/2292/5040/2/392.pdf.txt
f3b2d412b15ad7c4a25d36d21a40c888
oai:researchspace.auckland.ac.nz:2292/5041
2009-08-28T12:39:43Z
com_2292_122
col_2292_4963
2009-08-28T03:21:34Z
2009-08-28T03:21:34Z
1998-03
1998-03
http://hdl.handle.net/2292/5041
$D$-representability of Lipschitz functions defined on arbitrary Banach spaces reduces to the study of these properties on separable Banach spaces.
Separable determination of integrability and minimality of the Clarke subdifferential mapping
Borwein, Jonathan M.
Moors, Warren B.
$D$-representability of Lipschitz functions defined on arbitrary Banach spaces reduces to the study of these properties on separable Banach spaces.
Technical Report
Department of Mathematics - Research Reports-391 (1998)
1173-0889
http://hdl.handle.net/2292/5041
Research Reports - Department of Mathematics
https://researchspace.auckland.ac.nz/docs/uoa-docs/rights.htm
The author(s)
Department of Mathematics, The University of Auckland, New Zealand
http://www.math.auckland.ac.nz/Research/Reports/view.php?id=391
https://researchspace.auckland.ac.nz/bitstream/2292/5041/1/391.pdf
e87877dd392c6a60770c4901ce4b622b
https://researchspace.auckland.ac.nz/bitstream/2292/5041/2/391.pdf.txt
d1141f4ff9cc05841e5cf331e1f53ebf
oai:researchspace.auckland.ac.nz:2292/5042
2009-08-28T12:39:44Z
com_2292_122
col_2292_4963
2009-08-28T03:21:35Z
2009-08-28T03:21:35Z
1998-03
1998-03
http://hdl.handle.net/2292/5042
[no abstract available]
CONTINUOUS BRANCHES OF INVERSES OF THE 12 JACOBI ELLIPTIC FUNCTIONS FOR REAL ARGUMENT
Tee, Garry J.
[no abstract available]
Technical Report
Department of Mathematics - Research Reports-390 (1998)
1173-0889
http://hdl.handle.net/2292/5042
Research Reports - Department of Mathematics
https://researchspace.auckland.ac.nz/docs/uoa-docs/rights.htm
The author(s)
Department of Mathematics, The University of Auckland, New Zealand
http://www.math.auckland.ac.nz/Research/Reports/view.php?id=390
https://researchspace.auckland.ac.nz/bitstream/2292/5042/1/390.pdf
c163bb4e552ce441521de43f62ba497b
https://researchspace.auckland.ac.nz/bitstream/2292/5042/2/390.pdf.txt
56eb2bd9e7a769ada7dd0a3842ea6bf0
oai:researchspace.auckland.ac.nz:2292/5043
2009-08-28T12:39:45Z
com_2292_122
col_2292_4963
2009-08-28T03:21:35Z
2009-08-28T03:21:35Z
2006-03
2006-03
http://hdl.handle.net/2292/5043
The main purpose of this paper is to prove the following two theorems, an order hereditary closure preserving sum theorem and an hereditary theorem: (1) If a topological property $mathcal{P}$ satisfies $(sum')$ and is closed hereditary, and if $mathcal{V}$ is an order hereditary closure preserving open cover of $X$ and each $V inmathcal{V}$ is elementary and possesses $mathcal{P}$, then $X$ possesses $mathcal{P}$. (2) Let a topological property $mathcal{P}$ satisfy $(sum')$ and $(beta),$ and be closed hereditary. Let $X$ be a topological space which possesses $mathcal{P}$. If every open subset $G$ of $X$ can be written as an order hereditary closure preserving (in $G$) collection of elementary sets, then every subset of $X$ possesses $mathcal{P}$.
On the Order Hereditary Closure Preserving Sum Theorem
Gong, Jianhua
Reilly, Ivan
The main purpose of this paper is to prove the following two theorems, an order hereditary closure preserving sum theorem and an hereditary theorem: (1) If a topological property $mathcal{P}$ satisfies $(sum')$ and is closed hereditary, and if $mathcal{V}$ is an order hereditary closure preserving open cover of $X$ and each $V inmathcal{V}$ is elementary and possesses $mathcal{P}$, then $X$ possesses $mathcal{P}$. (2) Let a topological property $mathcal{P}$ satisfy $(sum')$ and $(beta),$ and be closed hereditary. Let $X$ be a topological space which possesses $mathcal{P}$. If every open subset $G$ of $X$ can be written as an order hereditary closure preserving (in $G$) collection of elementary sets, then every subset of $X$ possesses $mathcal{P}$.
Technical Report
Department of Mathematics - Research Reports-546 (2006)
1173-0889
http://hdl.handle.net/2292/5043
Research Reports - Department of Mathematics
https://researchspace.auckland.ac.nz/docs/uoa-docs/rights.htm
The author(s)
Department of Mathematics, The University of Auckland, New Zealand
http://www.math.auckland.ac.nz/Research/Reports/view.php?id=546
https://researchspace.auckland.ac.nz/bitstream/2292/5043/1/546.pdf
31b669af69d11ada2d3a82204928d157
https://researchspace.auckland.ac.nz/bitstream/2292/5043/2/546.pdf.txt
3afe385116e7dd2b0c74720f2baef9ad
oai:researchspace.auckland.ac.nz:2292/5044
2009-08-28T12:39:45Z
com_2292_122
col_2292_4963
2009-08-28T03:21:36Z
2009-08-28T03:21:36Z
1998-03
1998-03
http://hdl.handle.net/2292/5044
barrier is compared with one corresponding to a finite periodic chain of $N$ potential barriers or wells. It is proved, that even for small periodic potentials the exponential decreasing of the transmission coefficient for growing $N$ takes place in lacunas of the corresponding periodic operator on the whole real line. Using the Landauer formula we express the conductivity of the corresponding onedimensional conductor in terms of the transmission coefficient.
LANDAUER FORMULA AND FORMING OF SPECTRAL BANDS
Pavlov, B.
Roach, G.
Yafyasov, A.
barrier is compared with one corresponding to a finite periodic chain of $N$ potential barriers or wells. It is proved, that even for small periodic potentials the exponential decreasing of the transmission coefficient for growing $N$ takes place in lacunas of the corresponding periodic operator on the whole real line. Using the Landauer formula we express the conductivity of the corresponding onedimensional conductor in terms of the transmission coefficient.
Technical Report
Department of Mathematics - Research Reports-389 (1998)
1173-0889
http://hdl.handle.net/2292/5044
Research Reports - Department of Mathematics
https://researchspace.auckland.ac.nz/docs/uoa-docs/rights.htm
The author(s)
Department of Mathematics, The University of Auckland, New Zealand
http://www.math.auckland.ac.nz/Research/Reports/view.php?id=389
https://researchspace.auckland.ac.nz/bitstream/2292/5044/1/389.pdf
30875b4dc5bafd6bad03f9b089d96075
https://researchspace.auckland.ac.nz/bitstream/2292/5044/2/389.pdf.txt
90873aeb5116ca3ecf10e3b790f79456
oai:researchspace.auckland.ac.nz:2292/5045
2009-08-28T12:39:46Z
com_2292_122
col_2292_4963
2009-08-28T03:21:37Z
2009-08-28T03:21:37Z
1998-03
1998-03
http://hdl.handle.net/2292/5045
[no abstract available]
A Note on Arc-transitive Circulants
Morton, Margaret
[no abstract available]
Technical Report
Department of Mathematics - Research Reports-388 (1998)
1173-0889
http://hdl.handle.net/2292/5045
Research Reports - Department of Mathematics
https://researchspace.auckland.ac.nz/docs/uoa-docs/rights.htm
The author(s)
Department of Mathematics, The University of Auckland, New Zealand
http://www.math.auckland.ac.nz/Research/Reports/view.php?id=388
https://researchspace.auckland.ac.nz/bitstream/2292/5045/1/388.pdf
ac29ebbd2df6652ebf33c04097099abf
https://researchspace.auckland.ac.nz/bitstream/2292/5045/2/388.pdf.txt
d25ad43d5190c29559cf696587c930bf
oai:researchspace.auckland.ac.nz:2292/5046
2009-08-28T12:39:46Z
com_2292_122
col_2292_4963
2009-08-28T03:21:38Z
2009-08-28T03:21:38Z
1998-03
1998-03
http://hdl.handle.net/2292/5046
those graphs which are also concentric a recurrence relation is given which determines the growth rate. In the more general case lower bounds on the growth rate are given. In both the concentric and the general cases, the formulae involve the local condition of excess at a vertex.
Growth of Infinite Planar Graphs
Brand, Neal
Morton, Margaret
Vertigan, Dirk
those graphs which are also concentric a recurrence relation is given which determines the growth rate. In the more general case lower bounds on the growth rate are given. In both the concentric and the general cases, the formulae involve the local condition of excess at a vertex.
Technical Report
Department of Mathematics - Research Reports-387 (1998)
1173-0889
http://hdl.handle.net/2292/5046
Research Reports - Department of Mathematics
https://researchspace.auckland.ac.nz/docs/uoa-docs/rights.htm
The author(s)
Department of Mathematics, The University of Auckland, New Zealand
http://www.math.auckland.ac.nz/Research/Reports/view.php?id=387
https://researchspace.auckland.ac.nz/bitstream/2292/5046/1/387.pdf
f0afa2a34318952c7fc8f2c46f751a3a
https://researchspace.auckland.ac.nz/bitstream/2292/5046/2/387.pdf.txt
c8a05cea83dc6c3881369d87198ba7e2
oai:researchspace.auckland.ac.nz:2292/5047
2009-11-19T00:50:08Z
com_2292_122
col_2292_4963
2009-08-28T03:21:39Z
2009-08-28T03:21:39Z
1998-03
1998-03
http://hdl.handle.net/2292/5047
We prove that for any $ninomegacup{omega}$ there exists a ring with exactly $n$ computable isomorphism types. We also investigate the relationship between the number of computable isomorphism types of a ring and the number of computable isomorphism types of its expansion by a finite number of constants.
Nonassociative Computable Rings and Their Isomorphisms. (1998)
Khoussainov, B.
Slinko, A.
We prove that for any $ninomegacup{omega}$ there exists a ring with exactly $n$ computable isomorphism types. We also investigate the relationship between the number of computable isomorphism types of a ring and the number of computable isomorphism types of its expansion by a finite number of constants.
Technical Report
Department of Mathematics - Research Reports-386 (1998)
1173-0889
http://hdl.handle.net/2292/5047
Research Reports - Department of Mathematics
https://researchspace.auckland.ac.nz/docs/uoa-docs/rights.htm
The author(s)
Department of Mathematics, The University of Auckland, New Zealand
http://www.math.auckland.ac.nz/Research/Reports/view.php?id=386
https://researchspace.auckland.ac.nz/bitstream/2292/5047/1/386.pdf
6426144c9ba19bde75a5a0d0ebc5d2eb
https://researchspace.auckland.ac.nz/bitstream/2292/5047/2/386.pdf.txt
e5931ef6b07bdc4baf483321e1609a2e
oai:researchspace.auckland.ac.nz:2292/5048
2019-12-19T03:30:19Z
com_2292_122
col_2292_4963
2009-08-28T03:21:40Z
2009-08-28T03:21:40Z
1997-07
1997-07
http://hdl.handle.net/2292/5048
[no abstract available]
DADE'S INVARIANT CONJECTURE FOR CHEVALLEY GROUPS $G_2(q)$ IN NON-DEFINING CHARACTERISTICS
An, Jianbei
[no abstract available]
Technical Report
Department of Mathematics - Research Reports-385 (1997)
1173-0889
http://hdl.handle.net/2292/5048
Research Reports - Department of Mathematics
2041
16440
7379
7344
https://researchspace.auckland.ac.nz/docs/uoa-docs/rights.htm
The author(s)
Department of Mathematics, The University of Auckland, New Zealand
http://www.math.auckland.ac.nz/Research/Reports/view.php?id=385
https://researchspace.auckland.ac.nz/bitstream/2292/5048/1/385.pdf
a0fdf833227f35020e6f642c3c014e05
https://researchspace.auckland.ac.nz/bitstream/2292/5048/2/385.pdf.txt
46120427439a04ddecd1e370fc1cd4f9
oai:researchspace.auckland.ac.nz:2292/5049
2009-08-28T12:39:51Z
com_2292_122
col_2292_4963
2009-08-28T03:21:41Z
2009-08-28T03:21:41Z
1997-07
1997-07
http://hdl.handle.net/2292/5049
Using the Nagy-Foias functional model for contractions we reduce the spectral problem for Wiener-Hopf Operators with rational symbols to the spectral problem for finite matrices. In particular we suggest a simple approach to calculation of Wiener-Hopf determinants for analytic symbols.
Spectral Theory of Wiener-Hopf Operators and Functional Model
MacCormick, J.P.
Pavlov, B.
Using the Nagy-Foias functional model for contractions we reduce the spectral problem for Wiener-Hopf Operators with rational symbols to the spectral problem for finite matrices. In particular we suggest a simple approach to calculation of Wiener-Hopf determinants for analytic symbols.
Technical Report
Department of Mathematics - Research Reports-384 (1997)
1173-0889
http://hdl.handle.net/2292/5049
Research Reports - Department of Mathematics
https://researchspace.auckland.ac.nz/docs/uoa-docs/rights.htm
The author(s)
Department of Mathematics, The University of Auckland, New Zealand
http://www.math.auckland.ac.nz/Research/Reports/view.php?id=384
https://researchspace.auckland.ac.nz/bitstream/2292/5049/1/384.pdf
c7ae8844f3737d945e1891c42120f1b1
https://researchspace.auckland.ac.nz/bitstream/2292/5049/2/384.pdf.txt
8ee5b42954611dd3f078d9bac5ae67cd
oai:researchspace.auckland.ac.nz:2292/5050
2009-08-28T12:39:51Z
com_2292_122
col_2292_4963
2009-08-28T03:21:42Z
2009-08-28T03:21:42Z
1997-07
1997-07
http://hdl.handle.net/2292/5050
The mathematical model of the 2D-system of electrons in the subsurface space of the homogeneous narrow-gap semiconductor was developed for accumulation layers. The calculation of the 2D-systems parameters was carried out by numerical self-consistent integration of the Schr"odinger and Poisson equations by using the Fermi and quasi-classical (WKB) descriptions of the eigenfunctions of the continuous spectrum - the states of electrons "in continuum". par It is shown that the quasi-classical approximation is preferable in comparison with the Fermi one for the description of the continuum for 2D-systems. The parameters of the two-dimensional gas were computed in wide range of temperatures (200---300,K) and potentials (0---0.2,V). There exists possibility of experimental observation of quantum subbands in accumulation layers in the subsurface space of the narrow-gap semiconductor at room temperature.
Mathematical modelling and self-consistent calculation of the charge density of two-dimensional electrons system
Ivankiv, I.M.
Yafyasov, A.M.
Bogevolnov, V.B.
Pavlov, B.
Rudakova, T.V.
The mathematical model of the 2D-system of electrons in the subsurface space of the homogeneous narrow-gap semiconductor was developed for accumulation layers. The calculation of the 2D-systems parameters was carried out by numerical self-consistent integration of the Schr"odinger and Poisson equations by using the Fermi and quasi-classical (WKB) descriptions of the eigenfunctions of the continuous spectrum - the states of electrons "in continuum". par It is shown that the quasi-classical approximation is preferable in comparison with the Fermi one for the description of the continuum for 2D-systems. The parameters of the two-dimensional gas were computed in wide range of temperatures (200---300,K) and potentials (0---0.2,V). There exists possibility of experimental observation of quantum subbands in accumulation layers in the subsurface space of the narrow-gap semiconductor at room temperature.
Technical Report
Department of Mathematics - Research Reports-383 (1997)
1173-0889
http://hdl.handle.net/2292/5050
Research Reports - Department of Mathematics
https://researchspace.auckland.ac.nz/docs/uoa-docs/rights.htm
The author(s)
Department of Mathematics, The University of Auckland, New Zealand
http://www.math.auckland.ac.nz/Research/Reports/view.php?id=383
https://researchspace.auckland.ac.nz/bitstream/2292/5050/1/383.pdf
4faf4d0abb47fb5f767a3b43c8442618
https://researchspace.auckland.ac.nz/bitstream/2292/5050/2/383.pdf.txt
c4f317776b69eb39cea5e2ce7b97bb00
oai:researchspace.auckland.ac.nz:2292/5051
2009-08-28T12:39:52Z
com_2292_122
col_2292_4963
2009-08-28T03:21:43Z
2009-08-28T03:21:43Z
1997-05
1997-05
http://hdl.handle.net/2292/5051
[no abstract available]
Mean value interpolation for points in general position
Waldron, Shayne
[no abstract available]
Technical Report
Department of Mathematics - Research Reports-382 (1997)
1173-0889
http://hdl.handle.net/2292/5051
Research Reports - Department of Mathematics
https://researchspace.auckland.ac.nz/docs/uoa-docs/rights.htm
The author(s)
Department of Mathematics, The University of Auckland, New Zealand
http://www.math.auckland.ac.nz/Research/Reports/view.php?id=382
https://researchspace.auckland.ac.nz/bitstream/2292/5051/1/382.pdf
a23df3475ce12cfdb8060116c144fe91
https://researchspace.auckland.ac.nz/bitstream/2292/5051/2/382.pdf.txt
8945a79c58db0f994167377cc117cc33
oai:researchspace.auckland.ac.nz:2292/5052
2009-08-28T12:39:53Z
com_2292_122
col_2292_4963
2009-08-28T03:21:44Z
2009-08-28T03:21:44Z
1997-05
1997-05
http://hdl.handle.net/2292/5052
Some basic properties of what are called `B(ernstein)-monotone' seminorms are investigated. These lie between the classes of monotone and sign-monotone seminorms. It is seen that these seminorms arise naturally in Bernstein's comparison theorem, the description of Peano kernels of constant sign, and in near-minimax approximations. A number of new results are obtained including some sufficient conditions for a projection to be near-minimax which are easily seen to be satisfied by all the known examples, and a characterisation of the Peano kernels of constant sign where derivatives are replaced by divided differences
On Bernstein's comparison theorem, Peano kernels of constant sign and near-minimax approximation
Waldron, Shayne
Some basic properties of what are called `B(ernstein)-monotone' seminorms are investigated. These lie between the classes of monotone and sign-monotone seminorms. It is seen that these seminorms arise naturally in Bernstein's comparison theorem, the description of Peano kernels of constant sign, and in near-minimax approximations. A number of new results are obtained including some sufficient conditions for a projection to be near-minimax which are easily seen to be satisfied by all the known examples, and a characterisation of the Peano kernels of constant sign where derivatives are replaced by divided differences
Technical Report
Department of Mathematics - Research Reports-381 (1997)
1173-0889
http://hdl.handle.net/2292/5052
Research Reports - Department of Mathematics
https://researchspace.auckland.ac.nz/docs/uoa-docs/rights.htm
The author(s)
Department of Mathematics, The University of Auckland, New Zealand
http://www.math.auckland.ac.nz/Research/Reports/view.php?id=381
https://researchspace.auckland.ac.nz/bitstream/2292/5052/1/381.pdf
5c55da37c2377a40f5d5f4744677fc40
https://researchspace.auckland.ac.nz/bitstream/2292/5052/2/381.pdf.txt
2ef739ebdfa35ec5f3e4dcf32153d711
oai:researchspace.auckland.ac.nz:2292/5053
2009-08-28T12:39:53Z
com_2292_122
col_2292_4963
2009-08-28T03:21:45Z
2009-08-28T03:21:45Z
1997-05
1997-05
http://hdl.handle.net/2292/5053
It is shown that the standard method of obtaining direct (Jackson) theorems for the order of best uniform approximation by algebraic polynomials from those for trigonometric polynomials also provides inverse (Bernstein) theorems.
Inverse and direct theorems for best uniform approximation by polynomials
Waldron, Shayne
It is shown that the standard method of obtaining direct (Jackson) theorems for the order of best uniform approximation by algebraic polynomials from those for trigonometric polynomials also provides inverse (Bernstein) theorems.
Technical Report
Department of Mathematics - Research Reports-380 (1997)
1173-0889
http://hdl.handle.net/2292/5053
Research Reports - Department of Mathematics
https://researchspace.auckland.ac.nz/docs/uoa-docs/rights.htm
The author(s)
Department of Mathematics, The University of Auckland, New Zealand
http://www.math.auckland.ac.nz/Research/Reports/view.php?id=380
https://researchspace.auckland.ac.nz/bitstream/2292/5053/1/380.pdf
bb6fc645a58249dbd82ba8ed7e370e24
https://researchspace.auckland.ac.nz/bitstream/2292/5053/2/380.pdf.txt
0aece7566cc857ddac8cab18ae10854b
oai:researchspace.auckland.ac.nz:2292/5054
2009-08-28T12:39:55Z
com_2292_122
col_2292_4963
2009-08-28T03:21:45Z
2009-08-28T03:21:45Z
2005-08
2005-08
http://hdl.handle.net/2292/5054
The main aim of this paper is to construct the character tables of the parabolic subgroups of the Chevalley groups G_2(q), where q is a power of a prime p > 3.
Character Tables of Parabolic Subgroups of the Chevalley Groups of Type G_2
An, Jianbei
Huang, Shih-chang
The main aim of this paper is to construct the character tables of the parabolic subgroups of the Chevalley groups G_2(q), where q is a power of a prime p > 3.
Technical Report
Department of Mathematics - Research Reports-545 (2005)
1173-0889
http://hdl.handle.net/2292/5054
Research Reports - Department of Mathematics
https://researchspace.auckland.ac.nz/docs/uoa-docs/rights.htm
The author(s)
Department of Mathematics, The University of Auckland, New Zealand
http://www.math.auckland.ac.nz/Research/Reports/view.php?id=545
https://researchspace.auckland.ac.nz/bitstream/2292/5054/1/545.pdf
5720f4b27410351a5fdfed2583ea15db
https://researchspace.auckland.ac.nz/bitstream/2292/5054/2/545.pdf.txt
5a666087ce00122d183de995b96417b9
oai:researchspace.auckland.ac.nz:2292/5055
2009-08-28T12:39:55Z
com_2292_122
col_2292_4963
2009-08-28T03:21:46Z
2009-08-28T03:21:46Z
1997-04
1997-04
http://hdl.handle.net/2292/5055
A <em>sharp</em> pointwise error estimate is given for multivariate positive linear operators which reproduce the linear polynomials. This quantitative Korovkin--type theorem generalises a known univariate result. It is applied to a number of operators including the multivariate Bernstein operators, and the recently introduced Bernstein--Schoenberg type operators of Dahmen, Micchelli and Seidel.
Sharp error estimates for multivariate positive linear operators which reproduce the linear polynomials
Waldron, Shayne
A <em>sharp</em> pointwise error estimate is given for multivariate positive linear operators which reproduce the linear polynomials. This quantitative Korovkin--type theorem generalises a known univariate result. It is applied to a number of operators including the multivariate Bernstein operators, and the recently introduced Bernstein--Schoenberg type operators of Dahmen, Micchelli and Seidel.
Technical Report
Department of Mathematics - Research Reports-379 (1997)
1173-0889
http://hdl.handle.net/2292/5055
Research Reports - Department of Mathematics
https://researchspace.auckland.ac.nz/docs/uoa-docs/rights.htm
The author(s)
Department of Mathematics, The University of Auckland, New Zealand
http://www.math.auckland.ac.nz/Research/Reports/view.php?id=379
https://researchspace.auckland.ac.nz/bitstream/2292/5055/1/379.pdf
e9fcc7d719cd94042f073bef17eae15b
https://researchspace.auckland.ac.nz/bitstream/2292/5055/2/379.pdf.txt
5446cad4bf8b101037ff7b68cf1bed54
oai:researchspace.auckland.ac.nz:2292/5056
2009-08-28T12:39:57Z
com_2292_122
col_2292_4963
2009-08-28T03:21:47Z
2009-08-28T03:21:47Z
1997-04
1997-04
http://hdl.handle.net/2292/5056
The aim of this report is to survey some aspects of implict differential equations, differential algebraic equations, and their numerical solution. We will formulate an algorithm to solve implicitly defined differential systems by singly implicit Runge-Kutta methods, and see how estimates of the local error can be computed. Then we will give some convergence results for Runge-Kutta methods applied to differential algebraic systems. As a part of the project we have implemented an experimental version of the stiff ODE solver STRIDE by J.C. Butcher, K. Burrage and F.H. Chipman. The new code is capable of solving systems in implicit form and some differential algebraic systems. We have used the code to verify the convergence results and the local error estimates for SIRK methods. Furthermore we have tested the experimental code on some real applications.
The Implementation of SIRK Methods for Differential Algebraic Equations
Nilsen, E.H.
The aim of this report is to survey some aspects of implict differential equations, differential algebraic equations, and their numerical solution. We will formulate an algorithm to solve implicitly defined differential systems by singly implicit Runge-Kutta methods, and see how estimates of the local error can be computed. Then we will give some convergence results for Runge-Kutta methods applied to differential algebraic systems. As a part of the project we have implemented an experimental version of the stiff ODE solver STRIDE by J.C. Butcher, K. Burrage and F.H. Chipman. The new code is capable of solving systems in implicit form and some differential algebraic systems. We have used the code to verify the convergence results and the local error estimates for SIRK methods. Furthermore we have tested the experimental code on some real applications.
Technical Report
Department of Mathematics - Research Reports-378 (1997)
1173-0889
http://hdl.handle.net/2292/5056
Research Reports - Department of Mathematics
https://researchspace.auckland.ac.nz/docs/uoa-docs/rights.htm
The author(s)
Department of Mathematics, The University of Auckland, New Zealand
http://www.math.auckland.ac.nz/Research/Reports/view.php?id=378
https://researchspace.auckland.ac.nz/bitstream/2292/5056/1/378.pdf
85dcb8c6e696aab77cd2f302a9f4004b
https://researchspace.auckland.ac.nz/bitstream/2292/5056/2/378.pdf.txt
bdfb848bbceaec078ca0cc6a49f604d7
oai:researchspace.auckland.ac.nz:2292/5057
2009-08-28T12:39:59Z
com_2292_122
col_2292_4963
2009-08-28T03:21:48Z
2009-08-28T03:21:48Z
1997-04
1997-04
http://hdl.handle.net/2292/5057
This report surveys the method of lines as a method for solving partial differential equations. This method involves discretising of all independent variables except one, and integration of the resulting system of ordinary differential equations in the remaining variable. An introduction to space discretisation is given, and different Runge--Kutta methods and linear multi step methods are considered with emphasis on their linear stability properties.
Numerical integration of systems arising from the method of lines
Mageroy, Einar
This report surveys the method of lines as a method for solving partial differential equations. This method involves discretising of all independent variables except one, and integration of the resulting system of ordinary differential equations in the remaining variable. An introduction to space discretisation is given, and different Runge--Kutta methods and linear multi step methods are considered with emphasis on their linear stability properties.
Technical Report
Department of Mathematics - Research Reports-377 (1997)
1173-0889
http://hdl.handle.net/2292/5057
Research Reports - Department of Mathematics
https://researchspace.auckland.ac.nz/docs/uoa-docs/rights.htm
The author(s)
Department of Mathematics, The University of Auckland, New Zealand
http://www.math.auckland.ac.nz/Research/Reports/view.php?id=377
https://researchspace.auckland.ac.nz/bitstream/2292/5057/1/377.pdf
b1e08c7ac13e71e1a0f4dbe52d477057
https://researchspace.auckland.ac.nz/bitstream/2292/5057/2/377.pdf.txt
bbda4de86614d26de1c2530a746c634c
oai:researchspace.auckland.ac.nz:2292/5058
2009-08-28T12:40:00Z
com_2292_122
col_2292_4963
2009-08-28T03:21:49Z
2009-08-28T03:21:49Z
1997-04
1997-04
http://hdl.handle.net/2292/5058
In this paper quasi-developable spaces, quasi-WDelta-spaces, quasi-semi-stratifiable spaces and spaces with quasi-${G}^{*}_delta$-diagonal are studied. It is shown that every quasi-WDelta, quasi-semi-stratifiable space is a quasi-developable space. A regular space is quasi-semi-stratifiable if and only if it is a quasi-$beta$-space with
quasi-${G}^{*}_delta$-diagonal. A regular space is quasi-semi-stratifiable if and only if it is a quasi-$alpha$ quasi-$beta$-space. A regular quasi-$beta$-space is a quasi-Moore space if and only if it is a quasi-$gamma$-space. A quasi-first-countable quasi-semi-stratifiable space is quasi-developable. A regular quasi-$q$-space is a quasi-Moore space if and only if it is a quasi-semi-stratifiable space.
Some conditions which imply quasi-developability
Mohamad, A.M.
In this paper quasi-developable spaces, quasi-WDelta-spaces, quasi-semi-stratifiable spaces and spaces with quasi-${G}^{*}_delta$-diagonal are studied. It is shown that every quasi-WDelta, quasi-semi-stratifiable space is a quasi-developable space. A regular space is quasi-semi-stratifiable if and only if it is a quasi-$beta$-space with
quasi-${G}^{*}_delta$-diagonal. A regular space is quasi-semi-stratifiable if and only if it is a quasi-$alpha$ quasi-$beta$-space. A regular quasi-$beta$-space is a quasi-Moore space if and only if it is a quasi-$gamma$-space. A quasi-first-countable quasi-semi-stratifiable space is quasi-developable. A regular quasi-$q$-space is a quasi-Moore space if and only if it is a quasi-semi-stratifiable space.
Technical Report
Department of Mathematics - Research Reports-376 (1997)
1173-0889
http://hdl.handle.net/2292/5058
Research Reports - Department of Mathematics
https://researchspace.auckland.ac.nz/docs/uoa-docs/rights.htm
The author(s)
Department of Mathematics, The University of Auckland, New Zealand
http://www.math.auckland.ac.nz/Research/Reports/view.php?id=376
https://researchspace.auckland.ac.nz/bitstream/2292/5058/1/376.pdf
2dec778769db1faa01fa23e84486dc21
https://researchspace.auckland.ac.nz/bitstream/2292/5058/2/376.pdf.txt
68dfb92bc6178bbedaf855c441dcd133
oai:researchspace.auckland.ac.nz:2292/5059
2009-08-28T12:40:01Z
com_2292_122
col_2292_4963
2009-08-28T03:21:50Z
2009-08-28T03:21:50Z
1997-04
1997-04
http://hdl.handle.net/2292/5059
The research was supported by Marsden Fund grant 96-UOA-MIS-0098
On a projection from one co-invariant subspace onto another in character-automorphic Hardy space on a multiply connected domain
Fedorov, Sergei
The research was supported by Marsden Fund grant 96-UOA-MIS-0098
Technical Report
Department of Mathematics - Research Reports-375 (1997)
1173-0889
http://hdl.handle.net/2292/5059
Research Reports - Department of Mathematics
https://researchspace.auckland.ac.nz/docs/uoa-docs/rights.htm
The author(s)
Department of Mathematics, The University of Auckland, New Zealand
http://www.math.auckland.ac.nz/Research/Reports/view.php?id=375
https://researchspace.auckland.ac.nz/bitstream/2292/5059/1/375.pdf
08962193b77684fd7ac0c1ad2680e073
https://researchspace.auckland.ac.nz/bitstream/2292/5059/2/375.pdf.txt
fe02be50661d41ec81e0a9c88ce342a0
oai:researchspace.auckland.ac.nz:2292/5060
2009-08-28T12:40:02Z
com_2292_122
col_2292_4963
2009-08-28T03:21:51Z
2009-08-28T03:21:51Z
1997-04
1997-04
http://hdl.handle.net/2292/5060
This paper is a study of conditions under which a space with $S_2$ is metrizable, o-semimetrizable or semimetrizable. It is shown that: a $wMN$, $wgamma$-space is metrizable if and only if it has $S_2$, a quasi-$gamma$-space is metrizable if and only if it is a pseudo $wN$-space with $S_2$, a separable manifold is metrizable if and only if it has $S_2$ with property $(*)$, a perfectly normal manifold with quasi-${G}^{*}_delta$-diagonal is metrizable and a separable manifold is a hereditarily separable metrizable if and only if it has $theta$-${alpha}_2$.
Metrization and semimetrization theorems with applications to manifolds
Mohamad, A.M.
This paper is a study of conditions under which a space with $S_2$ is metrizable, o-semimetrizable or semimetrizable. It is shown that: a $wMN$, $wgamma$-space is metrizable if and only if it has $S_2$, a quasi-$gamma$-space is metrizable if and only if it is a pseudo $wN$-space with $S_2$, a separable manifold is metrizable if and only if it has $S_2$ with property $(*)$, a perfectly normal manifold with quasi-${G}^{*}_delta$-diagonal is metrizable and a separable manifold is a hereditarily separable metrizable if and only if it has $theta$-${alpha}_2$.
Technical Report
Department of Mathematics - Research Reports-374 (1997)
1173-0889
http://hdl.handle.net/2292/5060
Research Reports - Department of Mathematics
https://researchspace.auckland.ac.nz/docs/uoa-docs/rights.htm
The author(s)
Department of Mathematics, The University of Auckland, New Zealand
http://www.math.auckland.ac.nz/Research/Reports/view.php?id=374
https://researchspace.auckland.ac.nz/bitstream/2292/5060/1/374.pdf
d6a8fc1114ff03396059542604979e8d
https://researchspace.auckland.ac.nz/bitstream/2292/5060/2/374.pdf.txt
bb1553cc3b804841236aa51b940dc0d3
oai:researchspace.auckland.ac.nz:2292/5061
2009-08-28T12:40:03Z
com_2292_122
col_2292_4963
2009-08-28T03:21:52Z
2009-08-28T03:21:52Z
1997-04
1997-04
http://hdl.handle.net/2292/5061
In this paper we introduce the concepts of a quasi-$G^{*}_delta$-diagonal and quasi-wDelta-space as generalizations of the concepts of $G^{*}_delta$-diagonal and wDelta-space respectively. It is shown that a quasi-Moore space may be characterised in terms of these concepts. As a consequence we obtain the following metrization theorems: every paracompact wDelta-space with quasi-$G_delta$-diagonal is metrizable and every collectionwise normal $sigma$ quasi-wDelta-space is metrizable.
Generalization of $G^{*}_delta$-diagonals and wDelta-spaces
Mohamad, A.M.
In this paper we introduce the concepts of a quasi-$G^{*}_delta$-diagonal and quasi-wDelta-space as generalizations of the concepts of $G^{*}_delta$-diagonal and wDelta-space respectively. It is shown that a quasi-Moore space may be characterised in terms of these concepts. As a consequence we obtain the following metrization theorems: every paracompact wDelta-space with quasi-$G_delta$-diagonal is metrizable and every collectionwise normal $sigma$ quasi-wDelta-space is metrizable.
Technical Report
Department of Mathematics - Research Reports-373 (1997)
1173-0889
http://hdl.handle.net/2292/5061
Research Reports - Department of Mathematics
https://researchspace.auckland.ac.nz/docs/uoa-docs/rights.htm
The author(s)
Department of Mathematics, The University of Auckland, New Zealand
http://www.math.auckland.ac.nz/Research/Reports/view.php?id=373
https://researchspace.auckland.ac.nz/bitstream/2292/5061/1/373.pdf
022d6b861d6a95844e9a3bcd0c4c5951
https://researchspace.auckland.ac.nz/bitstream/2292/5061/2/373.pdf.txt
c5be2c0f418d0e0ddaf06b28e5ec9acc
oai:researchspace.auckland.ac.nz:2292/5062
2009-08-28T12:40:04Z
com_2292_122
col_2292_4963
2009-08-28T03:21:52Z
2009-08-28T03:21:52Z
1997-04
1997-04
http://hdl.handle.net/2292/5062
We prove two basic facts about finite intervals in the lattice of topologies on a set. One result states that a finite lattice is isomorphic to an interval of topologies if and only if it is isomorphic to an interval of topologies on a finite set, the other that not every finite lattice is an interval of topologies, although every finite lattice may be embedded into the lattice of topologies on a finite set.
Finite Intervals in the Lattice of Topologies
McIntyre, D.W.
We prove two basic facts about finite intervals in the lattice of topologies on a set. One result states that a finite lattice is isomorphic to an interval of topologies if and only if it is isomorphic to an interval of topologies on a finite set, the other that not every finite lattice is an interval of topologies, although every finite lattice may be embedded into the lattice of topologies on a finite set.
Technical Report
Department of Mathematics - Research Reports-372 (1997)
1173-0889
http://hdl.handle.net/2292/5062
Research Reports - Department of Mathematics
https://researchspace.auckland.ac.nz/docs/uoa-docs/rights.htm
The author(s)
Department of Mathematics, The University of Auckland, New Zealand
http://www.math.auckland.ac.nz/Research/Reports/view.php?id=372
https://researchspace.auckland.ac.nz/bitstream/2292/5062/1/372.pdf
f72f87179d0b6a48aa181f194b83ac4c
https://researchspace.auckland.ac.nz/bitstream/2292/5062/2/372.pdf.txt
afff29b146aa0bc6fce725f40a75edea
oai:researchspace.auckland.ac.nz:2292/5063
2009-08-28T12:40:05Z
com_2292_122
col_2292_4963
2009-08-28T03:21:53Z
2009-08-28T03:21:53Z
1997-03
1997-03
http://hdl.handle.net/2292/5063
This paper surveys a number of aspects of numerical methods for ordinary differential equations. The discussion includes the method of Euler and introduces Runge-Kutta methods and linear multistep methods as generalizations of Euler. Stability considerations arising from stiffness lead to a discussion of implicit methods and implementation issues. To the extent possible within this short survey, numerical methods are looked at in the context of problems arising in practical applications.
Basic intervals between metrizable topologies]{Basic intervals in the partial order of metrizable topologies
McIntyre, D.W.
Watson, W.S.
This paper surveys a number of aspects of numerical methods for ordinary differential equations. The discussion includes the method of Euler and introduces Runge-Kutta methods and linear multistep methods as generalizations of Euler. Stability considerations arising from stiffness lead to a discussion of implicit methods and implementation issues. To the extent possible within this short survey, numerical methods are looked at in the context of problems arising in practical applications.
Technical Report
Department of Mathematics - Research Reports-371 (1997)
1173-0889
http://hdl.handle.net/2292/5063
Research Reports - Department of Mathematics
https://researchspace.auckland.ac.nz/docs/uoa-docs/rights.htm
The author(s)
Department of Mathematics, The University of Auckland, New Zealand
http://www.math.auckland.ac.nz/Research/Reports/view.php?id=371
https://researchspace.auckland.ac.nz/bitstream/2292/5063/1/371.pdf
da67315b199d901752b248d15c7d0569
https://researchspace.auckland.ac.nz/bitstream/2292/5063/2/371.pdf.txt
8e88775a3d23b3b977386f269dc844bb
oai:researchspace.auckland.ac.nz:2292/5064
2009-08-28T12:40:05Z
com_2292_122
col_2292_4963
2009-08-28T03:21:54Z
2009-08-28T03:21:54Z
1997-03
1997-03
http://hdl.handle.net/2292/5064
This paper surveys a number of aspects of numerical methods for ordinary differential equations. The discussion includes the method of Euler and introduces Runge-Kutta methods and linear multistep methods as generalizations of Euler. Stability considerations arising from stiffness lead to a discussion of implicit methods and implementation issues. To the extent possible within this short survey, numerical methods are looked at in the context of problems arising in practical applications.
Numerical Methods for Differential Equations and Applications
Butcher, J.C.
This paper surveys a number of aspects of numerical methods for ordinary differential equations. The discussion includes the method of Euler and introduces Runge-Kutta methods and linear multistep methods as generalizations of Euler. Stability considerations arising from stiffness lead to a discussion of implicit methods and implementation issues. To the extent possible within this short survey, numerical methods are looked at in the context of problems arising in practical applications.
Technical Report
Department of Mathematics - Research Reports-370 (1997)
1173-0889
http://hdl.handle.net/2292/5064
Research Reports - Department of Mathematics
https://researchspace.auckland.ac.nz/docs/uoa-docs/rights.htm
The author(s)
Department of Mathematics, The University of Auckland, New Zealand
http://www.math.auckland.ac.nz/Research/Reports/view.php?id=370
https://researchspace.auckland.ac.nz/bitstream/2292/5064/1/370.pdf
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