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New Zealand Journal of Mathematics最新文献

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Multiplicative functions arising from the study of mutually unbiased bases 由相互无偏基的研究而产生的乘法函数
New Zealand Journal of Mathematics Pub Date : 2020-03-08 DOI: 10.53733/99
H. Chan, B. Englert
{"title":"Multiplicative functions arising from the study of mutually unbiased bases","authors":"H. Chan, B. Englert","doi":"10.53733/99","DOIUrl":"https://doi.org/10.53733/99","url":null,"abstract":"We introduce two families of multiplicative functions, which generalize the somewhat unusual function that was serendipitously discovered in 2010 during a study of mutually unbiased bases in the Hilbert space of quantum physics. In addition, we report yet another multiplicative function, which is also suggested by that example; it can be used to express the squarefree part of an integer in terms of an exponential sum.","PeriodicalId":30137,"journal":{"name":"New Zealand Journal of Mathematics","volume":"35 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-03-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83499226","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Trisections and link surgeries 三节切除和连接手术
New Zealand Journal of Mathematics Pub Date : 2019-09-30 DOI: 10.53733/94
R. Kirby, A. Thompson
{"title":"Trisections and link surgeries","authors":"R. Kirby, A. Thompson","doi":"10.53733/94","DOIUrl":"https://doi.org/10.53733/94","url":null,"abstract":"We examine questions about surgery on links which arise naturally from the trisection decomposition of 4-manifolds developed by Gay and Kirby cite{G-K3}. These links lie on Heegaard surfaces in $#^j S^1 times S^2$ and have surgeries yielding $#^k S^1 times S^2$. We describe families of links which have such surgeries. One can ask whether all links with such surgeries lie in these families; the answer is almost certainly no. We nevertheless give a small piece of evidence in favor of a positive answer.","PeriodicalId":30137,"journal":{"name":"New Zealand Journal of Mathematics","volume":"4 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2019-09-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78308349","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
closure-complement-frontier problem in saturated polytopological spaces 饱和拓扑空间中的闭补边问题
New Zealand Journal of Mathematics Pub Date : 2019-07-18 DOI: 10.53733/151
Sara Canilang, Michael P. Cohen, Nicolas Graese, Ian Seong
{"title":"closure-complement-frontier problem in saturated polytopological spaces","authors":"Sara Canilang, Michael P. Cohen, Nicolas Graese, Ian Seong","doi":"10.53733/151","DOIUrl":"https://doi.org/10.53733/151","url":null,"abstract":"Let $X$ be a space equipped with $n$ topologies $tau_1,ldots,tau_n$ which are pairwise comparable and saturated, and for each $1leq ileq n$ let $k_i$ and $f_i$ be the associated topological closure and frontier operators, respectively. Inspired by the closure-complement theorem of Kuratowski, we prove that the monoid of set operators $mathcal{KF}_n$ generated by ${k_i,f_i:1leq ileq n}cup{c}$ (where $c$ denotes the set complement operator) has cardinality no more than $2p(n)$ where $p(n)=frac{5}{24}n^4+frac{37}{12}n^3+frac{79}{24}n^2+frac{101}{12}n+2$. The bound is sharp in the following sense: for each $n$ there exists a saturated polytopological space $(X,tau_1,...,tau_n)$ and a subset $Asubseteq X$ such that repeated application of the operators $k_i, f_i, c$ to $A$ will yield exactly $2p(n)$ distinct sets. In particular, following the tradition for Kuratowski-type problems, we exhibit an explicit initial set in $mathbb{R}$, equipped with the usual and Sorgenfrey topologies, which yields $2p(2)=120$ distinct sets under the action of the monoid $mathcal{KF}_2$.","PeriodicalId":30137,"journal":{"name":"New Zealand Journal of Mathematics","volume":"52 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2019-07-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90067345","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 3
Embedding Heegaard Decompositions 嵌入标准分解
New Zealand Journal of Mathematics Pub Date : 2019-06-07 DOI: 10.53733/189
I. Agol, M. Freedman
{"title":"Embedding Heegaard Decompositions","authors":"I. Agol, M. Freedman","doi":"10.53733/189","DOIUrl":"https://doi.org/10.53733/189","url":null,"abstract":"A smooth embedding of a closed $3$-manifold $M$ in $mathbb{R}^4$ may generically be composed with projection to the fourth coordinate to determine a Morse function on $M$ and hence a Heegaard splitting $M=Xcup_Sigma Y$.  However, starting with a Heegaard splitting, we find an obstruction coming from the geometry of the curve complex $C(Sigma)$ to realizing a corresponding embedding $Mhookrightarrow mathbb{R}^4$.","PeriodicalId":30137,"journal":{"name":"New Zealand Journal of Mathematics","volume":"55 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2019-06-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89863481","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
Construction of ball spaces and the notion of continuity 球空间的构造和连续性的概念
New Zealand Journal of Mathematics Pub Date : 2018-10-19 DOI: 10.53733/157
Ren'e Bartsch, K. Kuhlmann, F. Kuhlmann
{"title":"Construction of ball spaces and the notion of continuity","authors":"Ren'e Bartsch, K. Kuhlmann, F. Kuhlmann","doi":"10.53733/157","DOIUrl":"https://doi.org/10.53733/157","url":null,"abstract":"Spherically complete ball spaces provide a simple framework for the encoding of completeness properties of various spaces and ordered structures. This allows to prove generic versions of theorems that work with these completeness properties, such as fixed point theorems and related results. For the purpose of applying the generic theorems, it is important to have methods for the construction of new spherically complete ball spaces from existing ones. Given various ball spaces on the same underlying set, we discuss the construction of new ball spaces through set theoretic operations on the balls. A definition of continuity for functions on ball spaces leads to the notion of quotient spaces. Further, we show the existence of products and coproducts and use this to derive a topological category associated with ball spaces.","PeriodicalId":30137,"journal":{"name":"New Zealand Journal of Mathematics","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2018-10-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81748503","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 3
Profinite Completions, Cohomology and JSJ Decompositions of Compact 3-Manifolds 紧3-流形的无限补全、上同调和JSJ分解
New Zealand Journal of Mathematics Pub Date : 2018-02-26 DOI: 10.17863/CAM.37668
G. Wilkes
{"title":"Profinite Completions, Cohomology and JSJ Decompositions of Compact 3-Manifolds","authors":"G. Wilkes","doi":"10.17863/CAM.37668","DOIUrl":"https://doi.org/10.17863/CAM.37668","url":null,"abstract":"In this paper we extend previous results concerning the behaviour of JSJ decompositions of closed 3-manifolds with respect to the profinite completion to the case of compact 3-manifolds with boundary. \u0000We also illustrate an alternative and perhaps more natural approach to part of the original theorem, using relative cohomology to analyse the actions of an-annular atoroidal group pairs on profinite trees. \u0000 ","PeriodicalId":30137,"journal":{"name":"New Zealand Journal of Mathematics","volume":"58 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2018-02-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84773306","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 6
Free transport for convex potentials 凸势的自由输运
New Zealand Journal of Mathematics Pub Date : 2016-12-31 DOI: 10.53733/102
Y. Dabrowski, A. Guionnet, D. Shlyakhtenko
{"title":"Free transport for convex potentials","authors":"Y. Dabrowski, A. Guionnet, D. Shlyakhtenko","doi":"10.53733/102","DOIUrl":"https://doi.org/10.53733/102","url":null,"abstract":"We construct non-commutative analogs of transport maps among free Gibbs state satisfying a certain convexity condition. Unlike previous constructions, our approach is non-perturbative in nature and thus can be used to construct transport maps between free Gibbs states associated to potentials which are far from quadratic, i.e., states which are far from the semicircle law. An essential technical ingredient in our approach is the extension of free stochastic analysis to non-commutative spaces of functions based on the Haagerup tensor product.","PeriodicalId":30137,"journal":{"name":"New Zealand Journal of Mathematics","volume":"19 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2016-12-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86439433","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 15
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