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New Zealand Journal of Mathematics最新文献

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The 2-fold pure extensions need not split 2倍纯扩展不需要拆分
New Zealand Journal of Mathematics Pub Date : 2023-06-25 DOI: 10.53733/277
A. Alijani
{"title":"The 2-fold pure extensions need not split","authors":"A. Alijani","doi":"10.53733/277","DOIUrl":"https://doi.org/10.53733/277","url":null,"abstract":"In this paper, we give an example of locally compact abelian groups $A$ and $C$ such that ${rm Pext}^{2}(C,A)neq 0$.","PeriodicalId":30137,"journal":{"name":"New Zealand Journal of Mathematics","volume":"8 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-06-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78739481","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
The conjugate locus in convex 3-manifolds 凸3流形的共轭轨迹
New Zealand Journal of Mathematics Pub Date : 2022-10-31 DOI: 10.53733/139
T. Waters, Matthew Cherrie
{"title":"The conjugate locus in convex 3-manifolds","authors":"T. Waters, Matthew Cherrie","doi":"10.53733/139","DOIUrl":"https://doi.org/10.53733/139","url":null,"abstract":"In this paper we study the conjugate locus in convex manifolds. Our main tool is Jacobi fields, which we use to define a special coordinate system on the unit sphere of the tangent space; this provides a natural coordinate system to study and classify the singularities of the conjugate locus. We pay particular attention to 3-dimensional manifolds, and describe a novel method for determining conjugate points. We then make a study of a special case: the 3-dimensional (quadraxial) ellipsoid. We emphasise the similarities with the focal sets of 2-dimensional ellipsoids.","PeriodicalId":30137,"journal":{"name":"New Zealand Journal of Mathematics","volume":"90 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-10-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76561175","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
Equation discovery from data: promise and pitfalls, from rabbits to Mars 从数据中发现方程:从兔子到火星，希望与陷阱
New Zealand Journal of Mathematics Pub Date : 2022-10-12 DOI: 10.53733/216
Graham Donovan, Qing Su
{"title":"Equation discovery from data: promise and pitfalls, from rabbits to Mars","authors":"Graham Donovan, Qing Su","doi":"10.53733/216","DOIUrl":"https://doi.org/10.53733/216","url":null,"abstract":"The problem of equation discovery seeks to reconstruct the underlying dynamics of a time-varying system from observations of the system, and moreover to do so in an instructive way such that we may understand these underlying dynamics from the reconstruction.This article illustrates one type of modern equation discovery method (sparse identification of nonlinear dynamics, or SINDy) in the context of two classic problems. The presentation is in a tutorial style intended to be accessible to students, and could form a useful module in undergraduate or graduate courses in modelling, data analysis, or numerical methods. In this style we explore the strengths and limitations of these methods. We also demonstrate, through use of a carefully constructed example, a new result about the relationship between the reconstructed and true models when a na\"ive polynomial basis is used.","PeriodicalId":30137,"journal":{"name":"New Zealand Journal of Mathematics","volume":"68 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-10-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85686052","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
Exact value of integrals involving product of sine or cosine function 包含正弦或余弦函数积的积分的精确值
New Zealand Journal of Mathematics Pub Date : 2022-10-12 DOI: 10.53733/235
Ratinan Boonklurb, Atiratch Laoharenoo
{"title":"Exact value of integrals involving product of sine or cosine function","authors":"Ratinan Boonklurb, Atiratch Laoharenoo","doi":"10.53733/235","DOIUrl":"https://doi.org/10.53733/235","url":null,"abstract":"By considering the number of all choices of signs $+$ and $-$ such that $pm alpha_1 pm alpha_2 pm alpha_3 cdots pm alpha_n = 0$ and the number of sign $-$ appeared therein, this paper can give the exact value of $int_{0}^{2pi} prod_{k=1}^{n} sin (alpha_k x) dx$. In addition, without using the Fourier transformation technique, we can also find the exact value of $int_{0}^{infty}frac{(cosalpha x - cosbeta x)^p}{x^q} dx$. These two integrals are motivated by the work of Andrican and Bragdasar in 2021, Andria and Tomescu in 2002, and Borwein and Borwein in 2001, respectively.","PeriodicalId":30137,"journal":{"name":"New Zealand Journal of Mathematics","volume":"2 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-10-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75548567","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
On a Theorem of Cooper 关于库珀的一个定理
New Zealand Journal of Mathematics Pub Date : 2022-10-12 DOI: 10.53733/197
S Sundar
{"title":"On a Theorem of Cooper","authors":"S Sundar","doi":"10.53733/197","DOIUrl":"https://doi.org/10.53733/197","url":null,"abstract":"\u0000\u0000\u0000The classical result of Cooper states that every pure strongly continuous semigroup of isometries ${V_t}_{t geq 0}$ on a Hilbert space is unitarily equivalent to the shift semigroup on $L^{2}([0,infty))$ with some multiplicity. The purpose of this note is to record a proof which has an algebraic flavour. The proof is based on the groupoid approach to semigroups of isometries initiated in [8]. We also indicate how our proof can be adapted to the Hilbert module setting and gives another proof of the main result of [3]. \u0000\u0000\u0000","PeriodicalId":30137,"journal":{"name":"New Zealand Journal of Mathematics","volume":"33 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-10-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73820805","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
Numerical radius points of ${mathcal L}(^m l_{infty}^n:l_{infty}^n)$ 的数值半径点 ${mathcal L}(^m l_{infty}^n:l_{infty}^n)$
New Zealand Journal of Mathematics Pub Date : 2022-10-12 DOI: 10.53733/179
Sung Guen Kim
{"title":"Numerical radius points of ${mathcal L}(^m l_{infty}^n:l_{infty}^n)$","authors":"Sung Guen Kim","doi":"10.53733/179","DOIUrl":"https://doi.org/10.53733/179","url":null,"abstract":"For $ngeq 2$ and a real Banach space $E,$ ${mathcal L}(^n E:E)$ denotes the space of all continuous $n$-linear mappings from $E$ to itself.Let $$Pi(E)=Big{~[x^*, (x_1, ldots, x_n)]: x^{*}(x_j)=|x^{*}|=|x_j|=1~mbox{for}~{j=1, ldots, n}~Big}.$$For $Tin {mathcal L}(^n E:E),$ we define $${rm Nrad}({T})=Big{~[x^*, (x_1, ldots, x_n)]in Pi(E): |x^{*}(T(x_1, ldots, x_n))|=v(T)~Big},$$where $v(T)$ denotes the numerical radius of $T$.$T$ is called {em numerical radius peak mapping} if there is $[x^{*}, (x_1, ldots, x_n)]in Pi(E)$ that satisfies ${rm Nrad}({T})=Big{~pm [x^{*}, (x_1, ldots, x_n)]~Big}.$\u0000In this paper we classify ${rm Nrad}({T})$ for every $Tin {mathcal L}(^2 l_{infty}^2: l_{infty}^2)$ in connection with the set of the norm attaining points of $T$.We also characterize all numerical radius peak mappings in ${mathcalL}(^m l_{infty}^n:l_{infty}^n)$ for $n, mgeq 2,$ where $l_{infty}^n=mathbb{R}^n$ with the supremum norm.","PeriodicalId":30137,"journal":{"name":"New Zealand Journal of Mathematics","volume":"41 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-10-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75609544","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
Capacitability for Co-Analytic Sets 协分析集的可性
New Zealand Journal of Mathematics Pub Date : 2022-05-16 DOI: 10.53733/170
T. Slaman
{"title":"Capacitability for Co-Analytic Sets","authors":"T. Slaman","doi":"10.53733/170","DOIUrl":"https://doi.org/10.53733/170","url":null,"abstract":"\u0000\u0000\u0000It follows from a theorem of Davies (1952) that if A is an analytic subset of the Cantor middle third set, λ is positive and the Hausdorff s-measure of A is greater than λ, then there is a compact subset C of A such that the Hausdorff s-measure of C is greater than λ. We exhibit a counterpoint to Davies’s theorem: In Gödel’s universe of sets, there is a co-analytic subset B of the Cantor set which has full Hausdorff dimension such that if C is a closed subset of B then C is countable.\u0000\u0000\u0000","PeriodicalId":30137,"journal":{"name":"New Zealand Journal of Mathematics","volume":"4 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-05-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83126726","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
Turing Determinacy and Suslin sets 图灵确定性和Suslin集
New Zealand Journal of Mathematics Pub Date : 2022-05-12 DOI: 10.53733/140
W. Woodin
{"title":"Turing Determinacy and Suslin sets","authors":"W. Woodin","doi":"10.53733/140","DOIUrl":"https://doi.org/10.53733/140","url":null,"abstract":"The relationship between the Axiom of Determinacy (AD) and the Axiom of Turing Determinacy has been open for over 50 years, and the attempts to understand that relationship has had a profound influence on Set Theory in a variety of ways. The prevailing conjecture is that these two determinacy hypotheses are actually equivalent, and the main theorem of this paper is that Turing Determinacy implies that every Suslin set is determined.","PeriodicalId":30137,"journal":{"name":"New Zealand Journal of Mathematics","volume":"461 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-05-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76333283","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
Two new proofs of the fact that triangle groups are distinguished by their finite quotients 关于三角群可由有限商区分的两个新证明
New Zealand Journal of Mathematics Pub Date : 2022-03-03 DOI: 10.53733/193
M. Conder
{"title":"Two new proofs of the fact that triangle groups are distinguished by their finite quotients","authors":"M. Conder","doi":"10.53733/193","DOIUrl":"https://doi.org/10.53733/193","url":null,"abstract":"In a 2016 paper by Alan Reid, Martin Bridson and the author, it was shown using the theory of profinite groups  that if $Gamma$ is a finitely-generated Fuchsian group and $Sigma$ is a lattice in a connected Lie group,  such that $Gamma$ and $Sigma$ have exactly the same finite quotients, then $Gamma$ is isomorphic to $Sigma$.  As a consequence, two triangle groups $Delta(r,s,t)$ and $Delta(u,v,w)$ have the same finite quotients  if and only if $(u,v,w)$ is a permutation of $(r,s,t)$.  A direct proof of this property of triangle groups was given in the final section of that paper,  with the purpose of exhibiting explicit finite quotients that can distinguish one triangle group from another. Unfortunately, part of the latter direct proof was flawed. In this paper two new direct proofs are given,  one being a corrected version using the same approach as before (involving direct products of small quotients),  and the other being a shorter one that uses the same preliminary observations as in the earlier version  but then takes a different direction (involving further use of the `Macbeath trick').","PeriodicalId":30137,"journal":{"name":"New Zealand Journal of Mathematics","volume":"35 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-03-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76313028","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
Global well-posedness for the 3D magneto-micropolar equations with fractional dissipation 具有分数阶耗散的三维磁微极方程的全局适定性
New Zealand Journal of Mathematics Pub Date : 2021-12-31 DOI: 10.53733/161
Baoquan Yuan, Panpan Zhang
{"title":"Global well-posedness for the 3D magneto-micropolar equations with fractional dissipation","authors":"Baoquan Yuan, Panpan Zhang","doi":"10.53733/161","DOIUrl":"https://doi.org/10.53733/161","url":null,"abstract":"This paper focus on the Cauchy problem of the 3D incompressible magneto-micropolar equations with fractional dissipation in the Sobolev space. Liu, Sun and Xin obtained the global solutions to the 3D magneto-micropolar equations with $alpha=beta=gamma=frac{5}{4}$. Deng and Shang established the global well-posedness of the 3D magneto-micropolar equations in the case of $alphageqfrac{5}{4}$, $alpha+betageqfrac{5}{2}$ and $gammageq2-alphageqfrac{3}{4}$. In this paper, we establish the global well-posedness of the 3D magneto-micropolar equations with $alpha=beta=frac{5}{4}$ and $gamma=frac{1}{2}$, which improves the results of Liu-Sun-Xin and Deng-Shang by reducing the value of $gamma$ to $frac{1}{2}$.","PeriodicalId":30137,"journal":{"name":"New Zealand Journal of Mathematics","volume":"72 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-12-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74133259","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
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