发布求助
文献互助 智能选刊 最新文献

Bulletin of the Australian Mathematical Society最新文献

筛选
英文 中文
SOME COUNTING QUESTIONS FOR MATRIX PRODUCTS 矩阵乘积的几个计数问题
4区 数学
Bulletin of the Australian Mathematical Society Pub Date : 2023-10-09 DOI: 10.1017/s0004972723001004
MUHAMMAD AFIFURRAHMAN
{"title":"SOME COUNTING QUESTIONS FOR MATRIX PRODUCTS","authors":"MUHAMMAD AFIFURRAHMAN","doi":"10.1017/s0004972723001004","DOIUrl":"https://doi.org/10.1017/s0004972723001004","url":null,"abstract":"Abstract Given a set X of $ntimes n$ matrices and a positive integer m , we consider the problem of estimating the cardinalities of the product sets $A_1 cdots A_m$ , where $A_iin X$ . When $X={mathcal M}_n(mathbb {Z};H)$ , the set of $ntimes n$ matrices with integer elements of size at most H , we give several bounds on the cardinalities of the product sets and solution sets of related equations such as $A_1 cdots A_m=C$ and $A_1 cdots A_m=B_1 cdots B_m$ . We also consider the case where X is the subset of matrices in ${mathcal M}_n(mathbb {F})$ , where $mathbb {F}$ is a field with bounded rank $kleq n$ . In this case, we completely classify the related product set.","PeriodicalId":50720,"journal":{"name":"Bulletin of the Australian Mathematical Society","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135095359","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
FINITE BASIS PROBLEM FOR INVOLUTION MONOIDS OF ORDER FIVE 五阶对合模群的有限基问题
4区 数学
Bulletin of the Australian Mathematical Society Pub Date : 2023-10-09 DOI: 10.1017/s0004972723000989
BIN BIN HAN, WEN TING ZHANG, YAN FENG LUO
{"title":"FINITE BASIS PROBLEM FOR INVOLUTION MONOIDS OF ORDER FIVE","authors":"BIN BIN HAN, WEN TING ZHANG, YAN FENG LUO","doi":"10.1017/s0004972723000989","DOIUrl":"https://doi.org/10.1017/s0004972723000989","url":null,"abstract":"Abstract An example of a nonfinitely based involution monoid of order five has recently been discovered. We confirm that this example is, up to isomorphism, the unique smallest among all involution monoids.","PeriodicalId":50720,"journal":{"name":"Bulletin of the Australian Mathematical Society","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135095668","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
A NOTE ON NORMALISED GROUND STATES FOR THE TWO-DIMENSIONAL CUBIC-QUINTIC NONLINEAR SCHRÖDINGER EQUATION 二维三次五次非线性schrÖdinger方程的归一化基态注释
4区 数学
Bulletin of the Australian Mathematical Society Pub Date : 2023-10-09 DOI: 10.1017/s0004972723000977
DEKE LI, QINGXUAN WANG
{"title":"A NOTE ON NORMALISED GROUND STATES FOR THE TWO-DIMENSIONAL CUBIC-QUINTIC NONLINEAR SCHRÖDINGER EQUATION","authors":"DEKE LI, QINGXUAN WANG","doi":"10.1017/s0004972723000977","DOIUrl":"https://doi.org/10.1017/s0004972723000977","url":null,"abstract":"Abstract We consider the two-dimensional minimisation problem for $inf { E_a(varphi ):varphi in H^1(mathbb {R}^2) text {and} |varphi |_2^2=1}$ , where the energy functional $ E_a(varphi )$ is a cubic-quintic Schrödinger functional defined by $E_a(varphi ):=tfrac 12int _{mathbb {R}^2}|nabla varphi |^2,dx-tfrac 14aint _{mathbb {R}^2}|varphi |^4,dx+tfrac 16a^2int _{mathbb {R}^2}|varphi |^6,dx$ . We study the existence and asymptotic behaviour of the ground state. The ground state $varphi _{a}$ exists if and only if the $L^2$ mass a satisfies $a>a_*={lVert QrVert }^2_2$ , where Q is the unique positive radial solution of $-Delta u+ u-u^3=0$ in $mathbb {R}^2$ . We show the optimal vanishing rate $int _{mathbb {R}^2}|nabla varphi _{a}|^2,dxsim (a-a_*)$ as $asearrow a_*$ and obtain the limit profile.","PeriodicalId":50720,"journal":{"name":"Bulletin of the Australian Mathematical Society","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135044550","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
HARMONIC-MEASURE DISTRIBUTION FUNCTIONS AND RELATED FUNCTIONS FOR SIMPLY CONNECTED AND MULTIPLY CONNECTED TWO-DIMENSIONAL REGIONS 单连通和多连通二维区域的谐波测度分布函数及相关函数
4区 数学
Bulletin of the Australian Mathematical Society Pub Date : 2023-10-06 DOI: 10.1017/s0004972723000990
ARUNMARAN MAHENTHIRAM
{"title":"HARMONIC-MEASURE DISTRIBUTION FUNCTIONS AND RELATED FUNCTIONS FOR SIMPLY CONNECTED AND MULTIPLY CONNECTED TWO-DIMENSIONAL REGIONS","authors":"ARUNMARAN MAHENTHIRAM","doi":"10.1017/s0004972723000990","DOIUrl":"https://doi.org/10.1017/s0004972723000990","url":null,"abstract":"An abstract is not available for this content. As you have access to this content, full HTML content is provided on this page. A PDF of this content is also available in through the ‘Save PDF’ action button.","PeriodicalId":50720,"journal":{"name":"Bulletin of the Australian Mathematical Society","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135350335","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
THE LIFTING PROBLEM FOR UNIVERSAL QUADRATIC FORMS OVER SIMPLEST CUBIC FIELDS 最简三次域上通用二次型的提升问题
4区 数学
Bulletin of the Australian Mathematical Society Pub Date : 2023-10-06 DOI: 10.1017/s0004972723000953
DANIEL GIL-MUÑOZ, MAGDALÉNA TINKOVÁ
{"title":"THE LIFTING PROBLEM FOR UNIVERSAL QUADRATIC FORMS OVER SIMPLEST CUBIC FIELDS","authors":"DANIEL GIL-MUÑOZ, MAGDALÉNA TINKOVÁ","doi":"10.1017/s0004972723000953","DOIUrl":"https://doi.org/10.1017/s0004972723000953","url":null,"abstract":"Abstract The lifting problem for universal quadratic forms over a totally real number field K consists of determining the existence or otherwise of a quadratic form with integer coefficients (or $mathbb {Z}$ -form) that is universal over K . We prove the nonexistence of universal $mathbb {Z}$ -forms over simplest cubic fields for which the integer parameter is big enough. The monogenic case is already known. We prove the nonexistence in the nonmonogenic case by using the existence of a totally positive nonunit algebraic integer in K with minimal (codifferent) trace equal to one.","PeriodicalId":50720,"journal":{"name":"Bulletin of the Australian Mathematical Society","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135351411","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
ON EXTERIOR POWERS OF REFLECTION REPRESENTATIONS 论反射表征的外部幂
4区 数学
Bulletin of the Australian Mathematical Society Pub Date : 2023-10-06 DOI: 10.1017/s0004972723000965
HONGSHENG HU
{"title":"ON EXTERIOR POWERS OF REFLECTION REPRESENTATIONS","authors":"HONGSHENG HU","doi":"10.1017/s0004972723000965","DOIUrl":"https://doi.org/10.1017/s0004972723000965","url":null,"abstract":"Abstract In 1968, Steinberg [ Endomorphisms of Linear Algebraic Groups , Memoirs of the American Mathematical Society, 80 (American Mathematical Society, Providence, RI, 1968)] proved a theorem stating that the exterior powers of an irreducible reflection representation of a Euclidean reflection group are again irreducible and pairwise nonisomorphic. We extend this result to a more general context where the inner product invariant under the group action may not necessarily exist.","PeriodicalId":50720,"journal":{"name":"Bulletin of the Australian Mathematical Society","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135351407","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
TRIPLE-PRODUCT-FREE SETS TRIPLE-PRODUCT-FREE集
4区 数学
Bulletin of the Australian Mathematical Society Pub Date : 2023-10-06 DOI: 10.1017/s0004972723000941
PRECIOUS U. AGIGOR-MIKE, SARAH B. HART, MARTIN C. OBI
{"title":"TRIPLE-PRODUCT-FREE SETS","authors":"PRECIOUS U. AGIGOR-MIKE, SARAH B. HART, MARTIN C. OBI","doi":"10.1017/s0004972723000941","DOIUrl":"https://doi.org/10.1017/s0004972723000941","url":null,"abstract":"Abstract In this paper, we study triple-product-free sets, which are analogous to the widely studied concept of product-free sets. A nonempty subset S of a group G is triple-product-free if $abc notin S$ for all $a, b, c in S$ . If S is triple-product-free and is not a proper subset of any other triple-product-free set, we say that S is locally maximal. We classify all groups containing a locally maximal triple-product-free set of size 1. We then derive necessary and sufficient conditions for a subset of a group to be locally maximal triple-product-free, and conclude with some observations and comparisons with the situation for standard product-free sets.","PeriodicalId":50720,"journal":{"name":"Bulletin of the Australian Mathematical Society","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135350331","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
SUMSETS CONTAINING A TERM OF A SEQUENCE 包含一个序列项的集合
4区 数学
Bulletin of the Australian Mathematical Society Pub Date : 2023-09-18 DOI: 10.1017/s0004972723000904
MIN CHEN, MIN TANG
{"title":"SUMSETS CONTAINING A TERM OF A SEQUENCE","authors":"MIN CHEN, MIN TANG","doi":"10.1017/s0004972723000904","DOIUrl":"https://doi.org/10.1017/s0004972723000904","url":null,"abstract":"Abstract Let $S={s_{1}, s_{2}, ldots }$ be an unbounded sequence of positive integers with $s_{n+1}/s_{n}$ approaching $alpha $ as $nrightarrow infty $ and let $beta>max (alpha , 2)$ . We show that for all sufficiently large positive integers l , if $Asubset [0, l]$ with $lin A$ , $gcd A=1$ and $|A|geq (2-{k}/{lambda beta })l/(lambda +1)$ , where $lambda =lceil {k}/{beta }rceil $ , then $kAcap Sneq emptyset $ for $2<beta leq 3$ and $kgeq {2beta }/{(beta -2)}$ or for $beta>3$ and $kgeq 3$ .","PeriodicalId":50720,"journal":{"name":"Bulletin of the Australian Mathematical Society","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-09-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135203016","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
CORRECTION TO ‘ON THE COMPLEMENT OF THE ZERO-DIVISOR GRAPH OF A PARTIALLY ORDERED SET’ 对“部分有序集的零因子图的补上”的修正
4区 数学
Bulletin of the Australian Mathematical Society Pub Date : 2023-09-18 DOI: 10.1017/s0004972723000849
SARIKA DEVHARE, VINAYAK JOSHI, JOHN LAGRANGE
{"title":"CORRECTION TO ‘ON THE COMPLEMENT OF THE ZERO-DIVISOR GRAPH OF A PARTIALLY ORDERED SET’","authors":"SARIKA DEVHARE, VINAYAK JOSHI, JOHN LAGRANGE","doi":"10.1017/s0004972723000849","DOIUrl":"https://doi.org/10.1017/s0004972723000849","url":null,"abstract":"An abstract is not available for this content so a preview has been provided. Please use the Get access link above for information on how to access this content.","PeriodicalId":50720,"journal":{"name":"Bulletin of the Australian Mathematical Society","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-09-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135110028","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
GEOMETRIC AND TOPOLOGICAL SHAPE ANALYSIS: INVESTIGATING AND SUMMARISING THE SHAPE OF DATA 几何和拓扑形状分析:调查和总结数据的形状
4区 数学
Bulletin of the Australian Mathematical Society Pub Date : 2023-09-15 DOI: 10.1017/s0004972723000916
YOSSI BOKOR BLEILE
{"title":"GEOMETRIC AND TOPOLOGICAL SHAPE ANALYSIS: INVESTIGATING AND SUMMARISING THE SHAPE OF DATA","authors":"YOSSI BOKOR BLEILE","doi":"10.1017/s0004972723000916","DOIUrl":"https://doi.org/10.1017/s0004972723000916","url":null,"abstract":"","PeriodicalId":50720,"journal":{"name":"Bulletin of the Australian Mathematical Society","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-09-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135396565","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
首页 上一页
0
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
提示
您的信息不完整，为了账户安全，请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
现在去查看 取消
×
提示
确定
请完成安全验证×
相关产品
×
本文献相关产品
联系我们：info@booksci.cn Book学术提供免费学术资源搜索服务，方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。 Copyright © 2023 布克学术 All rights reserved.
京ICP备2023020795号-1
ghs 京公网安备 11010802042870号
Book学术文献互助
Book学术文献互助群
群 号：481959085
Book学术官方微信