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Bulletin of the Australian Mathematical Society最新文献

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EVENTUAL POSITIVITY AND ASYMPTOTIC BEHAVIOUR FOR HIGHER-ORDER EVOLUTION EQUATIONS 高阶演化方程的最终正性和渐近性
4区 数学
Bulletin of the Australian Mathematical Society Pub Date : 2023-10-26 DOI: 10.1017/s0004972723001065
JONATHAN MUI
{"title":"EVENTUAL POSITIVITY AND ASYMPTOTIC BEHAVIOUR FOR HIGHER-ORDER EVOLUTION EQUATIONS","authors":"JONATHAN MUI","doi":"10.1017/s0004972723001065","DOIUrl":"https://doi.org/10.1017/s0004972723001065","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":"164 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136381371","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
LINEAR INDEPENDENCE OF VALUES OF THE q-EXPONENTIAL AND RELATED FUNCTIONS q指数和相关函数值的线性无关性
4区 数学
Bulletin of the Australian Mathematical Society Pub Date : 2023-10-23 DOI: 10.1017/s0004972723001028
ANUP B. DIXIT, VEEKESH KUMAR, SIDDHI S. PATHAK
{"title":"LINEAR INDEPENDENCE OF VALUES OF THE <i>q</i>-EXPONENTIAL AND RELATED FUNCTIONS","authors":"ANUP B. DIXIT, VEEKESH KUMAR, SIDDHI S. PATHAK","doi":"10.1017/s0004972723001028","DOIUrl":"https://doi.org/10.1017/s0004972723001028","url":null,"abstract":"Abstract We establish the linear independence of values of the q -analogue of the exponential function and its derivatives at specified algebraic arguments, when q is a Pisot–Vijayaraghavan number. We also deduce similar results for cognate functions, such as the Tschakaloff function and certain generalised q -series.","PeriodicalId":50720,"journal":{"name":"Bulletin of the Australian Mathematical Society","volume":"46 5","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135368326","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
NOWHERE-ZERO -FLOWS IN CAYLEY GRAPHS OF ORDER 无处零流在有序的凯利图中
4区 数学
Bulletin of the Australian Mathematical Society Pub Date : 2023-10-20 DOI: 10.1017/s000497272300103x
JUNYANG ZHANG, HANG ZHOU
{"title":"NOWHERE-ZERO -FLOWS IN CAYLEY GRAPHS OF ORDER","authors":"JUNYANG ZHANG, HANG ZHOU","doi":"10.1017/s000497272300103x","DOIUrl":"https://doi.org/10.1017/s000497272300103x","url":null,"abstract":"Abstract It is proved that Tutte’s $3$ -flow conjecture is true for Cayley graphs on groups of order $8p$ where p is an odd prime.","PeriodicalId":50720,"journal":{"name":"Bulletin of the Australian Mathematical Society","volume":"5 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135570151","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 THE EXCEPTIONAL SET OF TRANSCENDENTAL ENTIRE FUNCTIONS IN SEVERAL VARIABLES 关于多元超越全函数的例外集
4区 数学
Bulletin of the Australian Mathematical Society Pub Date : 2023-10-20 DOI: 10.1017/s0004972723001041
DIEGO ALVES, JEAN LELIS, DIEGO MARQUES, PAVEL TROJOVSKÝ
{"title":"ON THE EXCEPTIONAL SET OF TRANSCENDENTAL ENTIRE FUNCTIONS IN SEVERAL VARIABLES","authors":"DIEGO ALVES, JEAN LELIS, DIEGO MARQUES, PAVEL TROJOVSKÝ","doi":"10.1017/s0004972723001041","DOIUrl":"https://doi.org/10.1017/s0004972723001041","url":null,"abstract":"Abstract We prove that any subset of $overline {mathbb {Q}}^m$ (closed under complex conjugation and which contains the origin) is the exceptional set of uncountably many transcendental entire functions over $mathbb {C}^m$ with rational coefficients. This result solves a several variables version of a question posed by Mahler for transcendental entire functions [ Lectures on Transcendental Numbers , Lecture Notes in Mathematics, 546 (Springer-Verlag, Berlin, 1976)].","PeriodicalId":50720,"journal":{"name":"Bulletin of the Australian Mathematical Society","volume":"2 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135570154","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
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":"3 1","pages":"0"},"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":"119 1","pages":"0"},"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 $a&gt;a_*={lVert QrVert }^2_2$ , 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":"29 1","pages":"0"},"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":"67 1","pages":"0"},"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
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":"54 1","pages":"0"},"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":"29 1","pages":"0"},"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
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