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Bulletin of the Australian Mathematical Society最新文献

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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":"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
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":"41 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":"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":"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
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":"3 1","pages":"0"},"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":"184 1","pages":"0"},"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":"37 1","pages":"0"},"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
ON THE N-POINT CORRELATION OF VAN DER CORPUT SEQUENCES van der corput序列的n点相关
4区 数学
Bulletin of the Australian Mathematical Society Pub Date : 2023-09-15 DOI: 10.1017/s000497272300093x
CHRISTIAN WEIß
{"title":"ON THE <i>N</i>-POINT CORRELATION OF VAN DER CORPUT SEQUENCES","authors":"CHRISTIAN WEIß","doi":"10.1017/s000497272300093x","DOIUrl":"https://doi.org/10.1017/s000497272300093x","url":null,"abstract":"Abstract We derive an explicit formula for the N -point correlation $F_N(s)$ of the van der Corput sequence in base $2$ for all $N in mathbb {N}$ and $s geq 0$ . The formula can be evaluated without explicit knowledge about the elements of the van der Corput sequence. This constitutes the first example of an exact closed-form expression of $F_N(s)$ for all $N in mathbb {N}$ and all $s geq 0$ which does not require explicit knowledge about the involved sequence. Moreover, it can be immediately read off that $lim _{N to infty } F_N(s)$ exists only for $0 leq s leq 1/2$ .","PeriodicalId":50720,"journal":{"name":"Bulletin of the Australian Mathematical Society","volume":"40 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-09-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135436645","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
CAYLEY GRAPHS AND GRAPHICAL REGULAR REPRESENTATIONS 凯莱图和图形规则表示
4区 数学
Bulletin of the Australian Mathematical Society Pub Date : 2023-09-15 DOI: 10.1017/s0004972723000928
SHASHA ZHENG
{"title":"CAYLEY GRAPHS AND GRAPHICAL REGULAR REPRESENTATIONS","authors":"SHASHA ZHENG","doi":"10.1017/s0004972723000928","DOIUrl":"https://doi.org/10.1017/s0004972723000928","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":"17 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-09-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135436823","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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