Bulletin of the Australian Mathematical Society最新文献

{"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}

{"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}

{"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}

{"title":"BAYESIAN SPATIOTEMPORAL MODELS FOR INFECTIOUS DISEASES IN RELATION TO HEALTH INEQUALITY","authors":"Dinah Jane Lope","doi":"10.1017/s0004972723000886","DOIUrl":"https://doi.org/10.1017/s0004972723000886","url":null,"abstract":"","PeriodicalId":50720,"journal":{"name":"Bulletin of the Australian Mathematical Society","volume":" ","pages":""},"PeriodicalIF":0.7,"publicationDate":"2023-08-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42884780","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}

{"title":"MONTE CARLO VARIANCE REDUCTION METHODS WITH APPLICATIONS IN STRUCTURAL RELIABILITY ANALYSIS","authors":"Chenxiao Song","doi":"10.1017/s0004972723000874","DOIUrl":"https://doi.org/10.1017/s0004972723000874","url":null,"abstract":"","PeriodicalId":50720,"journal":{"name":"Bulletin of the Australian Mathematical Society","volume":" ","pages":""},"PeriodicalIF":0.7,"publicationDate":"2023-08-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45762192","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}

{"title":"ON SUMS INVOLVING THE EULER TOTIENT FUNCTION","authors":"I. Kiuchi, Yuki Tsuruta","doi":"10.1017/s0004972723000825","DOIUrl":"https://doi.org/10.1017/s0004972723000825","url":null,"abstract":"\u0000\t <jats:p>Let <jats:inline-formula>\u0000\t <jats:alternatives>\u0000\t\t<jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0004972723000825_inline1.png\" />\u0000\t\t<jats:tex-math>\u0000$gcd (n_{1},ldots ,n_{k})$\u0000</jats:tex-math>\u0000\t </jats:alternatives>\u0000\t </jats:inline-formula> denote the greatest common divisor of positive integers <jats:inline-formula>\u0000\t <jats:alternatives>\u0000\t\t<jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0004972723000825_inline2.png\" />\u0000\t\t<jats:tex-math>\u0000$n_{1},ldots ,n_{k}$\u0000</jats:tex-math>\u0000\t </jats:alternatives>\u0000\t </jats:inline-formula> and let <jats:inline-formula>\u0000\t <jats:alternatives>\u0000\t\t<jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0004972723000825_inline3.png\" />\u0000\t\t<jats:tex-math>\u0000$phi $\u0000</jats:tex-math>\u0000\t </jats:alternatives>\u0000\t </jats:inline-formula> be the Euler totient function. For any real number <jats:inline-formula>\u0000\t <jats:alternatives>\u0000\t\t<jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0004972723000825_inline4.png\" />\u0000\t\t<jats:tex-math>\u0000$x>3$\u0000</jats:tex-math>\u0000\t </jats:alternatives>\u0000\t </jats:inline-formula> and any integer <jats:inline-formula>\u0000\t <jats:alternatives>\u0000\t\t<jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0004972723000825_inline5.png\" />\u0000\t\t<jats:tex-math>\u0000$kgeq 2$\u0000</jats:tex-math>\u0000\t </jats:alternatives>\u0000\t </jats:inline-formula>, we investigate the asymptotic behaviour of <jats:inline-formula>\u0000\t <jats:alternatives>\u0000\t\t<jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0004972723000825_inline6.png\" />\u0000\t\t<jats:tex-math>\u0000$sum _{n_{1}ldots n_{k}leq x}phi (gcd (n_{1},ldots ,n_{k})). $\u0000</jats:tex-math>\u0000\t </jats:alternatives>\u0000\t </jats:inline-formula></jats:p>","PeriodicalId":50720,"journal":{"name":"Bulletin of the Australian Mathematical Society","volume":"18 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2023-08-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"56724602","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}

{"title":"EXTRACTING FEATURES FROM EIGENFUNCTIONS: HIGHER CHEEGER CONSTANTS AND SPARSE EIGENBASIS APPROXIMATION","authors":"Christopher P. Rock","doi":"10.1017/s0004972723000473","DOIUrl":"https://doi.org/10.1017/s0004972723000473","url":null,"abstract":"","PeriodicalId":50720,"journal":{"name":"Bulletin of the Australian Mathematical Society","volume":" ","pages":""},"PeriodicalIF":0.7,"publicationDate":"2023-08-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46018025","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}

{"title":"Inventory of tiger- and ground-beetles (Coleoptera, Caraboidea, Cicindelidae and Carabidae) in two sampling seasons of the Gorongosa National Park, Mozambique.","authors":"Artur R M Serrano, Martim Baptista, Rui Carvalho, Mário Boieiro, Sara Mendes, Marie Bartz, Sérgio Timóteo, Henrique M V S Azevedo-Pereira, Carlos A S Aguiar, António Alves da Silva, Joana Alves, Maria Jesús I Briones, Paulo A V Borges, José P Sousa, Pedro Martins da Silva","doi":"10.3897/BDJ.11.e101280","DOIUrl":"10.3897/BDJ.11.e101280","url":null,"abstract":"<p><strong>Background: </strong>The Gorongosa National Park (Mozambique) is one of the most emblematic protected areas in Africa, well known for its vertebrate biodiversity and restoration ecology efforts following the Mozambican civil war in 1992. The invertebrate biodiversity of Gorongosa National Park is still poorly studied, although the scarce information available indicates the existence of a rich number of species, namely in the case of tiger- and ground-beetles (Coleoptera, Caraboidea). Moreover, the study of arthropod assemblages is key for designing conservation practices since they are potentially accurate biodiversity and ecological indicators. Hence, the diversity assessment of Caraboidea beetles using standardised methodologies is likely to provide a new insight for future conservation planning and help to quantify the effects of climate change in areas identified as vulnerable to anthropogenic pressures, such as the Gorongosa National Park.</p><p><strong>New information: </strong>We report the occurrence of five tiger beetles (Cicindelidae) and 93 ground-beetles (Carabidae) species/morphospecies in Gorongosa National Park from a field survey funded by the ECOASSESS project. Sampling was performed in the four main habitat types present in the Park (miombo tropical forest, mixed dry forest, transitional forest and grasslands) between 25 October and 25 November 2019. In this sampling window, the turnover of Caraboidea species from the dry season to the wet season was recorded for the first time. Twenty-eight species of ground-beetles are new records to Mozambique, including three new subgenera and three new genera. Additional information on species phenology and habitat preferences is also provided.</p>","PeriodicalId":50720,"journal":{"name":"Bulletin of the Australian Mathematical Society","volume":"90 1","pages":"e101280"},"PeriodicalIF":1.0,"publicationDate":"2023-08-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC10848835/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78667563","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"MECHANISTIC MARKOV MODELS FOR THE EVOLUTION OF GENE FAMILIES","authors":"Jiahao Diao","doi":"10.1017/s0004972723000801","DOIUrl":"https://doi.org/10.1017/s0004972723000801","url":null,"abstract":"","PeriodicalId":50720,"journal":{"name":"Bulletin of the Australian Mathematical Society","volume":" ","pages":""},"PeriodicalIF":0.7,"publicationDate":"2023-08-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41809777","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}

{"title":"A COUNTEREXAMPLE TO A RESULT OF JABERI AND MAHMOODI","authors":"A. Sahami, S. Shariati","doi":"10.1017/s0004972723000813","DOIUrl":"https://doi.org/10.1017/s0004972723000813","url":null,"abstract":"\u0000\t <jats:p>We show that <jats:inline-formula>\u0000\t <jats:alternatives>\u0000\t\t<jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0004972723000813_inline1.png\" />\u0000\t\t<jats:tex-math>\u0000$ell ^1(mathbb {N}_wedge )$\u0000</jats:tex-math>\u0000\t </jats:alternatives>\u0000\t </jats:inline-formula> is <jats:inline-formula>\u0000\t <jats:alternatives>\u0000\t\t<jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0004972723000813_inline2.png\" />\u0000\t\t<jats:tex-math>\u0000$varphi $\u0000</jats:tex-math>\u0000\t </jats:alternatives>\u0000\t </jats:inline-formula>-amenable for each multiplicative linear functional <jats:inline-formula>\u0000\t <jats:alternatives>\u0000\t\t<jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0004972723000813_inline3.png\" />\u0000\t\t<jats:tex-math>\u0000$varphi :ell ^1(mathbb {N}_wedge )rightarrow mathbb {C}.$\u0000</jats:tex-math>\u0000\t </jats:alternatives>\u0000\t </jats:inline-formula> This is a counterexample to the final corollary of Jaberi and Mahmoodi [‘On <jats:inline-formula>\u0000\t <jats:alternatives>\u0000\t\t<jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0004972723000813_inline4.png\" />\u0000\t\t<jats:tex-math>\u0000$varphi $\u0000</jats:tex-math>\u0000\t </jats:alternatives>\u0000\t </jats:inline-formula>-amenability of dual Banach algebras’, <jats:italic>Bull. Aust. Math. Soc.</jats:italic><jats:bold>105</jats:bold> (2022), 303–313] and shows that the final theorem in that paper is not valid.</jats:p>","PeriodicalId":50720,"journal":{"name":"Bulletin of the Australian Mathematical Society","volume":" ","pages":""},"PeriodicalIF":0.7,"publicationDate":"2023-08-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41908069","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}