{"title":"On boundary discreteness of mappings with a modulus condition","authors":"E. Sevost’yanov","doi":"10.1007/s10474-023-01381-z","DOIUrl":"10.1007/s10474-023-01381-z","url":null,"abstract":"<div><p>We study the boundary behavior of spatial mappings that distort the\u0000modulus of families of paths in the same way as the inverse Poletsky\u0000inequality. Under certain conditions on the boundaries of the\u0000corresponding domains, we have shown that such mappings have a\u0000continuous boundary extension. Separately, we study the problem of\u0000discreteness of the indicated extension. It is shown that under\u0000some requirements, it is light, and under some more strong\u0000conditions, it is discrete in the closure of a domain.\u0000</p></div>","PeriodicalId":50894,"journal":{"name":"Acta Mathematica Hungarica","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2023-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134878220","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"A small ultrafilter number at every singular cardinal","authors":"T. Benhamou, S. Jirattikansakul","doi":"10.1007/s10474-023-01377-9","DOIUrl":"10.1007/s10474-023-01377-9","url":null,"abstract":"<div><p>We obtain a small ultrafilter number at <span>(aleph_{omega_1})</span>. Moreover, we develop a version of the overlapping strong extender forcing with collapses which can keep the top cardinal <span>(kappa)</span> inaccessible. We apply this forcing to construct a model where <span>(kappa)</span> is the least inaccessible and <span>( V_kappa )</span> is a model of GCH at regulars, failures of SCH at singulars, and the ultrafilter numbers at all singulars are small. \u0000</p></div>","PeriodicalId":50894,"journal":{"name":"Acta Mathematica Hungarica","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2023-10-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134795542","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Spectrality of a class of Moran measures on the plane","authors":"Z.-S. Liu","doi":"10.1007/s10474-023-01378-8","DOIUrl":"10.1007/s10474-023-01378-8","url":null,"abstract":"<div><p>\u0000Let <span>({(R_k,D_k)}_{k=1}^infty)</span> be a sequence of pairs, where \u0000</p><div><div><span>$$D_k={0,1,ldots,q_k-1}(1,1)^T$$</span></div></div><p> is an integer vector set and <span>(R_k)</span> is an integer diagonal matrix or upper triangular matrix, i.e.,\u0000<span>(R_k={begin{pmatrix} s_k & 0 0 & t_k end{pmatrix}})</span>\u0000or\u0000<span>(R_k={begin{pmatrix} u_k & 1 0 & v_k end{pmatrix}})</span>.\u0000Associated with the sequence <span>({(R_k,D_k)}_{k=1}^infty)</span>\u0000 , Moran measure <span>(mu_{{R_k},{D_k}})</span> is defined by\u0000</p><div><div><span>$$mu_{{R_k},{D_k}}=delta_{R_{1}^{-1}D_{1}}astdelta_{R_{1}^{-1}R_{2}^{-1}D_{2}}astcdotsast delta_{R_{1}^{-1}R_{2}^{-1}cdots R_{k}^{-1}D_{k}}ast cdots.$$</span></div></div><p>\u0000In this paper, we consider the spectrality of <span>(mu_{{R_k},{D_k}})</span>. We prove that <span>(mu_{{R_k},{D_k}})</span> is a spectral measure under certain conditions in terms of <span>((R_k,D_k))</span>, i.e., there exists a Fourier basis for <span>(L^2(mu_{{R_k},{D_k}}))</span>.</p></div>","PeriodicalId":50894,"journal":{"name":"Acta Mathematica Hungarica","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2023-10-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10474-023-01378-8.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134797830","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"The sum of squares of degrees of bipartite graphs","authors":"M. G. Neubauer","doi":"10.1007/s10474-023-01379-7","DOIUrl":"10.1007/s10474-023-01379-7","url":null,"abstract":"<div><p>Let <i>G</i> be a subgraph of the complete bipartite graph <span>(K_{l,m},{l leq m})</span>, with <span>(e=qm+p>0)</span>, <span>(0 leq p <m)</span>, edges. The maximal value of the sum of the squares of the degrees of the vertices of <i>G</i> is <span>(qm^2+p^2+ p (q+1)^2+(m-p) q^2)</span>. We classify all graphs that attain this bound using the diagonal sequence of a partition. </p></div>","PeriodicalId":50894,"journal":{"name":"Acta Mathematica Hungarica","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2023-10-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134795539","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"c-Normality and coprime action in finite groups","authors":"A. Beltrán, C. Shao","doi":"10.1007/s10474-023-01376-w","DOIUrl":"10.1007/s10474-023-01376-w","url":null,"abstract":"<div><p>A subgroup <i>H</i> of a finite group <i>G</i> is called <i>c</i>-normal if there \u0000exists a normal subgroup <i>N</i> in <i>G</i> such that <i>G = HN</i> and <span>(Hcap N leq core_G (H))</span>, the largest normal subgroup of <i>G</i> contained in <i>H</i>. <i>c</i>-Normality is a weaker form\u0000of normality, introduced by Y.M. Wang, that has led to interesting results and\u0000structural criteria of finite groups. In this paper we study <i>c</i>-normality in the\u0000coprime action setting so as to obtain several solvability and <i>p</i>-nilpotency criteria\u0000in terms of certain subsets of maximal invariant subgroups of a group or of its\u0000Sylow subgroups.</p></div>","PeriodicalId":50894,"journal":{"name":"Acta Mathematica Hungarica","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2023-10-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10474-023-01376-w.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134878446","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Arithmetic properties of colored p-ary partitions","authors":"B. Żmija","doi":"10.1007/s10474-023-01382-y","DOIUrl":"10.1007/s10474-023-01382-y","url":null,"abstract":"<div><p>We study divisibility properties of p-ary partitions colored with k(p − 1) colors for some positive integer k. In particular, we obtain a precise description of p-adic valuations in the case of <span>(k=p^{alpha})</span> and <span>(k=p^{alpha}-1)</span>.</p><p>We also prove a general result concerning the case in which finitely many parts can be colored with a number of colors smaller than k(p − 1) and all others with exactly k(p − 1) colors, where k is arbitrary (but fixed).</p></div>","PeriodicalId":50894,"journal":{"name":"Acta Mathematica Hungarica","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2023-10-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10474-023-01382-y.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134878447","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"The Baire category method for intermittent convex integration","authors":"G. Sattig, L. Székelyhidi","doi":"10.1007/s10474-023-01380-0","DOIUrl":"10.1007/s10474-023-01380-0","url":null,"abstract":"<div><p>We use a convex integration construction from [22] in a Baire\u0000category argument to show that weak solutions to the transport equation with\u0000incompressible vector fields with Sobolev regularity are generic in the Baire category\u0000sense. Using the construction of [7] we prove an analog statement for the\u00003D Navier–Stokes equations.</p></div>","PeriodicalId":50894,"journal":{"name":"Acta Mathematica Hungarica","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2023-10-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134878253","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Properties of complex-valued power means of random variables and their applications","authors":"Y. Akaoka, K. Okamura, Y. Otobe","doi":"10.1007/s10474-023-01372-0","DOIUrl":"10.1007/s10474-023-01372-0","url":null,"abstract":"<div><p>We consider power means of independent and identically distributed\u0000(i.i.d.) non-integrable random variables. The power mean is an example\u0000of a homogeneous quasi-arithmetic mean. Under certain conditions, several limit\u0000theorems hold for the power mean, similar to the case of the arithmetic mean of\u0000i.i.d. integrable random variables. Our feature is that the generators of the power\u0000means are allowed to be complex-valued, which enables us to consider the power\u0000mean of random variables supported on the whole set of real numbers. We establish\u0000integrabilities of the power mean of i.i.d. non-integrable random variables\u0000and a limit theorem for the variances of the power mean. We also consider the\u0000behavior of the power mean as the parameter of the power varies. The complex-valued\u0000power means are unbiased, strongly-consistent, robust estimators for the\u0000joint of the location and scale parameters of the Cauchy distribution.</p></div>","PeriodicalId":50894,"journal":{"name":"Acta Mathematica Hungarica","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2023-10-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134797364","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"A universal bound concerning t-intersecting families","authors":"P. Frankl","doi":"10.1007/s10474-023-01373-z","DOIUrl":"10.1007/s10474-023-01373-z","url":null,"abstract":"<div><p>A very short inductive proof is given for the maximal size of a <i>k</i>-graph on <i>n</i> vertices in which any two edges overlap in at least <i>t</i> vertices.</p></div>","PeriodicalId":50894,"journal":{"name":"Acta Mathematica Hungarica","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2023-09-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134797294","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"On transitive Cayley graphs of homogeneous inverse semigroups","authors":"E. Ilić-Georgijević","doi":"10.1007/s10474-023-01375-x","DOIUrl":"10.1007/s10474-023-01375-x","url":null,"abstract":"<div><p>Let <i>S</i> be a pseudo-unitary homogeneous (graded) inverse semigroup\u0000with zero 0, that is, an inverse semigroup with zero, and with a family <span>({S_delta}_{deltainDelta})</span> of nonzero subsets of <i>S</i>, called components of <i>S</i>,\u0000indexed by a partial groupoid <span>(Delta)</span>, that is, by a set with a partial binary operation, such that\u0000<span>(S=bigcup_{deltainDelta}S_delta)</span>, \u0000and: i) <span>(S_xicap S_etasubseteq{0})</span> for all distinct <span>(xi,etainDelta;)</span>\u0000ii) <span>(S_xi S_etasubseteq S_{xieta})</span> whenever <span>(xieta)</span> is defined;\u0000iii) <span>(S_xi S_etansubseteq{0})</span> if and only if the product <span>(xieta)</span> is defined;\u0000iv) for every idempotent element <span>(epsiloninDelta)</span>, the subsemigroup <span>(S_epsilon)</span> is with identity <span>(1_epsilon;)</span>\u0000v) for every <span>(xin S)</span> there exist idempotent elements <span>(xi, etainDelta)</span> such that <span>(1_xi x=x=x1_eta;)</span>\u0000vi) <span>(1_xi1_eta=1_{xieta})</span> whenever <span>(xietainDelta)</span> is an idempotent element, where <span>(xi)</span>, <span>(eta)</span> are idempotent elements of <span>(Delta)</span>.\u0000Let <i>A</i> be a subset of the union of the subsemigroup components of <i>S</i>, which does not contain 0. By <span>(operatorname{Cay}(S^*,A))</span> we denote a graph obtained \u0000from the Cayley graph <span>(operatorname{Cay}(S,A))</span> by removing 0 and its incident\u0000edges. We characterize vertex-transitivity of <span>(operatorname{Cay}(S^*,A))</span> and relate it \u0000to the vertex-transitivity of its subgraph whose vertex set is <span>(S_musetminus{0})</span>, where <span>(mu)</span> is the maximum element of the set of all idempotent elements of <span>(Delta)</span>,\u0000with respect to the natural order.\u0000</p></div>","PeriodicalId":50894,"journal":{"name":"Acta Mathematica Hungarica","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2023-09-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134797297","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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