Acta Mathematica Hungarica最新文献

{"title":"Representation of convex geometries of convex dimension 3 by spheres","authors":"K. Adaricheva,&nbsp;A. Agarwal,&nbsp;N. Nevo","doi":"10.1007/s10474-024-01487-y","DOIUrl":"10.1007/s10474-024-01487-y","url":null,"abstract":"<div><p>A convex geometry is a closure system satisfying the anti-exchange property. This paper, following the work of Adaricheva and Bolat [1] and the Polymath REU (2020), continues to investigate representations of convex geometries with small convex dimension by convex shapes on the plane and in spaces of higher dimension. In particular, we answer in the negative the question raised by Polymath REU (2020): whether every convex geometry of convex dimension 3 is representable by circles on the plane. We show there are geometries of convex dimension 3 that cannot be represented by spheres in any <span>(mathbb{R}^k)</span>, and this connects to posets not representable by spheres from the paper of Felsner, Fishburn and Trotter [44]. On the positive side, we use the result of Kincses [55] to show that every finite poset is an ellipsoid order.</p></div>","PeriodicalId":50894,"journal":{"name":"Acta Mathematica Hungarica","volume":"174 2","pages":"578 - 591"},"PeriodicalIF":0.6,"publicationDate":"2024-12-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10474-024-01487-y.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142994699","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":"Truncated polynomials with restricted digits","authors":"H. Liu,&nbsp;Z. Liu","doi":"10.1007/s10474-024-01490-3","DOIUrl":"10.1007/s10474-024-01490-3","url":null,"abstract":"<div><p>Many remarkable results have been obtained on important problems combining arithmetic properties of the integers and some restricted conditions of their digits in a given base. Maynard considered the number of the polynomial values with missing digits and gave an asymptotic formula. In this paper we study truncated polynomials with restricted digits by using the estimates for character sums and exponential sums modulo prime powers. In the case where the polynomials are monomial we further give exact identities.</p></div>","PeriodicalId":50894,"journal":{"name":"Acta Mathematica Hungarica","volume":"174 2","pages":"462 - 481"},"PeriodicalIF":0.6,"publicationDate":"2024-12-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142994341","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":"The solution of Drygas functional equations with additional conditions","authors":"M. Dehghanian,&nbsp;S. Izadi,&nbsp;S. Jahedi","doi":"10.1007/s10474-024-01488-x","DOIUrl":"10.1007/s10474-024-01488-x","url":null,"abstract":"<div><p>We determine the solution of the Drygas functional equation that satisfies the additional condition <span>((y^2+y)f(x)= (x^2+x)f(y))</span> on a restricted domain. Also, some other properties of Drygas functions are given as well.</p></div>","PeriodicalId":50894,"journal":{"name":"Acta Mathematica Hungarica","volume":"174 2","pages":"510 - 521"},"PeriodicalIF":0.6,"publicationDate":"2024-12-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142994568","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":"The distribution of coefficients attached to the Dedekind zeta function over certain sparse sequences","authors":"G. D. Hua","doi":"10.1007/s10474-024-01489-w","DOIUrl":"10.1007/s10474-024-01489-w","url":null,"abstract":"<div><p>Let <span>(K_{3})</span> be a non-normal cubic extension over <span>(mathbb{Q})</span>, and let <span>(a_{K_{3}}(n))</span> be the <span>(n)</span>-th coefficient of the Dedekind zeta function <span>(zeta_{K_{3}}(s))</span>. In this paper, we investigate the asymptotic behaviour of the type\u0000</p><div><div><span>$$ notag sum_{nleq x}a_{K_{3}}^{2}(n^{ell}),$$</span></div></div><p>\u0000where <span>(ellgeq 2)</span> is any fixed integer. As an application, we also establish the asymptotic formulae of the variance of <span>(a_{K_{3}}^{2}(n^{ell}))</span>. Furthermore, we also consider the asymptotic relations for shifted convolution sums associated to <span>(a_{K_{3}}(n))</span> with classical divisor function.\u0000</p></div>","PeriodicalId":50894,"journal":{"name":"Acta Mathematica Hungarica","volume":"174 2","pages":"376 - 407"},"PeriodicalIF":0.6,"publicationDate":"2024-12-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142994570","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 (p)-radical covers of pentavalent arc-transitive graphs","authors":"H. L. Liu,&nbsp;Y. L. Ma","doi":"10.1007/s10474-024-01491-2","DOIUrl":"10.1007/s10474-024-01491-2","url":null,"abstract":"<div><p>Let <span>(Gamma)</span> be a finite connected pentavalent graph admitting a nonabelian simple arc-transitive automorphism group <span>(T)</span> and soluble vertex stabilizers. Let <span>(p&gt;|T|_{2})</span> be an odd prime and <span>((p,|T|)=1)</span>, where <span>(|T|_{2})</span> is the largest power of 2 dividing the order <span>(|T|)</span> of <span>(|T|)</span>. Then we prove that there exists a <span>(p)</span>-radical cover <span>(widetilde{Gamma})</span> of <span>(Gamma)</span> such that the full automorphism group <span>(text{Aut}(widetilde{Gamma}))</span> of <span>(widetilde{Gamma})</span> is equal to <span>(O_{p}(text{Aut}(widetilde{Gamma})).T)</span> and the covering transformation group is <span>(O_{p}(text{Aut}(widetilde{Gamma})))</span>, where <span>(O_{p}(text{Aut}(widetilde{Gamma})))</span> is the <span>(p)</span>-radical of <span>(text{Aut}(widetilde{Gamma}))</span>.</p></div>","PeriodicalId":50894,"journal":{"name":"Acta Mathematica Hungarica","volume":"174 2","pages":"539 - 544"},"PeriodicalIF":0.6,"publicationDate":"2024-12-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142994567","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":"Representation and normality of hyponormal operators in the closure of (mathcal{AN})-operators","authors":"G. Ramesh,&nbsp;S. S. Sequeira","doi":"10.1007/s10474-024-01493-0","DOIUrl":"10.1007/s10474-024-01493-0","url":null,"abstract":"<div><p>A bounded linear operator <span>(T)</span> on a Hilbert space <span>(H)</span> is said to be absolutely norm attaining <span>((T in mathcal{AN}(H)))</span> if the restriction of <span>(T)</span> to any non-zero closed subspace attains its norm and absolutely minimum attaining <span>((T in mathcal{AM}(H)))</span> if every restriction to a non-zero closed subspace attains its minimum modulus.</p><p>In this article, we characterize normal operators in <span>(overline{mathcal{AN}(H)})</span>, the operator norm closure of <span>(mathcal{AN}(H))</span>, in terms of the essential spectrum. Later, we study representations of quasinormal and hyponormal operators in <span>(overline{mathcal{AN}(H)})</span>. Explicitly, we prove that any hyponormal operator in <span>(overline{mathcal{AN}(H)})</span> is a direct sum of a normal <span>(mathcal{AN})</span>-operator and a <span>(2times2)</span> upper triangular <span>(mathcal{AM})</span>-operator matrix. Finally, we deduce some sufficient conditions implying the normality of them.</p></div>","PeriodicalId":50894,"journal":{"name":"Acta Mathematica Hungarica","volume":"174 2","pages":"341 - 359"},"PeriodicalIF":0.6,"publicationDate":"2024-12-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142994569","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 class operators for the lower radical class and semisimple closure constructions","authors":"N. R. McConnell,&nbsp;R. G. McDougall,&nbsp;T. Stokes,&nbsp;L. K. Thornton","doi":"10.1007/s10474-024-01492-1","DOIUrl":"10.1007/s10474-024-01492-1","url":null,"abstract":"<div><p>We construct the lower radical class and the semisimple closure\u0000for a given class using class operators and detail some of the properties of these\u0000operators and their interplay with the operators already used in radical theory.\u0000The setting is the class of algebras introduced by Puczy lowski which ensures the\u0000results hold in groups, multi-operator groups such as rings, as well as loops and\u0000hoops.</p></div>","PeriodicalId":50894,"journal":{"name":"Acta Mathematica Hungarica","volume":"174 2","pages":"275 - 288"},"PeriodicalIF":0.6,"publicationDate":"2024-12-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142994755","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 an application of the lattice of (sigma)-permutable subgroups of a finite group","authors":"A. -M. Liu,&nbsp;V. G. Safonov,&nbsp;A. N. Skiba,&nbsp;S. Wang","doi":"10.1007/s10474-024-01476-1","DOIUrl":"10.1007/s10474-024-01476-1","url":null,"abstract":"<div><p>Let <span>(sigma ={sigma_{i} mid iin I})</span> be some partition of the set of all primes and <span>(G)</span> a finite group. Then <span>(G)</span> is said to be <span>(sigma)</span>-full if <span>(G)</span> has a Hall <span>(sigma _{i})</span>-subgroup for all <span>(i)</span>; <span>(sigma)</span>-primary if <span>(G)</span> is a <span>(sigma _{i})</span>-group for some <span>(i)</span>; <span>(sigma)</span>-soluble if every chief factor of <span>(G)</span> is <span>(sigma)</span>-primary; <span>(sigma)</span>-nilpotent if <span>(G)</span> is the direct product of <span>(sigma)</span>-primary groups; <span>(G^{mathfrak{N}_{sigma}})</span> denotes the <span>(sigma)</span>-nilpotent residual of <span>(G)</span>, that is, the intersection of all normal subgroups <span>(N)</span> of <span>(G)</span> with <span>(sigma)</span>-nilpotent quotient <span>(G/N)</span>.</p><p>A subgroup <span>(A)</span> of <span>(G)</span> is said to be: <span>(sigma)</span>-permutable in <span>(G)</span> provided <span>(G)</span> is <span>(sigma)</span>-full and <span>(A)</span> permutes with all Hall <span>(sigma _{i})</span>-subgroups <span>(H)</span> of <span>(G)</span> (that is, <span>(AH=HA)</span>) for all <span>(i)</span>; <span>(sigma)</span>-subnormal in <span>(G)</span> if there is a subgroup chain <span>(A=A_{0} leq A_{1} leq cdots leq A_{n}=G)</span> such that either <span>(A_{i-1} trianglelefteq A_{i})</span> or <span>(A_{i}/(A_{i-1})_{A_{i}})</span> is <span>(sigma)</span>-primary for all <span>(i=1, ldots , n)</span>.</p><p>Let <span>(A_{sigma G})</span> be the subgroup of <span>(A)</span> generated by all <span>(sigma)</span>-permutable subgroups of <span>(G)</span> contained in <span>(A)</span> and <span>(A^{sigma G})</span> be the intersection of all <span>(sigma)</span>-permutable subgroups of <span>(G)</span> containing <span>(A)</span>.</p><p>We prove that if <span>(G)</span> is a finite <span>(sigma)</span>-soluble group, then the <span>(sigma)</span>-permutability is a transitive relation in <span>(G)</span> if and only if <span>(G^{mathfrak{N}_{sigma}})</span> avoids the pair <span>((A^{sigma G}, A_{sigma G}))</span>, that is, <span>(G^{mathfrak{N}_{sigma}}cap A^{sigma G}= G^{mathfrak{N}_{sigma}}cap A_{sigma G})</span> for every <span>(sigma)</span>-subnormal subgroup <span>(A)</span> of <span>(G)</span>.\u0000</p></div>","PeriodicalId":50894,"journal":{"name":"Acta Mathematica Hungarica","volume":"174 2","pages":"482 - 497"},"PeriodicalIF":0.6,"publicationDate":"2024-11-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142995003","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 the second irreducibility theorem of I. Schur","authors":"A. Jakhar,&nbsp;R. Kalwaniya","doi":"10.1007/s10474-024-01478-z","DOIUrl":"10.1007/s10474-024-01478-z","url":null,"abstract":"<div><p>Let <span>(n)</span> be a positive integer different from <span>(8)</span> and <span>(n+1 neq 2^u)</span> for any integer <span>(ugeq 2)</span>. Let <span>(phi(x))</span> belonging to <span>(Z[x])</span> be a monic polynomial which is irreducible modulo all primes less than or equal to <span>(n+1)</span>. Let <span>(a_j(x))</span> with <span>(0leq jleq n-1)</span> belonging to <span>(Z[x])</span> be polynomials having degree less than <span>(degphi(x))</span>. Assume that the content of <span>(a_na_0(x))</span> is not divisible by any prime less than or equal to <span>(n+1)</span>. We prove that the polynomial \u0000</p><div><div><span>$$\u0000f(x) = a_nfrac{phi(x)^n}{(n+1)!}+ sum _{j=0}^{n-1}a_j(x)frac{phi(x)^{j}}{(j+1)!}\u0000$$</span></div></div><p>\u0000is irreducible over the field <span>(Q)</span> of rational numbers. This generalises a well-known result of Schur which states that the polynomial <span>( sum _{j=0}^{n}a_jfrac{x^{j}}{(j+1)!})</span> with <span>(a_j in Z)</span> and <span>(|a_0| = |a_n| = 1)</span> is irreducible over <span>(Q)</span>. For proving our results, we use the notion of <span>(phi)</span>-Newton polygons and a few results on primes from number theory. We illustrate our result through examples.\u0000</p></div>","PeriodicalId":50894,"journal":{"name":"Acta Mathematica Hungarica","volume":"174 2","pages":"289 - 298"},"PeriodicalIF":0.6,"publicationDate":"2024-11-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142994899","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":"Geodesic loops on tetrahedra in spaces of constant sectional curvature","authors":"A. Borisenko,&nbsp;V. Miquel","doi":"10.1007/s10474-024-01475-2","DOIUrl":"10.1007/s10474-024-01475-2","url":null,"abstract":"<div><p>Geodesic loops on tetrahedra were studied only for the Euclidean space and it was known that there are no simple geodesic loops on regular tetrahedra. Here we prove that: 1) In the spherical space, there are no simple geodesic loops on tetrahedra with internal angles <span>(pi/3 &lt; a_i&lt;pi/2)</span>or regular tetrahedra with <span>(a_i=pi/2)</span>, and there are three simple geodesic loops for each vertex of a tetrahedra with <span>(a_i &gt; pi/2)</span>and the lengths of the edges <span>(a_i&gt;pi/2)</span>. 2) We obtain also a new theorem on simple closed geodesics: If the angles <span>(a_i)</span>of the faces of a tetraedron satisfy <span>(pi/3 &lt; a_i&lt;pi/2)</span>and all faces of the tetrahedron are congruent, then there exist at least <span>(3)</span> simple closed geodesics.\u00003) In the hyperbolic space, for every regular tetrahedron <span>(T)</span>and every pair of coprime numbers <span>((p,q))</span>, there is one simple geodesic loop of type <span>((p,q))</span> through every vertex of <span>(T)</span>.\u0000The geodesic loops that we have found on the tetrahedra in the hyperbolic space are also quasi-geodesics.</p></div>","PeriodicalId":50894,"journal":{"name":"Acta Mathematica Hungarica","volume":"174 2","pages":"360 - 375"},"PeriodicalIF":0.6,"publicationDate":"2024-11-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10474-024-01475-2.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142994708","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}