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An almost p-standard system of parameters and approximately Cohen–Macaulay modules 近似 p 标准参数系统和近似 Cohen-Macaulay 模块
IF 0.6 3区 数学
Acta Mathematica Hungarica Pub Date : 2024-07-23 DOI: 10.1007/s10474-024-01447-6
P. H. Nam
{"title":"An almost p-standard system of parameters and approximately Cohen–Macaulay modules","authors":"P. H. Nam","doi":"10.1007/s10474-024-01447-6","DOIUrl":"10.1007/s10474-024-01447-6","url":null,"abstract":"<div><p>We characterize the approximate Cohen–Macaulayness of a\u0000module in terms of the length function and the Hilbert coefficient of the module\u0000with respect to an almost p-standard system of parameters (a strict subclass of\u0000d-sequences). As applications, we characterize the approximate Cohen–Macaulay\u0000property of Stanley–Reisner rings, localizations, idealizations, and power series\u0000rings. Furthermore, for power series rings, we construct almost p-standard systems\u0000of parameters of them. From this result, we give a class of Cohen–Macaulay\u0000Rees algebras and give precise formulas computing all Hilbert coefficients of the\u0000formal power series ring with respect to an almost p-standard system of parameters.</p></div>","PeriodicalId":50894,"journal":{"name":"Acta Mathematica Hungarica","volume":"173 2","pages":"366 - 391"},"PeriodicalIF":0.6,"publicationDate":"2024-07-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141775247","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}
引用次数: 0
On approximate A-seminorm and A-numerical radius orthogonality of operators 论算子的近似 A-最小值和 A-数值半径正交性
IF 0.6 3区 数学
Acta Mathematica Hungarica Pub Date : 2024-06-25 DOI: 10.1007/s10474-024-01439-6
C. Conde, K. Feki
{"title":"On approximate A-seminorm and A-numerical radius orthogonality of operators","authors":"C. Conde,&nbsp;K. Feki","doi":"10.1007/s10474-024-01439-6","DOIUrl":"10.1007/s10474-024-01439-6","url":null,"abstract":"<div><p>This paper explores the concept of approximate Birkhoff–James orthogonality in the context of operators on semi-Hilbert spaces. These spaces are generated by positive semi-definite sesquilinear forms. We delve into the fundamental properties of this concept and provide several characterizations of it. Using innovative arguments, we extend a widely known result initially proposed by Magajna [17]. Additionally, we improve a recent result by Sen and Paul [24] regarding a characterization of approximate numerical radius orthogonality of two semi-Hilbert space operators, such that one of them is <span>(A)</span>-positive. Here, <span>(A)</span> is assumed to be a positive semi-definite operator.</p></div>","PeriodicalId":50894,"journal":{"name":"Acta Mathematica Hungarica","volume":"173 1","pages":"227 - 245"},"PeriodicalIF":0.6,"publicationDate":"2024-06-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141549243","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}
引用次数: 0
A note on the 2-colored rectilinear crossing number of random point sets in the unit square 关于单位正方形中随机点集的双色直线交叉数的说明
IF 0.6 3区 数学
Acta Mathematica Hungarica Pub Date : 2024-06-18 DOI: 10.1007/s10474-024-01436-9
S. Cabello, É Czabarka, R. Fabila-Monroy, Y. Higashikawa, R. Seidel, L. Székely, J. Tkadlec, A. Wesolek
{"title":"A note on the 2-colored rectilinear crossing number of random point sets in the unit square","authors":"S. Cabello,&nbsp;É Czabarka,&nbsp;R. Fabila-Monroy,&nbsp;Y. Higashikawa,&nbsp;R. Seidel,&nbsp;L. Székely,&nbsp;J. Tkadlec,&nbsp;A. Wesolek","doi":"10.1007/s10474-024-01436-9","DOIUrl":"10.1007/s10474-024-01436-9","url":null,"abstract":"<div><p>Let <span>(S)</span> be a set of four points chosen independently, uniformly at random from a square. Join every pair of points of <span>(S)</span> with a straight line segment. Color these edges red if they have positive slope and blue, otherwise. We show that the probability that <span>(S)</span> defines a pair of crossing edges of the same color is equal to <span>(1/4)</span>. This is connected to a recent result of Aichholzer et al. [1] who showed that by 2-colouring the edges of a geometric graph and counting monochromatic crossings instead of crossings, the number of crossings can be more than halved. \u0000Our result shows that for the described random drawings, there is a coloring of the edges such that the number of monochromatic crossings is in expectation <span>(frac{1}{2}-frac{7}{50})</span> of the total number of crossings.</p></div>","PeriodicalId":50894,"journal":{"name":"Acta Mathematica Hungarica","volume":"173 1","pages":"214 - 226"},"PeriodicalIF":0.6,"publicationDate":"2024-06-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10474-024-01436-9.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141549244","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}
引用次数: 0
Jordan derivable mappings on (B(H)) B(H)$$上的乔丹可导映射
IF 0.6 3区 数学
Acta Mathematica Hungarica Pub Date : 2024-06-15 DOI: 10.1007/s10474-024-01438-7
L. Chen, F. Guo, Z.-J. Qin
{"title":"Jordan derivable mappings on (B(H))","authors":"L. Chen,&nbsp;F. Guo,&nbsp;Z.-J. Qin","doi":"10.1007/s10474-024-01438-7","DOIUrl":"10.1007/s10474-024-01438-7","url":null,"abstract":"<div><p>Let <span>(H)</span> be a real or complex Hilbert space with the dimension greater than one and <span>(B(H))</span> the algebra of all bounded linear operators on <span>(H)</span>. Assume that <span>(delta)</span> is a linear mapping from <span>(B(H))</span> into itself which is Jordan derivable at a given element <span>(Omegain B(H))</span>, in the sense that <span>(delta(Acirc B)=delta(A)circ B+Acircdelta (B))</span> holds for all <span>(A,Bin B(H))</span> with <span>(Acirc B = Omega)</span>, where <span>(circ)</span> denotes the Jordan product <span>( {Acirc B } =AB+BA)</span>. In this paper, we show that if <span>(Omega)</span> is an arbitrary but fixed nonzero operator, then <span>(delta)</span> is a derivation; if <span>(Omega)</span> is a zero operator, then <span>(delta)</span> is a generalized derivation.</p></div>","PeriodicalId":50894,"journal":{"name":"Acta Mathematica Hungarica","volume":"173 1","pages":"112 - 121"},"PeriodicalIF":0.6,"publicationDate":"2024-06-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141337673","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}
引用次数: 0
E-unitary and F-inverse monoids, and closure operators on group Cayley graphs E 单元和 F 逆单元，以及 Cayley 群图上的闭包算子
IF 0.6 3区 数学
Acta Mathematica Hungarica Pub Date : 2024-06-14 DOI: 10.1007/s10474-024-01443-w
N. Szakács
{"title":"E-unitary and F-inverse monoids, and closure operators on group Cayley graphs","authors":"N. Szakács","doi":"10.1007/s10474-024-01443-w","DOIUrl":"10.1007/s10474-024-01443-w","url":null,"abstract":"<div><p>We show that the category of <i>X</i>-generated <i>E</i>-unitary inverse monoids with greatest group image <i>G</i> is equivalent to the category of <i>G</i>-invariant, finitary closure operators on the set of connected subgraphs of the Cayley graph of <i>G</i>. Analogously, we study <i>F</i>-inverse monoids in the extended signature <span>((cdot, 1, ^{-1}, ^mathfrak m))</span>, and show that the category of <i>X</i>-generated <i>F</i>-inverse monoids with greatest group image <i>G</i> is equivalent to the category of <i>G</i>-invariant, finitary closure operators on the set of all subgraphs of the Cayley graph of <i>G</i>. As an application, we show that presentations of <i>F</i>-inverse monoids in the extended signature can be studied by tools analogous to Stephen’s procedure in inverse monoids, in particular, we introduce the notions of <i>F</i>-Schützenberger graphs and <i>P</i>-expansions.</p></div>","PeriodicalId":50894,"journal":{"name":"Acta Mathematica Hungarica","volume":"173 1","pages":"297 - 316"},"PeriodicalIF":0.6,"publicationDate":"2024-06-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10474-024-01443-w.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141338640","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}
引用次数: 0
Markov processes on quasi-random graphs 准随机图上的马尔可夫过程
IF 0.6 3区 数学
Acta Mathematica Hungarica Pub Date : 2024-06-11 DOI: 10.1007/s10474-024-01441-y
D. Keliger
{"title":"Markov processes on quasi-random graphs","authors":"D. Keliger","doi":"10.1007/s10474-024-01441-y","DOIUrl":"10.1007/s10474-024-01441-y","url":null,"abstract":"<div><p>We study Markov population processes on large graphs, with the local state transition rates of a single vertex being a linear function of its neighborhood. A simple way to approximate such processes is by a system of ODEs called the homogeneous mean-field approximation (HMFA). Our main result is showing that HMFA is guaranteed to be the large graph limit of the stochastic dynamics on a finite time horizon if and only if the graph-sequence is quasi-random. An explicit error bound is given and it is <span>(frac{1}{sqrt{N}})</span> plus the largest discrepancy of the graph. For Erdős–Rényi and random regular graphs we show an error bound of order the inverse square root of the average degree. In general, diverging average degrees is shown to be a necessary condition for the HMFA to be accurate. Under special conditions, some of these results also apply to more detailed type of approximations like the inhomogenous mean field approximation (IHMFA). We pay special attention to epidemic applications such as the SIS process.</p></div>","PeriodicalId":50894,"journal":{"name":"Acta Mathematica Hungarica","volume":"173 1","pages":"20 - 51"},"PeriodicalIF":0.6,"publicationDate":"2024-06-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10474-024-01441-y.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141549245","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}
引用次数: 0
Tight contact structures on some families of small Seifert fiber spaces 小塞弗特纤维空间某些族上的紧密接触结构
IF 0.6 3区 数学
Acta Mathematica Hungarica Pub Date : 2024-06-10 DOI: 10.1007/s10474-024-01444-9
S. Wan
{"title":"Tight contact structures on some families of small Seifert fiber spaces","authors":"S. Wan","doi":"10.1007/s10474-024-01444-9","DOIUrl":"10.1007/s10474-024-01444-9","url":null,"abstract":"<div><p>Suppose <i>K</i> is a knot in a 3-manifold <i>Y</i>, and that <i>Y</i> admits a pair of distinct contact structures. Assume that <i>K</i> has Legendrian representatives in each of these contact structures, such that the corresponding Thurston-Bennequin framings are equivalent. This paper provides a method to prove that the contact structures resulting from Legendrian surgery along these two representatives remain distinct. Applying this method to the situation where the starting manifold is <span>(-Sigma(2,3,6m+1))</span> and the knot is a singular fiber, together with convex surface theory we can classify the tight contact structures on certain families of Seifert fiber spaces.\u0000</p></div>","PeriodicalId":50894,"journal":{"name":"Acta Mathematica Hungarica","volume":"173 1","pages":"286 - 296"},"PeriodicalIF":0.6,"publicationDate":"2024-06-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10474-024-01444-9.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141549246","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}
引用次数: 0
Extremal problems for typically real odd polynomials 典型实奇数多项式的极值问题
IF 0.6 3区 数学
Acta Mathematica Hungarica Pub Date : 2024-06-08 DOI: 10.1007/s10474-024-01440-z
D. Dmitrishin, D. Gray, A. Stokolos, I. Tarasenko
{"title":"Extremal problems for typically real odd polynomials","authors":"D. Dmitrishin,&nbsp;D. Gray,&nbsp;A. Stokolos,&nbsp;I. Tarasenko","doi":"10.1007/s10474-024-01440-z","DOIUrl":"10.1007/s10474-024-01440-z","url":null,"abstract":"<div><p>On the class of typically real odd polynomials of degree <span>(2N-1)</span>\u0000</p><div><div><span>$$F(z)=z+sum_{j=2}^Na_jz^{2j-1}$$</span></div></div><p>\u0000we consider two problems: 1) stretching the central \u0000unit disc under the above polynomial mappings and 2) estimating the coefficient <span>(a_2.)</span>\u0000It is shown that \u0000</p><div><div><span>$$begin{gathered} |{F(z)}|le frac12csc^2left({frac{pi}{2N+2}}right),-1+4sin^2left({frac{pi}{2N+4}}right)le a_2le-1+4cos^2left({frac{pi}{N+2}}right) quad text{for odd $N$,}end{gathered} $$</span></div></div><p>\u0000and\u0000</p><div><div><span>$$-1+4(nu_N)^2le a_2le -1+4cos^2left({frac{pi}{N+2}}right) quad text{for even $N$,}$$</span></div></div><p>\u0000where <span>(nu_N)</span> is a minimal positive root of the equation <span>(U'_{N+1}(x) = 0)</span> with <span>(U'_{N + 1}(x))</span> being the derivative of the Chebyshev polynomial of the second kind of the corresponding order.\u0000The above boundaries are sharp, the corresponding estremizers are unique and the coefficients are determined. \u0000</p></div>","PeriodicalId":50894,"journal":{"name":"Acta Mathematica Hungarica","volume":"173 1","pages":"1 - 19"},"PeriodicalIF":0.6,"publicationDate":"2024-06-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141370450","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Characterizing AF-embeddable (C^*)-algebras by representations 用表示法表征可嵌入 AF 的 $$C^*$-gebras
IF 0.6 3区 数学
Acta Mathematica Hungarica Pub Date : 2024-06-08 DOI: 10.1007/s10474-024-01442-x
Y. Liu
{"title":"Characterizing AF-embeddable (C^*)-algebras by representations","authors":"Y. Liu","doi":"10.1007/s10474-024-01442-x","DOIUrl":"10.1007/s10474-024-01442-x","url":null,"abstract":"<div><p>A major open problem of AF-embedding is whether every separable exact quasidiagonal <span>(C^*)</span>-algebra can be embedded into an AF-algebra. In this paper we characterize AF-embeddable <span>(C^*)</span>-algebras by representations to observe their similarity to the separable exact quasidiagonal <span>(C^*)</span>-algebras. As an application, we show that every separable exact quasidiagonal <span>(C^*)</span>-algebra is AF-embeddable if and only if every faithful essential representation of a separable exact quasidiagonal <span>(C^*)</span>-algebra is a certain kind of <span>(*)</span>-representation. We also show that a separable <span>(C^*)</span>-algebra is AF-embeddable if and only if it can be embedded into a particular <span>(C^*)</span>-algebra.</p></div>","PeriodicalId":50894,"journal":{"name":"Acta Mathematica Hungarica","volume":"173 1","pages":"139 - 153"},"PeriodicalIF":0.6,"publicationDate":"2024-06-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141369248","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}
引用次数: 0
Mixed volumes and the Blaschke–Lebesgue theorem 混合体积和布拉什克-勒贝格定理
IF 0.6 3区 数学
Acta Mathematica Hungarica Pub Date : 2024-06-05 DOI: 10.1007/s10474-024-01435-w
B. Bogosel
{"title":"Mixed volumes and the Blaschke–Lebesgue theorem","authors":"B. Bogosel","doi":"10.1007/s10474-024-01435-w","DOIUrl":"10.1007/s10474-024-01435-w","url":null,"abstract":"<div><p>The mixed area of a Reuleaux polygon and its symmetric with respect to the origin is expressed in terms of the mixed area of two explicit polygons. This gives a geometric explanation of a classical proof due to Chakerian. Mixed areas and volumes are also used to reformulate the minimization of the volume under constant width constraint as isoperimetric problems. In the two dimensional case, the equivalent formulation is solved, providing another proof of the Blaschke–Lebesgue theorem. In the three dimensional case the proposed relaxed formulation involves the mean width, the area and inclusion constraints.</p></div>","PeriodicalId":50894,"journal":{"name":"Acta Mathematica Hungarica","volume":"173 1","pages":"122 - 138"},"PeriodicalIF":0.6,"publicationDate":"2024-06-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141519647","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}
引用次数: 0
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