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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
The orthogonality principle for Osserman manifolds 奥瑟曼流形的正交原理
IF 0.6 3区 数学
Acta Mathematica Hungarica Pub Date : 2024-06-05 DOI: 10.1007/s10474-024-01434-x
V. Andrejić, K. Lukić
{"title":"The orthogonality principle for Osserman manifolds","authors":"V. Andrejić,&nbsp;K. Lukić","doi":"10.1007/s10474-024-01434-x","DOIUrl":"10.1007/s10474-024-01434-x","url":null,"abstract":"<div><p>We introduce a new potential characterization of Osserman algebraic curvature tensors. \u0000An algebraic curvature tensor is Jacobi-orthogonal if <span>(mathcal{J}_XYperpmathcal{J}_YX)</span> holds for all <span>(Xperp Y)</span>,\u0000where <span>(mathcal{J})</span> denotes the Jacobi operator.\u0000We prove that any Jacobi-orthogonal tensor is Osserman, while all known Osserman tensors are Jacobi-orthogonal.</p></div>","PeriodicalId":50894,"journal":{"name":"Acta Mathematica Hungarica","volume":"173 1","pages":"246 - 252"},"PeriodicalIF":0.6,"publicationDate":"2024-06-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141385938","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
The prime-counting Copeland–Erdős constant 素数哥白兰-厄尔多常数
IF 0.6 3区 数学
Acta Mathematica Hungarica Pub Date : 2024-06-05 DOI: 10.1007/s10474-024-01437-8
J. M. Campbell
{"title":"The prime-counting Copeland–Erdős constant","authors":"J. M. Campbell","doi":"10.1007/s10474-024-01437-8","DOIUrl":"10.1007/s10474-024-01437-8","url":null,"abstract":"<div><p>Let <span>((a(n) : n in mathbb{N}))</span> denote a sequence of nonnegative integers. Let <span>(0.a(1)a(2) ldots )</span> denote the real number obtained by concatenating the digit expansions, in a fixed base, of consecutive entries of <span>((a(n) : n in mathbb{N}))</span>. Research on digit expansions of this form has mainly to do with the normality of <span>(0.a(1)a(2) ldots )</span> for a given base. Famously, the Copeland-Erdős constant <span>(0.2357111317 ldots {})</span>, for the case whereby <span>(a(n))</span> equals the <span>(n^{text{th}})</span> prime number <span>(p_{n})</span>, is normal in base 10. However, it seems that the “inverse” construction given by concatenating the decimal digits of <span>((pi(n) : n in mathbb{N}))</span>, where <span>(pi)</span> denotes the prime-counting function, has not previously been considered. Exploring the distribution of sequences of digits in this new constant <span>(0.0122 ldots 9101011 ldots )</span> would be comparatively difficult, since the number of times a fixed <span>(m in mathbb{N} )</span> appears in <span>((pi(n) : n in mathbb{N}))</span> is equal to the prime gap <span>(g_{m} = p_{m+1} - p_{m})</span>, with the behaviour of prime gaps notoriously elusive. Using a combinatorial method due to Szüsz and Volkmann, we prove that Cramér’s conjecture on prime gaps implies the normality of <span>(0.a(1)a(2) ldots )</span> in a given base <span>(g geq 2)</span>, for <span>(a(n) = pi(n))</span>.</p></div>","PeriodicalId":50894,"journal":{"name":"Acta Mathematica Hungarica","volume":"173 1","pages":"101 - 111"},"PeriodicalIF":0.6,"publicationDate":"2024-06-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141500537","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
No selection lemma for empty triangles 没有空三角形的选择 Lemma
IF 0.6 3区 数学
Acta Mathematica Hungarica Pub Date : 2024-05-23 DOI: 10.1007/s10474-024-01431-0
R. Fabila-Monroy, C. Hidalgo-Toscano, D. Perz, B. Vogtenhuber
{"title":"No selection lemma for empty triangles","authors":"R. Fabila-Monroy,&nbsp;C. Hidalgo-Toscano,&nbsp;D. Perz,&nbsp;B. Vogtenhuber","doi":"10.1007/s10474-024-01431-0","DOIUrl":"10.1007/s10474-024-01431-0","url":null,"abstract":"<div><p>\u0000Let <i>P</i> be a set of <i>n</i> points in general position in the plane. \u0000The Second Selection Lemma states that for any family of <span>(Theta(n^3))</span> triangles spanned by <i>P</i>, there exists a point of the plane that lies in a constant fraction of them.\u0000For families of <span>(Theta(n^{3-alpha}))</span> triangles, with <span>(0le alpha le 1)</span>, there might not be a point in more than <span>(Theta(n^{3-2alpha}))</span> of those triangles.\u0000An empty triangle of <i>P</i> is a triangle spanned by <i>P</i>\u0000not containing any point of <i>P</i> in its interior. Bárány conjectured that there exists an edge\u0000spanned by <i>P</i> that is incident to a super-constant number of empty triangles of <i>P</i>. The number of empty triangles\u0000of <i>P</i> might be as low as <span>(Theta(n^2))</span>; in such a case, on average, every edge spanned by <i>P</i> is incident to a constant number\u0000of empty triangles. The conjecture of Bárány suggests that for the class of empty triangles the above upper bound\u0000might not hold. In this paper we show that, somewhat surprisingly,\u0000the above upper bound does in fact hold for empty triangles. \u0000Specifically, we show that for any integer <i>n</i> and real number <span>(0leq alpha leq 1)</span> there exists a point set of size <i>n</i> with <span>(Theta(n^{3-alpha}))</span> empty triangles such that any point of the plane is only in <span>(O(n^{3-2alpha}))</span> empty triangles.\u0000</p></div>","PeriodicalId":50894,"journal":{"name":"Acta Mathematica Hungarica","volume":"173 1","pages":"52 - 73"},"PeriodicalIF":0.6,"publicationDate":"2024-05-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10474-024-01431-0.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141103518","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
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