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A limit theorem for runs containing two types of contaminations 包含两类污染的运行极限定理
IF 0.8 3区 数学
Periodica Mathematica Hungarica Pub Date : 2024-07-06 DOI: 10.1007/s10998-024-00600-6
István Fazekas, Borbála Fazekas, Michael Ochieng Suja
{"title":"A limit theorem for runs containing two types of contaminations","authors":"István Fazekas, Borbála Fazekas, Michael Ochieng Suja","doi":"10.1007/s10998-024-00600-6","DOIUrl":"https://doi.org/10.1007/s10998-024-00600-6","url":null,"abstract":"<p>In this paper, sequences of trials having three outcomes are studied. The outcomes are labelled as success, failure of type I and failure of type II. A run is called at most <span>(1+1)</span> contaminated, if it contains at most one failure of type I and at most one failure of type II. The accompanying distribution for the length of the longest at most <span>(1+1)</span> contaminated run is obtained. The proof is based on a powerful lemma of Csáki, Földes and Komlós. Besides a mathematical proof, simulation results supporting our theorem are also presented.</p>","PeriodicalId":49706,"journal":{"name":"Periodica Mathematica Hungarica","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2024-07-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141572596","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
Bounded and homoclinic-like solutions of second-order singular difference equations 二阶奇异差分方程的有界解和类同解
IF 0.8 3区 数学
Periodica Mathematica Hungarica Pub Date : 2024-07-06 DOI: 10.1007/s10998-024-00596-z
Ruyun Ma, Jiao Zhao
{"title":"Bounded and homoclinic-like solutions of second-order singular difference equations","authors":"Ruyun Ma, Jiao Zhao","doi":"10.1007/s10998-024-00596-z","DOIUrl":"https://doi.org/10.1007/s10998-024-00596-z","url":null,"abstract":"<p>We are concerned with the existence of positive solutions for the boundary value problem </p><span>$$begin{aligned} left{ begin{array}{ll} -D^{2}u(n-1)+c(n)Du(n)+a(n)u(n)=frac{b(n)}{(u(n))^p},&amp;{}quad nin mathbb {Z}, lim _{|n|rightarrow +infty }u(n)=0, end{array}right. end{aligned}$$</span><p>where <span>(a,b:mathbb {Z}rightarrow mathbb {R})</span>, <span>(c:mathbb {Z}rightarrow (0,1))</span>, <span>(p&gt;0)</span>, and <i>D</i> is the forward difference operator. The main tools used are fixed point theorems of cone-compressing and cone-condensing type.</p>","PeriodicalId":49706,"journal":{"name":"Periodica Mathematica Hungarica","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2024-07-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141572594","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
New characterization of Hopf hypersurfaces in nonflat complex space forms 非平面复数空间形式中霍普夫超曲面的新特征
IF 0.8 3区 数学
Periodica Mathematica Hungarica Pub Date : 2024-07-05 DOI: 10.1007/s10998-024-00604-2
Wenjie Wang
{"title":"New characterization of Hopf hypersurfaces in nonflat complex space forms","authors":"Wenjie Wang","doi":"10.1007/s10998-024-00604-2","DOIUrl":"https://doi.org/10.1007/s10998-024-00604-2","url":null,"abstract":"<p>It is proved that the <span>(*)</span>-Ricci operator of a real hypersurface in a nonflat complex space form is Reeb parallel if and only if the hypersurface is Hopf. As an application of this result, we obtain a classification theorem of real hypersurfaces with parallel <span>(*)</span>-Ricci operators. These results answer some open questions posed by Kaimakamis and Panagiotidou a decade ago.</p>","PeriodicalId":49706,"journal":{"name":"Periodica Mathematica Hungarica","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2024-07-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141572595","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
Shadowing, hyperbolicity, and Aluthge transforms 阴影、双曲性和阿鲁特奇变换
IF 0.8 3区 数学
Periodica Mathematica Hungarica Pub Date : 2024-07-05 DOI: 10.1007/s10998-024-00597-y
C. A. Morales, T. T. Linh
{"title":"Shadowing, hyperbolicity, and Aluthge transforms","authors":"C. A. Morales, T. T. Linh","doi":"10.1007/s10998-024-00597-y","DOIUrl":"https://doi.org/10.1007/s10998-024-00597-y","url":null,"abstract":"<p>We introduce the concept of <span>(epsilon )</span>-homoclinic points for invertible linear operators on Banach spaces. We establish that an operator is hyperbolic if and only if it possesses the shadowing property without any nonzero <span>(epsilon )</span>-homoclinic points (for some <span>(epsilon &gt;0)</span>). Additionally, we demonstrate that a linear operator on a Banach space <i>X</i> exhibiting the shadowing property is uniformly contracting, uniformly expanding, possesses a nontrivial invariant closed subspace, or has a dense set of bounded orbits in <i>X</i>. Moreover, we demonstrate the invariance of the set of generalized hyperbolic operators under <span>(lambda )</span>-Aluthge transforms, where <span>(lambda in left( 0, 1right) )</span>. Additionally, we establish that the Aluthge iterates of an invertible operator converge to a hyperbolic operator solely when the initial operator is hyperbolic. Finally, we prove that the Aluthge iterates of hyponormal shifted hyperbolic weighted shifts diverge and also the existence of hyperbolic weighted shifts with divergent Aluthge iterates.</p>","PeriodicalId":49706,"journal":{"name":"Periodica Mathematica Hungarica","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2024-07-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141553025","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 the number of A-transversals in hypergraphs 关于超图中的A遍数
IF 0.8 3区 数学
Periodica Mathematica Hungarica Pub Date : 2024-07-04 DOI: 10.1007/s10998-024-00586-1
János Barát, Dániel Gerbner, Anastasia Halfpap
{"title":"On the number of A-transversals in hypergraphs","authors":"János Barát, Dániel Gerbner, Anastasia Halfpap","doi":"10.1007/s10998-024-00586-1","DOIUrl":"https://doi.org/10.1007/s10998-024-00586-1","url":null,"abstract":"<p>A set <i>S</i> of vertices in a hypergraph is <i>strongly independent</i> if every hyperedge shares at most one vertex with <i>S</i>. We prove a sharp result for the number of maximal strongly independent sets in a 3-uniform hypergraph analogous to the Moon-Moser theorem. Given an <i>r</i>-uniform hypergraph <span>({{mathcal {H}}})</span> and a non-empty set <i>A</i> of non-negative integers, we say that a set <i>S</i> is an <i>A</i>-<i>transversal</i> of <span>({{mathcal {H}}})</span> if for any hyperedge <i>H</i> of <span>({{mathcal {H}}})</span>, we have <span>(|Hcap S| in A)</span>. Independent sets are <span>({0,1,dots ,r{-}1})</span>-transversals, while strongly independent sets are <span>({0,1})</span>-transversals. Note that for some sets <i>A</i>, there may exist hypergraphs without any <i>A</i>-transversals. We study the maximum number of <i>A</i>-transversals for every <i>A</i>, but we focus on the more natural sets, <span>(A={a})</span>, <span>(A={0,1,dots ,a})</span> or <i>A</i> being the set of odd integers or the set of even integers.\u0000</p>","PeriodicalId":49706,"journal":{"name":"Periodica Mathematica Hungarica","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2024-07-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141552547","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
n-convexity and weighted majorization with applications to f-divergences and Zipf–Mandelbrot law n-凸性和加权大化在 f-发散和 Zipf-Mandelbrot 定律中的应用
IF 0.8 3区 数学
Periodica Mathematica Hungarica Pub Date : 2024-07-03 DOI: 10.1007/s10998-024-00601-5
Slavica Ivelić Bradanović, Ɖilda Pečarić, Josip Pečarić
{"title":"n-convexity and weighted majorization with applications to f-divergences and Zipf–Mandelbrot law","authors":"Slavica Ivelić Bradanović, Ɖilda Pečarić, Josip Pečarić","doi":"10.1007/s10998-024-00601-5","DOIUrl":"https://doi.org/10.1007/s10998-024-00601-5","url":null,"abstract":"<p>In this paper we obtain refinement of Sherman’s generalization of classical majorization inequality for convex functions (2-convex functions). Using some nice properties of Green’s functions we introduce new identities that include Sherman’s difference, deduced from Sherman’s inequality, which enable us to extend Sherman’s results to the class of convex functions of higher order, i.e. to <i>n</i>-convex functions (<span>(nge 3)</span>). We connect this approach with Csiszár <i>f</i>-divergence and specified divergences as the Kullback–Leibler divergence, Hellinger divergence, Harmonic divergence, Bhattacharya distance, Triangular discrimination, Rényi divergence and derive new estimates for them. We also observe results in the context of the Zipf–Mandelbrot law and its special form Zipf’s law and give one linguistic example using experimentally obtained values of coefficients from Zipf’s law assigned to different languages.\u0000</p>","PeriodicalId":49706,"journal":{"name":"Periodica Mathematica Hungarica","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2024-07-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141547326","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
Multiplicative group generated by quotients of integral parts 由积分部分的商生成的乘法群
IF 0.8 3区 数学
Periodica Mathematica Hungarica Pub Date : 2024-07-03 DOI: 10.1007/s10998-024-00599-w
Artūras Dubickas
{"title":"Multiplicative group generated by quotients of integral parts","authors":"Artūras Dubickas","doi":"10.1007/s10998-024-00599-w","DOIUrl":"https://doi.org/10.1007/s10998-024-00599-w","url":null,"abstract":"<p>For fixed positive numbers <span>(alpha ne beta )</span>, we consider the multiplicative group <span>({mathcal {F}}_{alpha ,beta })</span> generated by the rational numbers of the form <span>(frac{lfloor alpha nrfloor }{lfloor beta nrfloor })</span>, where <span>(n in {mathbb {N}})</span> and <span>(n ge max big (frac{1}{alpha },frac{1}{beta }big ))</span>. For <span>(0&lt;alpha &lt;1)</span> and <span>(beta =1)</span>, we prove that <span>({mathcal {F}}_{alpha ,1})</span> is the maximal possible group, namely, it is the multiplicative group of all positive rational numbers <span>({mathbb {Q}}^{+})</span>. The same equality <span>({mathcal {F}}_{alpha ,beta }={mathbb {Q}}^{+})</span> holds in the case when <span>(0&lt; 10 alpha le beta &lt;1)</span>. These results produce infinitely many pairs <span>((alpha ,beta ))</span>, <span>(alpha ne beta )</span>, for which a conjecture posed by Kátai and Phong can be confirmed. The only previously known such example is <span>((alpha ,beta )=(sqrt{2},1))</span>. We also give a new proof in that case, which is much simpler than the original proof of Kátai and Phong. More generally, we conjecture that <span>({mathcal {F}}_{alpha ,beta }={mathbb {Q}}^{+})</span> for <span>(alpha ne beta )</span> if at least one of the numbers <span>(alpha ,beta &gt;0)</span> is not an integer.</p>","PeriodicalId":49706,"journal":{"name":"Periodica Mathematica Hungarica","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2024-07-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141519219","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
Signed zero sum problems for metacyclic group 元环组的有符号零和问题
IF 0.8 3区 数学
Periodica Mathematica Hungarica Pub Date : 2024-07-03 DOI: 10.1007/s10998-024-00593-2
B. K. Moriya
{"title":"Signed zero sum problems for metacyclic group","authors":"B. K. Moriya","doi":"10.1007/s10998-024-00593-2","DOIUrl":"https://doi.org/10.1007/s10998-024-00593-2","url":null,"abstract":"<p>Let <i>A</i> be a nonempty subset of the integers and <i>G</i> a finite group written multiplicatively. The constant <span>(eta _A(G))</span> (<span>(s_A(G))</span>) is defined to be the smallest positive integer <i>t</i> such that any sequence of length <i>t</i> of elements of <i>G</i> contains a nonempty <i>A</i>-weighted product one subsequence (that is, the terms of the subsequence could be ordered so that their <i>A</i>-weighted product is the multiplicative identity of the group <i>G</i>) of length at most <span>(exp (G))</span> (of length <span>(exp (G))</span>). In this note, we shall calculate the value of <span>(eta _pm (G),D_pm (G),E_pm (G) text{ and } s_pm (G))</span> for some metacyclic groups. In 2007, Gao et al. conjectured that <span>(s(G)=eta (G)+exp (G)-1)</span> holds for any finite abelian group <i>G</i> (see Gao et al. in Integers 7:A21, 2007). We will prove that this conjecture is true for some metacyclic groups. Furthermore, we study the Harborth constant <span>(mathfrak {g}_pm (G))</span>, where <i>G</i> is a group among one specific class of metacyclic groups.</p>","PeriodicalId":49706,"journal":{"name":"Periodica Mathematica Hungarica","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2024-07-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141519218","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 sum-of-digits function in rings of residue classes 残差类环中的位数和函数
IF 0.8 3区 数学
Periodica Mathematica Hungarica Pub Date : 2024-07-02 DOI: 10.1007/s10998-024-00595-0
Huaning Liu, Zehua Liu
{"title":"The sum-of-digits function in rings of residue classes","authors":"Huaning Liu, Zehua Liu","doi":"10.1007/s10998-024-00595-0","DOIUrl":"https://doi.org/10.1007/s10998-024-00595-0","url":null,"abstract":"<p>Dartyge and Sárközy introduced the notion of digits in finite fields and studied the properties of polynomial values of <span>({mathbb {F}}_q)</span> with a fixed sum of digits. Swaenepoel provided sharp estimates for the number of elements of special sequences of <span>({mathbb {F}}_q)</span> whose sum of digits is prescribed. In this paper we study the sum-of-digits function in rings of residue classes and give a few asymptotic formulas and exact identities by using estimates for character sums and exponential sums modulo prime powers.</p>","PeriodicalId":49706,"journal":{"name":"Periodica Mathematica Hungarica","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2024-07-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141519216","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 a ternary diophantine inequality with prime numbers of a special type II 关于有特殊类型素数 II 的三元二叉不等式
IF 0.8 3区 数学
Periodica Mathematica Hungarica Pub Date : 2024-07-02 DOI: 10.1007/s10998-024-00602-4
Li Zhu
{"title":"On a ternary diophantine inequality with prime numbers of a special type II","authors":"Li Zhu","doi":"10.1007/s10998-024-00602-4","DOIUrl":"https://doi.org/10.1007/s10998-024-00602-4","url":null,"abstract":"<p>Suppose that <i>N</i> is a sufficiently large real number and <i>E</i> is an arbitrarily large constant. In this paper, it is proved that, for <span>(1&lt; c &lt; frac{7}{6})</span>, the Diophantine inequality </p><span>$$begin{aligned} |p_1^c+p_2^c+p_3^c-N|&lt;(log N)^{-E} end{aligned}$$</span><p>is solvable in prime variables <span>(p_1,p_2,p_3)</span> so that each of the numbers <span>(p_i+2,,i=1,2,3)</span>, has at most <span>(big [3.43655+{frac{12.12}{7-6c}}big ])</span> prime factors counted with multiplicity.</p>","PeriodicalId":49706,"journal":{"name":"Periodica Mathematica Hungarica","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2024-07-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141503331","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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