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Turán number of two vertex-disjoint copies of cliques 两个顶点不相连的小群副本的图兰数
IF 0.5 4区 数学
Czechoslovak Mathematical Journal Pub Date : 2024-06-17 DOI: 10.21136/cmj.2024.0461-23
Caiyun Hu
{"title":"Turán number of two vertex-disjoint copies of cliques","authors":"Caiyun Hu","doi":"10.21136/cmj.2024.0461-23","DOIUrl":"https://doi.org/10.21136/cmj.2024.0461-23","url":null,"abstract":"<p>The Turán number of a given graph <i>H</i>, denoted by ex(<i>n, H</i>), is the maximum number of edges in an <i>H</i>-free graph on n vertices. Applying a well-known result of Hajnal and Szemerédi, we determine the Turán number ex(<i>n</i>, <i>K</i><sub><i>p</i></sub> ∪ <i>K</i><sub><i>q</i></sub>) of a vertex-disjoint union of cliques <i>K</i><sub><i>p</i></sub> and <i>K</i><sub><i>q</i></sub> for all values of <i>n</i>.</p>","PeriodicalId":50596,"journal":{"name":"Czechoslovak Mathematical Journal","volume":"20 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2024-06-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141929854","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Bounds for the derivative of certain meromorphic functions and on meromorphic Bloch-type functions 某些分形函数的导数和分形布洛赫型函数的界限
IF 0.5 4区 数学
Czechoslovak Mathematical Journal Pub Date : 2024-05-31 DOI: 10.21136/cmj.2024.0332-23
Bappaditya Bhowmik, Sambhunath Sen
{"title":"Bounds for the derivative of certain meromorphic functions and on meromorphic Bloch-type functions","authors":"Bappaditya Bhowmik, Sambhunath Sen","doi":"10.21136/cmj.2024.0332-23","DOIUrl":"https://doi.org/10.21136/cmj.2024.0332-23","url":null,"abstract":"<p>It is known that if f is holomorphic in the open unit disc <span>(mathbb{D})</span> of the complex plane and if, for some <i>c</i> &gt; 0, ∣<i>f</i>(<i>z</i>)∣ ⩽ 1/(1−∣<i>z</i>∣<sup>2</sup>)<sup><i>c</i></sup>, <span>(z in mathbb{D})</span>, then ∣<i>f</i>′(<i>z</i>)∣ ⩽ 2(<i>c</i>+1)/(1−∣<i>z</i>∣<sup>2</sup>)<sup><i>c</i>+1</sup>. We consider a meromorphic analogue of this result. Furthermore, we introduce and study the class of meromorphic Bloch-type functions that possess a nonzero simple pole in D. In particular, we obtain bounds for the modulus of the Taylor coefficients of functions in this class.</p>","PeriodicalId":50596,"journal":{"name":"Czechoslovak Mathematical Journal","volume":"78 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2024-05-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141501950","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Partitioning planar graph of girth 5 into two forests with maximum degree 4 将周长为 5 的平面图划分为两个最大度数为 4 的森林
IF 0.5 4区 数学
Czechoslovak Mathematical Journal Pub Date : 2024-05-30 DOI: 10.21136/cmj.2024.0394-21
Min Chen, André Raspaud, Weifan Wang, Weiqiang Yu
{"title":"Partitioning planar graph of girth 5 into two forests with maximum degree 4","authors":"Min Chen, André Raspaud, Weifan Wang, Weiqiang Yu","doi":"10.21136/cmj.2024.0394-21","DOIUrl":"https://doi.org/10.21136/cmj.2024.0394-21","url":null,"abstract":"<p>Given a graph <i>G</i> = (<i>V, E</i>), if we can partition the vertex set <i>V</i> into two nonempty subsets <i>V</i><sub>1</sub> and <i>V</i><sub>2</sub> which satisfy Δ(<i>G</i>[<i>V</i><sub>1</sub>]) ⩽ <i>d</i><sub>1</sub> and Δ(<i>G</i>[<i>V</i><sub>2</sub>]) ⩽ <i>d</i><sub>2</sub>, then we say <i>G</i> has a (<span>({{rm{Delta }}_{{d_1}}},,{{rm{Delta }}_{{d_2}}})</span>)-partition. And we say <i>G</i> admits an (<span>({F_{d_{1}}}, {F_{d_{2}}})</span>)-partition if <i>G</i>[<i>V</i><sub>1</sub>] and <i>G</i>[<i>V</i><sub>2</sub>] are both forests whose maximum degree is at most <i>d</i><sub>1</sub> and <i>d</i><sub>2</sub>, respectively. We show that every planar graph with girth at least 5 has an (<i>F</i><sub>4</sub>, <i>F</i><sub>4</sub>)-partition.</p>","PeriodicalId":50596,"journal":{"name":"Czechoslovak Mathematical Journal","volume":"39 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2024-05-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141501951","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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 finite groups whose enhanced power graphs have universal vertices 增强幂图具有普遍顶点的有限群的特征
IF 0.5 4区 数学
Czechoslovak Mathematical Journal Pub Date : 2024-04-29 DOI: 10.21136/cmj.2024.0065-24
David G. Costanzo, Mark L. Lewis, Stefano Schmidt, Eyob Tsegaye, Gabe Udell
{"title":"Characterizing finite groups whose enhanced power graphs have universal vertices","authors":"David G. Costanzo, Mark L. Lewis, Stefano Schmidt, Eyob Tsegaye, Gabe Udell","doi":"10.21136/cmj.2024.0065-24","DOIUrl":"https://doi.org/10.21136/cmj.2024.0065-24","url":null,"abstract":"<p>Let <i>G</i> be a finite group and construct a graph Δ(<i>G</i>) by taking <i>G</i> {1} as the vertex set of Δ(<i>G</i>) and by drawing an edge between two vertices <i>x</i> and <i>y</i> if 〈<i>x</i>, <i>y</i>〉 is cyclic. Let <i>K</i>(<i>G</i>) be the set consisting of the universal vertices of Δ(<i>G</i>) along the identity element. For a solvable group <i>G</i>, we present a necessary and sufficient condition for <i>K</i>(<i>G</i>) to be nontrivial. We also develop a connection between Δ(<i>G</i>) and <i>K</i>(<i>G</i>) when ∣<i>G</i>∣ is divisible by two distinct primes and the diameter of Δ(<i>G</i>) is 2.</p>","PeriodicalId":50596,"journal":{"name":"Czechoslovak Mathematical Journal","volume":"59 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2024-04-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141525284","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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 average behaviour of the Fourier coefficients of jth symmetric power L-function over certain sparse sequence of positive integers 关于第 j 次对称幂 L 函数在某些正整数稀疏序列上的傅立叶系数平均行为的说明
IF 0.5 4区 数学
Czechoslovak Mathematical Journal Pub Date : 2024-04-29 DOI: 10.21136/cmj.2024.0038-24
Youjun Wang
{"title":"A note on average behaviour of the Fourier coefficients of jth symmetric power L-function over certain sparse sequence of positive integers","authors":"Youjun Wang","doi":"10.21136/cmj.2024.0038-24","DOIUrl":"https://doi.org/10.21136/cmj.2024.0038-24","url":null,"abstract":"<p>Let <i>j</i> ⩾ 2 be a given integer. Let <i>H</i><sub><i>k</i></sub>* be the set of all normalized primitive holomorphic cusp forms of even integral weight <i>k</i> ⩾ 2 for the full modulo group SL(2, ℤ). For <i>f</i> ∈ <i>H</i><sub><i>k</i></sub>*, denote by <span>({{rm{lambda }}_{{rm{sy}}{{rm{m}}^j}{kern 1pt} f}}(n))</span> the <i>n</i>th normalized Fourier coefficient of <i>j</i>th symmetric power <i>L</i>-function (<i>L</i>(<i>s</i>, sym<sup><i>j</i></sup><i>f</i>)) attached to <i>f</i>. We are interested in the average behaviour of the sum </p><span>$$sumlimits_{scriptstyle n, = ,a_1^2 + a_2^2 + a_3^2 + a_4^2 + a_5^2 + a_6^2x atop scriptstyle ,,,,,,,({a_1},{a_2},{a_3},{a_4},{a_5},{a_6}{rm{)}} in ,{{mathbb{Z}}^6}} {{rm{lambda }}_{{rm{sy}}{{rm{m}}^j},fleft( n right),}^2}$$</span><p> where <i>x</i> is sufficiently large, which improves the recent work of A. Sharma and A. Sankaranarayanan (2023).</p>","PeriodicalId":50596,"journal":{"name":"Czechoslovak Mathematical Journal","volume":"25 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2024-04-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141525283","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Non-differentiability of Feynman paths 费曼路径的不可分性
IF 0.5 4区 数学
Czechoslovak Mathematical Journal Pub Date : 2024-03-08 DOI: 10.21136/cmj.2024.0493-22
Pat Muldowney
{"title":"Non-differentiability of Feynman paths","authors":"Pat Muldowney","doi":"10.21136/cmj.2024.0493-22","DOIUrl":"https://doi.org/10.21136/cmj.2024.0493-22","url":null,"abstract":"<p>A well-known mathematical property of the particle paths of Brownian motion is that such paths are, with probability one, everywhere continuous and nowhere differentiable. R. Feynman (1965) and elsewhere asserted without proof that an analogous property holds for the sample paths (or possible paths) of a non-relativistic quantum mechanical particle to which a conservative force is applied. Using the non-absolute integration theory of Kurzweil and Henstock, this article provides an introductory proof of Feynman’s assertion.</p>","PeriodicalId":50596,"journal":{"name":"Czechoslovak Mathematical Journal","volume":"65 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2024-03-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140886046","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Bilinear fractional Hardy-type operators with rough kernels on central Morrey spaces with variable exponents 具有可变指数的莫里中心空间上粗糙核的双线性分数哈代型算子
IF 0.5 4区 数学
Czechoslovak Mathematical Journal Pub Date : 2024-02-16 DOI: 10.21136/cmj.2024.0431-23
{"title":"Bilinear fractional Hardy-type operators with rough kernels on central Morrey spaces with variable exponents","authors":"","doi":"10.21136/cmj.2024.0431-23","DOIUrl":"https://doi.org/10.21136/cmj.2024.0431-23","url":null,"abstract":"<h3>Abstract</h3> <p>We introduce a type of <em>n</em>-dimensional bilinear fractional Hardy-type operators with rough kernels and prove the boundedness of these operators and their commutators on central Morrey spaces with variable exponents. Furthermore, the similar definitions and results of multilinear fractional Hardy-type operators with rough kernels are obtained.</p>","PeriodicalId":50596,"journal":{"name":"Czechoslovak Mathematical Journal","volume":"77 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2024-02-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139926730","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Lipschitz constants for a hyperbolic type metric under Möbius transformations 莫比乌斯变换下双曲型度量的 Lipschitz 常量
IF 0.5 4区 数学
Czechoslovak Mathematical Journal Pub Date : 2024-02-12 DOI: 10.21136/cmj.2024.0366-23
{"title":"Lipschitz constants for a hyperbolic type metric under Möbius transformations","authors":"","doi":"10.21136/cmj.2024.0366-23","DOIUrl":"https://doi.org/10.21136/cmj.2024.0366-23","url":null,"abstract":"<h3>Abstract</h3> <p>Let <em>D</em> be a nonempty open set in a metric space (<em>X, d</em>) with <em>∂D</em> ≠ Ø. Define <span> <span>$$h_{D,c}(x,y)=logleft(1+c{{{d(x,y)}}over{{sqrt{d_{D}(x)d_{D}(y)}}}}right).$$</span> </span> where <em>d</em><sub><em>D</em></sub>(<em>x</em>) = <em>d</em>(<em>x, ∂D</em>) is the distance from <em>x</em> to the boundary of <em>D</em>. For every <em>c</em> ⩾ 2, <em>h</em><sub><em>D,c</em></sub> is a metric. We study the sharp Lipschitz constants for the metric <em>h</em><sub><em>D,c</em></sub> under Möbius transformations of the unit ball, the upper half space, and the punctured unit ball.</p>","PeriodicalId":50596,"journal":{"name":"Czechoslovak Mathematical Journal","volume":"11 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2024-02-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139980488","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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 conjecture on minimum permanents 关于最小永久点的猜想
IF 0.5 4区 数学
Czechoslovak Mathematical Journal Pub Date : 2023-12-11 DOI: 10.21136/cmj.2023.0186-23
Gi-Sang Cheon, Seok-Zun Song
{"title":"A conjecture on minimum permanents","authors":"Gi-Sang Cheon, Seok-Zun Song","doi":"10.21136/cmj.2023.0186-23","DOIUrl":"https://doi.org/10.21136/cmj.2023.0186-23","url":null,"abstract":"<p>We consider the permanent function on the faces of the polytope of certain doubly stochastic matrices, whose nonzero entries coincide with those of fully indecomposable square (0, 1)-matrices containing the identity submatrix. We show that a conjecture in K. Pula, S. Z. Song, I. M. Wanless (2011), is true for some cases by determining the minimum permanent on some faces of the polytope of doubly stochastic matrices.</p>","PeriodicalId":50596,"journal":{"name":"Czechoslovak Mathematical Journal","volume":"1 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2023-12-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138630549","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Boundary value problems with bounded ϕ-Laplacian and nonlocal conditions of integral type 有界拉普拉卡矩和积分型非局部条件的边值问题
IF 0.5 4区 数学
Czechoslovak Mathematical Journal Pub Date : 2023-12-08 DOI: 10.21136/cmj.2023.0154-23
Daria Bugajewska, Jean Mawhin
{"title":"Boundary value problems with bounded ϕ-Laplacian and nonlocal conditions of integral type","authors":"Daria Bugajewska, Jean Mawhin","doi":"10.21136/cmj.2023.0154-23","DOIUrl":"https://doi.org/10.21136/cmj.2023.0154-23","url":null,"abstract":"<p>We study the existence of solutions to nonlinear boundary value problems for second order quasilinear ordinary differential equations involving bounded <i>ϕ</i>-Laplacian, subject to integral boundary conditions formulated in terms of Riemann-Stieltjes integrals.</p>","PeriodicalId":50596,"journal":{"name":"Czechoslovak Mathematical Journal","volume":"80 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2023-12-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138632526","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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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