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On some maximal and minimal sets 关于一些最大集和最小集
IF 0.8 3区 数学
Periodica Mathematica Hungarica Pub Date : 2023-12-12 DOI: 10.1007/s10998-023-00559-w
Jin-Hui Fang, Xue-Qin Cao
{"title":"On some maximal and minimal sets","authors":"Jin-Hui Fang, Xue-Qin Cao","doi":"10.1007/s10998-023-00559-w","DOIUrl":"https://doi.org/10.1007/s10998-023-00559-w","url":null,"abstract":"<p>A set <i>A</i> of positive integers is called 3-free if it contains no 3-term arithmetic progression. Furthermore, such <i>A</i> is called <i>maximal</i> if it is not properly contained in any other 3-free set. In 2006, by confirming a question posed by Erdős et al., Savchev and Chen proved that there exists a maximal 3-free set <span>({a_1&lt;a_2&lt;cdots&lt;a_n&lt;cdots })</span> of positive integers with the property that <span>(lim _{nrightarrow infty }(a_{n+1}-a_n)=infty )</span>. In this paper, we generalize their result. On the other hand, a set <i>A</i> of nonnegative integers is called an asymptotic basis of order <i>h</i> if every sufficiently large integer can be represented as a sum of <i>h</i> elements of <i>A</i>. Such <i>A</i> is defined as <i>minimal</i> if no proper subset of <i>A</i> has this property. We also extend a result of Jańczak and Schoen about the minimal asymptotic basis.</p>","PeriodicalId":49706,"journal":{"name":"Periodica Mathematica Hungarica","volume":"22 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2023-12-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138580311","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 Greenberg’s conjecture for certain real biquadratic fields 关于格林伯格对某些实双曲域的猜想
IF 0.8 3区 数学
Periodica Mathematica Hungarica Pub Date : 2023-12-09 DOI: 10.1007/s10998-023-00560-3
Abdelakder El Mahi, M’hammed Ziane
{"title":"On Greenberg’s conjecture for certain real biquadratic fields","authors":"Abdelakder El Mahi, M’hammed Ziane","doi":"10.1007/s10998-023-00560-3","DOIUrl":"https://doi.org/10.1007/s10998-023-00560-3","url":null,"abstract":"<p>In this paper, we give the structure of the Iwasawa module <span>(X=X(k_{infty }))</span> of the <span>(mathbb {Z}_{2})</span>-extension of infinitely many real biquadratic fields <i>k</i>. Denote by <span>(lambda , mu )</span> and <span>(nu )</span> the Iwasawa invariants of the cyclotomic <span>(mathbb {Z}_{2})</span>-extension of <i>k</i>. Then <span>(lambda =mu =0 )</span> and <span>(nu =2)</span>.</p>","PeriodicalId":49706,"journal":{"name":"Periodica Mathematica Hungarica","volume":"118 26 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2023-12-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138560445","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 c-differential uniformity of the perturbed inverse function via a trace function $$ {{,textrm{Tr},}}big (frac{x^2}{x+1}big )$$ 通过痕量函数计算扰动反函数的 c 微分均匀性 $$ {{,textrm{Tr},}}big (frac{x^2}{x+1}big )$$
IF 0.8 3区 数学
Periodica Mathematica Hungarica Pub Date : 2023-12-09 DOI: 10.1007/s10998-023-00561-2
Kübra Kaytancı, Ferruh Özbudak
{"title":"The c-differential uniformity of the perturbed inverse function via a trace function $$ {{,textrm{Tr},}}big (frac{x^2}{x+1}big )$$","authors":"Kübra Kaytancı, Ferruh Özbudak","doi":"10.1007/s10998-023-00561-2","DOIUrl":"https://doi.org/10.1007/s10998-023-00561-2","url":null,"abstract":"<p>Differential uniformity is one of the most crucial concepts in cryptography. Recently Ellingsen et al. (IEEE Trans Inf Theory 66:5781–5789, 2020) introduced a new concept, the c-Difference Distribution Table and the c-differential uniformity, by extending the usual differential notion. The motivation behind this new concept is based on having the ability to resist some known differential attacks which is shown by Borisov et. al. (Multiplicative Differentials, 2002). In 2022, Hasan et al. (IEEE Trans Inf Theory 68:679–691, 2022) gave an upper bound of the c-differential uniformity of the perturbed inverse function <i>H</i> via a trace function <span>( {{,textrm{Tr},}}big (frac{x^2}{x+1}big ))</span>. In their work, they also presented an open question on the exact c-differential uniformity of <i>H</i>. By using a new method based on algebraic curves over finite fields, we solve the open question in the case <span>( {{,textrm{Tr},}}(c)=1= {{,textrm{Tr},}}(frac{1}{c}))</span> for <span>( c in {mathbb {F}}_{2^n}setminus {0,1} )</span> completely and we show that the exact c-differential uniformity of <i>H</i> is 8. In the remaining case, we almost completely solve the problem and we show that the c-differential uniformity of <i>H</i> is either 8 or 9.</p>","PeriodicalId":49706,"journal":{"name":"Periodica Mathematica Hungarica","volume":"47 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2023-12-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138560260","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 Three Problems of Y.–G. Chen 论陈永刚的三个问题
IF 0.8 3区 数学
Periodica Mathematica Hungarica Pub Date : 2023-12-07 DOI: 10.1007/s10998-023-00563-0
Yuchen Ding
{"title":"On Three Problems of Y.–G. Chen","authors":"Yuchen Ding","doi":"10.1007/s10998-023-00563-0","DOIUrl":"https://doi.org/10.1007/s10998-023-00563-0","url":null,"abstract":"<p>In this short note, we answer two questions of Chen and Ruzsa negatively and answer a question of Ma and Chen affirmatively.</p>","PeriodicalId":49706,"journal":{"name":"Periodica Mathematica Hungarica","volume":"32 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2023-12-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138547417","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 degenerate Kirchhoff-type problem involving variable $$s(cdot )$$ -order fractional $$p(cdot )$$ -Laplacian with weights 涉及带权重的变量$$s(cdot )$$ -阶分数$$p(cdot )$$ -拉普拉奇的退化基尔霍夫型问题
IF 0.8 3区 数学
Periodica Mathematica Hungarica Pub Date : 2023-12-07 DOI: 10.1007/s10998-023-00562-1
Mostafa Allaoui, Mohamed Karim Hamdani, Lamine Mbarki
{"title":"A degenerate Kirchhoff-type problem involving variable $$s(cdot )$$ -order fractional $$p(cdot )$$ -Laplacian with weights","authors":"Mostafa Allaoui, Mohamed Karim Hamdani, Lamine Mbarki","doi":"10.1007/s10998-023-00562-1","DOIUrl":"https://doi.org/10.1007/s10998-023-00562-1","url":null,"abstract":"<p>This paper deals with a class of nonlocal variable <i>s</i>(.)-order fractional <i>p</i>(.)-Kirchhoff type equations: </p><span>$$begin{aligned} left{ begin{array}{ll} {mathcal {K}}left( int _{{mathbb {R}}^{2N}}frac{1}{p(x,y)}frac{|varphi (x)-varphi (y)|^{p(x,y)}}{|x-y|^{N+s(x,y){p(x,y)}}} ,dx,dyright) (-Delta )^{s(cdot )}_{p(cdot )}varphi (x) =f(x,varphi ) quad text{ in } Omega , varphi =0 quad text{ on } {mathbb {R}}^Nbackslash Omega . end{array} right. end{aligned}$$</span><p>Under some suitable conditions on the functions <span>(p,s, {mathcal {K}})</span> and <i>f</i>, the existence and multiplicity of nontrivial solutions for the above problem are obtained. Our results cover the degenerate case in the <span>(p(cdot ))</span> fractional setting.\u0000</p>","PeriodicalId":49706,"journal":{"name":"Periodica Mathematica Hungarica","volume":"17 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2023-12-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138547241","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 regular Tóth identity and a Menon-type identity in residually finite Dedekind domains 剩余有限Dedekind域中的正则Tóth恒等式和menon型恒等式
IF 0.8 3区 数学
Periodica Mathematica Hungarica Pub Date : 2023-11-24 DOI: 10.1007/s10998-023-00555-0
Tianfang Qi
{"title":"A regular Tóth identity and a Menon-type identity in residually finite Dedekind domains","authors":"Tianfang Qi","doi":"10.1007/s10998-023-00555-0","DOIUrl":"https://doi.org/10.1007/s10998-023-00555-0","url":null,"abstract":"<p>In this paper, we define the <i>s</i>-dimensional regular generalized Euler function and give a variant of Tóth’s identity in residually finite Dedekind domains, which can be viewed as a multidimensional version of the results by Wang, Zhang, Ji (2019) and Ji, Wang (2020).</p>","PeriodicalId":49706,"journal":{"name":"Periodica Mathematica Hungarica","volume":"26 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2023-11-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138520895","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 convergence of multiple Richardson extrapolation combined with explicit Runge–Kutta methods 结合显式龙格-库塔方法的多重Richardson外推的收敛性
IF 0.8 3区 数学
Periodica Mathematica Hungarica Pub Date : 2023-11-23 DOI: 10.1007/s10998-023-00557-y
Teshome Bayleyegn, István Faragó, Ágnes Havasi
{"title":"On the convergence of multiple Richardson extrapolation combined with explicit Runge–Kutta methods","authors":"Teshome Bayleyegn, István Faragó, Ágnes Havasi","doi":"10.1007/s10998-023-00557-y","DOIUrl":"https://doi.org/10.1007/s10998-023-00557-y","url":null,"abstract":"<p>The order of accuracy of any convergent time integration method for systems of differential equations can be increased by using the sequence acceleration method known as Richardson extrapolation, as well as its variants (classical Richardson extrapolation and multiple Richardson extrapolation). The original (classical) version of Richardson extrapolation consists in taking a linear combination of numerical solutions obtained by two different time-steps with time-step sizes <i>h</i> and <i>h</i>/2 by the same numerical method. Multiple Richardson extrapolation is a generalization of this procedure, where the extrapolation is applied to the combination of some underlying numerical method and the classical Richardson extrapolation. This procedure increases the accuracy order of the underlying method from <i>p</i> to <span>(p+2)</span>, and with each repetition, the order is further increased by one. In this paper we investigate the convergence of multiple Richardson extrapolation in the case where the underlying numerical method is an explicit Runge–Kutta method, and the computational efficiency is also checked.</p>","PeriodicalId":49706,"journal":{"name":"Periodica Mathematica Hungarica","volume":"2 4","pages":""},"PeriodicalIF":0.8,"publicationDate":"2023-11-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138520928","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
Inverse results for restricted sumsets in $${mathbb {Z}/pmathbb {Z}}$$ 中的限制集合的逆结果 $${mathbb {Z}/pmathbb {Z}}$$
IF 0.8 3区 数学
Periodica Mathematica Hungarica Pub Date : 2023-11-22 DOI: 10.1007/s10998-023-00554-1
Mario Huicochea
{"title":"Inverse results for restricted sumsets in $${mathbb {Z}/pmathbb {Z}}$$","authors":"Mario Huicochea","doi":"10.1007/s10998-023-00554-1","DOIUrl":"https://doi.org/10.1007/s10998-023-00554-1","url":null,"abstract":"<p>Let <i>p</i> be a prime, <i>A</i> and <i>B</i> be subsets of <span>({mathbb {Z}/pmathbb {Z}})</span> and <i>S</i> be a subset of <span>(Atimes B)</span>. We write <span>(A{{mathop {+}limits ^{S}}}B:={a+b:;(a,b)in S})</span>. In the first inverse result of this paper, we show that if <span>(left| A{{mathop {+}limits ^{S}}}Bright| )</span> and <span>(|(Atimes B)setminus S|)</span> are small, then <i>A</i> has a big subset with small difference set. In the second theorem of this paper, we use the previous result to show that if <span>(left| A{{mathop {+}limits ^{S}}}Bright| )</span>, |<i>A</i>| and |<i>B</i>| are small, then big parts of <i>A</i> and <i>B</i> are contained in short arithmetic progressions with the same difference. As an application of this result, we get an inverse of Pollard’s theorem.\u0000</p>","PeriodicalId":49706,"journal":{"name":"Periodica Mathematica Hungarica","volume":"28 4","pages":""},"PeriodicalIF":0.8,"publicationDate":"2023-11-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138520894","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
Unlimited accumulation by Shelah’s PCF operator 希拉的PCF操作员无限积累
3区 数学
Periodica Mathematica Hungarica Pub Date : 2023-11-14 DOI: 10.1007/s10998-023-00553-2
Mohammad Golshani
{"title":"Unlimited accumulation by Shelah’s PCF operator","authors":"Mohammad Golshani","doi":"10.1007/s10998-023-00553-2","DOIUrl":"https://doi.org/10.1007/s10998-023-00553-2","url":null,"abstract":"","PeriodicalId":49706,"journal":{"name":"Periodica Mathematica Hungarica","volume":"36 8","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-11-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134954099","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 Arestov’s inequalities concerning the Shur–Szegő composition of polynomials 关于多项式的舒尔-塞格格复合的Arestov不等式
3区 数学
Periodica Mathematica Hungarica Pub Date : 2023-11-11 DOI: 10.1007/s10998-023-00558-x
Mudassir A. Bhat, Ravinder Kumar, Suhail Gulzar
{"title":"On Arestov’s inequalities concerning the Shur–Szegő composition of polynomials","authors":"Mudassir A. Bhat, Ravinder Kumar, Suhail Gulzar","doi":"10.1007/s10998-023-00558-x","DOIUrl":"https://doi.org/10.1007/s10998-023-00558-x","url":null,"abstract":"","PeriodicalId":49706,"journal":{"name":"Periodica Mathematica Hungarica","volume":"17 3","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-11-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135042889","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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