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Spanning trees of $$K_{1,4}$$ -free graphs whose reducible stems have few leaves 无$$K_{1,4}$$图的生成树，其可还原茎的叶子很少
IF 0.8 3区 数学
Periodica Mathematica Hungarica Pub Date : 2024-02-19 DOI: 10.1007/s10998-024-00572-7
Pham Hoang Ha, Le Dinh Nam, Ngoc Diep Pham
{"title":"Spanning trees of $$K_{1,4}$$ -free graphs whose reducible stems have few leaves","authors":"Pham Hoang Ha, Le Dinh Nam, Ngoc Diep Pham","doi":"10.1007/s10998-024-00572-7","DOIUrl":"https://doi.org/10.1007/s10998-024-00572-7","url":null,"abstract":"<p>Let <i>T</i> be a tree; a vertex of degree 1 is a <i>leaf</i> of <i>T</i> and a vertex of degree at least 3 is a <i>branch vertex</i> of <i>T</i>. The <i>reducible stem</i> of <i>T</i> is the smallest subtree that contains all branch vertices of <i>T</i>. In this paper, we give some sharp sufficient conditions for <span>(K_{1,4})</span>-free graphs to have a spanning tree whose reducible stem has few leaves.</p>","PeriodicalId":49706,"journal":{"name":"Periodica Mathematica Hungarica","volume":"34 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2024-02-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139928714","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 q-statistical convergence of double sequences 论双重序列的 q 统计收敛性
IF 0.8 3区 数学
Periodica Mathematica Hungarica Pub Date : 2024-01-19 DOI: 10.1007/s10998-023-00556-z
Mohammad Mursaleen, Sabiha Tabassum, Ruqaiyya Fatma
{"title":"On the q-statistical convergence of double sequences","authors":"Mohammad Mursaleen, Sabiha Tabassum, Ruqaiyya Fatma","doi":"10.1007/s10998-023-00556-z","DOIUrl":"https://doi.org/10.1007/s10998-023-00556-z","url":null,"abstract":"<p>In this paper, we study <i>q</i>-statistical convergence for double sequences. The definitions of <i>q</i>-analog of statistical Cauchy and statistical pre-Cauchy for double sequences are given. The necessary and sufficient condition for a double sequence to have different statistical limits is also obtained. We show that a <i>q</i>-statistical convergent sequence is <i>q</i>-statistical Cauchy and vice-versa.</p>","PeriodicalId":49706,"journal":{"name":"Periodica Mathematica Hungarica","volume":"60 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2024-01-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139509859","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
Correction to: On Greenberg’s conjecture for certain real biquadratic fields 更正：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 : 2024-01-09 DOI: 10.1007/s10998-023-00571-0
Abdelkader El Mahi, M’hammed Ziane
{"title":"Correction to: On Greenberg’s conjecture for certain real biquadratic fields","authors":"Abdelkader El Mahi, M’hammed Ziane","doi":"10.1007/s10998-023-00571-0","DOIUrl":"https://doi.org/10.1007/s10998-023-00571-0","url":null,"abstract":"","PeriodicalId":49706,"journal":{"name":"Periodica Mathematica Hungarica","volume":"35 39","pages":""},"PeriodicalIF":0.8,"publicationDate":"2024-01-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139442842","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
Non-vanishing and cofiniteness of generalized local cohomology modules 广义局部同调模块的非凡性和同完备性
IF 0.8 3区 数学
Periodica Mathematica Hungarica Pub Date : 2024-01-02 DOI: 10.1007/s10998-023-00567-w
Tran Tuan Nam, Nguyen Minh Tri
{"title":"Non-vanishing and cofiniteness of generalized local cohomology modules","authors":"Tran Tuan Nam, Nguyen Minh Tri","doi":"10.1007/s10998-023-00567-w","DOIUrl":"https://doi.org/10.1007/s10998-023-00567-w","url":null,"abstract":"<p>In this paper, we show some results on the non-vanishing of the generalized local cohomology modules <span>(H^i_I(M,N))</span>. In a Cohen–Macaulay local ring <span>((R,mathop {mathfrak {m}}))</span>, we prove, by using induction on <span>(dim N)</span>, that if <i>M</i>, <i>N</i> are two finitely generated <i>R</i>-modules with <span>({text {id}},M&lt;infty )</span> and <span>({text {Gid}},N&lt;infty )</span>, then <span>(H^{dim R-grade _R({text {Ann}}_RN,M)}_{mathop {mathfrak {m}}}(M,N)ne 0)</span>. We also study the <i>I</i>-cofiniteness of the generalized local cohomology module <span>(H^i_{mathop {mathfrak {m}}}(M,N))</span>.\u0000</p>","PeriodicalId":49706,"journal":{"name":"Periodica Mathematica Hungarica","volume":"6 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2024-01-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139078725","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 boundedness of general partial sums 论一般偏和的有界性
IF 0.8 3区 数学
Periodica Mathematica Hungarica Pub Date : 2023-12-24 DOI: 10.1007/s10998-023-00565-y
Vakhtang Tsagareishvili
{"title":"On the boundedness of general partial sums","authors":"Vakhtang Tsagareishvili","doi":"10.1007/s10998-023-00565-y","DOIUrl":"https://doi.org/10.1007/s10998-023-00565-y","url":null,"abstract":"<p>From S. Banach’s results it follows that even for the function <span>(f(x)=1)</span> <span>((xin [0,1]))</span> the general partial sums of its general Fourier series are not bounded a.e. on [0, 1]. In the present paper, we find conditions for the functions <span>(varphi _n)</span> of an orthonormal system <span>((varphi _n)</span>) under which the partial sums of functions from some differentiable class are bounded. We prove that the obtained results are best possible. We also investigate the properties of subsequences of general orthonormal systems.</p>","PeriodicalId":49706,"journal":{"name":"Periodica Mathematica Hungarica","volume":"30 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2023-12-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139028762","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
Bifurcation and hybrid control in a discrete predator–prey model with Holling type-IV functional response 具有霍林IV型功能响应的离散捕食者-猎物模型中的分岔和混合控制
IF 0.8 3区 数学
Periodica Mathematica Hungarica Pub Date : 2023-12-16 DOI: 10.1007/s10998-023-00568-9
Wenxian Zhang, Shengfu Deng
{"title":"Bifurcation and hybrid control in a discrete predator–prey model with Holling type-IV functional response","authors":"Wenxian Zhang, Shengfu Deng","doi":"10.1007/s10998-023-00568-9","DOIUrl":"https://doi.org/10.1007/s10998-023-00568-9","url":null,"abstract":"<p>In this paper we investigate the 1:1 resonance and the hybrid control in a discrete predator–prey model with Holling-IV functional response, which is derived from a 2-dimensional continuous one of Gause type. When the parameters satisfy some conditions, this discrete model has a positive fixed point, which has a double eigenvalue 1 with geometric multiplicity 1. With the Picard iteration and the time-one map, this discrete one is converted into an ordinary differential system. It is shown that a Bogdanov–Takens bifurcation for this ordinary differential system happens by the bifurcation theory. This implies that this discrete model undergoes a Neimark–Sacker bifurcation and a homoclinic bifurcation. The stability of its fixed point is obtained. Then, the hybrid control strategy is applied to control the stability of this fixed point. Finally, the local phase portraits of these systems are also simulated by the Matlab software.</p>","PeriodicalId":49706,"journal":{"name":"Periodica Mathematica Hungarica","volume":"10 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2023-12-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138693124","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
Sums of divisors on arithmetic progressions 算术级数上的除数之和
IF 0.8 3区 数学
Periodica Mathematica Hungarica Pub Date : 2023-12-15 DOI: 10.1007/s10998-023-00566-x
Prapanpong Pongsriiam
{"title":"Sums of divisors on arithmetic progressions","authors":"Prapanpong Pongsriiam","doi":"10.1007/s10998-023-00566-x","DOIUrl":"https://doi.org/10.1007/s10998-023-00566-x","url":null,"abstract":"<p>For each <span>(sin {mathbb {R}})</span> and <span>(nin {mathbb {N}})</span>, let <span>(sigma _s(n) = sum _{dmid n}d^s)</span>. In this article, we study the number of sign changes in the difference <span>(sigma _s(an+b)-sigma _s(cn+d))</span> where <i>a</i>, <i>b</i>, <i>c</i>, <i>d</i>, <i>s</i> are fixed, the vectors (<i>a</i>, <i>b</i>) and (<i>c</i>, <i>d</i>) are linearly independent over <span>({mathbb {Q}})</span>, and <i>n</i> runs over all positive integers. We also give several examples and propose some problems.</p>","PeriodicalId":49706,"journal":{"name":"Periodica Mathematica Hungarica","volume":"90 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2023-12-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138688175","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 class of Lebesgue-Ramanujan-Nagell equations 关于一类 Lebesgue-Ramanujan-Nagell 方程
IF 0.8 3区 数学
Periodica Mathematica Hungarica Pub Date : 2023-12-14 DOI: 10.1007/s10998-023-00564-z
Azizul Hoque
{"title":"On a class of Lebesgue-Ramanujan-Nagell equations","authors":"Azizul Hoque","doi":"10.1007/s10998-023-00564-z","DOIUrl":"https://doi.org/10.1007/s10998-023-00564-z","url":null,"abstract":"<p>We deeply investigate the Diophantine equation <span>(cx^2+d^{2m+1}=2y^n)</span> in integers <span>(x, yge 1, mge 0)</span> and <span>(nge 3)</span>, where <i>c</i> and <i>d</i> are coprime positive integers satisfying <span>(cdnot equiv 3 pmod 4)</span>. We first solve this equation for prime <i>n</i> under the condition <span>(gcd (n, h(-cd))=1)</span>, where <span>(h(-cd))</span> denotes the class number of the imaginary quadratic field <span>({mathbb {Q}}(sqrt{-cd}))</span>. We then completely solve this equation for both <i>c</i> and <i>d</i> primes under the assumption <span>(gcd (n, h(-cd))=1)</span>. We also completely solve this equation for <span>(c=1)</span> and <span>(dequiv 1 pmod 4)</span> under the condition <span>(gcd (n, h(-d))=1)</span>. For some fixed values of <i>c</i> and <i>d</i>, we derive some results concerning the solvability of this equation.</p>","PeriodicalId":49706,"journal":{"name":"Periodica Mathematica Hungarica","volume":"55 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2023-12-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138688297","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
Extensions of a Diophantine triple by adjoining smaller elements II 通过邻接较小元素扩展 Diophantine 三元组 II
IF 0.8 3区 数学
Periodica Mathematica Hungarica Pub Date : 2023-12-14 DOI: 10.1007/s10998-023-00569-8
Mihai Cipu, Andrej Dujella, Yasutsugu Fujita
{"title":"Extensions of a Diophantine triple by adjoining smaller elements II","authors":"Mihai Cipu, Andrej Dujella, Yasutsugu Fujita","doi":"10.1007/s10998-023-00569-8","DOIUrl":"https://doi.org/10.1007/s10998-023-00569-8","url":null,"abstract":"<p>Let <span>({a_1,b,c})</span> and <span>({a_2,b,c})</span> be Diophantine triples with <span>(a_1&lt;b&lt;a_2&lt;c)</span> and <span>(a_2ne b+c-2sqrt{bc+1})</span>. Put <span>(d_2=a_2+b+c+2a_2bc-2r_2st)</span>, where <span>(r_2=sqrt{a_2b+1})</span>, <span>(s=sqrt{ac+1})</span> and <span>(t=sqrt{bc+1})</span>. In this paper, we prove that if <span>(c le 16mu ^2 b^3)</span>, where <span>(mu =min {a_1,d_2})</span>, then <span>({a_1,a_2,b,c})</span> is a Diophantine quadruple. Combining this result with one of our previous results implies that if <span>({a_i,b,c,d})</span> <span>((iin {1,2,3}))</span> are Diophantine quadruples with <span>(a_1&lt;a_2&lt;b&lt;a_3&lt;c&lt;d)</span>, then <span>(a_3=b+c-2sqrt{bc+1})</span>. It immediately follows that there does not exist a septuple <span>({a_1,a_2,a_3,a_4,b,c,d})</span> with <span>(a_1&lt;a_2&lt;b&lt;a_3&lt;a_4&lt;c&lt;d)</span> such that <span>({a_i,b,c,d})</span> <span>((i in {1,2,3,4}))</span> are Diophantine quadruples. Moreover, it is shown that there are only finitely many sextuples <span>({a_1,a_2,a_3,b,c,d})</span> with <span>(a_1&lt;b&lt;a_2&lt;a_3&lt;c&lt;d)</span> such that <span>({a_i,b,c,d})</span> <span>((i in {1,2,3}))</span> are Diophantine quadruples.</p>","PeriodicalId":49706,"journal":{"name":"Periodica Mathematica Hungarica","volume":"2 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2023-12-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138688294","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 ascending chain condition on principal right ideals for semigroup constructions 半群构造的主权利理想的升链条件
IF 0.8 3区 数学
Periodica Mathematica Hungarica Pub Date : 2023-12-14 DOI: 10.1007/s10998-023-00570-1
Craig Miller
{"title":"The ascending chain condition on principal right ideals for semigroup constructions","authors":"Craig Miller","doi":"10.1007/s10998-023-00570-1","DOIUrl":"https://doi.org/10.1007/s10998-023-00570-1","url":null,"abstract":"<p>We call a semigroup <span>({mathcal {R}})</span><i>-noetherian</i> if it satisfies the ascending chain condition on principal right ideals, or, equivalently, the ascending chain condition on <span>({mathcal {R}})</span>-classes. We investigate the behaviour of the property of being <span>({mathcal {R}}text {-noetherian})</span> under the following standard semigroup-theoretic constructions: semidirect products, Schützenberger products, free products, Rees matrix semigroups, Brandt extensions, Bruck–Reilly extensions and semilattices of semigroups.</p>","PeriodicalId":49706,"journal":{"name":"Periodica Mathematica Hungarica","volume":"98 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2023-12-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138627975","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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