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Indian Journal of Pure and Applied Mathematics最新文献

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Biases amongst products of two Beatty primes in arithmetic progressions 算术级数中两个比蒂素数乘积之间的偏差
Indian Journal of Pure and Applied Mathematics Pub Date : 2024-04-26 DOI: 10.1007/s13226-024-00596-2
Walid Wannes
{"title":"Biases amongst products of two Beatty primes in arithmetic progressions","authors":"Walid Wannes","doi":"10.1007/s13226-024-00596-2","DOIUrl":"https://doi.org/10.1007/s13226-024-00596-2","url":null,"abstract":"<p>Motivated by a recently observed bias in products of two prime numbers with congruence conditions by Dummit, Granville and Kisilevsky, we try to observe some bias in the distribution of integers which are product of two distinct primes taken from Beatty sequences with each one is in an arithmetic progression.</p>","PeriodicalId":501427,"journal":{"name":"Indian Journal of Pure and Applied Mathematics","volume":"131 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-04-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140801165","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Bijections between different combinatorial models for q-Whittaker and modified Hall-Littlewood polynomials q-维特克多项式和修正霍尔-利特尔伍德多项式的不同组合模型之间的双射
Indian Journal of Pure and Applied Mathematics Pub Date : 2024-04-24 DOI: 10.1007/s13226-024-00598-0
T. V. Ratheesh
{"title":"Bijections between different combinatorial models for q-Whittaker and modified Hall-Littlewood polynomials","authors":"T. V. Ratheesh","doi":"10.1007/s13226-024-00598-0","DOIUrl":"https://doi.org/10.1007/s13226-024-00598-0","url":null,"abstract":"<p>We consider the monomial expansion of the <i>q</i>-Whittaker polynomials and the modified Hall-Littlewood polynomials arising from specialization of the modified Macdonald polynomial. The two combinatorial formulas for the latter, due to Haglund, Haiman, and Loehr and Ayyer, Mandelshtam and Martin, give rise to two different parameterizing sets in each case. We produce bijections between the parameterizing sets, which preserve the content and major index statistics. We identify the major index with the charge or cocharge of appropriate words, and use descriptions of the latter due to Lascoux–Schützenberger and Killpatrick to show that our bijections have the desired properties.</p>","PeriodicalId":501427,"journal":{"name":"Indian Journal of Pure and Applied Mathematics","volume":"8 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-04-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140801166","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Hamilton and Souplet–Zhang type estimations on semilinear parabolic system along geometric flow 半线性抛物系统沿几何流的汉密尔顿和苏普莱特-张式估计
Indian Journal of Pure and Applied Mathematics Pub Date : 2024-04-20 DOI: 10.1007/s13226-024-00586-4
Sujit Bhattacharyya, Shahroud Azami, Shyamal Kumar Hui
{"title":"Hamilton and Souplet–Zhang type estimations on semilinear parabolic system along geometric flow","authors":"Sujit Bhattacharyya, Shahroud Azami, Shyamal Kumar Hui","doi":"10.1007/s13226-024-00586-4","DOIUrl":"https://doi.org/10.1007/s13226-024-00586-4","url":null,"abstract":"<p>In this article we derive both Hamilton type and Souplet–Zhang type gradient estimations for a system of semilinear equations along a geometric flow on a weighted Riemannian manifold.</p>","PeriodicalId":501427,"journal":{"name":"Indian Journal of Pure and Applied Mathematics","volume":"38 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-04-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140626856","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Congruence relation between Stirling numbers of the first and second kinds 第一类和第二类斯特林数之间的一致关系
Indian Journal of Pure and Applied Mathematics Pub Date : 2024-04-20 DOI: 10.1007/s13226-024-00593-5
A. Lalchhuangliana, S. S. Singh
{"title":"Congruence relation between Stirling numbers of the first and second kinds","authors":"A. Lalchhuangliana, S. S. Singh","doi":"10.1007/s13226-024-00593-5","DOIUrl":"https://doi.org/10.1007/s13226-024-00593-5","url":null,"abstract":"<p>This paper consists of certain congruence properties of Stirling numbers of the first and second kinds. Some congruence relations between <i>s</i>(<i>n</i>, <i>k</i>) and <i>S</i>(<i>n</i>, <i>k</i>) for different modulo are obtained through their generating functions. We also present some exact <i>p</i>-adic valuations of <i>s</i>(<i>n</i>, <i>k</i>) and <i>S</i>(<i>n</i>, <i>k</i>) for some cases, mainly when <span>(n-k)</span> is divisible by <span>(p-1)</span> for odd prime <i>p</i>. Some estimates of the <i>p</i>-adic valuation of these two numbers are also presented when <span>(p-1)</span> does not divide <span>(n-k)</span>.</p>","PeriodicalId":501427,"journal":{"name":"Indian Journal of Pure and Applied Mathematics","volume":"29 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-04-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140630825","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Point-wise time-space estimates for a class of oscillatory integrals and their applications 一类振荡积分的点时空估计及其应用
Indian Journal of Pure and Applied Mathematics Pub Date : 2024-04-20 DOI: 10.1007/s13226-024-00589-1
JinMyong Kim, JinMyong An
{"title":"Point-wise time-space estimates for a class of oscillatory integrals and their applications","authors":"JinMyong Kim, JinMyong An","doi":"10.1007/s13226-024-00589-1","DOIUrl":"https://doi.org/10.1007/s13226-024-00589-1","url":null,"abstract":"<p>This paper investigates the point-wise time-space estimates for a class of oscillatory integrals given by <span>(int _{mathbb R^{n} }e^{i&lt;x,; xi &gt;pm itP^{frac{1}{2} } (xi )} P^{-frac{alpha }{2} } (xi )dxi )</span>, where <i>P</i> is a real non-degenerate elliptic polynomial of order <span>(mge 4)</span> on <span>(mathbb R^{n} )</span>. These estimates are applied to obtain time-space integrability estimates with regularity for solutions to higher order wave-type equations.</p>","PeriodicalId":501427,"journal":{"name":"Indian Journal of Pure and Applied Mathematics","volume":"222 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-04-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140630566","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Homogenization of the Neumann boundary value problem: polygonal domains 诺伊曼边界值问题的均质化：多边形域
Indian Journal of Pure and Applied Mathematics Pub Date : 2024-04-20 DOI: 10.1007/s13226-024-00590-8
Jie Zhao, Juan Wang, Jianlin Zhang
{"title":"Homogenization of the Neumann boundary value problem: polygonal domains","authors":"Jie Zhao, Juan Wang, Jianlin Zhang","doi":"10.1007/s13226-024-00590-8","DOIUrl":"https://doi.org/10.1007/s13226-024-00590-8","url":null,"abstract":"<p>In this paper, we study the convergence rates for homogenization problems for solutions of partial differential equations with rapidly oscillating Neumann boundary data in the convex polygonal domains. As a consequence, we obtain the pointwise and <span>(L^{p})</span> convergence results. Our techniques are based on using Fourier analysis method as well as Diophantine condition on the boundary</p>","PeriodicalId":501427,"journal":{"name":"Indian Journal of Pure and Applied Mathematics","volume":"14 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-04-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140635663","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","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 diophantine inequality involving prime numbers of a special form 关于涉及特殊形式素数的二项不等式
Indian Journal of Pure and Applied Mathematics Pub Date : 2024-04-18 DOI: 10.1007/s13226-024-00592-6
Yuhui Liu
{"title":"On a diophantine inequality involving prime numbers of a special form","authors":"Yuhui Liu","doi":"10.1007/s13226-024-00592-6","DOIUrl":"https://doi.org/10.1007/s13226-024-00592-6","url":null,"abstract":"<p>Let <i>N</i> be a sufficiently large real number. In this paper, we prove that for <span>(2&lt;c&lt; frac{68}{33})</span> and for any arbitrary large number <span>(E&gt;0)</span> , the Diophantine inequality </p><span>$$begin{aligned} left| p_{1}^{c}+p_{2}^{c}+p_{3}^{c}+p_{4}^{c}+p_{5}^{c}-Nright| &lt;left( log Nright) ^{-E} end{aligned}$$</span><p>is solvable in prime variables <span>(p_1,p_2,p_3,p_4,p_5)</span> such that, each of the numbers <span>(p_{i}+2,, (1le ile 5))</span> has at most <span>(big [frac{214467}{136000-66000c}big ])</span> prime factors, counted with multiplicity.</p>","PeriodicalId":501427,"journal":{"name":"Indian Journal of Pure and Applied Mathematics","volume":"5 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-04-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140626770","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Integer partitions with restricted odd and even parts 有限制奇数和偶数部分的整数分区
Indian Journal of Pure and Applied Mathematics Pub Date : 2024-04-17 DOI: 10.1007/s13226-024-00584-6
Nipen Saikia
{"title":"Integer partitions with restricted odd and even parts","authors":"Nipen Saikia","doi":"10.1007/s13226-024-00584-6","DOIUrl":"https://doi.org/10.1007/s13226-024-00584-6","url":null,"abstract":"<p>In this note, two generalized partition functions <span>(p_o^alpha (n))</span> and <span>(p_e^beta (n))</span> are considered, where for any odd positive integer <span>(alpha )</span>, <span>(p_o^alpha (n))</span> denotes the number of partitions of <i>n</i> into odd parts such that no parts is congruent to <span>(alpha )</span> modulo <span>(2alpha )</span>, and for any even positive integer <span>(beta )</span>, <span>(p_e^beta (n))</span> denotes the number of partitions of <i>n</i> into even parts such that no parts is congruent to <span>(beta )</span> modulo <span>(2beta )</span>. Some divisibility properties of <span>(p_o^alpha (n))</span> and <span>(p_e^beta (n))</span> are discussed for some particular values of <span>(alpha )</span> and <span>(beta )</span>.</p>","PeriodicalId":501427,"journal":{"name":"Indian Journal of Pure and Applied Mathematics","volume":"31 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-04-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140614387","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Joint Functional Independence of the Riemann Zeta-Function 黎曼 Zeta 函数的联合函数独立性
Indian Journal of Pure and Applied Mathematics Pub Date : 2024-04-16 DOI: 10.1007/s13226-024-00585-5
Maxim Korolev, Antanas Laurinčikas
{"title":"Joint Functional Independence of the Riemann Zeta-Function","authors":"Maxim Korolev, Antanas Laurinčikas","doi":"10.1007/s13226-024-00585-5","DOIUrl":"https://doi.org/10.1007/s13226-024-00585-5","url":null,"abstract":"<p>By the Ostrowski theorem, the Riemann zeta-function <span>(zeta (s))</span> does not satisfy any algebraic-differential equation. Voronin proved that the function <span>(zeta (s))</span> does not satisfy algebraic-differential equation with continuous coefficients. In the paper, a joint generalization of the Voronin theorem is given, i. e., that a collection <span>((zeta (s_1), dots , zeta (s_r)))</span> does not satisfy a certain algebraic-differential equation with continuous coefficients.</p>","PeriodicalId":501427,"journal":{"name":"Indian Journal of Pure and Applied Mathematics","volume":"8 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-04-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140614112","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Higher order numerical methods for fractional delay differential equations 分数延迟微分方程的高阶数值方法
Indian Journal of Pure and Applied Mathematics Pub Date : 2024-04-05 DOI: 10.1007/s13226-024-00579-3
Manoj Kumar, Aman Jhinga, Varsha Daftardar-Gejji
{"title":"Higher order numerical methods for fractional delay differential equations","authors":"Manoj Kumar, Aman Jhinga, Varsha Daftardar-Gejji","doi":"10.1007/s13226-024-00579-3","DOIUrl":"https://doi.org/10.1007/s13226-024-00579-3","url":null,"abstract":"<p>In this paper, we present a new family of higher-order numerical methods for solving non-linear fractional delay differential equations (FDDEs) along with the error analysis. Further, we solve various non-trivial systems of FDDEs to illustrate their applicability and utility. By using the proposed numerical methods, computational time is reduced drastically. These methods take only 5 to 10 percent of the time required for other methods such as the fractional Adams method (FAM). Furthermore, these methods converge for very small values of fractional derivative while FAM and the new predictor-corrector method (NPCM) introduced by Daftardar-Gejji <i>et al.</i> [1] do not converge. The order of convergence of the proposed methods is <span>(r+alpha )</span>, where <i>r</i> is the order of fractional backward difference formulae and <span>(alpha )</span> denotes the order of the fractional derivative. Thus these methods have a higher order of accuracy than FAM or NPCM.</p>","PeriodicalId":501427,"journal":{"name":"Indian Journal of Pure and Applied Mathematics","volume":"35 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-04-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140572992","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","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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