发布求助
文献互助 智能选刊 最新文献

arXiv - MATH - General Mathematics最新文献

筛选
英文 中文
The BiGamma Function and some of its Related Inequalities 毕伽马函数及其一些相关不等式
arXiv - MATH - General Mathematics Pub Date : 2024-05-26 DOI: arxiv-2405.19368
Raissoulii, Mohamed Chergui
{"title":"The BiGamma Function and some of its Related Inequalities","authors":"Raissoulii, Mohamed Chergui","doi":"arxiv-2405.19368","DOIUrl":"https://doi.org/arxiv-2405.19368","url":null,"abstract":"In this article, we define a special function called the Bigamma function. It\u0000provides a generalization of Euler's gamma function. Several algebraic\u0000properties of this new function are studied. In particular, results linking\u0000this new function to the standard Beta function have been provided. We have\u0000also established inequalities, which allow to approximate this new function.","PeriodicalId":501502,"journal":{"name":"arXiv - MATH - General Mathematics","volume":"35 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-05-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141197279","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
Decreasing and complete monotonicity of two functions defined by three derivatives of a completely monotonic function involving the trigamma function 由涉及三角函数的完全单调函数的三个导数定义的两个函数的递减性和完全单调性
arXiv - MATH - General Mathematics Pub Date : 2024-05-24 DOI: arxiv-2405.19361
Hong-Ping Yin, Ling-Xiong Han, Feng Qi
{"title":"Decreasing and complete monotonicity of two functions defined by three derivatives of a completely monotonic function involving the trigamma function","authors":"Hong-Ping Yin, Ling-Xiong Han, Feng Qi","doi":"arxiv-2405.19361","DOIUrl":"https://doi.org/arxiv-2405.19361","url":null,"abstract":"In the paper, by convolution theorem of the Laplace transforms, a\u0000monotonicity rule for the ratio of two Laplace transforms, Bernstein's theorem\u0000for completely monotonic functions, and other analytic techniques, the authors\u0000verify decreasing property of a ratio between three derivatives of a function\u0000involving trigamma function and find necessary and sufficient conditions for a\u0000function defined by three derivatives of a function involving trigamma function\u0000to be completely monotonic. These results confirm previous guesses posed by Qi\u0000and generalize corresponding known conclusions.","PeriodicalId":501502,"journal":{"name":"arXiv - MATH - General Mathematics","volume":"51 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-05-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141189206","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 Concatenations of Two $ k $-Generalized Fibonacci Numbers 论两个 $ k $ 广义斐波那契数的并集
arXiv - MATH - General Mathematics Pub Date : 2024-05-23 DOI: arxiv-2405.15001
Alaa Altassan, Murat Alan
{"title":"On Concatenations of Two $ k $-Generalized Fibonacci Numbers","authors":"Alaa Altassan, Murat Alan","doi":"arxiv-2405.15001","DOIUrl":"https://doi.org/arxiv-2405.15001","url":null,"abstract":"Let $ k geq 2 $ be an integer. The $ k- $generalized Fibonacci sequence is a\u0000sequence defined by the recurrence relation $ F_{n}^{(k)}=F_{n-1}^{(k)} +\u0000cdots + F_{n-k}^{(k)}$ for all $ n geq 2$ with the initial values $\u0000F_{i}^{(k)}=0 $ for $ i=2-k, ldots, 0 $ and $ F_{1}^{(k)}=1.$ In 2020, Banks\u0000and Luca, among other things, determined all Fibonacci numbers which are\u0000concatenations of two Fibonacci numbers. In this paper, we consider the\u0000analogue of this problem by taking into account $ k-$generalized Fibonacci\u0000numbers as concatenations of two terms of the same sequence. We completely\u0000solve this problem for all $ k geq 3.","PeriodicalId":501502,"journal":{"name":"arXiv - MATH - General Mathematics","volume":"63 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-05-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141170201","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
Rotations of Gödel algebras with modal operators 哥德尔代数的模态算子旋转
arXiv - MATH - General Mathematics Pub Date : 2024-05-23 DOI: arxiv-2405.19354
Tommaso Flaminio, Lluis Godo, Paula Menchón, Ricardo O. Rodriguez
{"title":"Rotations of Gödel algebras with modal operators","authors":"Tommaso Flaminio, Lluis Godo, Paula Menchón, Ricardo O. Rodriguez","doi":"arxiv-2405.19354","DOIUrl":"https://doi.org/arxiv-2405.19354","url":null,"abstract":"The present paper is devoted to study the effect of connected and\u0000disconnected rotations of G\"odel algebras with operators grounded on directly\u0000indecomposable structures. The structures resulting from this construction we\u0000will present are nilpotent minimum (with or without negation fixpoint,\u0000depending on whether the rotation is connected or disconnected) with special\u0000modal operators defined on a directly indecomposable algebra. In this paper we\u0000will present a (quasi-)equational definition of these latter structures. Our\u0000main results show that directly indecomposable nilpotent minimum algebras (with\u0000or without negation fixpoint) with modal operators are fully characterized as\u0000connected and disconnected rotations of directly indecomposable G\"odel\u0000algebras endowed with modal operators.","PeriodicalId":501502,"journal":{"name":"arXiv - MATH - General Mathematics","volume":"43 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-05-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141197275","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
New identities for the Laplace, Glasser, and Widder potential transforms and their applications 拉普拉斯、格拉斯和维德势变换的新特性及其应用
arXiv - MATH - General Mathematics Pub Date : 2024-05-23 DOI: arxiv-2405.14248
Abdulhafeez A. Abdulsalam, Ammar K. Mohammed, Hemza Djahel
{"title":"New identities for the Laplace, Glasser, and Widder potential transforms and their applications","authors":"Abdulhafeez A. Abdulsalam, Ammar K. Mohammed, Hemza Djahel","doi":"arxiv-2405.14248","DOIUrl":"https://doi.org/arxiv-2405.14248","url":null,"abstract":"In this paper, we begin by applying the Laplace transform to derive closed\u0000forms for several challenging integrals that seem nearly impossible to\u0000evaluate. By utilizing the solution to the Pythagorean equation $a^2 + b^2 =\u0000c^2$, these closed forms become even more intriguing. This method allows us to\u0000provide new integral representations for the error function. Following this, we\u0000use the Fourier transform to derive formulas for the Glasser and Widder\u0000potential transforms, leading to several new and interesting corollaries. As\u0000part of the applications, we demonstrate the use of one of these integral\u0000formulas to provide a new real analytic proof of Euler's reflection formula for\u0000the gamma function. Of particular interest is a generalized integral involving\u0000the Riemann zeta function, which we also present as an application.","PeriodicalId":501502,"journal":{"name":"arXiv - MATH - General Mathematics","volume":"74 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-05-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141146263","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
The $A$-philosophy for the Hardy $Z$-Function 哈代 Z$函数的 A$哲学
arXiv - MATH - General Mathematics Pub Date : 2024-05-23 DOI: arxiv-2406.06548
Yochay Jerby
{"title":"The $A$-philosophy for the Hardy $Z$-Function","authors":"Yochay Jerby","doi":"arxiv-2406.06548","DOIUrl":"https://doi.org/arxiv-2406.06548","url":null,"abstract":"In recent works we have introduced the parameter space $mathcal{Z}_N$ of\u0000$A$-variations of the Hardy $Z$-function, $Z(t)$, whose elements are functions\u0000of the form begin{equation} label{eq:Z-sections} Z_N(t ; overline{a} ) =\u0000cos(theta(t))+ sum_{k=1}^{N} frac{a_k}{sqrt{k+1} } cos ( theta (t) -\u0000ln(k+1) t), end{equation} where $overline{a} = (a_1,...,a_N) in\u0000mathbb{R}^N$. The ( A )-philosophy advocates that studying the discriminant\u0000hypersurface forming within such parameter spaces, often reveals essential\u0000insights about the original mathematical object and its zeros. In this paper we\u0000apply the $A$-philosophy to our space $mathcal{Z}_N$ by introducing (\u0000Delta_n(overline{a} ) ) the $n$-th Gram discriminant of ( Z(t) ). We show\u0000that the Riemann Hypothesis (RH) is equivalent to the corrected Gram's law [\u0000(-1)^n Delta_n(overline{1}) > 0, ] for any $n in mathbb{Z}$. We further\u0000show that the classical Gram's law ( (-1)^n Z(g_n) >0) can be considered as a\u0000first-order approximation of our corrected law. The second-order approximation\u0000of $Delta_n (overline{a})$ is then shown to be related to shifts of Gram\u0000points along the ( t )-axis. This leads to the discovery of a new, previously\u0000unobserved, repulsion phenomena [ left| Z'(g_n) right| > 4 left| Z(g_n)\u0000right|, ] for bad Gram points $g_n$ whose consecutive neighbours $g_{n pm\u00001}$ are good. Our analysis of the (A)-variation space (mathcal{Z}_N)\u0000introduces a wealth of new results on the zeros of (Z(t)), casting new light\u0000on classical questions such as Gram's law, the Montgomery pair-correlation\u0000conjecture, and the RH, and also unveils previously unknown fundamental\u0000properties.","PeriodicalId":501502,"journal":{"name":"arXiv - MATH - General Mathematics","volume":"161 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-05-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141504905","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
Introduction to generalized Leonardo-Alwyn hybrid numbers 广义莱昂纳多-阿尔文混合数介绍
arXiv - MATH - General Mathematics Pub Date : 2024-05-21 DOI: arxiv-2405.13074
Gamaliel Cerda-Morales
{"title":"Introduction to generalized Leonardo-Alwyn hybrid numbers","authors":"Gamaliel Cerda-Morales","doi":"arxiv-2405.13074","DOIUrl":"https://doi.org/arxiv-2405.13074","url":null,"abstract":"In cite{Go}, G\"okbac{s} defined a new type of number sequence called\u0000Leonardo-Alwyn sequence. In this paper, we consider the generalized\u0000Leonardo-Alwyn hybrid numbers and investigate some of their properties. We also\u0000give some applications related to the generalized Leonardo-Alwyn hybrid numbers\u0000in matrices.","PeriodicalId":501502,"journal":{"name":"arXiv - MATH - General Mathematics","volume":"17 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-05-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141146262","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
Small Prime $k$th Power Residues and Nonresidues in Arithmetic Progressions 算术级数中的小质数 k 次幂残差和非残差
arXiv - MATH - General Mathematics Pub Date : 2024-05-21 DOI: arxiv-2405.13159
N. A. Carella
{"title":"Small Prime $k$th Power Residues and Nonresidues in Arithmetic Progressions","authors":"N. A. Carella","doi":"arxiv-2405.13159","DOIUrl":"https://doi.org/arxiv-2405.13159","url":null,"abstract":"Let $p$ be a large odd prime, let $x=(log p)^{1+varepsilon}$ and let\u0000$qllloglog p$ be an integer, where $varepsilon>0$ is a small number. This\u0000note proves the existence of small prime quadratic residues and prime quadratic\u0000nonresidues in the arithmetic progression $a+qmll x$, with relatively prime\u0000$1leq a<q$, unconditionally. The same results are generalized to small prime\u0000$k$th power residues and nonresidues, where $kmid p-1$ and $kllloglog p$.","PeriodicalId":501502,"journal":{"name":"arXiv - MATH - General Mathematics","volume":"59 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-05-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141146265","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
Approximation by $T$ means with respect to Vilenkin system in Lebesgue spaces and Lipschitz classes 关于 Lebesgue 空间和 Lipschitz 类中的 Vilenkin 系统的 $T$ 近似手段
arXiv - MATH - General Mathematics Pub Date : 2024-05-21 DOI: arxiv-2405.19350
N. Anakidze, N. Areshidze, L. -E. Persson, G. Tephnadze
{"title":"Approximation by $T$ means with respect to Vilenkin system in Lebesgue spaces and Lipschitz classes","authors":"N. Anakidze, N. Areshidze, L. -E. Persson, G. Tephnadze","doi":"arxiv-2405.19350","DOIUrl":"https://doi.org/arxiv-2405.19350","url":null,"abstract":"In this paper we present and prove some new results concerning approximation\u0000properties of $T$ means with respect to the Vilenkin system in Lebesgue spaces\u0000and Lipschitz classes for any $1leq p<infty$. As applications, we obtain\u0000extension of some known approximation inequalities.","PeriodicalId":501502,"journal":{"name":"arXiv - MATH - General Mathematics","volume":"29 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-05-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141189204","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
Padovan and Perrin Hyperbolic Spinors 帕多万和佩林双曲旋光子
arXiv - MATH - General Mathematics Pub Date : 2024-05-21 DOI: arxiv-2405.13163
Zehra İşbilir, Işıl Arda Kösal, Murat Tosun
{"title":"Padovan and Perrin Hyperbolic Spinors","authors":"Zehra İşbilir, Işıl Arda Kösal, Murat Tosun","doi":"arxiv-2405.13163","DOIUrl":"https://doi.org/arxiv-2405.13163","url":null,"abstract":"In this study, we intend to bring together Padovan and Perrin number\u0000sequences, which are one of the most popular third-order recurrence sequences,\u0000and hyperbolic spinors, which are used in several disciplines from physics to\u0000mathematics, with the help of the split quaternions. This paper especially\u0000improves the relationship between hyperbolic spinors both a physical and\u0000mathematical concept, and number theory. For this aim, we combine the\u0000hyperbolic spinors and Padovan and Perrin numbers concerning the split Padovan\u0000and Perrin quaternions, and we determine two new special recurrence sequences\u0000named Padovan and Perrin hyperbolic spinors. Then, we give Binet formulas,\u0000generating functions, exponential generating functions, Poisson generating\u0000functions, and summation formulas. Additionally, we present some matrix and\u0000determinant equations with respect to them. Then, we construct some numerical\u0000algorithms for these special number systems, as well. Further, we give an\u0000introduction for $(s,t)$-Padovan and $(s,t)$-Perrin hyperbolic spinors.","PeriodicalId":501502,"journal":{"name":"arXiv - MATH - General Mathematics","volume":"76 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-05-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141153808","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
首页 上一页 下一页 尾页
0
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
提示
您的信息不完整，为了账户安全，请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
现在去查看 取消
×
提示
确定
请完成安全验证×
相关产品
×
本文献相关产品
联系我们：info@booksci.cn Book学术提供免费学术资源搜索服务，方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。 Copyright © 2023 布克学术 All rights reserved.
京ICP备2023020795号-1
ghs 京公网安备 11010802042870号
Book学术文献互助
Book学术文献互助群
群 号：481959085
Book学术官方微信