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GAPS IN A SUMSET OF A POLYNOMIAL WITH ITSELF 多项式与自身的和集中的间隙
IF 0.1 4区 数学
Mathematical Reports Pub Date : 2023-01-01 DOI: 10.59277/mrar.2023.25.75.2.313
A. Dubickas
{"title":"GAPS IN A SUMSET OF A POLYNOMIAL WITH ITSELF","authors":"A. Dubickas","doi":"10.59277/mrar.2023.25.75.2.313","DOIUrl":"https://doi.org/10.59277/mrar.2023.25.75.2.313","url":null,"abstract":"In this note, we give some lower and upper bounds for the gaps between consecutive elements of an integer sequence whose elements are expressible in the form P(m) + P(n), where P is a degree d polynomial with integer coefficients, and m, n are nonnegative","PeriodicalId":49858,"journal":{"name":"Mathematical Reports","volume":"31 1","pages":""},"PeriodicalIF":0.1,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75535585","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
EULER–ZAGIER SUMS VIA TRIGONOMETRIC SERIES 通过三角级数的欧拉-扎吉尔和
4区 数学
Mathematical Reports Pub Date : 2023-01-01 DOI: 10.59277/mrar.2023.25.75.3.381
SERMIN CAM CELIK, HAYDAR GORAL
{"title":"EULER–ZAGIER SUMS VIA TRIGONOMETRIC SERIES","authors":"SERMIN CAM CELIK, HAYDAR GORAL","doi":"10.59277/mrar.2023.25.75.3.381","DOIUrl":"https://doi.org/10.59277/mrar.2023.25.75.3.381","url":null,"abstract":"In this note, we study the evaluations of Euler sums via trigonometric series. It is a commonly believed conjecture that for an even weight greater than seven, Euler sums cannot be evaluated in terms of the special values of the Riemann zeta function. For an even weight, we reduce the evaluations of Euler sums into the evaluations of double series and integrals of products of Clausen functions. We also re-evaluate Euler sums of odd weight using a new method based on trigonometric series.","PeriodicalId":49858,"journal":{"name":"Mathematical Reports","volume":"295 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135953773","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
ARMENDARIZ MODULES AND NILTORSIONLESS MODULES Armendariz模块和niltorsion模块
IF 0.1 4区 数学
Mathematical Reports Pub Date : 2023-01-01 DOI: 10.59277/mrar.2023.25.75.2.319
KH HERA SINGH, A. M. Buhphang, M. B. Rege
{"title":"ARMENDARIZ MODULES AND NILTORSIONLESS MODULES","authors":"KH HERA SINGH, A. M. Buhphang, M. B. Rege","doi":"10.59277/mrar.2023.25.75.2.319","DOIUrl":"https://doi.org/10.59277/mrar.2023.25.75.2.319","url":null,"abstract":"In this paper, we introduce the concepts niltorsionless modules and NSmodules (which are generalisations of NI-rings). We prove that the class of niltorsionless modules contains the classes of semiprime and in particular, the class of regular modules. We","PeriodicalId":49858,"journal":{"name":"Mathematical Reports","volume":"75 1","pages":""},"PeriodicalIF":0.1,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77241419","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
ON COMMUTATORS IN FINITE P-GROUPS OF ALMOST MAXIMAL CLASS 几乎极大类的有限p群中的交换子
IF 0.1 4区 数学
Mathematical Reports Pub Date : 2023-01-01 DOI: 10.59277/mrar.2023.25.75.2.279
N. Azimi Shahrabi, M. Akhavan-Malayeri
{"title":"ON COMMUTATORS IN FINITE P-GROUPS OF ALMOST MAXIMAL CLASS","authors":"N. Azimi Shahrabi, M. Akhavan-Malayeri","doi":"10.59277/mrar.2023.25.75.2.279","DOIUrl":"https://doi.org/10.59277/mrar.2023.25.75.2.279","url":null,"abstract":"Let Γ(G) denote the set of commutators of a group G, G′ = ⟨Γ(G)⟩ and c(G) (or cw(G)) the minimal number such that every element of G′ can be expressed as a product of at most c(G) commutators. Recently we proved that if G is a finite p-group of maximal cl","PeriodicalId":49858,"journal":{"name":"Mathematical Reports","volume":"1 1","pages":""},"PeriodicalIF":0.1,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88037644","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
HOPF CO-BRACE, BRAID EQUATION AND BICROSSED Hopf共括号，编织方程和交叉
4区 数学
Mathematical Reports Pub Date : 2023-01-01 DOI: 10.59277/mrar.2023.25.75.3.481
HUIHUI ZHENG, FANGSHU LI, TIANSHUI MA
{"title":"HOPF CO-BRACE, BRAID EQUATION AND BICROSSED","authors":"HUIHUI ZHENG, FANGSHU LI, TIANSHUI MA","doi":"10.59277/mrar.2023.25.75.3.481","DOIUrl":"https://doi.org/10.59277/mrar.2023.25.75.3.481","url":null,"abstract":"In this paper, we mainly give some equivalent characterisations of Hopf cobraces, show that the full subcategory HCB(A) of Hopf co-braces is equivalent to the full subcategory C(A) of bijective 1-cocycles, and prove that the full subcategory HCB(A) is also equivalent to the category M(A) of Hopf matched pairs. Moreover, we construct many Hopf co-braces on polynomial Hopf algebras, Long copaired Hopf algebras and Drinfel’d doubles of finite dimensional Hopf algebras. And we also give a sufficient and necessary condition for a given bicrossed coproduct A ▷◁ H to be a Hopf co-brace if A or H is a Hopf co-brace","PeriodicalId":49858,"journal":{"name":"Mathematical Reports","volume":"26 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135953488","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
CHARACTERIZATIONS OF COMMUTATORS OF SINGULAR INTEGRAL OPERATORS ON MORREY TRIEBEL-LIZORKIN morrey triiebel - lizorkin上奇异积分算子的交换子的刻画
4区 数学
Mathematical Reports Pub Date : 2023-01-01 DOI: 10.59277/mrar.2023.25.75.3.425
CHENGLONG FANG
{"title":"CHARACTERIZATIONS OF COMMUTATORS OF SINGULAR INTEGRAL OPERATORS ON MORREY TRIEBEL-LIZORKIN","authors":"CHENGLONG FANG","doi":"10.59277/mrar.2023.25.75.3.425","DOIUrl":"https://doi.org/10.59277/mrar.2023.25.75.3.425","url":null,"abstract":"In this paper, we obtain the characterizations of Morrey Triebel-Lizorkin spaces by two families of operators. Applying the characterizations of Morrey TriebelLizorkin spaces, it is proved that b is a Lipschitz function if and only if the commutator [b, T] is bounded from Morrey spaces to Morrey Triebel-Lizorkin spaces, where T is singular integral operator or Riesz potential operator.","PeriodicalId":49858,"journal":{"name":"Mathematical Reports","volume":"13 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135953720","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
HOMOLOGY THEORY OF MULTIPLICATIVE HOM-LIE ALGEBRAS 乘法同李代数的同调理论
IF 0.1 4区 数学
Mathematical Reports Pub Date : 2023-01-01 DOI: 10.59277/mrar.2023.25.75.2.331
Maosen Xu, Zhixiang Wu
{"title":"HOMOLOGY THEORY OF MULTIPLICATIVE HOM-LIE ALGEBRAS","authors":"Maosen Xu, Zhixiang Wu","doi":"10.59277/mrar.2023.25.75.2.331","DOIUrl":"https://doi.org/10.59277/mrar.2023.25.75.2.331","url":null,"abstract":"In this article, we establish Serre-Hochschild spectral sequences of Hom-Lie algebras. By using these spectral sequences, we describe homology groups of finite dimensional multiplicative Hom-Lie algebras in terms of homology groups of Lie algebras and abe","PeriodicalId":49858,"journal":{"name":"Mathematical Reports","volume":"1 1","pages":""},"PeriodicalIF":0.1,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84583444","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
UNITARY PARTS OF CONTRACTIVE LITTLE HANKEL OPERATORS ON THE BERGMAN SPACE bergman空间上压缩小hankel算子的酉部
IF 0.1 4区 数学
Mathematical Reports Pub Date : 2023-01-01 DOI: 10.59277/mrar.2023.25.75.2.247
N. Das, Satyajit Sahoo
{"title":"UNITARY PARTS OF CONTRACTIVE LITTLE HANKEL OPERATORS ON THE BERGMAN SPACE","authors":"N. Das, Satyajit Sahoo","doi":"10.59277/mrar.2023.25.75.2.247","DOIUrl":"https://doi.org/10.59277/mrar.2023.25.75.2.247","url":null,"abstract":"In this paper, we consider little Hankel operators Γφ defined on the Bergman space L2 a(D) with symbol φ ∈ H∞(D) that are contractions. Necessary and sufficient conditions are obtained for the existence of a nontrivial unitary part of these little Hankel","PeriodicalId":49858,"journal":{"name":"Mathematical Reports","volume":"9 1","pages":""},"PeriodicalIF":0.1,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87743033","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
CORRIGENDUM TO “INTRANSITIVE PERMUTATION GROUPS “不可传递置换群”的勘误
4区 数学
Mathematical Reports Pub Date : 2023-01-01 DOI: 10.59277/mrar.2023.25.75.3.451
MEHDI REZAEI, MEHDI ALAEIYAN, ZEINAB FORUZANFAR
{"title":"CORRIGENDUM TO “INTRANSITIVE PERMUTATION GROUPS","authors":"MEHDI REZAEI, MEHDI ALAEIYAN, ZEINAB FORUZANFAR","doi":"10.59277/mrar.2023.25.75.3.451","DOIUrl":"https://doi.org/10.59277/mrar.2023.25.75.3.451","url":null,"abstract":"In this note, we point out a mistake in part (II) of Theorem 1.1 of [1] and correct it here. In [1], the authors investigated the structure of intransitive permutation groups with bounded movement having maximum degree.","PeriodicalId":49858,"journal":{"name":"Mathematical Reports","volume":"42 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135953230","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
ANALYTICAL AND NUMERICAL SOLUTIONS FOR SOME 一些问题的解析解和数值解
4区 数学
Mathematical Reports Pub Date : 2023-01-01 DOI: 10.59277/mrar.2023.25.75.3.465
ABDUL RAUF, TAHIR MUSHTAQ QURESHI, CONSTANTIN FETECAU
{"title":"ANALYTICAL AND NUMERICAL SOLUTIONS FOR SOME","authors":"ABDUL RAUF, TAHIR MUSHTAQ QURESHI, CONSTANTIN FETECAU","doi":"10.59277/mrar.2023.25.75.3.465","DOIUrl":"https://doi.org/10.59277/mrar.2023.25.75.3.465","url":null,"abstract":"Oscillatory motions of incompressible viscous fluids with exponential dependence of viscosity on the pressure between infinite horizontal parallel plates are analytically and numerically studied. The fluid motion is generated by the lower plate that oscillates in its plane and exact expressions are established for the steady-state solutions. The convergence of starting solutions to the corresponding steady-state solutions is graphically proved. The steady solutions corresponding to the simple Couette flow of the same fluids are obtained as limiting cases of the previous solutions. As expected, the fluid velocity diminishes for increasing values of the pressure-viscosity coefficient and ordinary fluids flow faster. The time required to reach the steady-state is graphically approximated. The spatial profiles of the starting solutions are presented both for oscillatory motions and the simple Couette flow.","PeriodicalId":49858,"journal":{"name":"Mathematical Reports","volume":"4 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135953457","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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