Results in Mathematics最新文献_第4页

Discrete Bessel Functions and Discrete Wave Equation 离散贝塞尔函数和离散波方程

IF 2.2 3区数学

Results in Mathematics Pub Date : 2024-07-30 DOI: 10.1007/s00025-024-02235-y

Amar Bašić, Lejla Smajlović, Zenan Šabanac

{"title":"Discrete Bessel Functions and Discrete Wave Equation","authors":"Amar Bašić, Lejla Smajlović, Zenan Šabanac","doi":"10.1007/s00025-024-02235-y","DOIUrl":"https://doi.org/10.1007/s00025-024-02235-y","url":null,"abstract":"In this paper, we study four discrete Bessel functions which are solutions to the discretization of Bessel differential equations when the time derivative is replaced by the forward and the backward difference. We focus on discrete Bessel equations with the time derivative being the backward difference and derive their solutions: the discrete I-Bessel function (overline{I}_n^c(t)) and the discrete J-Bessel function (overline{J}_n^c(t)), (tin mathbb {Z}), (nin mathbb {N}_0). We then study transformation properties of those functions and describe their asymptotic behaviour as (trightarrow infty ) and as (nrightarrow infty ). Moreover, we prove that the (unilateral) Laplace transform of (overline{I}_n^c) and (overline{J}_n^c) in the timescale (T=mathbb {Z}) with the delta derivative being the backward difference equals the Laplace transform of classical I-Bessel and J-Bessel functions (mathcal {I}_n(cx)) and (mathcal {J}_n(cx)), respectively. As an application, we study the discrete wave equation on the integers in the timescale (T=mathbb {Z}) and express its fundamental and general solution in terms of (overline{J}_n^c(t)). Going further, we show that the first fundamental solution of this discrete wave equation oscillates with the exponentially decaying amplitude as time tends to infinity.","PeriodicalId":54490,"journal":{"name":"Results in Mathematics","volume":null,"pages":null},"PeriodicalIF":2.2,"publicationDate":"2024-07-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141865284","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

Analysis in Function Spaces Associated with the Group $$ax+b$$ 与组$ax+b$$相关的函数空间分析

IF 2.2 3区数学

Results in Mathematics Pub Date : 2024-07-30 DOI: 10.1007/s00025-024-02245-w

Isaac Z. Pesenson

引用次数: 0

Sublinear Elliptic Equations with Unbounded Coefficients in Lipschitz Domains Lipschitz 域中系数无界的亚线性椭圆方程

IF 2.2 3区数学

Results in Mathematics Pub Date : 2024-07-30 DOI: 10.1007/s00025-024-02246-9

Kentaro Hirata

引用次数: 0

Isometric Jordan Isomorphisms of Group Algebras 群代数的等距约旦同构

IF 2.2 3区数学

Results in Mathematics Pub Date : 2024-07-30 DOI: 10.1007/s00025-024-02244-x

J. Alaminos, J. Extremera, C. Godoy, A. R. Villena

引用次数: 0

Local and 2-Local $$frac{1}{2}$$ -Derivations on Finite-Dimensional Lie Algebras 有限维李代数上的局部和 2 局部 $$frac{1}{2}$ 衍生

IF 2.2 3区数学

Results in Mathematics Pub Date : 2024-07-27 DOI: 10.1007/s00025-024-02228-x

Abror Khudoyberdiyev, Bakhtiyor Yusupov

引用次数: 0

Cube Tilings with Linear Constraints 带线性约束的立方体结构

IF 2.2 3区数学

Results in Mathematics Pub Date : 2024-07-27 DOI: 10.1007/s00025-024-02243-y

Dae Gwan Lee, Götz E. Pfander, David Walnut

{"title":"Cube Tilings with Linear Constraints","authors":"Dae Gwan Lee, Götz E. Pfander, David Walnut","doi":"10.1007/s00025-024-02243-y","DOIUrl":"https://doi.org/10.1007/s00025-024-02243-y","url":null,"abstract":"We consider tilings ((mathcal {Q},Phi )) of (mathbb {R}^d) where (mathcal {Q}) is the d-dimensional unit cube and the set of translations (Phi ) is constrained to lie in a pre-determined lattice (A mathbb {Z}^d) in (mathbb {R}^d). We provide a full characterization of matrices A for which such cube tilings exist when (Phi ) is a sublattice of (Amathbb {Z}^d) with any (d in mathbb {N}) or a generic subset of (Amathbb {Z}^d) with (dle 7). As a direct consequence of our results, we obtain a criterion for the existence of linearly constrained frequency sets, that is, (Phi subseteq Amathbb {Z}^d), such that the respective set of complex exponential functions (mathcal {E} (Phi )) is an orthogonal Fourier basis for the space of square integrable functions supported on a parallelepiped (Bmathcal {Q}), where (A, B in mathbb {R}^{d times d}) are nonsingular matrices given a priori. Similarly constructed Riesz bases are considered in a companion paper (Lee et al., Exponential bases for parallelepipeds with frequencies lying in a prescribed lattice, 2024. arXiv:2401.08042).","PeriodicalId":54490,"journal":{"name":"Results in Mathematics","volume":null,"pages":null},"PeriodicalIF":2.2,"publicationDate":"2024-07-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141781322","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

New Identities Associated with Ranks and Cranks of Partitions Modulo 7 与模数为 7 的分区的秩和曲相关的新特性

IF 2.2 3区数学

Results in Mathematics Pub Date : 2024-07-27 DOI: 10.1007/s00025-024-02242-z

Yongqiang Chen, Olivia X. M. Yao

{"title":"New Identities Associated with Ranks and Cranks of Partitions Modulo 7","authors":"Yongqiang Chen, Olivia X. M. Yao","doi":"10.1007/s00025-024-02242-z","DOIUrl":"https://doi.org/10.1007/s00025-024-02242-z","url":null,"abstract":"Beck introduced two important partition statistics NT(r, m, n) and (M_{omega }(r,m,n)) which count the total number of parts in the partitions of n with rank congruent to r modulo m and the total number of ones in the partitions of n with crank congruent to r modulo m, respectively. Andrews confirmed two conjectures of Beck on congruences of NT(r, m, n). Inspired by Andrews’ work, Chern discovered a number of congruences modulo 5, 7, 11 and 13 of NT(r, m, n) and (M_{omega }(r,m,n) ). Recently, Mao, and Xia, Yan and Yao established several identities on NT(r, 7, n) and (M_{omega }(r,7,n)) which yield some congruences modulo 7 due to Chern. Unfortunately, there are six congruences modulo 7 of Chern which are not implied by the identities given by Mao, and Xia, Yan and Yao. In this paper, we establish several new identities on NT(r, 7, n) and (M_{omega }(r,7,n)). In particular, we prove six identities which are analogous to “Ramanujan’s most beautiful identity”and imply Chern’s six congruences.","PeriodicalId":54490,"journal":{"name":"Results in Mathematics","volume":null,"pages":null},"PeriodicalIF":2.2,"publicationDate":"2024-07-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141781318","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

Pinched Constantly Curved Holomorphic Two-Spheres in the Complex Grassmann Manifolds 复格拉斯曼流形中的捏合恒定弯曲全态双球面

IF 2.2 3区数学

Results in Mathematics Pub Date : 2024-07-23 DOI: 10.1007/s00025-024-02236-x

Jie Fei, Jun Wang

引用次数: 0

Generalizations of Guo and Schlosser’s Two q-Supercongruences 郭和施洛瑟的两个 q 超矛盾的一般化

IF 2.2 3区数学

Results in Mathematics Pub Date : 2024-07-23 DOI: 10.1007/s00025-024-02237-w

Caihuan Zhang

引用次数: 0

On Conformally Flat Manifolds with Semi-parallel Ricci Tensor and Applications to the Study of Affine Hyperspheres 论具有半平行里奇张量的共形平坦曲面及其在仿射超球研究中的应用

IF 2.2 3区数学

Results in Mathematics Pub Date : 2024-07-20 DOI: 10.1007/s00025-024-02232-1

Weilin Duan, Zejun Hu, Cheng Xing

引用次数: 0