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A note on equivalent conditions for majorization 关于主要化的同等条件的说明
IF 2.2 3区 数学
AIMS Mathematics Pub Date : 2024-05-13 DOI: 10.3934/math.2024419
Roberto Bruno, Ugo Vaccaro
{"title":"A note on equivalent conditions for majorization","authors":"Roberto Bruno, Ugo Vaccaro","doi":"10.3934/math.2024419","DOIUrl":"https://doi.org/10.3934/math.2024419","url":null,"abstract":"In this paper, we introduced novel characterizations of the classical concept of majorization in terms of upper triangular (resp., lower triangular) row-stochastic matrices, and in terms of sequences of linear transforms on vectors. We used our new characterizations of majorization to derive an improved entropy inequality.","PeriodicalId":48562,"journal":{"name":"AIMS Mathematics","volume":null,"pages":null},"PeriodicalIF":2.2,"publicationDate":"2024-05-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140983701","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 conjugacy diameters of non-abelian finite $ p $-groups with cyclic maximal subgroups 具有循环最大子群的非阿贝尔有限 $ p $ 群的共轭直径
IF 2.2 3区 数学
AIMS Mathematics Pub Date : 2024-01-17 DOI: 10.3934/math.2024524
Fawaz Aseeri, J. Kaspczyk
{"title":"The conjugacy diameters of non-abelian finite $ p $-groups with cyclic maximal subgroups","authors":"Fawaz Aseeri, J. Kaspczyk","doi":"10.3934/math.2024524","DOIUrl":"https://doi.org/10.3934/math.2024524","url":null,"abstract":"Let $ G $ be a group. A subset $ S $ of $ G $ is said to normally generate $ G $ if $ G $ is the normal closure of $ S $ in $ G. $ In this case, any element of $ G $ can be written as a product of conjugates of elements of $ S $ and their inverses. If $ gin G $ and $ S $ is a normally generating subset of $ G, $ then we write $ | g|_{S} $ for the length of a shortest word in $ mbox{Conj}_{G}(S^{pm 1}): = {h^{-1}sh | hin G, sin S , mbox{or} , s{^{-1}}in S } $ needed to express $ g. $ For any normally generating subset $ S $ of $ G, $ we write $ |G|_{S} = mbox{sup}{|g|_{S} , |, , gin G}. $ Moreover, we write $ Delta(G) $ for the supremum of all $ |G|_{S}, $ where $ S $ is a finite normally generating subset of $ G, $ and we call $ Delta(G) $ the conjugacy diameter of $ G. $ In this paper, we derive the conjugacy diameters of the semidihedral $ 2 $-groups, the generalized quaternion groups and the modular $ p $-groups. This is a natural step after the determination of the conjugacy diameters of dihedral groups.","PeriodicalId":48562,"journal":{"name":"AIMS Mathematics","volume":null,"pages":null},"PeriodicalIF":2.2,"publicationDate":"2024-01-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140505170","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
$ mathcal{N} = 2 $ double graded supersymmetric quantum mechanics via dimensional reduction $ mathcal{N} = 2 $ 通过降维的双梯度超对称量子力学
IF 2.2 3区 数学
AIMS Mathematics Pub Date : 2024-01-05 DOI: 10.3934/math.2024513
N. Aizawa, Ren Ito, Toshiya Tanaka
{"title":"$ mathcal{N} = 2 $ double graded supersymmetric quantum mechanics via dimensional reduction","authors":"N. Aizawa, Ren Ito, Toshiya Tanaka","doi":"10.3934/math.2024513","DOIUrl":"https://doi.org/10.3934/math.2024513","url":null,"abstract":"We presented a novel $ mathcal{N} = 2 $ $ mathbb{Z}_2^2 $-graded supersymmetric quantum mechanics ($ {mathbb{Z}_2^2} $-SQM) which has different features from those introduced so far. It is a two-dimensional (two-particle) system and was the first example of the quantum mechanical realization of an eight-dimensional irreducible representation (irrep) of the $ mathcal{N} = 2 $ $ mathbb{Z}_2^2 $-supersymmetry algebra. The $ {mathbb{Z}_2^2} $-SQM was obtained by quantizing the one-dimensional classical system derived by dimensional reduction from the two-dimensional $ {mathbb{Z}_2^2} $-supersymmetric Lagrangian of $ mathcal{N} = 1 $, which we constructed in our previous work. The ground states of the $ {mathbb{Z}_2^2} $-SQM were also investigated.","PeriodicalId":48562,"journal":{"name":"AIMS Mathematics","volume":null,"pages":null},"PeriodicalIF":2.2,"publicationDate":"2024-01-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140513415","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
Fejér type inequalities for harmonically convex functions 调和凸函数的fejsamr型不等式
IF 2.2 3区 数学
AIMS Mathematics Pub Date : 2023-08-18 DOI: 10.3934/math.2022835
Muhammad Amer Latif
{"title":"Fejér type inequalities for harmonically convex functions","authors":"Muhammad Amer Latif","doi":"10.3934/math.2022835","DOIUrl":"https://doi.org/10.3934/math.2022835","url":null,"abstract":"In this study, some mappings related to the Fejér-type inequalities for harmonically convex functions are defined over $ left[ 0, 1right] $. Some Fejér-type inequalities for harmonically convex functions are proved using these mappings. Properties of these mappings are considered and consequently, refinements are obtained of some known results.","PeriodicalId":48562,"journal":{"name":"AIMS Mathematics","volume":null,"pages":null},"PeriodicalIF":2.2,"publicationDate":"2023-08-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46984565","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: 3
Angle in the space of $ p $-summable sequences $ p $-可和序列空间中的角
IF 2.2 3区 数学
AIMS Mathematics Pub Date : 2023-07-16 DOI: 10.3934/math.2022155
M. Nur, M. Bahri, A. Islamiyati, Harmanus Batkunde
{"title":"Angle in the space of $ p $-summable sequences","authors":"M. Nur, M. Bahri, A. Islamiyati, Harmanus Batkunde","doi":"10.3934/math.2022155","DOIUrl":"https://doi.org/10.3934/math.2022155","url":null,"abstract":"The aim of this paper is to investigate completness of $ A $ that equipped with usual norm on $ p $-summable sequences space where $ A $ is subspace in $ p $-summable sequences space and $ 1le p < infty $. We also introduce a new inner product on $ A $ and prove completness of $ A $ using a new norm that corresponds this new inner product. Moreover, we discuss the angle between two vectors and two subspaces in $ A $. In particular, we discuss the angle between $ 1 $-dimensional subspace and $ (s-1) $-dimensional subspace where $ sge 2 $ of $ A $.","PeriodicalId":48562,"journal":{"name":"AIMS Mathematics","volume":null,"pages":null},"PeriodicalIF":2.2,"publicationDate":"2023-07-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48080725","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
Cohomologies of modified $ lambda $-differential Lie triple systems and applications 修正$ λ $-微分李三元系统的上同调及其应用
IF 2.2 3区 数学
AIMS Mathematics Pub Date : 2023-07-12 DOI: 10.3934/math.20231280
Wen Teng, Fengshan Long, Yu Zhang
{"title":"Cohomologies of modified $ lambda $-differential Lie triple systems and applications","authors":"Wen Teng, Fengshan Long, Yu Zhang","doi":"10.3934/math.20231280","DOIUrl":"https://doi.org/10.3934/math.20231280","url":null,"abstract":"In this paper, we introduce the concept and representation of modified $ lambda $-differential Lie triple systems. Next, we define the cohomology of modified $ lambda $-differential Lie triple systems with coefficients in a suitable representation. As applications of the proposed cohomology theory, we study 1-parameter formal deformations and abelian extensions of modified $ lambda $-differential Lie triple systems.","PeriodicalId":48562,"journal":{"name":"AIMS Mathematics","volume":null,"pages":null},"PeriodicalIF":2.2,"publicationDate":"2023-07-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42483532","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 lifespan of classical solutions of one dimensional wave equations with semilinear terms of the spatial derivative 具有空间导数的双线性项的一维波动方程经典解的寿命
IF 2.2 3区 数学
AIMS Mathematics Pub Date : 2023-06-12 DOI: 10.3934/math.20231300
Takiko Sasaki, Shuhei Takamatsu, H. Takamura
{"title":"The lifespan of classical solutions of one dimensional wave equations with semilinear terms of the spatial derivative","authors":"Takiko Sasaki, Shuhei Takamatsu, H. Takamura","doi":"10.3934/math.20231300","DOIUrl":"https://doi.org/10.3934/math.20231300","url":null,"abstract":"This paper is devoted to the lifespan estimates of small classical solutions of the initial value problems for one dimensional wave equations with semilinear terms of the spatial derivative of the unknown function. It is natural that the result is same as the one for semilinear terms of the time-derivative. But there are so many differences among their proofs. Moreover, it is meaningful to study this problem in the sense that it may help us to investigate its blow-up boundary in the near future.","PeriodicalId":48562,"journal":{"name":"AIMS Mathematics","volume":null,"pages":null},"PeriodicalIF":2.2,"publicationDate":"2023-06-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47127415","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: 1
Stability of stochastic dynamic systems of a random structure with Markov switching in the presence of concentration points 具有马尔可夫切换的随机结构动态系统在集中点下的稳定性
IF 2.2 3区 数学
AIMS Mathematics Pub Date : 2023-05-19 DOI: 10.3934/math.20231245
T. Lukashiv, I. Malyk, Maryna K. Chepeleva, P. Nazarov
{"title":"Stability of stochastic dynamic systems of a random structure with Markov switching in the presence of concentration points","authors":"T. Lukashiv, I. Malyk, Maryna K. Chepeleva, P. Nazarov","doi":"10.3934/math.20231245","DOIUrl":"https://doi.org/10.3934/math.20231245","url":null,"abstract":"This article aims to investigate sufficient conditions for the stability of the trivial solution of stochastic differential equations with a random structure, particularly in contexts involving the presence of concentration points. The proof of asymptotic stability leverages the use of Lyapunov functions, supplemented by additional constraints on the magnitudes of jumps and jump times, as well as the Markov property of the system solutions. The findings are elucidated with an example, demonstrating both stable and unstable conditions of the system. The novelty of this work is in the consideration of jump concentration points, which are not considered in classical works. The assumption of the existence of concentration points leads to additional constraints on jumps, jump times and relations between them.","PeriodicalId":48562,"journal":{"name":"AIMS Mathematics","volume":null,"pages":null},"PeriodicalIF":2.2,"publicationDate":"2023-05-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45589800","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
Mixed radial-angular bounds for Hardy-type operators on Heisenberg group Heisenberg群上hardy型算子的混合径向-角界
IF 2.2 3区 数学
AIMS Mathematics Pub Date : 2023-04-24 DOI: 10.3934/math.20231070
Zhongci Hang, Xiang Li, D. Yan
{"title":"Mixed radial-angular bounds for Hardy-type operators on Heisenberg group","authors":"Zhongci Hang, Xiang Li, D. Yan","doi":"10.3934/math.20231070","DOIUrl":"https://doi.org/10.3934/math.20231070","url":null,"abstract":"In this paper, we study $ n $-dimensional Hardy operator and its dual in mixed radial-angular spaces on Heisenberg group and obtain their sharp bounds by using the rotation method. Furthermore, the sharp bounds of $ n $-dimensional weighted Hardy operator and weighted Cesàro operator are also obtained.","PeriodicalId":48562,"journal":{"name":"AIMS Mathematics","volume":null,"pages":null},"PeriodicalIF":2.2,"publicationDate":"2023-04-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41319140","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: 1
Exact solutions and superposition rules for Hamiltonian systems generalizing time-dependent SIS epidemic models with stochastic fluctuations 具有随机波动的时变SIS流行病模型的hamilton系统的精确解和叠加规则
IF 2.2 3区 数学
AIMS Mathematics Pub Date : 2023-04-18 DOI: 10.3934/math.20231225
R. Campoamor-Stursberg, Eduardo Fernández-Saiz, F. J. Herranz
{"title":"Exact solutions and superposition rules for Hamiltonian systems generalizing time-dependent SIS epidemic models with stochastic fluctuations","authors":"R. Campoamor-Stursberg, Eduardo Fernández-Saiz, F. J. Herranz","doi":"10.3934/math.20231225","DOIUrl":"https://doi.org/10.3934/math.20231225","url":null,"abstract":"Using the theory of Lie-Hamilton systems, formal generalized time-dependent Hamiltonian systems that extend a recently proposed SIS epidemic model with a variable infection rate are considered. It is shown that, independently on the particular interpretation of the time-dependent coefficients, these systems generally admit an exact solution, up to the case of the maximal extension within the classification of Lie-Hamilton systems, for which a superposition rule is constructed. The method provides the algebraic frame to which any SIS epidemic model that preserves the above-mentioned properties is subjected. In particular, we obtain exact solutions for generalized SIS Hamiltonian models based on the book and oscillator algebras, denoted by $ mathfrak{b}_2 $ and $ mathfrak{h}_4 $, respectively. The last generalization corresponds to an SIS system possessing the so-called two-photon algebra symmetry $ mathfrak{h}_6 $, according to the embedding chain $ mathfrak{b}_2subset mathfrak{h}_4subset mathfrak{h}_6 $, for which an exact solution cannot generally be found but a nonlinear superposition rule is explicitly given.","PeriodicalId":48562,"journal":{"name":"AIMS Mathematics","volume":null,"pages":null},"PeriodicalIF":2.2,"publicationDate":"2023-04-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43783486","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: 1
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