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Further representations and computations of the generalized Moore-Penrose inverse 广义Moore-Penrose逆的进一步表示和计算
IF 2.2 3区 数学
AIMS Mathematics Pub Date : 2023-01-01 DOI: 10.3934/math.20231191
Kezheng Zuo, Yang Chen, Li Yuan
{"title":"Further representations and computations of the generalized Moore-Penrose inverse","authors":"Kezheng Zuo, Yang Chen, Li Yuan","doi":"10.3934/math.20231191","DOIUrl":"https://doi.org/10.3934/math.20231191","url":null,"abstract":"The aim of this paper is to provide new representations and computations of the generalized Moore-Penrose inverse. Based on the Moore-Penrose inverse, group inverse, Bott-Duffin inverse and certain projections, some representations for the generalized Moore-Penrose inverse are given. An equivalent condition for the continuity of the generalized Moore-Penrose inverse is proposed. Splitting methods and successive matrix squaring algorithm for computing the generalized Moore-Penrose inverse are presented.","PeriodicalId":48562,"journal":{"name":"AIMS Mathematics","volume":"1 1","pages":""},"PeriodicalIF":2.2,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70162999","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
Riccati equation and metric geometric means of positive semidefinite matrices involving semi-tensor products 涉及半张量积的正半定矩阵的Riccati方程和度量几何均值
IF 2.2 3区 数学
AIMS Mathematics Pub Date : 2023-01-01 DOI: 10.3934/math.20231195
P. Chansangiam, Arnon Ploymukda
{"title":"Riccati equation and metric geometric means of positive semidefinite matrices involving semi-tensor products","authors":"P. Chansangiam, Arnon Ploymukda","doi":"10.3934/math.20231195","DOIUrl":"https://doi.org/10.3934/math.20231195","url":null,"abstract":"We investigate the Riccati matrix equation $ X A^{-1} X = B $ in which the conventional matrix products are generalized to the semi-tensor products $ ltimes $. When $ A $ and $ B $ are positive definite matrices satisfying the factor-dimension condition, this equation has a unique positive definite solution, which is defined to be the metric geometric mean of $ A $ and $ B $. We show that this geometric mean is the maximum solution of the Riccati inequality. We then extend the notion of the metric geometric mean to positive semidefinite matrices by a continuity argument and investigate its algebraic properties, order properties and analytic properties. Moreover, we establish some equations and inequalities of metric geometric means for matrices involving cancellability, positive linear map and concavity. Our results generalize the conventional metric geometric means of matrices.","PeriodicalId":48562,"journal":{"name":"AIMS Mathematics","volume":"1 1","pages":""},"PeriodicalIF":2.2,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70163285","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
A new subclass of analytic and bi-univalent functions associated with Legendre polynomials 与勒让德多项式相关的解析函数和双一元函数的一个新子类
IF 2.2 3区 数学
AIMS Mathematics Pub Date : 2023-01-01 DOI: 10.3934/math.20231196
Abeer O. Badghaish, Abdel Moneim Y. Lashin, Amani Z. Bajamal, Fayzah A. Alshehri
{"title":"A new subclass of analytic and bi-univalent functions associated with Legendre polynomials","authors":"Abeer O. Badghaish, Abdel Moneim Y. Lashin, Amani Z. Bajamal, Fayzah A. Alshehri","doi":"10.3934/math.20231196","DOIUrl":"https://doi.org/10.3934/math.20231196","url":null,"abstract":"In this paper, we introduce a new subclass of analytic and bi-univalent functions in the open unit disc $ U. $ For this subclass of functions, estimates of the initial coefficients $ leftvert A_{2}rightvert $ and $ leftvert A_{3}rightvert $ of the Taylor-Maclaurin series are given. An application of Legendre polynomials to this subclass of functions is presented. Furthermore, our study discusses several special cases.","PeriodicalId":48562,"journal":{"name":"AIMS Mathematics","volume":"42 1","pages":""},"PeriodicalIF":2.2,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70163671","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: 2
Fixed-point results via $ alpha_{i}^{j} $-$ left({bf D}_{{mathscr{C}}}left(mathfrak{P}_{hat E}right)right) $-contractions in partial $ flat $-metric spaces 不动点结果通过$ alpha_{i}^{j} $ - $ left({bf D}_{{mathscr{C}}}left(mathfrak{P}_{hat E}right)right) $ -缩在部分$ flat $ -度量空间
IF 2.2 3区 数学
AIMS Mathematics Pub Date : 2023-01-01 DOI: 10.3934/math.20231204
Leyla Sağ Dönmez, Abdurrahman Büyükkaya, M. Öztürk
{"title":"Fixed-point results via $ alpha_{i}^{j} $-$ left({bf D}_{{mathscr{C}}}left(mathfrak{P}_{hat E}right)right) $-contractions in partial $ flat $-metric spaces","authors":"Leyla Sağ Dönmez, Abdurrahman Büyükkaya, M. Öztürk","doi":"10.3934/math.20231204","DOIUrl":"https://doi.org/10.3934/math.20231204","url":null,"abstract":"In this study, we characterize a novel contraction mapping referred to as $ alpha_{i}^{j} $-$ left({bf D}_{{mathscr{C}}}left(mathfrak{P}_{hat E}right)right) $-contraction in light of $ {bf D}_{mathscr{C}} $-contraction mappings associated with the Geraghty-type contraction and $ E $-type contraction. Besides, a novel common fixed-point theorem providing such mappings is demonstrated in the context of partial $ flat $-metric spaces. It is stated that the main theorem is a generalization of the existing literature, and its comparisons with the results are expressed. Additionally, the efficiency of the result of this study is demonstrated through some examples and an application to homotopy theory.","PeriodicalId":48562,"journal":{"name":"AIMS Mathematics","volume":"1 1","pages":""},"PeriodicalIF":2.2,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70163768","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
A new error bound for linear complementarity problems involving $ B- $matrices 涉及$ B- $矩阵的线性互补问题的一个新的误差界
IF 2.2 3区 数学
AIMS Mathematics Pub Date : 2023-01-01 DOI: 10.3934/math.20231218
Hongmin Mo, Yingxue Dong
{"title":"A new error bound for linear complementarity problems involving $ B- $matrices","authors":"Hongmin Mo, Yingxue Dong","doi":"10.3934/math.20231218","DOIUrl":"https://doi.org/10.3934/math.20231218","url":null,"abstract":"In this paper, a new error bound for the linear complementarity problems of $ B- $matrices which is a subclass of the $ P- $matrices is presented. Theoretical analysis and numerical example illustrate that the new error bound improves some existing results.","PeriodicalId":48562,"journal":{"name":"AIMS Mathematics","volume":"1 1","pages":""},"PeriodicalIF":2.2,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70164314","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
Continuous Tsallis and Renyi extropy with pharmaceutical market application 连续的沙利和仁义外倾与医药市场应用
IF 2.2 3区 数学
AIMS Mathematics Pub Date : 2023-01-01 DOI: 10.3934/math.20231233
M. Mohamed, Najwan Alsadat, O. S. Balogun
{"title":"Continuous Tsallis and Renyi extropy with pharmaceutical market application","authors":"M. Mohamed, Najwan Alsadat, O. S. Balogun","doi":"10.3934/math.20231233","DOIUrl":"https://doi.org/10.3934/math.20231233","url":null,"abstract":"In this paper, the Tsallis and Renyi extropy is presented as a continuous measure of information under the continuous distribution. Furthermore, the features and their connection to other information measures are introduced. Some stochastic comparisons and results on the order statistics and upper records are given. Moreover, some theorems about the maximum Tsallis and Renyi extropy are discussed. On the other hand, numerical results of the non-parametric estimation of Tsallis extropy are calculated for simulated and real data with application to time series model and its forecasting.","PeriodicalId":48562,"journal":{"name":"AIMS Mathematics","volume":"1 1","pages":""},"PeriodicalIF":2.2,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70164915","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
Unreliable retrial queueing system with working vacation 带工作假期的不可靠重审排队系统
IF 2.2 3区 数学
AIMS Mathematics Pub Date : 2023-01-01 DOI: 10.3934/math.20231234
Bharathy Shanmugam, M. C. Saravanarajan
{"title":"Unreliable retrial queueing system with working vacation","authors":"Bharathy Shanmugam, M. C. Saravanarajan","doi":"10.3934/math.20231234","DOIUrl":"https://doi.org/10.3934/math.20231234","url":null,"abstract":"This paper investigates an unreliable $ M/G(P_{1}, P_{2})/1 $ retrial queueing system with a woking vacation. An arriving customer successfully starts the first phase service with the probability $ alpha $ or the server fails with the probability $ bar{alpha} $. Once failure happens, the serving customer is taken to the orbit. The failed server is taken for repair with some delay. Once the repair is comleted, the server is ready to provide service once again. In this background, we implemented the working vacation scenario. During working vacation, the service will be provided at a slower rate, rather than entirely stopping the service. The supplementary variable method was adopted to find the orbit and system lengths. Additionally, some unique results and numerical evaluations have been presented.","PeriodicalId":48562,"journal":{"name":"AIMS Mathematics","volume":"1 1","pages":""},"PeriodicalIF":2.2,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70165316","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 mass formula for self-orthogonal and self-dual codes over a non-unitary commutative ring 非酉交换环上自正交码和自对偶码的质量公式
IF 2.2 3区 数学
AIMS Mathematics Pub Date : 2023-01-01 DOI: 10.3934/math.20231242
A. Alahmadi, A. Alshuhail, P. Solé
{"title":"The mass formula for self-orthogonal and self-dual codes over a non-unitary commutative ring","authors":"A. Alahmadi, A. Alshuhail, P. Solé","doi":"10.3934/math.20231242","DOIUrl":"https://doi.org/10.3934/math.20231242","url":null,"abstract":"In this paper, we establish a mass formula for self-orthogonal codes, quasi self-dual codes, and self-dual codes over commutative non-unital rings $ {{mathit {I}_p}} = left < a, b | pa = pb = 0, a^2 = b, ab = 0 right > $, where $ p $ is an odd prime. We also give a classification of the three said classes of codes over $ {{mathit {I}_p}} $ where $ p = 3, 5, $ and $ 7 $, with lengths up to $ 3 $.","PeriodicalId":48562,"journal":{"name":"AIMS Mathematics","volume":"1 1","pages":""},"PeriodicalIF":2.2,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70165454","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
Unbalanced signed graphs with eigenvalue properties 具有特征值性质的不平衡符号图
IF 2.2 3区 数学
AIMS Mathematics Pub Date : 2023-01-01 DOI: 10.3934/math.20231262
Rashad Ismail, S. Hameed, Uzma Ahmad, Khadija Majeed, M. Javaid
{"title":"Unbalanced signed graphs with eigenvalue properties","authors":"Rashad Ismail, S. Hameed, Uzma Ahmad, Khadija Majeed, M. Javaid","doi":"10.3934/math.20231262","DOIUrl":"https://doi.org/10.3934/math.20231262","url":null,"abstract":"For a signature function $ Psi:E({H}) longrightarrow {pm 1} $ with underlying graph $ H $, a signed graph (S.G) $ hat{H} = (H, Psi) $ is a graph in which edges are assigned the signs using the signature function $ Psi $. An S.G $ hat{H} $ is said to fulfill the symmetric eigenvalue property if for every eigenvalue $ hat{h}(hat{H}) $ of $ hat{H} $, $ -hat{h}(hat{H}) $ is also an eigenvalue of $ hat{H} $. A non singular S.G $ hat{H} $ is said to fulfill the property $ (mathcal{SR}) $ if for every eigenvalue $ hat{h}(hat{H}) $ of $ hat{H} $, its reciprocal is also an eigenvalue of $ hat{H} $ (with multiplicity as that of $ hat{h}(hat{H}) $). A non singular S.G $ hat{H} $ is said to fulfill the property $ (-mathcal{SR}) $ if for every eigenvalue $ hat{h}(hat{H}) $ of $ hat{H} $, its negative reciprocal is also an eigenvalue of $ hat{H} $ (with multiplicity as that of $ hat{h}(hat{H}) $). In this article, non bipartite unbalanced S.Gs $ hat{mathfrak{C}}^{(m, 1)}_{3} $ and $ hat{mathfrak{C}}^{(m, 2)}_{5} $, where $ m $ is even positive integer have been constructed and it has been shown that these graphs fulfill the symmetric eigenvalue property, the S.Gs $ hat{mathfrak{C}}^{(m, 1)}_{3} $ also fulfill the properties $ (-mathcal{SR}) $ and $ (mathcal{SR}) $, whereas the S.Gs $ hat{mathfrak{C}}^{(m, 2)}_{5} $ are close to fulfill the properties $ (-mathcal{SR}) $ and $ (mathcal{SR}) $.","PeriodicalId":48562,"journal":{"name":"AIMS Mathematics","volume":"1 1","pages":""},"PeriodicalIF":2.2,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70165991","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 $ g $-extra $ H $-structure connectivity and $ g $-extra $ H $-substructure connectivity of hypercubes 超立方体的$ g $-extra $ H $-结构连通性和$ g $-extra $ H $-子结构连通性
IF 2.2 3区 数学
AIMS Mathematics Pub Date : 2023-01-01 DOI: 10.3934/math.20231267
Bo Zhu, Shumin Zhang, Huifen Ge, Chengfu Ye
{"title":"The $ g $-extra $ H $-structure connectivity and $ g $-extra $ H $-substructure connectivity of hypercubes","authors":"Bo Zhu, Shumin Zhang, Huifen Ge, Chengfu Ye","doi":"10.3934/math.20231267","DOIUrl":"https://doi.org/10.3934/math.20231267","url":null,"abstract":"At present, the reliability of interconnection networks of multiprocessing systems has become a hot topic of research concern for parallel computer systems. Conditional connectivity is an important parameter to measure the reliability of an interconnected network. In reality, the failure of one node will inevitably have a negative impact on the surrounding nodes. Often it is the specific structures that fail in an interconnected network. Therefore, we propose two novel kinds of connectivity, called $ g $-extra $ H $-structure connectivity and $ g $-extra $ H $-substructure connectivity, to go for a more accurate measure of the reliability of the network. Hypercube network is the most dominant interconnection network topology used by computer systems today, for example, the famous parallel computing systems Cray $ T3D $, Cray $ T3E $, $ IBM $ Blue Gene, etc. are built with it as the interconnection network topology. In this paper, we obtain the results of the $ g $-extra $ H $-structure connectivity and the $ g $-extra $ H $-substructure connectivity of the hypercubes when the specific structure is $ P_k $ and $ g = 1 $.","PeriodicalId":48562,"journal":{"name":"AIMS Mathematics","volume":"1 1","pages":""},"PeriodicalIF":2.2,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70166766","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
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