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 $.
本文建立了可交换非一元环$ {{mathit {I}_p}} = 左< a, b | pa = pb = 0, a^2 = b, ab = 0 右> $上的自正交码、拟自对偶码和自对偶码的质量公式，其中$ p $为奇素数。我们还给出了$ {mathit {I}_p}} $上的三种代码类的分类，其中$ p = 3,5，$和$ 7 $，长度最多为$ 3 $。
{"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}
Rashad Ismail, S. Hameed, Uzma Ahmad, Khadija Majeed, M. Javaid
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}) $.
{"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}
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 $.
目前，多处理系统互连网络的可靠性问题已成为并行计算机系统研究的热点问题。条件连通性是衡量互联网络可靠性的重要参数。在现实中，一个节点的故障不可避免地会对周围的节点产生负面影响。通常是特定的结构在互联网络中失效。因此，我们提出了两种新的连接，称为$ g $-额外$ H $-结构连接和$ g $-额外$ H $-子结构连接，以更准确地衡量网络的可靠性。超立方体网络是当今计算机系统使用的最主流的互联网络拓扑，例如著名的并行计算系统Cray $ T3D $、Cray $ T3E $、IBM $ Blue Gene等都是以超立方体网络作为互联网络拓扑构建的。本文得到了超立方体在特定结构为$ P_k $和$ g = 1 $时的$ g $-extra $ H $-结构连通性和$ g $-extra $ H $-子结构连通性的结果。
{"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}
A bivariate extension of a flexible univariate family is proposed. The new family is called bivariate q-extended Weibull Morgenstern family of distributions which can be constructed based on the Farlie-Gumbel-Morgenstern (FGM) copula technique. After introducing the new family, four sub-models are discussed in detail from the theoretical and numerical coefficient of correlation point of view with pointing to the effect of the $ q $ parameter.
{"title":"Bivariate q-extended Weibull morgenstern family and correlation coefficient formulas for some of its sub-models","authors":"R. A. Attwa, T. Radwan, E. O. A. Zaid","doi":"10.3934/math.20231292","DOIUrl":"https://doi.org/10.3934/math.20231292","url":null,"abstract":"A bivariate extension of a flexible univariate family is proposed. The new family is called bivariate q-extended Weibull Morgenstern family of distributions which can be constructed based on the Farlie-Gumbel-Morgenstern (FGM) copula technique. After introducing the new family, four sub-models are discussed in detail from the theoretical and numerical coefficient of correlation point of view with pointing to the effect of the $ q $ parameter.","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":"70167690","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}
In this paper, we show that every continuous linear map between unital $ C^ast $-algebras is skew Lie triple derivable at the identity is a $ ast $-derivation and that every continuous linear map between unital $ C^ast $-algebras which is a skew Lie triple homomorphism at the identity is a Jordan $ ast $-homomorphism.
{"title":"Maps on $ C^ast $-algebras are skew Lie triple derivations or homomorphisms at one point","authors":"Zhonghua Wang, Xiuhai Fei","doi":"10.3934/math.20231305","DOIUrl":"https://doi.org/10.3934/math.20231305","url":null,"abstract":"In this paper, we show that every continuous linear map between unital $ C^ast $-algebras is skew Lie triple derivable at the identity is a $ ast $-derivation and that every continuous linear map between unital $ C^ast $-algebras which is a skew Lie triple homomorphism at the identity is a Jordan $ ast $-homomorphism.","PeriodicalId":48562,"journal":{"name":"AIMS Mathematics","volume":"49 1","pages":""},"PeriodicalIF":2.2,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70168965","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}
Linear isotropic elasticity is an interesting branch of continuum mechanics, described by the fundamental laws of Hooke and Newton, which are combined in order to construct the governing generalized Navier equation of the displacement within any material. Implying time-independence and in the absence of external body forces, the latter is reduced to the corresponding form of a homogeneous second-order partial differential equation, whose solution is given via the Papkovich differential representation, which expresses the displacement field in terms of harmonic functions. On the other hand, spherical geometry provides the most widely used framework in real-life applications, concerning interior and exterior problems in elasticity. The present work aims to provide a little progress, by producing ready-to-use basic functions for linear isotropic elasticity in spherical coordinates. Hence, we calculate the Papkovich eigensolutions, generated by the spherical harmonic eigenfunctions, obtaining connections between Navier and spherical harmonic kernels. A set of useful results are provided at the end of the paper in the form of examples, regarding the evaluation of displacement field inside and outside a sphere.
{"title":"Direct connection between Navier and spherical harmonic kernels in elasticity","authors":"D. Labropoulou, P. Vafeas, G. Dassios","doi":"10.3934/math.2023158","DOIUrl":"https://doi.org/10.3934/math.2023158","url":null,"abstract":"Linear isotropic elasticity is an interesting branch of continuum mechanics, described by the fundamental laws of Hooke and Newton, which are combined in order to construct the governing generalized Navier equation of the displacement within any material. Implying time-independence and in the absence of external body forces, the latter is reduced to the corresponding form of a homogeneous second-order partial differential equation, whose solution is given via the Papkovich differential representation, which expresses the displacement field in terms of harmonic functions. On the other hand, spherical geometry provides the most widely used framework in real-life applications, concerning interior and exterior problems in elasticity. The present work aims to provide a little progress, by producing ready-to-use basic functions for linear isotropic elasticity in spherical coordinates. Hence, we calculate the Papkovich eigensolutions, generated by the spherical harmonic eigenfunctions, obtaining connections between Navier and spherical harmonic kernels. A set of useful results are provided at the end of the paper in the form of examples, regarding the evaluation of displacement field inside and outside a sphere.","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":"70171122","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}
A. Fahmi, Rehan Ahmed, M. Aslam, T. Abdeljawad, Aziz Khan
In this paper, the use of the Fermatean fuzzy number (FFN) in a significant research problem of disaster decision-making by defining operational laws and score function is demonstrated. Generally, decision control authorities need to brand suitable and sensible disaster decisions in the direct conceivable period as unfitting decisions may consequence in enormous financial dead and thoughtful communal costs. To certify that a disaster comeback can be made, professionally, we propose a new disaster decision-making (DDM) technique by the Fermatean fuzzy Schweizer-Sklar environment. First, the Fermatean fuzzy Schweizer-Sklar operators are employed by decision-makers to rapidly analyze their indefinite and vague assessment information on disaster choices. Then, the DDM technique based on the FFN is planned to identify highly devastating disaster choices and the best available choices. Finally, the proposed regret philosophy DDM technique is shown functional to choose the ideal retort explanation for a communal fitness disaster in Pakistan. The dominance and realism of the intended technique are further defensible through a relative study with additional DDM systems.
{"title":"Disaster decision-making with a mixing regret philosophy DDAS method in Fermatean fuzzy number","authors":"A. Fahmi, Rehan Ahmed, M. Aslam, T. Abdeljawad, Aziz Khan","doi":"10.3934/math.2023192","DOIUrl":"https://doi.org/10.3934/math.2023192","url":null,"abstract":"In this paper, the use of the Fermatean fuzzy number (FFN) in a significant research problem of disaster decision-making by defining operational laws and score function is demonstrated. Generally, decision control authorities need to brand suitable and sensible disaster decisions in the direct conceivable period as unfitting decisions may consequence in enormous financial dead and thoughtful communal costs. To certify that a disaster comeback can be made, professionally, we propose a new disaster decision-making (DDM) technique by the Fermatean fuzzy Schweizer-Sklar environment. First, the Fermatean fuzzy Schweizer-Sklar operators are employed by decision-makers to rapidly analyze their indefinite and vague assessment information on disaster choices. Then, the DDM technique based on the FFN is planned to identify highly devastating disaster choices and the best available choices. Finally, the proposed regret philosophy DDM technique is shown functional to choose the ideal retort explanation for a communal fitness disaster in Pakistan. The dominance and realism of the intended technique are further defensible through a relative study with additional DDM systems.","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":"70171984","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}
A. Alanzi, Muhammad Imran, Muhammad Mohsin Tahir, C. Chesneau, Farrukh Jamal, Saima Shakoor, Waqas Sami
In this article, we make mathematical and practical contributions to the Bell-X family of absolutely continuous distributions. As a main member of this family, a special distribution extending the modeling perspectives of the famous Burr XII (BXII) distribution is discussed in detail. It is called the Bell-Burr XII (BBXII) distribution. It stands apart from the other extended BXII distributions because of its flexibility in terms of functional shapes. On the theoretical side, a linear representation of the probability density function and the ordinary and incomplete moments are among the key properties studied in depth. Some commonly used entropy measures, namely Rényi, Havrda and Charvat, Arimoto, and Tsallis entropy, are derived. On the practical (inferential) side, the associated parameters are estimated using seven different frequentist estimation methods, namely the methods of maximum likelihood estimation, percentile estimation, least squares estimation, weighted least squares estimation, Cramér von-Mises estimation, Anderson-Darling estimation, and right-tail Anderson-Darling estimation. A simulation study utilizing all these methods is offered to highlight their effectiveness. Subsequently, the BBXII model is successfully used in comparisons with other comparable models to analyze data on patients with acute bone cancer and arthritis pain. A group acceptance sampling plan for truncated life tests is also proposed when an item's lifetime follows a BBXII distribution. Convincing results are obtained.
在本文中，我们对绝对连续分布的Bell-X族做出了数学和实际的贡献。作为该家族的主要成员，详细讨论了扩展了著名的Burr XII (BXII)分布的建模视角的特殊分布。它被称为贝尔-伯尔十二(BBXII)分布。它与其他扩展BXII发行版的区别在于它在功能形状方面的灵活性。在理论方面，概率密度函数的线性表示以及普通矩和不完全矩是深入研究的关键性质。推导了一些常用的熵测度，即r尼、Havrda和Charvat、Arimoto和Tsallis熵。在实际(推理)方面，使用七种不同的频率估计方法对相关参数进行估计，即最大似然估计、百分位数估计、最小二乘估计、加权最小二乘估计、cram von-Mises估计、Anderson-Darling估计和右尾Anderson-Darling估计。利用所有这些方法进行了仿真研究，以突出它们的有效性。随后，BBXII模型成功用于与其他可比较模型的比较，分析急性骨癌和关节炎疼痛患者的数据。当一个项目的寿命遵循BBXII分布时，还提出了截断寿命试验的组验收抽样计划。得到了令人信服的结果。
{"title":"Simulation analysis, properties and applications on a new Burr XII model based on the Bell-X functionalities","authors":"A. Alanzi, Muhammad Imran, Muhammad Mohsin Tahir, C. Chesneau, Farrukh Jamal, Saima Shakoor, Waqas Sami","doi":"10.3934/math.2023352","DOIUrl":"https://doi.org/10.3934/math.2023352","url":null,"abstract":"In this article, we make mathematical and practical contributions to the Bell-X family of absolutely continuous distributions. As a main member of this family, a special distribution extending the modeling perspectives of the famous Burr XII (BXII) distribution is discussed in detail. It is called the Bell-Burr XII (BBXII) distribution. It stands apart from the other extended BXII distributions because of its flexibility in terms of functional shapes. On the theoretical side, a linear representation of the probability density function and the ordinary and incomplete moments are among the key properties studied in depth. Some commonly used entropy measures, namely Rényi, Havrda and Charvat, Arimoto, and Tsallis entropy, are derived. On the practical (inferential) side, the associated parameters are estimated using seven different frequentist estimation methods, namely the methods of maximum likelihood estimation, percentile estimation, least squares estimation, weighted least squares estimation, Cramér von-Mises estimation, Anderson-Darling estimation, and right-tail Anderson-Darling estimation. A simulation study utilizing all these methods is offered to highlight their effectiveness. Subsequently, the BBXII model is successfully used in comparisons with other comparable models to analyze data on patients with acute bone cancer and arthritis pain. A group acceptance sampling plan for truncated life tests is also proposed when an item's lifetime follows a BBXII distribution. Convincing results are obtained.","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":"70179632","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}
$ mathcal{H} $-tensors play a key role in identifying the positive definiteness of even-order real symmetric tensors. Some criteria have been given since it is difficult to judge whether a given tensor is an $ mathcal{H} $-tensor, and their range of judgment has been limited. In this paper, some new criteria, from an increasing constant $ k $ to scale the elements of a given tensor can expand the range of judgment, are obtained. Moreover, as an application of those new criteria, some sufficient conditions for judging positive definiteness of even-order real symmetric tensors are proposed. In addition, some numerical examples are presented to illustrate those new results.
$ mathcal{H} $-张量在确定偶阶实对称张量的正定性方面起着关键作用。由于很难判断给定张量是否为$ mathcal{H} $-张量，因此给出了一些准则，并且它们的判断范围受到限制。本文给出了从一个递增的常数$ k $缩放给定张量的元素可以扩大判断范围的一些新准则。此外，作为这些新准则的应用，给出了判定偶阶实对称张量正确定性的几个充分条件。此外，还给出了一些数值算例来说明这些新结果。
{"title":"Some new criteria for judging $ mathcal{H} $-tensors and their applications","authors":"Wenbin Gong, Yaqiang Wang","doi":"10.3934/math.2023381","DOIUrl":"https://doi.org/10.3934/math.2023381","url":null,"abstract":"$ mathcal{H} $-tensors play a key role in identifying the positive definiteness of even-order real symmetric tensors. Some criteria have been given since it is difficult to judge whether a given tensor is an $ mathcal{H} $-tensor, and their range of judgment has been limited. In this paper, some new criteria, from an increasing constant $ k $ to scale the elements of a given tensor can expand the range of judgment, are obtained. Moreover, as an application of those new criteria, some sufficient conditions for judging positive definiteness of even-order real symmetric tensors are proposed. In addition, some numerical examples are presented to illustrate those new 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":"70181534","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}
In this article, a Green's function for a fractional boundary value problem in connection with modified analytic kernel has been constructed to study the existence of multiple solutions of a type of characteristic fractional boundary value problems. It is done here by using a well-known result: Krasnoselskii fixed point theorem. Moreover, a practical example is created to understand the importance of main results regarding the existence of solution of a boundary value fractional differential problem with homogeneous conditions. This example analytically and graphically, explains circumstances under which the Green's functions with different types of differential operator are compatible.
{"title":"Existence and compatibility of positive solutions for boundary value fractional differential equation with modified analytic kernel","authors":"A. Kalsoom, Sehar Afsheen, A. Azam, Faryad Ali","doi":"10.3934/math.2023390","DOIUrl":"https://doi.org/10.3934/math.2023390","url":null,"abstract":"In this article, a Green's function for a fractional boundary value problem in connection with modified analytic kernel has been constructed to study the existence of multiple solutions of a type of characteristic fractional boundary value problems. It is done here by using a well-known result: Krasnoselskii fixed point theorem. Moreover, a practical example is created to understand the importance of main results regarding the existence of solution of a boundary value fractional differential problem with homogeneous conditions. This example analytically and graphically, explains circumstances under which the Green's functions with different types of differential operator are compatible.","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":"70182202","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}
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