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Advances in Applied Clifford Algebras最新文献

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The General Solution to a System of Linear Coupled Quaternion Matrix Equations with an Application 一类线性耦合四元数矩阵方程组的通解及其应用
IF 1.5 2区 数学
Advances in Applied Clifford Algebras Pub Date : 2023-08-09 DOI: 10.1007/s00006-023-01283-x
Long-Sheng Liu
{"title":"The General Solution to a System of Linear Coupled Quaternion Matrix Equations with an Application","authors":"Long-Sheng Liu","doi":"10.1007/s00006-023-01283-x","DOIUrl":"10.1007/s00006-023-01283-x","url":null,"abstract":"<div><p>Linear coupled matrix equations are widely utilized in applications, including stability analysis of control systems and robust control. In this paper, we establish the necessary and sufficient conditions for the consistency of the system of linear coupled matrix equations and derive an expression of the corresponding general solution (where it is solvable) over quaternion. Additionally, we investigate the necessary and sufficient conditions for the system of linear coupled matrix equations with construct to have a solution and derive a formula of its general solution (where it is solvable). Finally, an algorithm and an example were provided in order to further illustrate the primary outcomes of this paper.</p></div>","PeriodicalId":7330,"journal":{"name":"Advances in Applied Clifford Algebras","volume":"33 4","pages":""},"PeriodicalIF":1.5,"publicationDate":"2023-08-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45406355","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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
Bicomplex Weighted Bergman Spaces and Composition Operators 双复加权Bergman空间与复合算子
IF 1.5 2区 数学
Advances in Applied Clifford Algebras Pub Date : 2023-08-07 DOI: 10.1007/s00006-023-01291-x
Stanzin Dolkar, Sanjay Kumar
{"title":"Bicomplex Weighted Bergman Spaces and Composition Operators","authors":"Stanzin Dolkar,&nbsp;Sanjay Kumar","doi":"10.1007/s00006-023-01291-x","DOIUrl":"10.1007/s00006-023-01291-x","url":null,"abstract":"<div><p>In this paper, we study the bicomplex version of weighted Bergman spaces and the composition operators acting on them. We also investigate the Bergman kernel, duality properties and Berezin transform. This paper is essentially based on the work of Zhu (Operator Theory in Function Spaces of Math. Surveys and Monographs, vol. 138, 2nd edn. American Mathematical Society, Providence, 2007).</p></div>","PeriodicalId":7330,"journal":{"name":"Advances in Applied Clifford Algebras","volume":"33 4","pages":""},"PeriodicalIF":1.5,"publicationDate":"2023-08-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46018306","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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 Some Quaternionic Series 关于一些四元数级数
IF 1.5 2区 数学
Advances in Applied Clifford Algebras Pub Date : 2023-07-31 DOI: 10.1007/s00006-023-01293-9
J. Oscar González Cervantes, J. Emilio Paz Cordero, Daniel González Campos
{"title":"On Some Quaternionic Series","authors":"J. Oscar González Cervantes,&nbsp;J. Emilio Paz Cordero,&nbsp;Daniel González Campos","doi":"10.1007/s00006-023-01293-9","DOIUrl":"10.1007/s00006-023-01293-9","url":null,"abstract":"<div><p>The aim of this work is to show that given <span>(uin {mathbb {H}}{setminus }{mathbb {R}})</span>, there exists a differential operator <span>(G^{-u})</span> whose solutions expand in quaternionic power series expansion <span>( sum _{n=0}^infty (x-u)^n a_n)</span> in a neighborhood of <span>(uin {mathbb {H}})</span>. This paper also presents Stokes and Borel-Pompeiu formulas induced by <span>(G^{-u})</span> and as consequence we give some versions of Cauchy’s Theorem and Cauchy’s Formula associated to these kind of regular functions.</p></div>","PeriodicalId":7330,"journal":{"name":"Advances in Applied Clifford Algebras","volume":"33 4","pages":""},"PeriodicalIF":1.5,"publicationDate":"2023-07-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00006-023-01293-9.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42452252","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
On Some Lie Groups in Degenerate Clifford Geometric Algebras 简并Clifford几何代数中的若干李群
IF 1.5 2区 数学
Advances in Applied Clifford Algebras Pub Date : 2023-07-18 DOI: 10.1007/s00006-023-01290-y
Ekaterina Filimoshina, Dmitry Shirokov
{"title":"On Some Lie Groups in Degenerate Clifford Geometric Algebras","authors":"Ekaterina Filimoshina,&nbsp;Dmitry Shirokov","doi":"10.1007/s00006-023-01290-y","DOIUrl":"10.1007/s00006-023-01290-y","url":null,"abstract":"<div><p>In this paper, we introduce and study five families of Lie groups in degenerate Clifford geometric algebras. These Lie groups preserve the even and odd subspaces and some other subspaces under the adjoint representation and the twisted adjoint representation. The considered Lie groups contain degenerate spin groups, Lipschitz groups, and Clifford groups as subgroups in the case of arbitrary dimension and signature. The considered Lie groups can be of interest for various applications in physics, engineering, and computer science.</p></div>","PeriodicalId":7330,"journal":{"name":"Advances in Applied Clifford Algebras","volume":"33 4","pages":""},"PeriodicalIF":1.5,"publicationDate":"2023-07-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00006-023-01290-y.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46698511","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Various Characteristic Properties of Lipschitzian Elements in Clifford Algebras Clifford代数中Lipschitzian元素的各种特征性质
IF 1.5 2区 数学
Advances in Applied Clifford Algebras Pub Date : 2023-07-12 DOI: 10.1007/s00006-023-01288-6
Jacques Helmstetter
{"title":"Various Characteristic Properties of Lipschitzian Elements in Clifford Algebras","authors":"Jacques Helmstetter","doi":"10.1007/s00006-023-01288-6","DOIUrl":"10.1007/s00006-023-01288-6","url":null,"abstract":"<div><p>In most cases, the Lipschitz monoid <span>(textrm{Lip}(V,Q))</span> is the multiplicative monoid (or semi-group) generated in the Clifford algebra <span>(textrm{Cl}(V,Q))</span> by the vectors of <i>V</i>. But the elements of <span>(textrm{Lip}(V,Q))</span> satisfy many other characteristic properties, very different from one another, which may as well be used as definitions of <span>(textrm{Lip}(V,Q))</span>. The present work proposes several characteristic properties, and explores some of the ways that enable us to link one property to another.</p></div>","PeriodicalId":7330,"journal":{"name":"Advances in Applied Clifford Algebras","volume":"33 4","pages":""},"PeriodicalIF":1.5,"publicationDate":"2023-07-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45000800","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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 Way to Construct the Riemann Curvature Tensor Using Geometric Algebra and Division Algebraic Structure 利用几何代数和除法代数结构构造黎曼曲率张量的新方法
IF 1.5 2区 数学
Advances in Applied Clifford Algebras Pub Date : 2023-06-22 DOI: 10.1007/s00006-023-01286-8
Brian Jonathan Wolk
{"title":"A New Way to Construct the Riemann Curvature Tensor Using Geometric Algebra and Division Algebraic Structure","authors":"Brian Jonathan Wolk","doi":"10.1007/s00006-023-01286-8","DOIUrl":"10.1007/s00006-023-01286-8","url":null,"abstract":"<div><p>The Riemann curvature tensor is constructed using the Clifford-Dirac geometric algebra and division-algebraic operator structure.</p></div>","PeriodicalId":7330,"journal":{"name":"Advances in Applied Clifford Algebras","volume":"33 4","pages":""},"PeriodicalIF":1.5,"publicationDate":"2023-06-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43159617","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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
Mean Value Theorems for Bicomplex Harmonic Functions 双复调和函数的中值定理
IF 1.5 2区 数学
Advances in Applied Clifford Algebras Pub Date : 2023-06-21 DOI: 10.1007/s00006-023-01285-9
Abdelkader Abouricha, Aiad El Gourari, Allal Ghanmi
{"title":"Mean Value Theorems for Bicomplex Harmonic Functions","authors":"Abdelkader Abouricha,&nbsp;Aiad El Gourari,&nbsp;Allal Ghanmi","doi":"10.1007/s00006-023-01285-9","DOIUrl":"10.1007/s00006-023-01285-9","url":null,"abstract":"<div><p>Mean value theorems appear as fundamental tools in the analysis of harmonic functions and elliptic partial differential equations. In the present paper, we establish their bicomplex analogs for bicomplex harmonic and strongly harmonic functions with bicomplex values. Their analytical converse as well as geometrical converse characterizing open idempotent discus are also discussed.</p></div>","PeriodicalId":7330,"journal":{"name":"Advances in Applied Clifford Algebras","volume":"33 4","pages":""},"PeriodicalIF":1.5,"publicationDate":"2023-06-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00006-023-01285-9.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48301376","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Quaternion Quantum Neural Network for Classification 用于分类的四元数量子神经网络
IF 1.5 2区 数学
Advances in Applied Clifford Algebras Pub Date : 2023-06-21 DOI: 10.1007/s00006-023-01280-0
Guillermo Altamirano-Escobedo, Eduardo Bayro-Corrochano
{"title":"Quaternion Quantum Neural Network for Classification","authors":"Guillermo Altamirano-Escobedo,&nbsp;Eduardo Bayro-Corrochano","doi":"10.1007/s00006-023-01280-0","DOIUrl":"10.1007/s00006-023-01280-0","url":null,"abstract":"<div><p>We propose the quaternionic quantum neural network (QQNN) for pattern recognition based on the formulation of quaternionic qubits and the construction of activation operators. In this model, the inputs and targets are represented by quaternionic qubits. The proposed neural network is evaluated through a series of experiments using different benchmark datasets, where the results show its superiority as a classifier in terms of accuracy when it is compared to conventional (real-valued) neural networks.</p></div>","PeriodicalId":7330,"journal":{"name":"Advances in Applied Clifford Algebras","volume":"33 4","pages":""},"PeriodicalIF":1.5,"publicationDate":"2023-06-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48983285","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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
Propagators Beyond The Standard Model 超越标准模型的传播媒介
IF 1.5 2区 数学
Advances in Applied Clifford Algebras Pub Date : 2023-06-17 DOI: 10.1007/s00006-023-01287-7
Rodolfo José Bueno Rogerio, Luca Fabbri
{"title":"Propagators Beyond The Standard Model","authors":"Rodolfo José Bueno Rogerio,&nbsp;Luca Fabbri","doi":"10.1007/s00006-023-01287-7","DOIUrl":"10.1007/s00006-023-01287-7","url":null,"abstract":"<div><p>In this paper, we explore the field propagator with a structure that is general enough to encompas both the case of newly-defined mass-dimension 1 fermions and spin-1/2 bosons. The method we employ is to define a map between spinors of different Lounesto classes, and then write the propagator in terms of the corresponding dual structures.</p></div>","PeriodicalId":7330,"journal":{"name":"Advances in Applied Clifford Algebras","volume":"33 4","pages":""},"PeriodicalIF":1.5,"publicationDate":"2023-06-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00006-023-01287-7.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46541270","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 2
Clifford Algebras, Quantum Neural Networks and Generalized Quantum Fourier Transform Clifford代数，量子神经网络和广义量子傅里叶变换
IF 1.5 2区 数学
Advances in Applied Clifford Algebras Pub Date : 2023-06-13 DOI: 10.1007/s00006-023-01279-7
Marco A. S. Trindade, Vinícius N. A. Lula-Rocha, S. Floquet
{"title":"Clifford Algebras, Quantum Neural Networks and Generalized Quantum Fourier Transform","authors":"Marco A. S. Trindade,&nbsp;Vinícius N. A. Lula-Rocha,&nbsp;S. Floquet","doi":"10.1007/s00006-023-01279-7","DOIUrl":"10.1007/s00006-023-01279-7","url":null,"abstract":"<div><p>We propose models of quantum perceptrons and quantum neural networks based on Clifford algebras. These models are capable to capture geometric features of classical and quantum data as well as producing data entanglement. Due to their representations in terms of Pauli matrices, the Clifford algebras seem to be a natural framework for multidimensional data analysis in a quantum setting. In this context, the implementation of activation functions, and unitary learning rules are discussed. In this scheme, we also provide an algebraic generalization of the quantum Fourier transform containing additional parameters that allow performing quantum machine learning based on variational algorithms. Furthermore, some interesting properties of the generalized quantum Fourier transform have been proved.</p></div>","PeriodicalId":7330,"journal":{"name":"Advances in Applied Clifford Algebras","volume":"33 3","pages":""},"PeriodicalIF":1.5,"publicationDate":"2023-06-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00006-023-01279-7.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47016234","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 3
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