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Advances in Applied Clifford Algebras最新文献

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A Real Method for Solving Octonion Matrix Equation (AXB=C) Based on Semi-tensor Product of Matrices 基于矩阵半张量积的求解八音矩阵方程 $$AXB=C$$ 的实数法
IF 1.1 2区 数学
Advances in Applied Clifford Algebras Pub Date : 2024-03-23 DOI: 10.1007/s00006-024-01316-z
Xiaochen Liu, Ying Li, Wenxv Ding, Ruyu Tao
{"title":"A Real Method for Solving Octonion Matrix Equation (AXB=C) Based on Semi-tensor Product of Matrices","authors":"Xiaochen Liu,&nbsp;Ying Li,&nbsp;Wenxv Ding,&nbsp;Ruyu Tao","doi":"10.1007/s00006-024-01316-z","DOIUrl":"10.1007/s00006-024-01316-z","url":null,"abstract":"<div><p>In this paper, the octonion matrix equation <span>(AXB=C)</span> is studied based on semi-tensor product of matrices. Firstly, we propose the left real element representation and the right real element representation of octonion. Then we obtain the expression of the least squares Hermitian solution to the octonion matrix equation <span>(AXB=C)</span> by combining these representations with <span>(mathcal {H})</span>-representation of the special matrices. In addition, we also put forward the equivalent condition of existence and general expression of the Hermitian solution to the octonion matrix equation <span>(AXB=C.)</span> Finally, the validity and stability of our method is verified by numerical experiments.</p></div>","PeriodicalId":7330,"journal":{"name":"Advances in Applied Clifford Algebras","volume":"34 2","pages":""},"PeriodicalIF":1.1,"publicationDate":"2024-03-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140192587","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
Common Spectral Properties of Bounded Right Linear Operators AC and BA in the Quaternionic Setting 四元数背景下有界右线性算子 AC 和 BA 的共谱特性
IF 1.1 2区 数学
Advances in Applied Clifford Algebras Pub Date : 2024-03-18 DOI: 10.1007/s00006-024-01315-0
Rachid Arzini, Ali Jaatit
{"title":"Common Spectral Properties of Bounded Right Linear Operators AC and BA in the Quaternionic Setting","authors":"Rachid Arzini,&nbsp;Ali Jaatit","doi":"10.1007/s00006-024-01315-0","DOIUrl":"10.1007/s00006-024-01315-0","url":null,"abstract":"<div><p>Let <i>X</i> be a two-sided quaternionic Banach space and let <span>(A, B, C: X longrightarrow X)</span> be bounded right linear quaternionic operators such that <span>(ACA=ABA)</span>. Let <i>q</i> be a non-zero quaternion. In this paper, we investigate the common properties of <span>((AC)^{2}-2Re(q)AC+|q|^2I)</span> and <span>((BA)^{2}-2Re(q)BA+|q|^2I)</span> where <i>I</i> stands for the identity operator on <i>X</i>. In particular, we show that </p><div><div><span>$$begin{aligned} sigma ^{S}_{{mathcal {F}}}(AC)backslash {0} = sigma ^{S}_{{mathcal {F}}}(BA)backslash {0} end{aligned}$$</span></div></div><p>where <span>(sigma ^{S}_{{mathcal {F}}}(.))</span> is a distinguished part of the spherical spectrum.</p></div>","PeriodicalId":7330,"journal":{"name":"Advances in Applied Clifford Algebras","volume":"34 2","pages":""},"PeriodicalIF":1.1,"publicationDate":"2024-03-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140161940","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
Generalized Partial-Slice Monogenic Functions: A Synthesis of Two Function Theories 广义部分片单原函数：两种函数理论的合成
IF 1.1 2区 数学
Advances in Applied Clifford Algebras Pub Date : 2024-03-09 DOI: 10.1007/s00006-024-01314-1
Zhenghua Xu, Irene Sabadini
{"title":"Generalized Partial-Slice Monogenic Functions: A Synthesis of Two Function Theories","authors":"Zhenghua Xu,&nbsp;Irene Sabadini","doi":"10.1007/s00006-024-01314-1","DOIUrl":"10.1007/s00006-024-01314-1","url":null,"abstract":"<div><p>In this paper, we review the notion of generalized partial-slice monogenic functions that was introduced by the authors in Xu and Sabadini (Generalized partial-slice monogenic functions, arXiv:2309.03698, 2023). The class of these functions includes both the theory of monogenic functions and of slice monogenic functions over Clifford algebras and it is obtained via a synthesis operator which combines a generalized Cauchy–Riemann operator with an operator acting on slices. Besides recalling the fundamental features, we provide a notion of <span>(*)</span>-product based on the CK-extension and discuss the smoothness of generalized partial-slice functions.</p></div>","PeriodicalId":7330,"journal":{"name":"Advances in Applied Clifford Algebras","volume":"34 2","pages":""},"PeriodicalIF":1.1,"publicationDate":"2024-03-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00006-024-01314-1.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140067802","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
Heron’s Formula in Higher Dimensions 高维赫伦公式
IF 1.1 2区 数学
Advances in Applied Clifford Algebras Pub Date : 2024-02-17 DOI: 10.1007/s00006-023-01305-8
Timothy F. Havel
{"title":"Heron’s Formula in Higher Dimensions","authors":"Timothy F. Havel","doi":"10.1007/s00006-023-01305-8","DOIUrl":"10.1007/s00006-023-01305-8","url":null,"abstract":"<div><p>This paper shows how geometric algebra can be used to derive a novel generalization of Heron’s classical formula for the area of a triangle in the plane to higher dimensions. It begins by illustrating some of the many ways in which the conformal model of three-dimensional Euclidean space yields provocative insights into some of our most basic intuitive notions of solid geometry. It then uses this conceptual framework to elucidate the geometric meaning of Heron’s formula in the plane, and explains in detail how it extends naturally to the volumes of tetrahedra in space. The paper closes by outlining a proof of a previously conjectured extension of the formula to the hyper-volumes of simplices in all dimensions.</p></div>","PeriodicalId":7330,"journal":{"name":"Advances in Applied Clifford Algebras","volume":"34 2","pages":""},"PeriodicalIF":1.1,"publicationDate":"2024-02-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00006-023-01305-8.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139898782","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 Optimal Inequalities for Anti-invariant Riemannian Submersions from Conformal Sasakian Space Forms 论来自共形萨萨基空间形式的反不变黎曼潜影的最优不等式
IF 1.1 2区 数学
Advances in Applied Clifford Algebras Pub Date : 2024-01-21 DOI: 10.1007/s00006-023-01312-9
Mehraj Ahmad Lone, Towseef Ali Wani
{"title":"On Optimal Inequalities for Anti-invariant Riemannian Submersions from Conformal Sasakian Space Forms","authors":"Mehraj Ahmad Lone,&nbsp;Towseef Ali Wani","doi":"10.1007/s00006-023-01312-9","DOIUrl":"10.1007/s00006-023-01312-9","url":null,"abstract":"<div><p>The aim of this paper is two-fold. First, we obtain various inequalities which involve the Ricci and scalar curvatures of horizontal and vertical distributions of anti-invariant Riemannian submersion defined from conformal Sasakian space form onto a Riemannian manifold. Second, we obtain the Chen–Ricci inequality for the said Riemannian submersion.</p></div>","PeriodicalId":7330,"journal":{"name":"Advances in Applied Clifford Algebras","volume":"34 1","pages":""},"PeriodicalIF":1.1,"publicationDate":"2024-01-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139510875","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
Geometric Algebras of Light Cone Projective Graph Geometries 光锥投影图几何的几何代数
IF 1.1 2区 数学
Advances in Applied Clifford Algebras Pub Date : 2024-01-17 DOI: 10.1007/s00006-023-01307-6
Garret Sobczyk
{"title":"Geometric Algebras of Light Cone Projective Graph Geometries","authors":"Garret Sobczyk","doi":"10.1007/s00006-023-01307-6","DOIUrl":"10.1007/s00006-023-01307-6","url":null,"abstract":"<div><p>A null vector is an algebraic quantity with the property that its square is zero. I denote the universal algebra generated by taking all sums and products of null vectors over the real or complex numbers by <span>({{mathcal {N}}})</span>. The rules of addition and multiplication in <span>({{mathcal {N}}})</span> are taken to be the same as those for real and complex square matrices. A distinct pair of null vectors is <i>positively</i> or <i>negatively</i> correlated if their inner product is <i>positive</i> or <i>negative</i>, respectively. A <i>basis</i> of <span>(n+1)</span> null vectors, with pairwise inner products equal to plus or minus one half, defines the Clifford geometric algebras <span>({mathbb {G}}_{1,n})</span>, or <span>({mathbb {G}}_{n,1})</span>, respectively, and provides a foundation for a new Cayley–Grassman linear algebra, a theory of complete graphs, and other applications in pure and applied areas of science.</p></div>","PeriodicalId":7330,"journal":{"name":"Advances in Applied Clifford Algebras","volume":"34 1","pages":""},"PeriodicalIF":1.1,"publicationDate":"2024-01-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139489203","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
Algorithms for Conic Fitting Through Given Proper and Improper Waypoints in Geometric Algebra for Conics 圆锥曲线几何代数中通过给定适当和不适当航点进行圆锥拟合的算法
IF 1.5 2区 数学
Advances in Applied Clifford Algebras Pub Date : 2024-01-09 DOI: 10.1007/s00006-023-01308-5
Pavel Loučka, Petr Vašík
{"title":"Algorithms for Conic Fitting Through Given Proper and Improper Waypoints in Geometric Algebra for Conics","authors":"Pavel Loučka,&nbsp;Petr Vašík","doi":"10.1007/s00006-023-01308-5","DOIUrl":"10.1007/s00006-023-01308-5","url":null,"abstract":"<div><p>As an addition to proper points of the real plane, we introduce a representation of improper points, i.e. points at infinity, in terms of Geometric Algebra for Conics (GAC) and offer possible use of both types of points. More precisely, we present two algorithms fitting a conic to a dataset with a certain number of points lying on the conic precisely, referred to as the waypoints. Furthermore, we consider inclusion of one or two improper waypoints, which leads to the asymptotic directions of the fitted conic. The number of used waypoints may be up to four and we classify all the cases.</p></div>","PeriodicalId":7330,"journal":{"name":"Advances in Applied Clifford Algebras","volume":"34 1","pages":""},"PeriodicalIF":1.5,"publicationDate":"2024-01-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139400393","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
An Extension of Slice Regular Functions in Terms of Fiber Bundle Theory 从纤维束理论看片正则函数的扩展
IF 1.5 2区 数学
Advances in Applied Clifford Algebras Pub Date : 2024-01-08 DOI: 10.1007/s00006-023-01309-4
J. Oscar González-Cervantes
{"title":"An Extension of Slice Regular Functions in Terms of Fiber Bundle Theory","authors":"J. Oscar González-Cervantes","doi":"10.1007/s00006-023-01309-4","DOIUrl":"10.1007/s00006-023-01309-4","url":null,"abstract":"<div><p>This work presents an extension, called coordinate slice extension, of the union of a finite number of axially symmetric s domains according to the fiber bundle theory and a kind of slice regular functions are defined on this coordinate slice extension.</p></div>","PeriodicalId":7330,"journal":{"name":"Advances in Applied Clifford Algebras","volume":"34 1","pages":""},"PeriodicalIF":1.5,"publicationDate":"2024-01-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139400249","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
Concept of s-Numbers in Quaternionic Analysis and Schatten Classes 四元分析中的 s 数概念和沙腾类
IF 1.5 2区 数学
Advances in Applied Clifford Algebras Pub Date : 2023-12-30 DOI: 10.1007/s00006-023-01311-w
João Costa
{"title":"Concept of s-Numbers in Quaternionic Analysis and Schatten Classes","authors":"João Costa","doi":"10.1007/s00006-023-01311-w","DOIUrl":"10.1007/s00006-023-01311-w","url":null,"abstract":"<div><p>In this paper we introduce an axiomatic approach to the theory of s-numbers in quaternionic analysis. To this end, Pietsch’s approach to s-number theory is adapted to the quaternionic framework, following the works of Colombo and Sabadini on quaternionic spectral analysis. One of the main results of this paper is the uniqueness of s-numbers over quaternionic Hilbert spaces. Moreover, examples are given in the quaternionic framework together with the introduction of nuclear numbers. A consequence of the presented theory is a basis independent definition of the Schatten classes over quaternionic Hilbert and Banach spaces.</p></div>","PeriodicalId":7330,"journal":{"name":"Advances in Applied Clifford Algebras","volume":"34 1","pages":""},"PeriodicalIF":1.5,"publicationDate":"2023-12-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00006-023-01311-w.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139060443","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
New Versions of the Plemelj–Sochocki Formula in Clifford Analysis 克利福德分析中普莱梅利-索霍基公式的新版本
IF 1.5 2区 数学
Advances in Applied Clifford Algebras Pub Date : 2023-12-26 DOI: 10.1007/s00006-023-01310-x
Yufeng Wang, Zhongxiang Zhang
{"title":"New Versions of the Plemelj–Sochocki Formula in Clifford Analysis","authors":"Yufeng Wang,&nbsp;Zhongxiang Zhang","doi":"10.1007/s00006-023-01310-x","DOIUrl":"10.1007/s00006-023-01310-x","url":null,"abstract":"<div><p>In this paper, we give some new versions of the Plemelj–Sochocki formula under weaker condition in real Clifford Analysis which are different from the result in Luo and Du (Adv Appl Clifford Algebras 27:2531-2583, 2017). By the new versions of the Plemelj–Sochocki formula, we can give a different proof of the generalized Plemelj–Sochocki formula for the symmetric difference of boundary values, which is obtained in Luo and Du (2017), the classical Plemelj–Sochocki formula can be also derived.</p></div>","PeriodicalId":7330,"journal":{"name":"Advances in Applied Clifford Algebras","volume":"34 1","pages":""},"PeriodicalIF":1.5,"publicationDate":"2023-12-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139041333","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
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