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Advances in Applied Clifford Algebras最新文献

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Construction of an Infinite-Dimensional Family of Exact Solutions of a Three-Dimensional Biharmonic Equation by the Hypercomplex Method 用超复杂法构建三维双谐方程的无限维精确解族
IF 1.1 2区 数学
Advances in Applied Clifford Algebras Pub Date : 2024-11-25 DOI: 10.1007/s00006-024-01365-4
Vitalii Shpakivskyi
{"title":"Construction of an Infinite-Dimensional Family of Exact Solutions of a Three-Dimensional Biharmonic Equation by the Hypercomplex Method","authors":"Vitalii Shpakivskyi","doi":"10.1007/s00006-024-01365-4","DOIUrl":"10.1007/s00006-024-01365-4","url":null,"abstract":"<div><p>An infinite-dimensional family of exact solutions of a three-dimensional biharmonic equation was constructed by the hypercomplex method.</p></div>","PeriodicalId":7330,"journal":{"name":"Advances in Applied Clifford Algebras","volume":"35 1","pages":""},"PeriodicalIF":1.1,"publicationDate":"2024-11-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142694783","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
Eigenvalues of Quaternion Tensors: Properties, Algorithms and Applications 四元张量的特征值：特性、算法和应用
IF 1.1 2区 数学
Advances in Applied Clifford Algebras Pub Date : 2024-11-22 DOI: 10.1007/s00006-024-01366-3
Zhuo-Heng He, Ting-Ting Liu, Xiang-Xiang Wang
{"title":"Eigenvalues of Quaternion Tensors: Properties, Algorithms and Applications","authors":"Zhuo-Heng He,&nbsp;Ting-Ting Liu,&nbsp;Xiang-Xiang Wang","doi":"10.1007/s00006-024-01366-3","DOIUrl":"10.1007/s00006-024-01366-3","url":null,"abstract":"<div><p>In this paper, we investigate the eigenvalues of quaternion tensors under Einstein Product and their applications in color video processing. We present the Ger<span>(check{s})</span>gorin theorem for quaternion tensors. Furthermore, we have executed some experiments to validate the efficacy of our proposed theoretical framework and algorithms. Finally, we contemplate the application of this methodology in color video compression, in which the reconstruction of an approximate original image is achieved by computing a limited number of the largest eigenvalues, yielding a favorable outcome. In summary, by utilizing block tensors in its iterations, this method converges more rapidly to the desired eigenvalues and eigentensors, which significantly reduces the time required for videos compression.</p></div>","PeriodicalId":7330,"journal":{"name":"Advances in Applied Clifford Algebras","volume":"35 1","pages":""},"PeriodicalIF":1.1,"publicationDate":"2024-11-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142690705","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 Product of Two Oriented Points in Conformal Geometric Algebra 共形几何代数中两个定向点的几何积
IF 1.1 2区 数学
Advances in Applied Clifford Algebras Pub Date : 2024-11-15 DOI: 10.1007/s00006-024-01363-6
Eckhard Hitzer
{"title":"Geometric Product of Two Oriented Points in Conformal Geometric Algebra","authors":"Eckhard Hitzer","doi":"10.1007/s00006-024-01363-6","DOIUrl":"10.1007/s00006-024-01363-6","url":null,"abstract":"<div><p>We compute and explore the full geometric product of two oriented points in conformal geometric algebra <i>Cl</i>(4, 1) of three-dimensional Euclidean space. We comment on the symmetry of the various components, and state for all expressions also a representation in terms of point pair center and radius vectors.</p></div>","PeriodicalId":7330,"journal":{"name":"Advances in Applied Clifford Algebras","volume":"35 1","pages":""},"PeriodicalIF":1.1,"publicationDate":"2024-11-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142636951","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
Riemann–Hilbert Problems for Biaxially Symmetric Monogenic Functions in (mathbb {R}^{n}) Riemann-Hilbert Problems for Biaxially Symmetric Monogenic Functions in (mathbb {R}^{n})
IF 1.1 2区 数学
Advances in Applied Clifford Algebras Pub Date : 2024-11-13 DOI: 10.1007/s00006-024-01364-5
Dian Zuo, Min Ku, Fuli He
{"title":"Riemann–Hilbert Problems for Biaxially Symmetric Monogenic Functions in (mathbb {R}^{n})","authors":"Dian Zuo,&nbsp;Min Ku,&nbsp;Fuli He","doi":"10.1007/s00006-024-01364-5","DOIUrl":"10.1007/s00006-024-01364-5","url":null,"abstract":"<div><p>We are dedicated to addressing Riemann–Hilbert boundary value problems (RHBVPs) with variable coefficients, where the solutions are valued in the Clifford algebra of <span>(mathbb {R}_{0,n})</span>, for biaxially monogenic functions defined in the biaxially symmetric domains of the Euclidean space <span>(mathbb {R}^{n})</span>. Our research establishes the equivalence between RHBVPs for biaxially monogenic functions defined in biaxially domains and RHBVPs for generalized analytic functions on the complex plane. We derive explicit solutions and conditions for solvability of RHBVPs for biaxially monogenic functions. Additionally, we explore related Schwarz problems and RHBVPs for biaxially meta-monogenic functions.</p></div>","PeriodicalId":7330,"journal":{"name":"Advances in Applied Clifford Algebras","volume":"35 1","pages":""},"PeriodicalIF":1.1,"publicationDate":"2024-11-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142600706","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
Conics, Their Pencils and Intersections in Geometric Algebra 几何代数中的圆锥曲线、其铅笔和交点
IF 1.1 2区 数学
Advances in Applied Clifford Algebras Pub Date : 2024-11-05 DOI: 10.1007/s00006-024-01356-5
Clément Chomicki, Stéphane Breuils, Venceslas Biri, Vincent Nozick
{"title":"Conics, Their Pencils and Intersections in Geometric Algebra","authors":"Clément Chomicki,&nbsp;Stéphane Breuils,&nbsp;Venceslas Biri,&nbsp;Vincent Nozick","doi":"10.1007/s00006-024-01356-5","DOIUrl":"10.1007/s00006-024-01356-5","url":null,"abstract":"<div><p>This paper presents an approach for extracting points from conic intersections by using the concept of pencils. This method is based on QC2GA—the two-dimensional version of QCGA (Quadric Conformal Geometric Algebra)—that is demonstrated to be equivalent to GAC (Geometric Algebra for Conics). A new interpretation of QC2GA and its objects based on pencils of conics and point space elements is presented, enabling the creation, constraining, and exploitation of pencils of conics. A Geometric Algebra method for computing the discriminants and center point of a conic will also be presented, enabling the proposition of an algorithm for extracting points from a conic intersection object.</p></div>","PeriodicalId":7330,"journal":{"name":"Advances in Applied Clifford Algebras","volume":"35 1","pages":""},"PeriodicalIF":1.1,"publicationDate":"2024-11-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142579494","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
Fueter’s Theorem for One Class of Pseudoanalytic Functions 一类伪解析函数的 Fueter 定理
IF 1.1 2区 数学
Advances in Applied Clifford Algebras Pub Date : 2024-10-26 DOI: 10.1007/s00006-024-01361-8
Yuanyuan Han, Pan Lian
{"title":"Fueter’s Theorem for One Class of Pseudoanalytic Functions","authors":"Yuanyuan Han,&nbsp;Pan Lian","doi":"10.1007/s00006-024-01361-8","DOIUrl":"10.1007/s00006-024-01361-8","url":null,"abstract":"<div><p>In this paper, we extend Fueter’s theorem in hypercomplex function theory to encompass a class of pseudoanalytic functions associated with the main Vekua equation. This class includes Duffin’s <span>(mu )</span>-regular functions as special cases, which correspond to the Yukawa equation. As the parameter <span>(mu rightarrow 0)</span>, we recover the classical Fueter’s theorem.</p></div>","PeriodicalId":7330,"journal":{"name":"Advances in Applied Clifford Algebras","volume":"34 5","pages":""},"PeriodicalIF":1.1,"publicationDate":"2024-10-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142490663","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
Multivector Contractions Revisited, Part I 重温多向量收缩，第一部分
IF 1.1 2区 数学
Advances in Applied Clifford Algebras Pub Date : 2024-10-24 DOI: 10.1007/s00006-024-01357-4
André L. G. Mandolesi
{"title":"Multivector Contractions Revisited, Part I","authors":"André L. G. Mandolesi","doi":"10.1007/s00006-024-01357-4","DOIUrl":"10.1007/s00006-024-01357-4","url":null,"abstract":"<div><p>We reorganize, simplify and expand the theory of contractions or interior products of multivectors, and related topics like Hodge star duality. Many results are generalized and new ones are given, like: geometric characterizations of blade contractions and regressive products, higher-order graded Leibniz rules, determinant formulas, improved complex star operators, etc. Different contractions found in the literature are discussed and compared, in special those of Clifford Geometric Algebra. Applications of the theory are developed in a follow-up paper.</p></div>","PeriodicalId":7330,"journal":{"name":"Advances in Applied Clifford Algebras","volume":"34 5","pages":""},"PeriodicalIF":1.1,"publicationDate":"2024-10-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142488420","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
The Plemelj-Sokhotski Formulas Associated to the k-Cauchy-Fueter Operator 与 k-Cauchy-Fueter 算子相关的 Plemelj-Sokhotski 公式
IF 1.1 2区 数学
Advances in Applied Clifford Algebras Pub Date : 2024-10-21 DOI: 10.1007/s00006-024-01359-2
Haiyan Wang, Wei Xia
{"title":"The Plemelj-Sokhotski Formulas Associated to the k-Cauchy-Fueter Operator","authors":"Haiyan Wang,&nbsp;Wei Xia","doi":"10.1007/s00006-024-01359-2","DOIUrl":"10.1007/s00006-024-01359-2","url":null,"abstract":"<div><p>The Plemelj-Sokhotski formulas, which deal with limiting values of the Bochner-Martinelli type integral, are powerful tools for analyzing boundary value problems. This article aims to study the boundary behavior of the Bochner-Martinelli type integral formula for the <i>k</i>-Cauchy-Fueter operator. Specifically, we consider the Plemelj-Sokhotski formulas, which will extend the corresponding results in the complex analysis of several variables.</p></div>","PeriodicalId":7330,"journal":{"name":"Advances in Applied Clifford Algebras","volume":"34 5","pages":""},"PeriodicalIF":1.1,"publicationDate":"2024-10-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142453051","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
Multivector Contractions Revisited, Part II 重温多向量收缩，第二部分
IF 1.1 2区 数学
Advances in Applied Clifford Algebras Pub Date : 2024-10-19 DOI: 10.1007/s00006-024-01358-3
André L. G. Mandolesi
{"title":"Multivector Contractions Revisited, Part II","authors":"André L. G. Mandolesi","doi":"10.1007/s00006-024-01358-3","DOIUrl":"10.1007/s00006-024-01358-3","url":null,"abstract":"<div><p>The theory of contractions of multivectors, and star duality, was reorganized in a previous article, and here we present some applications. First, we study inner and outer spaces associated to a general multivector <i>M</i> via the equations <span>(v wedge M = 0)</span> and <span>(v mathbin {lrcorner }M=0)</span>. They are then used to analyze special decompositions, factorizations and ‘carvings’ of <i>M</i>, to define generalized grades, and to obtain new simplicity criteria, including a reduced set of Plücker-like relations. We also discuss how contractions are related to supersymmetry, and give formulas for supercommutators of multi-fermion creation and annihilation operators.</p></div>","PeriodicalId":7330,"journal":{"name":"Advances in Applied Clifford Algebras","volume":"34 5","pages":""},"PeriodicalIF":1.1,"publicationDate":"2024-10-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142451090","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
Scaled Global Operators and Fueter Variables on Non-zero Scaled Hypercomplex Numbers 非零标度超复数上的标度全局算子和 Fueter 变量
IF 1.1 2区 数学
Advances in Applied Clifford Algebras Pub Date : 2024-10-15 DOI: 10.1007/s00006-024-01347-6
Daniel Alpay, Ilwoo Cho, Mihaela Vajiac
{"title":"Scaled Global Operators and Fueter Variables on Non-zero Scaled Hypercomplex Numbers","authors":"Daniel Alpay,&nbsp;Ilwoo Cho,&nbsp;Mihaela Vajiac","doi":"10.1007/s00006-024-01347-6","DOIUrl":"10.1007/s00006-024-01347-6","url":null,"abstract":"<div><p>In this paper we describe the rise of global operators in the scaled quaternionic case, an important extension from the quaternionic case to the family of scaled hypercomplex numbers <span>(mathbb {H}_t,, tin mathbb {R}^*)</span>, of which the <span>(mathbb {H}_{-1}=mathbb {H})</span> is the space of quaternions and <span>(mathbb {H}_{1})</span> is the space of split quaternions. We also describe the scaled Fueter-type variables associated to these operators, developing a coherent theory in this field. We use these types of variables to build different types of function spaces on <span>(mathbb {H}_t)</span>. Counterparts of the Hardy space and of the Arveson space are also introduced and studied in the present setting. The two different adjoints in the scaled hypercomplex numbers lead to two parallel cases in each instance. Finally we introduce and study the notion of rational function.</p></div>","PeriodicalId":7330,"journal":{"name":"Advances in Applied Clifford Algebras","volume":"34 5","pages":""},"PeriodicalIF":1.1,"publicationDate":"2024-10-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00006-024-01347-6.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142434955","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
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