Advances in Applied Clifford Algebras最新文献_第4页

Hypercomplex Representation of Finite-Dimensional Unital Archimedean f-Algebras 有限维单元阿基米德 f 结构的超复数表示

IF 1.1 2区数学

Advances in Applied Clifford Algebras Pub Date : 2024-08-28 DOI: 10.1007/s00006-024-01352-9

Sayed Kossentini

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引用次数: 0

Geometric Structures on the Quaternionic Unit Ball and Slice Regular Möbius Transformations 四元单位球上的几何结构和切片正则莫比乌斯变换

IF 1.1 2区数学

Advances in Applied Clifford Algebras Pub Date : 2024-08-17 DOI: 10.1007/s00006-024-01343-w

Raul Quiroga-Barranco

引用次数: 0

Bounds for the Zeros of a Quaternionic Polynomial with Restricted Coefficients 具有受限系数的四元多项式的零点界限

IF 1.1 2区数学

Advances in Applied Clifford Algebras Pub Date : 2024-08-07 DOI: 10.1007/s00006-024-01344-9

Abdullah Mir, Abrar Ahmad

引用次数: 0

On the Construction of Beltrami Fields and Associated Boundary Value Problems 论贝尔特拉米场的构造及相关的边值问题

IF 1.1 2区数学

Advances in Applied Clifford Algebras Pub Date : 2024-08-01 DOI: 10.1007/s00006-024-01340-z

Pablo E. Moreira, Briceyda B. Delgado

引用次数: 0

Quaternionic Subspace Gabor Frames and Their Duals 四元子空间 Gabor 帧及其对偶

IF 1.1 2区数学

Advances in Applied Clifford Algebras Pub Date : 2024-07-14 DOI: 10.1007/s00006-024-01342-x

Yun-Zhang Li, Xiao-Li Zhang

引用次数: 0

On the Geometry of Quantum Spheres and Hyperboloids 论量子球和超球的几何学

IF 1.1 2区数学

Advances in Applied Clifford Algebras Pub Date : 2024-07-13 DOI: 10.1007/s00006-024-01339-6

Giovanni Landi, Chiara Pagani

引用次数: 0

Models of CR Manifolds and Their Symmetry Algebras CR 曼olds 的模型及其对称性代数

IF 1.1 2区数学

Advances in Applied Clifford Algebras Pub Date : 2024-07-05 DOI: 10.1007/s00006-024-01341-y

Jan Gregorovič, Martin Kolář, Francine Meylan, David Sykes

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引用次数: 0

A Multi-dimensional Unified Concavity and Convexity Detection Method Based on Geometric Algebra 基于几何代数的多维统一凹凸检测方法

IF 1.1 2区数学

Advances in Applied Clifford Algebras Pub Date : 2024-07-02 DOI: 10.1007/s00006-024-01332-z

Jiyi Zhang, Huanhuan Liu, Tianzi Wei, Ruitong Liu, Chunwang Jia, Fan Yang

{"title":"A Multi-dimensional Unified Concavity and Convexity Detection Method Based on Geometric Algebra","authors":"Jiyi Zhang, Huanhuan Liu, Tianzi Wei, Ruitong Liu, Chunwang Jia, Fan Yang","doi":"10.1007/s00006-024-01332-z","DOIUrl":"10.1007/s00006-024-01332-z","url":null,"abstract":"<div><p>Detecting the concavity and convexity of three-dimensional (3D) geometric objects is a well-established challenge in the realm of computer graphics. Serving as the cornerstone for various related graphics algorithms and operations, researchers have put forth numerous algorithms for discerning the concavity and convexity of such objects. The majority of existing methods primarily rely on Euclidean geometry, determining concavity and convexity by calculating the vertices of these objects. However, within the realm of Euclidean geometric space, there exists a lack of uniformity in the expression and calculation rules for geometric objects of differing dimensions. Consequently, distinct concavity and convexity detection algorithms must be tailored for geometric objects with varying dimensions. This approach inevitably results in heightened complexity and instability within the algorithmic structure. To address these aforementioned issues, this paper introduces geometric algebra theory into the domain of concavity and convexity detection within 3D spatial objects. With the algorithms devised in this study, it becomes feasible to detect concavity and convexity for geometric objects of varying dimensions, all based on a uniform set of criteria. In comparison to concavity-convexity detection algorithms grounded in Euclidean geometry, this research effectively streamlines the algorithmic structure.</p></div>","PeriodicalId":7330,"journal":{"name":"Advances in Applied Clifford Algebras","volume":"34 3","pages":""},"PeriodicalIF":1.1,"publicationDate":"2024-07-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141489601","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 Clifford Algebra of the Density Matrix: An Elementary Approach 密度矩阵的克利福德代数：初级方法

IF 1.1 2区数学

Advances in Applied Clifford Algebras Pub Date : 2024-06-29 DOI: 10.1007/s00006-024-01337-8

Pedro Amao, Hernan Castillo

引用次数: 0

Convex Characteristics of Quaternionic Positive Definite Functions on Abelian Groups 阿贝尔群上四元正定函数的凸特性

IF 1.1 2区数学

Advances in Applied Clifford Algebras Pub Date : 2024-06-25 DOI: 10.1007/s00006-024-01336-9

Jingning Liu, Zeping Zhu

引用次数: 0