Advances in Applied Clifford Algebras最新文献_第7页

Fourier-Poisson Transforms Associated with the Principal Series Representations of Sp(1, n) 与 Sp(1, n) 主数列表示相关的傅立叶-泊松变换

IF 1.1 2区数学

Advances in Applied Clifford Algebras Pub Date : 2024-05-28 DOI: 10.1007/s00006-024-01330-1

Xingya Fan, Jianxun He, Xiaoke Jia

引用次数: 0

Mobility Analysis of Multi-loop Coupling Mechanisms Using Geometric Algebra 利用几何代数分析多环耦合机制的流动性

IF 1.1 2区数学

Advances in Applied Clifford Algebras Pub Date : 2024-05-27 DOI: 10.1007/s00006-024-01329-8

Jinqun Guo, Yu Xiao, Qinchuan Li, Lingmin Xu, Xinxue Chai

引用次数: 0

On SVD and Polar Decomposition in Real and Complexified Clifford Algebras 论实数和复数克利福德代数中的 SVD 和极性分解

IF 1.1 2区数学

Advances in Applied Clifford Algebras Pub Date : 2024-05-27 DOI: 10.1007/s00006-024-01328-9

Dmitry Shirokov

引用次数: 0

Distribution Function and Nonincreasing Rearrangement of ({mathbb {B}}{mathbb {C}})-Valued Functions with ({mathbb {B}} {mathbb {C}})-Measure 有$${mathbb {B}}{mathbb {C}}$ 值函数的分布函数和非递增重排{{mathbb {C}}$ -度量

IF 1.1 2区数学

Advances in Applied Clifford Algebras Pub Date : 2024-05-18 DOI: 10.1007/s00006-024-01327-w

İlker Eryılmaz

引用次数: 0

Hausdorff–Young Inequalities for Fourier Transforms over Cayley–Dickson Algebras Cayley-Dickson 代数上傅立叶变换的 Hausdorff-Young 不等式

IF 1.1 2区数学

Advances in Applied Clifford Algebras Pub Date : 2024-05-10 DOI: 10.1007/s00006-024-01326-x

Shihao Fan, Guangbin Ren

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引用次数: 0

Machine Learning Clifford Invariants of ADE Coxeter Elements ADE Coxeter 元素的机器学习克利福德不变式

IF 1.1 2区数学

Advances in Applied Clifford Algebras Pub Date : 2024-05-04 DOI: 10.1007/s00006-024-01325-y

Siqi Chen, Pierre-Philippe Dechant, Yang-Hui He, Elli Heyes, Edward Hirst, Dmitrii Riabchenko

{"title":"Machine Learning Clifford Invariants of ADE Coxeter Elements","authors":"Siqi Chen, Pierre-Philippe Dechant, Yang-Hui He, Elli Heyes, Edward Hirst, Dmitrii Riabchenko","doi":"10.1007/s00006-024-01325-y","DOIUrl":"10.1007/s00006-024-01325-y","url":null,"abstract":"<div>There has been recent interest in novel Clifford geometric invariants of linear transformations. This motivates the investigation of such invariants for a certain type of geometric transformation of interest in the context of root systems, reflection groups, Lie groups and Lie algebras: the Coxeter transformations. We perform exhaustive calculations of all Coxeter transformations for (A_8), (D_8) and (E_8) for a choice of basis of simple roots and compute their invariants, using high-performance computing. This computational algebra paradigm generates a dataset that can then be mined using techniques from data science such as supervised and unsupervised machine learning. In this paper we focus on neural network classification and principal component analysis. Since the output—the invariants—is fully determined by the choice of simple roots and the permutation order of the corresponding reflections in the Coxeter element, we expect huge degeneracy in the mapping. This provides the perfect setup for machine learning, and indeed we see that the datasets can be machine learned to very high accuracy. This paper is a pump-priming study in experimental mathematics using Clifford algebras, showing that such Clifford algebraic datasets are amenable to machine learning, and shedding light on relationships between these novel and other well-known geometric invariants and also giving rise to analytic results.</div>","PeriodicalId":7330,"journal":{"name":"Advances in Applied Clifford Algebras","volume":"34 3","pages":""},"PeriodicalIF":1.1,"publicationDate":"2024-05-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00006-024-01325-y.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140845242","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

Exploring Quaternion Neural Network Loss Surfaces 探索四元数神经网络损失曲面

IF 1.1 2区数学

Advances in Applied Clifford Algebras Pub Date : 2024-04-24 DOI: 10.1007/s00006-024-01313-2

Jeremiah Bill, Bruce Cox

引用次数: 0

Fractional Elliptic Operators with Multiple Poles on Riemannian Manifold with Clifford Bundle 带克里福德束的黎曼曼体上具有多个极点的分数椭圆算子

IF 1.1 2区数学

Advances in Applied Clifford Algebras Pub Date : 2024-04-23 DOI: 10.1007/s00006-024-01318-x

Rami Ahmad El-Nabulsi, Waranont Anukool

引用次数: 0

Multidimensional Generalized Fractional ({pmb {S}}) Transform 多维广义分式 $${pmb {S}}$ 变换

IF 1.1 2区数学

Advances in Applied Clifford Algebras Pub Date : 2024-04-17 DOI: 10.1007/s00006-024-01317-y

Lakshmanan Subbiah, Roopkumar Rajakumar

{"title":"Multidimensional Generalized Fractional ({pmb {S}}) Transform","authors":"Lakshmanan Subbiah, Roopkumar Rajakumar","doi":"10.1007/s00006-024-01317-y","DOIUrl":"10.1007/s00006-024-01317-y","url":null,"abstract":"<div>In this paper, we introduce a new multidimensional fractional S transform (S_{phi ,varvec{alpha },lambda }) using a generalized fractional convolution (star _{varvec{alpha },lambda }) and a general window function (phi ) satisfying some admissibility condition. The value of (S_{phi ,varvec{alpha },lambda }f) is also written in the form of inner product of the input function f with a suitable function (phi _{textbf{t},textbf{u}}^{varvec{alpha }_{lambda }}). The representation of (S_{phi ,varvec{alpha },lambda }f) in terms of the generalized fractional convolution helps us to obtain the Parseval’s formula for (S_{phi ,varvec{alpha },lambda }) using the generalized fractional convolution theorem. Then, the inversion theorem is proved as a consequence of the Parseval’s identity. Using a generalized window function in the kernel of (S_{phi ,varvec{alpha },lambda }) gives option to choose window function whose Fourier transform as a compactly supported smooth function or a rapidly decreasing function. We also discuss about the characterization of range of (S_{phi ,varvec{alpha },lambda }) on (L^2(mathbb {R}^N, mathbb {C})). Finally, we extend the transform to a class of quaternion valued functions consistently.</div>","PeriodicalId":7330,"journal":{"name":"Advances in Applied Clifford Algebras","volume":"34 3","pages":""},"PeriodicalIF":1.1,"publicationDate":"2024-04-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140603899","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

A Note on Cohomology of Clifford Algebras 关于克利福德代数同调的说明

IF 1.1 2区数学

Advances in Applied Clifford Algebras Pub Date : 2024-04-09 DOI: 10.1007/s00006-024-01324-z

Bikram Banerjee, Goutam Mukherjee

引用次数: 0