发布求助
文献互助 智能选刊 最新文献

Advances in Applied Clifford Algebras最新文献

筛选
英文 中文
Fractional Powers of the Quaternionic d-Bar Derivative 四元数d-Bar导数的分数次幂
IF 1.5 2区 数学
Advances in Applied Clifford Algebras Pub Date : 2023-11-28 DOI: 10.1007/s00006-023-01306-7
Arran Fernandez, Cihan Güder, Walaa Yasin
{"title":"Fractional Powers of the Quaternionic d-Bar Derivative","authors":"Arran Fernandez,&nbsp;Cihan Güder,&nbsp;Walaa Yasin","doi":"10.1007/s00006-023-01306-7","DOIUrl":"10.1007/s00006-023-01306-7","url":null,"abstract":"<div><p>This work introduces fractional d-bar derivatives in the setting of quaternionic analysis, by giving meaning to fractional powers of the quaternionic d-bar derivative. The definition is motivated by starting from <i>n</i>th-order d-bar derivatives for <span>(nin {mathbb {N}})</span>, and further justified by various natural properties such as composition laws and its action on special functions such as Fueter polynomials.</p></div>","PeriodicalId":7330,"journal":{"name":"Advances in Applied Clifford Algebras","volume":"34 1","pages":""},"PeriodicalIF":1.5,"publicationDate":"2023-11-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138449100","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 Algebra Speaks Quantum Esperanto 几何代数讲量子世界语
IF 1.5 2区 数学
Advances in Applied Clifford Algebras Pub Date : 2023-11-11 DOI: 10.1007/s00006-023-01304-9
Sebastian Xambó-Descamps
{"title":"Geometric Algebra Speaks Quantum Esperanto","authors":"Sebastian Xambó-Descamps","doi":"10.1007/s00006-023-01304-9","DOIUrl":"10.1007/s00006-023-01304-9","url":null,"abstract":"<div><p>The goal of this paper is to elucidate the hermitian structure of the algebra of geometric quaternions <span>({textbf {H}})</span> (that is, the even algebra of the geometric algebra of the euclidean 3d space), use it to couch a geometric and dynamical presentation of the <i>q</i>-bit, and to see its bearing on the geometric structure of <i>q</i>-registers (arrangements of finite number of <i>q</i>-bits) and with that to pay a brief revisit to the formal structure of <i>q</i>-computations, with emphasis on the <i>algebra</i> structure of <span>(textbf{H}^{otimes n})</span>. The main underlying theme is the unraveling of the subtle geometric relations between <span>(textbf{H})</span> and the sphere <span>(S^2)</span> in the 3d euclidean space.</p></div>","PeriodicalId":7330,"journal":{"name":"Advances in Applied Clifford Algebras","volume":"34 1","pages":""},"PeriodicalIF":1.5,"publicationDate":"2023-11-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72365059","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
General Right-Sided Orthogonal 2D-Planes Split Quaternionic Wave-Packet Transform 一般右侧正交二维平面分割四元数波包变换
IF 1.5 2区 数学
Advances in Applied Clifford Algebras Pub Date : 2023-10-23 DOI: 10.1007/s00006-023-01303-w
Hakim Monaim, Said Fahlaoui
{"title":"General Right-Sided Orthogonal 2D-Planes Split Quaternionic Wave-Packet Transform","authors":"Hakim Monaim,&nbsp;Said Fahlaoui","doi":"10.1007/s00006-023-01303-w","DOIUrl":"10.1007/s00006-023-01303-w","url":null,"abstract":"<div><p>In this paper, we present the general right-sided quaternionic orthogonal 2D-planes split wave-packet transform that combines windowed and wavelet transforms. We derive fundamental properties: Plancherel–Parseval theorems, reconstruction formulas, and orthogonality relations, and we provide characterization range, convolutions, and some estimates. Additionally, we derive component-wise, directional and logarithmic uncertainty principles for the given transform and give a discrete formula on the square-integrable function space.\u0000</p></div>","PeriodicalId":7330,"journal":{"name":"Advances in Applied Clifford Algebras","volume":"33 5","pages":""},"PeriodicalIF":1.5,"publicationDate":"2023-10-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50509026","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 (mathcal {L_C})-Structure-Preserving Algorithms of Quaternion (LDL^H) Decomposition and Cholesky Decomposition 四元数分解和Cholesky分解的保结构算法
IF 1.5 2区 数学
Advances in Applied Clifford Algebras Pub Date : 2023-10-16 DOI: 10.1007/s00006-023-01298-4
Mingcui Zhang, Ying Li, Jianhua Sun, Wenxv Ding
{"title":"The (mathcal {L_C})-Structure-Preserving Algorithms of Quaternion (LDL^H) Decomposition and Cholesky Decomposition","authors":"Mingcui Zhang,&nbsp;Ying Li,&nbsp;Jianhua Sun,&nbsp;Wenxv Ding","doi":"10.1007/s00006-023-01298-4","DOIUrl":"10.1007/s00006-023-01298-4","url":null,"abstract":"<div><p>In this paper, the <span>(mathcal {L_C})</span>-structure-preserving algorithms of <span>(LDL^H)</span> decomposition and Cholesky decomposition of quaternion Hermitian positive definite matrices based on the semi-tensor product of matrices are studied. We first propose <span>(mathcal {L_C})</span>-representation by using the semi-tensor product of matries and the structure matrix of the product of the quaternion. Then, <span>(mathcal {L_C})</span>-structure-preserving algorithms of <span>(LDL^H)</span> decomposition and Cholesky decomposition of quaternion Hermitian positive definite matrices are proposed by using <span>(mathcal {L_C})</span>-representation, and the advantages of our method are obtained by comparing the operation time and error with the real structure-preserving algorithms in Wei et al. (Quaternion matrix computations. Nova Science Publishers, Hauppauge, 2018). Finally, we apply the <span>(mathcal {L_C})</span>-structure-preserving algorithm of Cholesky decomposition to strict authentication of color images.</p></div>","PeriodicalId":7330,"journal":{"name":"Advances in Applied Clifford Algebras","volume":"33 5","pages":""},"PeriodicalIF":1.5,"publicationDate":"2023-10-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50487941","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
Dual Boas Type Results for the Quaternion Transform and Generalized Lipschitz Spaces 四元数变换与广义Lipschitz空间的对偶Boas型结果
IF 1.5 2区 数学
Advances in Applied Clifford Algebras Pub Date : 2023-10-14 DOI: 10.1007/s00006-023-01301-y
Sergey Volosivets
{"title":"Dual Boas Type Results for the Quaternion Transform and Generalized Lipschitz Spaces","authors":"Sergey Volosivets","doi":"10.1007/s00006-023-01301-y","DOIUrl":"10.1007/s00006-023-01301-y","url":null,"abstract":"<div><p>For the quaternion algebra <span>({mathbb {H}})</span> and <span>(f:mathbb R^2rightarrow {mathbb {H}})</span>, we consider a two-sided quaternion Fourier transform <span>({widehat{f}})</span>. Necessary and sufficient conditions for <span>({widehat{f}})</span> to belong to generalized uniform Lipschitz spaces are given in terms of behavior of <i>f</i>.</p></div>","PeriodicalId":7330,"journal":{"name":"Advances in Applied Clifford Algebras","volume":"33 5","pages":""},"PeriodicalIF":1.5,"publicationDate":"2023-10-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50482888","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
Spinorial Representation of Submanifolds in a Product of Space Forms 空间形式乘积中子流形的自旋表示
IF 1.5 2区 数学
Advances in Applied Clifford Algebras Pub Date : 2023-10-11 DOI: 10.1007/s00006-023-01302-x
Alicia Basilio, Pierre Bayard, Marie-Amélie Lawn, Julien Roth
{"title":"Spinorial Representation of Submanifolds in a Product of Space Forms","authors":"Alicia Basilio,&nbsp;Pierre Bayard,&nbsp;Marie-Amélie Lawn,&nbsp;Julien Roth","doi":"10.1007/s00006-023-01302-x","DOIUrl":"10.1007/s00006-023-01302-x","url":null,"abstract":"<div><p>We present a method giving a spinorial characterization of an immersion into a product of spaces of constant curvature. As a first application we obtain a proof using spinors of the fundamental theorem of immersion theory for such target spaces. We also study special cases: we recover previously known results concerning immersions in <span>(mathbb {S}^2times mathbb {R})</span> and we obtain new spinorial characterizations of immersions in <span>(mathbb {S}^2times mathbb {R}^2)</span> and in <span>(mathbb {H}^2times mathbb {R}.)</span> We then study the theory of <span>(H=1/2)</span> surfaces in <span>(mathbb {H}^2times mathbb {R})</span> using this spinorial approach, obtain new proofs of some of its fundamental results and give a direct relation with the theory of <span>(H=1/2)</span> surfaces in <span>(mathbb {R}^{1,2})</span>.</p></div>","PeriodicalId":7330,"journal":{"name":"Advances in Applied Clifford Algebras","volume":"33 5","pages":""},"PeriodicalIF":1.5,"publicationDate":"2023-10-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00006-023-01302-x.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50472731","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
(Anti) de Sitter Geometry, Complex Conformal Gravity-Maxwell Theory from a Cl(4, C) Gauge Theory of Gravity and Grand Unification 从Cl（4，C）规范理论看（反）de Sitter几何、复共形引力Maxwell理论
IF 1.5 2区 数学
Advances in Applied Clifford Algebras Pub Date : 2023-09-18 DOI: 10.1007/s00006-023-01299-3
Carlos Castro Perelman
{"title":"(Anti) de Sitter Geometry, Complex Conformal Gravity-Maxwell Theory from a Cl(4, C) Gauge Theory of Gravity and Grand Unification","authors":"Carlos Castro Perelman","doi":"10.1007/s00006-023-01299-3","DOIUrl":"10.1007/s00006-023-01299-3","url":null,"abstract":"<div><p>We present the deep connections among (Anti) de Sitter geometry, and complex conformal gravity-Maxwell theory, stemming directly from a gauge theory of gravity based on the complex Clifford algebra <i>Cl</i>(4, <i>C</i>). This is attained by simply <i>promoting</i> the de (Anti) Sitter algebras <i>so</i>(4, 1), <i>so</i>(3, 2) to the real Clifford algebras <i>Cl</i>(4, 1, <i>R</i>), <i>Cl</i>(3, 2, <i>R</i>), respectively. This interplay between gauge theories of gravity based on <i>Cl</i>(4, 1, <i>R</i>), <i>Cl</i>(3, 2, <i>R</i>) , whose bivector-generators encode the de (Anti) Sitter algebras <i>so</i>(4, 1), <i>so</i>(3, 2), respectively, and 4<i>D</i> conformal gravity based on <i>Cl</i>(3, 1, <i>R</i>) is reminiscent of the <span>(AdS_{ D+1}/CFT_D)</span> correspondence between <span>(D+1)</span>-dim gravity in the bulk and conformal field theory in the <i>D</i>-dim boundary. Although a plausible cancellation mechanism of the cosmological constant terms appearing in the real-valued curvature components associated with complex conformal gravity is possible, it does <i>not</i> occur simultaneously in the imaginary curvature components. Nevertheless, by including a Lagrange multiplier term in the action, it is still plausible that one might be able to find a restricted set of on-shell field configurations leading to a cancellation of the cosmological constant in curvature-squared actions due to the coupling among the real and imaginary components of the vierbein. We finalize with a brief discussion related to <span>(U(4) times U(4))</span> grand-unification models with gravity based on <span>( Cl (5, C) = Cl(4,C) oplus Cl(4,C))</span>. It is plausible that these grand-unification models could also be traded for models based on <span>( GL (4, C) times GL(4, C) )</span>.</p></div>","PeriodicalId":7330,"journal":{"name":"Advances in Applied Clifford Algebras","volume":"33 5","pages":""},"PeriodicalIF":1.5,"publicationDate":"2023-09-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50494862","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 the Representations of Clifford and SO(1,9) Algebras for 8-Component Dirac Equation 关于8分量Dirac方程的Clifford和SO（1,9）代数的表示
IF 1.5 2区 数学
Advances in Applied Clifford Algebras Pub Date : 2023-09-04 DOI: 10.1007/s00006-023-01295-7
V. M. Simulik, I. I. Vyikon
{"title":"On the Representations of Clifford and SO(1,9) Algebras for 8-Component Dirac Equation","authors":"V. M. Simulik,&nbsp;I. I. Vyikon","doi":"10.1007/s00006-023-01295-7","DOIUrl":"10.1007/s00006-023-01295-7","url":null,"abstract":"<div><p>Extended gamma matrix Clifford–Dirac and SO(1,9) algebras in the terms of <span>(8 times 8)</span> matrices have been considered. The 256-dimensional gamma matrix representation of Clifford algebra for 8-component Dirac equation is suggested. Two isomorphic realizations <span>(textit{C}ell ^{texttt {R}})</span>(0,8) and <span>(textit{C}ell ^{texttt {R}})</span>(1,7) are considered. The corresponding gamma matrix representations of 45-dimensional SO(10) and SO(1,9) algebras, which contain standard and additional spin operators, are introduced as well. The SO(10), SO(1,9) and the corresponding <span>(textit{C}ell ^{texttt {R}})</span>(0,8)<span>(, textit{C}ell ^{texttt {R}})</span>(1,7) representations are determined as algebras over the field of real numbers. The suggested gamma matrix representations of the Lie algebras SO(10), SO(1,9) are constructed on the basis of the Clifford algebras <span>(textit{C}ell ^{texttt {R}})</span>(0,8)<span>(, textit{C}ell ^{texttt {R}})</span>(1,7) representations. Comparison with the corresponded algebras in the space of standard 4-component Dirac spinors is demonstrated. The proposed mathematical objects allow generalization of our results, obtained earlier for the standard Dirac equation, for equations of higher spin and, especially, for equations, describing particles with spin 3/2. The maximal 84-dimensional pure matrix algebra of invariance of the 8-component Dirac equation in the Foldy–Wouthuysen representation is found. The corresponding symmetry of the Dirac equation in ordinary representation is found as well. The possible generalizations of considered Lie algebras to the arbitrary dimensional SO(n) and SO(m,n) are discussed briefly.</p></div>","PeriodicalId":7330,"journal":{"name":"Advances in Applied Clifford Algebras","volume":"33 5","pages":""},"PeriodicalIF":1.5,"publicationDate":"2023-09-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48923275","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
Series Representation of Solutions of Polynomial Dirac Equations 多项式狄拉克方程解的级数表示
IF 1.5 2区 数学
Advances in Applied Clifford Algebras Pub Date : 2023-09-04 DOI: 10.1007/s00006-023-01297-5
Doan Cong Dinh
{"title":"Series Representation of Solutions of Polynomial Dirac Equations","authors":"Doan Cong Dinh","doi":"10.1007/s00006-023-01297-5","DOIUrl":"10.1007/s00006-023-01297-5","url":null,"abstract":"<div><p>In this paper, we consider the polynomial Dirac equation <span>( left( D^m+sum _{i=0}^{m-1}a_iD^iright) u=0, (a_iin {mathbb {C}}))</span>, where <i>D</i> is the Dirac operator in <span>({mathbb {R}}^n)</span>. We introduce a method of using series to represent explicit solutions of the polynomial Dirac equations.</p></div>","PeriodicalId":7330,"journal":{"name":"Advances in Applied Clifford Algebras","volume":"33 5","pages":""},"PeriodicalIF":1.5,"publicationDate":"2023-09-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45557662","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 New Type of Quaternionic Regularity 一类新的四元数正则性
IF 1.5 2区 数学
Advances in Applied Clifford Algebras Pub Date : 2023-08-29 DOI: 10.1007/s00006-023-01292-w
A. Vajiac
{"title":"A New Type of Quaternionic Regularity","authors":"A. Vajiac","doi":"10.1007/s00006-023-01292-w","DOIUrl":"10.1007/s00006-023-01292-w","url":null,"abstract":"<div><p>I introduce a notion of quaternionic regularity using techniques based on hypertwined analysis, a refined version of general hypercomplex theory. In the quaternionic and biquaternionic cases, I show that hypertwined holomorphic (regular) functions admit a decomposition in a hypertwined sum of regular functions in certain subalgebras. The hypertwined quaternionic regularity lies in between slice regularity and the modified Cauchy–Fueter theories, and proves to have a direct impact on reformulations of quaternionic and spacetime algebra quantum theories.</p></div>","PeriodicalId":7330,"journal":{"name":"Advances in Applied Clifford Algebras","volume":"33 5","pages":""},"PeriodicalIF":1.5,"publicationDate":"2023-08-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00006-023-01292-w.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42111341","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
首页 上一页 下一页 尾页
0
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
提示
您的信息不完整，为了账户安全，请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
现在去查看 取消
×
提示
确定
请完成安全验证×
相关产品
×
本文献相关产品
联系我们：info@booksci.cn Book学术提供免费学术资源搜索服务，方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。 Copyright © 2023 布克学术 All rights reserved.
京ICP备2023020795号-1
ghs 京公网安备 11010802042870号
Book学术文献互助
Book学术文献互助群
群 号：481959085
Book学术官方微信