Advances in Applied Clifford Algebras最新文献_第2页

Sliding Mode Control of Switched Hamiltonian Systems: A Geometric Algebra Approach 切换哈密顿系统的滑模控制：一种几何代数方法

IF 1.1 2区数学

Advances in Applied Clifford Algebras Pub Date : 2025-04-12 DOI: 10.1007/s00006-025-01380-z

H. Sira-Ramírez, B. C. Gómez-León, M. A. Aguilar-Orduña

{"title":"Sliding Mode Control of Switched Hamiltonian Systems: A Geometric Algebra Approach","authors":"H. Sira-Ramírez, B. C. Gómez-León, M. A. Aguilar-Orduña","doi":"10.1007/s00006-025-01380-z","DOIUrl":"10.1007/s00006-025-01380-z","url":null,"abstract":"<div>In this article, a Geometric Algebra (GA) and Geometric Calculus (GC) based exposition is carried out dealing with the formal characterization of sliding regimes for general Single-Input-Single-Output (SISO) nonlinear switched controlled Hamiltonian systems. Necessary and sufficient conditions for the local existence of a sliding regime on a given vector manifold are presented. Feedback controller design strategies for achieving local sliding regimes on a given smooth vector manifold—defined in the phase space of the system—are also derived using the GA-GC framework. One such controller design method, which is mathematically justified, is based on the invariance property of the leaves of the foliation induced by the sliding surface coordinate function level sets. The idealized average smooth sliding motions are shown to arise from an extrinsic projection operator whose geometric properties are exploited for characterizing robustness with respect to unknown exogenous perturbation vector fields. An application example is provided from the power electronics area.</div>","PeriodicalId":7330,"journal":{"name":"Advances in Applied Clifford Algebras","volume":"35 2","pages":""},"PeriodicalIF":1.1,"publicationDate":"2025-04-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00006-025-01380-z.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143824592","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 Second Order Elliptic Systems of Partial Differential Equations in Clifford Analysis 二阶椭圆型偏微分方程组的Clifford分析

IF 1.1 2区数学

Advances in Applied Clifford Algebras Pub Date : 2025-04-08 DOI: 10.1007/s00006-025-01377-8

Daniel Alfonso Santiesteban, Ricardo Abreu Blaya, Juan Bory Reyes

引用次数: 0

Quaternionic Generalized Norm Retrieval in Quaternion Euclidean Spaces 四元数欧几里得空间中的四元数广义范数检索

IF 1.1 2区数学

Advances in Applied Clifford Algebras Pub Date : 2025-04-04 DOI: 10.1007/s00006-025-01381-y

Ming Yang, Yun-Zhang Li

{"title":"Quaternionic Generalized Norm Retrieval in Quaternion Euclidean Spaces","authors":"Ming Yang, Yun-Zhang Li","doi":"10.1007/s00006-025-01381-y","DOIUrl":"10.1007/s00006-025-01381-y","url":null,"abstract":"<div>Quaternion algebra (mathbb {H}) is a noncommutative associative algebra, and recently quaternionic Fourier analysis has become the focus of an active research due to their potentials in signal analysis and color image processing. The problems related to quaternions are nontrivial and challenging due to noncommutativity of quaternion multiplication. This paper is devoted to establishing the framework of quaternionic generalized norm retrieval (QGNR) in quaternion Euclidean spaces (mathbb {H}^{M}). We introduce the concept of QGNR in (mathbb {H}^{M}) that is defined for general quaternionic self-adjoint matrix sequences. Recall that, even in (mathbb {C}^{M}) ((mathbb {R}^{M}))-setting, the existing literature on norm retrieval problems is only for orthogonal projection matrix sequences instead of general self-adjoint matrix sequences. We characterize QGNR-sequences in terms of their phaselift operators and induced real matrices, present an Edidin type theorem on QGNR for (mathbb {H}^{M}), and investigate the topological property of QGNR-sequences. Finally, we turn to constructing more QGNR-sequences. We prove that a quaternionic self-adjoint matrix sequence (mathcal {F}={F_{n}}_{nin mathbb {N}_{N}}) is such that all ({TF_{n}T^{*}}_{nin mathbb {N}_{N}}) with quaternionic invertible matrices T allow QGNR for (mathbb {H}^{M}) if and only if (mathcal {F}) allows quaternionic generalized phase retrieval, and characterize quaternionic generalized norm retrieval multipliers that transform every QGNR-sequence into another QGNR-sequence.</div>","PeriodicalId":7330,"journal":{"name":"Advances in Applied Clifford Algebras","volume":"35 2","pages":""},"PeriodicalIF":1.1,"publicationDate":"2025-04-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143775921","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 Generalized Eigenvector–Eigenvalue Identity from the Viewpoint of Exterior Algebra 外代数视域下的广义特征向量-特征值恒等式

IF 1.1 2区数学

Advances in Applied Clifford Algebras Pub Date : 2025-02-26 DOI: 10.1007/s00006-025-01375-w

Małgorzata Stawiska

引用次数: 0

General Aspects of Jackson Calculus in Clifford Analysis Clifford分析中Jackson微积分的一般问题

IF 1.1 2区数学

Advances in Applied Clifford Algebras Pub Date : 2025-02-25 DOI: 10.1007/s00006-025-01374-x

Martha Lina Zimmermann, Swanhild Bernstein, Baruch Schneider

{"title":"General Aspects of Jackson Calculus in Clifford Analysis","authors":"Martha Lina Zimmermann, Swanhild Bernstein, Baruch Schneider","doi":"10.1007/s00006-025-01374-x","DOIUrl":"10.1007/s00006-025-01374-x","url":null,"abstract":"<div>We consider an extension of Jackson calculus into higher dimensions and specifically into Clifford analysis for the case of commuting variables. In this case, Dirac is the operator of the first q-partial derivatives (or q-differences) ({_{q}}mathbf {mathcal {D}}= sum _{i=1}^n e_i,{_{q}}partial _i), where ({_{q}}partial _i) denotes the q-partial derivative with respect to (x_i). This Dirac operator factorizes the q-deformed Laplace operator. Similar to the case of classical Clifford analysis, we then consider the q-deformed Euler and Gamma operators and their relations to each other. Nullsolutions of this q-Dirac equation are called q-monogenic. Using the Fischer decomposition, we can decompose the space of homogeneous polynomials into spaces of q-monogenic polynomials. Using the q-deformed Cauchy–Kovalevskaya extension theorem, we can construct q-monogenic functions. Overall, we show the analogies and the differences between classical Clifford and Jackson-Clifford analysis. In particular, q-monogenic functions need not be monogenic and vice versa.</div>","PeriodicalId":7330,"journal":{"name":"Advances in Applied Clifford Algebras","volume":"35 2","pages":""},"PeriodicalIF":1.1,"publicationDate":"2025-02-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00006-025-01374-x.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143480923","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

Branching of Weil Representation for (G_2) 的分支表示 $$G_2$$

IF 1.1 2区数学

Advances in Applied Clifford Algebras Pub Date : 2025-01-29 DOI: 10.1007/s00006-025-01370-1

Zhiqiang Wang, Xingya Fan

引用次数: 0

Cubic Dirac operator for (U_q({mathfrak {sl}}_2)) 的三次狄拉克算子 $$U_q({mathfrak {sl}}_2)$$

IF 1.1 2区数学

Advances in Applied Clifford Algebras Pub Date : 2025-01-22 DOI: 10.1007/s00006-025-01372-z

Andrey Krutov, Pavle Pandžić

引用次数: 0

The Wigner Little Group for Photons is a Projective Subalgebra 光子的Wigner小群是一个射影子代数

IF 1.1 2区数学

Advances in Applied Clifford Algebras Pub Date : 2025-01-21 DOI: 10.1007/s00006-025-01369-8

Moab Croft, Hamish Todd, Edward Corbett

{"title":"The Wigner Little Group for Photons is a Projective Subalgebra","authors":"Moab Croft, Hamish Todd, Edward Corbett","doi":"10.1007/s00006-025-01369-8","DOIUrl":"10.1007/s00006-025-01369-8","url":null,"abstract":"<div>This paper presents the Geometric Algebra approach to the Wigner little group for photons using the Spacetime Algebra, incorporating a mirror-based view for physical interpretation. The shift from a point-based view to a mirror-based view is a modern movement that allows for a more intuitive representation of geometric and physical entities, with vectors and their higher-grade counterparts viewed as hyperplanes. This reinterpretation simplifies the implementation of homogeneous representations of geometric objects within the Spacetime Algebra and enables a relative view via projective geometry. Then, after utilizing the intrinsic properties of Geometric Algebra, the Wigner little group is seen to induce a projective geometric algebra as a subalgebra of the Spacetime Algebra. However, the dimension-agnostic nature of Geometric Algebra enables the generalization of induced subalgebras to ((1+n))-dimensional Minkowski geometric algebras, termed little photon algebras. The lightlike transformations (translations) in these little photon algebras are seen to leave invariant the (pseudo)canonical electromagetic field bivector. Geometrically, this corresponds to Lorentz transformations that do not change the intersection of the spacelike polarization hyperplane with the lightlike wavevector hyperplane while simultaneously not affecting the lightlike wavevector hyperplane. This provides for a framework that unifies the analysis of symmetries and substructures of point-based Geometric Algebra with mirror-based Geometric Algebra.</div>","PeriodicalId":7330,"journal":{"name":"Advances in Applied Clifford Algebras","volume":"35 1","pages":""},"PeriodicalIF":1.1,"publicationDate":"2025-01-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142991449","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

H-B Theorems of Cauchy Integral Operators in Clifford Analysis Clifford分析中Cauchy积分算子的H-B定理

IF 1.1 2区数学

Advances in Applied Clifford Algebras Pub Date : 2025-01-18 DOI: 10.1007/s00006-025-01371-0

Yufeng Wang, Zhongxiang Zhang

引用次数: 0

Multicomplex Ideals, Modules and Hilbert Spaces 多复理想、模与希尔伯特空间

IF 1.1 2区数学

Advances in Applied Clifford Algebras Pub Date : 2025-01-17 DOI: 10.1007/s00006-025-01373-y

Derek Courchesne, Sébastien Tremblay

引用次数: 0