Advances in Applied Clifford Algebras最新文献

Slice Regular Holomorphic Cliffordian Functions of Order k

IF 1.1 2区数学

Advances in Applied Clifford Algebras Pub Date : 2025-04-25 DOI: 10.1007/s00006-025-01376-9

Giulio Binosi

引用次数: 0

Additive Preservers of Invertibility or Zero Divisors in Quaternionic Setting

IF 1.1 2区数学

Advances in Applied Clifford Algebras Pub Date : 2025-04-22 DOI: 10.1007/s00006-025-01383-w

El Miloud Ouahabi, Khalid Souilah

引用次数: 0

On Monogenic Functions and the Dirac Complex of Two Vector Variables

IF 1.1 2区数学

Advances in Applied Clifford Algebras Pub Date : 2025-04-12 DOI: 10.1007/s00006-025-01378-7

Yun Shi, Wei Wang, Qingyan Wu

引用次数: 0

Uncertainty Principles Associated with the Multi-dimensional Quaternionic Offset Linear Canonical Transform

IF 1.1 2区数学

Advances in Applied Clifford Algebras Pub Date : 2025-04-12 DOI: 10.1007/s00006-025-01379-6

Yingchun Jiang, Sihua Ling, Yan Tang

引用次数: 0

Sliding Mode Control of Switched Hamiltonian Systems: A Geometric Algebra Approach

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

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

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

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

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)

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