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Advances in Applied Clifford Algebras最新文献

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A New Complex Structure-Preserving Quaternion Implicit Double Shift QR Algorithm 一种新的复杂保结构四元数隐式双移位QR算法
IF 1.2 2区 数学
Advances in Applied Clifford Algebras Pub Date : 2026-02-04 DOI: 10.1007/s00006-025-01424-4
Jianhua Sun, Ying Li, Mingcui Zhang, Musheng Wei
{"title":"A New Complex Structure-Preserving Quaternion Implicit Double Shift QR Algorithm","authors":"Jianhua Sun,&nbsp;Ying Li,&nbsp;Mingcui Zhang,&nbsp;Musheng Wei","doi":"10.1007/s00006-025-01424-4","DOIUrl":"10.1007/s00006-025-01424-4","url":null,"abstract":"<div><p>In this paper, we study an effective algorithm for the Schur decomposition of a quaternion matrix. Firstly, we give a complex structure-preserving algorithm for the Hessenberg decomposition of a quaternion matrix by Householder transformation. Secondly, we implement the implicit double shift QR strategy on the obtained Hessenberg matrix, and design the corresponding complex structure-preserving algorithm. Moreover, the effectiveness of the newly proposed algorithm is verified by numerical experiments. At last, the proposed algorithm is used to deal with a blind color image watermarking problem.</p></div>","PeriodicalId":7330,"journal":{"name":"Advances in Applied Clifford Algebras","volume":"36 2","pages":""},"PeriodicalIF":1.2,"publicationDate":"2026-02-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146138558","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
Construction of Special Conics in Pencils of Conics Using Geometric Algebra for Conics 用几何代数构造二次曲线铅笔中的特殊二次曲线
IF 1.2 2区 数学
Advances in Applied Clifford Algebras Pub Date : 2026-02-02 DOI: 10.1007/s00006-025-01434-2
Pavel Loučka
{"title":"Construction of Special Conics in Pencils of Conics Using Geometric Algebra for Conics","authors":"Pavel Loučka","doi":"10.1007/s00006-025-01434-2","DOIUrl":"10.1007/s00006-025-01434-2","url":null,"abstract":"<div><p>We present the ways of constructing special subsets of conics present in the pencils of conics using Geometric Algebra for Conics (GAC). In particular, we offer geometrically oriented approaches to obtain the line-pairs and generalised parabolas that can be found in the pencils, by applying the tools of GAC and the classical theory of projective conics. In addition, we also describe the construction of a conic passing through five points and, throughout the work, we demonstrate the usage of points at infinity in the mentioned problems as well. The text is accompanied by examples with corresponding figures and includes a partial classification of some of the cases one may encounter in the topic.</p></div>","PeriodicalId":7330,"journal":{"name":"Advances in Applied Clifford Algebras","volume":"36 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2026-02-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00006-025-01434-2.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146101460","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
Quadratic Motion Polynomials with Irregular Factorizations 具有不规则分解的二次运动多项式
IF 1.2 2区 数学
Advances in Applied Clifford Algebras Pub Date : 2026-01-24 DOI: 10.1007/s00006-025-01426-2
Daren A. Thimm, Zijia Li, Hans-Peter Schröcker, Johannes Siegele
{"title":"Quadratic Motion Polynomials with Irregular Factorizations","authors":"Daren A. Thimm,&nbsp;Zijia Li,&nbsp;Hans-Peter Schröcker,&nbsp;Johannes Siegele","doi":"10.1007/s00006-025-01426-2","DOIUrl":"10.1007/s00006-025-01426-2","url":null,"abstract":"<div><p>Motion polynomials are a specific type of polynomial over a Clifford algebra that can conveniently describe rational motions. There exists an algorithm for the factorization of motion polynomials that works in generic cases. It hinges on the invertibility of a certain coefficient occurring in the algorithm. If this coefficient is not invertible, factorizations may or may not exist. In the case of existence we call this an irregular factorization. We characterize quadratic motion polynomials with irregular factorizations in terms of algebraic equations and present examples whose number of unique factorizations range from one to infinitely many. For two special sub-cases we show the unique existence of such polynomials. In case of commuting factors we obtain the conformal Villarceau motion, in case of rigid body motions the circular translation.</p></div>","PeriodicalId":7330,"journal":{"name":"Advances in Applied Clifford Algebras","volume":"36 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2026-01-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00006-025-01426-2.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146048532","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
Restricted Quaternion Two-Sided Matrix Equations with Weighted Drazin-Star and Star-Drazin Solutions 具有加权Drazin-Star和Star-Drazin解的受限四元数双面矩阵方程
IF 1.2 2区 数学
Advances in Applied Clifford Algebras Pub Date : 2026-01-23 DOI: 10.1007/s00006-025-01420-8
Ivan I. Kyrchei, Dijana Mosić, Predrag Stanimirović
{"title":"Restricted Quaternion Two-Sided Matrix Equations with Weighted Drazin-Star and Star-Drazin Solutions","authors":"Ivan I. Kyrchei,&nbsp;Dijana Mosić,&nbsp;Predrag Stanimirović","doi":"10.1007/s00006-025-01420-8","DOIUrl":"10.1007/s00006-025-01420-8","url":null,"abstract":"<div><p>This paper extends the concepts of weighted Drazin-star (WDS) and weighted star-Drazin (WSD) matrices to domain of quaternion matrices. We develop determinantal representations for these matrices, leveraging the theory of noncommutative row-column determinants, considering both general and Hermitian cases. As specific instances, we derive the determinantal representations of the complex WDS and WSD matrices by employing minors of appropriately constructed complex matrices. Furthermore, we investigate two-sided quaternion equations, along with one-sided particular types, where the unique solutions are expressed using WDS and WSD matrices. Explicit solutions for these quaternion matrix equations are obtained using Cramer-type methods. Finally, a numerical example is provided to confirm applicability and efficacy of our findings.</p></div>","PeriodicalId":7330,"journal":{"name":"Advances in Applied Clifford Algebras","volume":"36 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2026-01-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146027483","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 Scattering Algebra of Physical Space: Squared Massive Constructive Amplitudes 物理空间的散射代数：平方质量构造振幅
IF 1.2 2区 数学
Advances in Applied Clifford Algebras Pub Date : 2026-01-13 DOI: 10.1007/s00006-025-01435-1
Moab Croft, Neil Christensen
{"title":"The Scattering Algebra of Physical Space: Squared Massive Constructive Amplitudes","authors":"Moab Croft,&nbsp;Neil Christensen","doi":"10.1007/s00006-025-01435-1","DOIUrl":"10.1007/s00006-025-01435-1","url":null,"abstract":"<div><p>The <i>Algebra of Physical Space</i> (APS) is used to explore the <i>Constructive Standard Model</i> (CSM) of particle physics. Namely, this paper connects the spinor formalism of the APS to massive amplitudes in the CSM. A novel equivalency between traditional CSM and APS-CSM formalisms is introduced, called the <i>Scattering Algebra</i> (SA), with example calculations confirming the consistency of results between both frameworks. Through this all, two significant insights are revealed: The identification of traditional CSM <i>spin spinors</i> with <i>Lorentz rotors</i> in the APS, and the connection of the CSM to various formalisms through <i>ray spinor structure</i>. The CSM’s results are replicated in massive cases, showcasing the power of the index-free, matrix-free, coordinate-free, geometric approach and paving the way for future research into massless cases, amplitude-construction, and Wigner little group methods within the APS.</p></div>","PeriodicalId":7330,"journal":{"name":"Advances in Applied Clifford Algebras","volume":"36 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2026-01-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00006-025-01435-1.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145955152","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
Flux Quantization in Type II Superconductors II型超导体的通量量子化
IF 1.2 2区 数学
Advances in Applied Clifford Algebras Pub Date : 2026-01-10 DOI: 10.1007/s00006-025-01409-3
Gene E. McClellan
{"title":"Flux Quantization in Type II Superconductors","authors":"Gene E. McClellan","doi":"10.1007/s00006-025-01409-3","DOIUrl":"10.1007/s00006-025-01409-3","url":null,"abstract":"<div><p>This paper explores the physics of magnetic and electric flux tubes supported by current vortices in condensed matter having a superconducting state in which bosonic charge carriers flow without resistance. The starting point is that the boson wave function satisfies the Klein–Gordon equation of relativistic quantum mechanics. Next, the electromagnetic fields within the superconducting medium are assumed to obey the quasistatic Maxwell equations expressed with geometric algebra and calculus and incorporating either electric or hypothetical magnetic currents. Finally, the Fundamental Theorem of Calculus is utilized in two forms to examine flux tubes, first in electric superconductors and then in hypothetical magnetic superconductors. Geometric algebra and calculus enable a consistent treatment of both analyses and an extension from three to four spatial dimensions.</p></div>","PeriodicalId":7330,"journal":{"name":"Advances in Applied Clifford Algebras","volume":"36 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2026-01-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145930775","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 Lie Groups Preserving Subspaces of Degenerate Clifford Algebras 退化Clifford代数的李群保持子空间
IF 1.2 2区 数学
Advances in Applied Clifford Algebras Pub Date : 2026-01-10 DOI: 10.1007/s00006-025-01431-5
Ekaterina Filimoshina, Dmitry Shirokov
{"title":"On Lie Groups Preserving Subspaces of Degenerate Clifford Algebras","authors":"Ekaterina Filimoshina,&nbsp;Dmitry Shirokov","doi":"10.1007/s00006-025-01431-5","DOIUrl":"10.1007/s00006-025-01431-5","url":null,"abstract":"<div><p>This paper introduces Lie groups in degenerate geometric (Clifford) algebras that preserve four fundamental subspaces determined by the grade involution and reversion under the adjoint and twisted adjoint representations. We prove that these Lie groups can be equivalently defined using norm functions of multivectors applied in the theory of spin groups. We also study the corresponding Lie algebras. Some of these Lie groups and algebras are closely related to Heisenberg Lie groups and algebras. The introduced groups are interesting for various applications in physics and computer science, in particular, for constructing equivariant neural networks.</p></div>","PeriodicalId":7330,"journal":{"name":"Advances in Applied Clifford Algebras","volume":"36 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2026-01-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145930776","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
Some Properties and the Teodorescu Transform in Higher Spin Clifford Analysis 高自旋Clifford分析中的一些性质及Teodorescu变换
IF 1.2 2区 数学
Advances in Applied Clifford Algebras Pub Date : 2026-01-08 DOI: 10.1007/s00006-025-01433-3
Chao Ding
{"title":"Some Properties and the Teodorescu Transform in Higher Spin Clifford Analysis","authors":"Chao Ding","doi":"10.1007/s00006-025-01433-3","DOIUrl":"10.1007/s00006-025-01433-3","url":null,"abstract":"<div><p>The Rarita–Schwinger fields are solutions to the relativistic field equation of spin-3/2 fermions in four dimensional flat spacetime, which are important in supergravity and superstring theories. Bureš et al. generalized it to an arbitrary spin <i>k</i>/2 in 2002 in the context of Clifford algebras. In this article, we introduce a mean value property, a Cauchy’s estimates, and a Liouville’s theorem for null solutions to the Rarita–Schwinger operator in the Euclidean spaces. Further, we investigate boundednesses to the Teodorescu transform and its derivatives. This gives rise to a Hodge decomposition of an <span>(L^2)</span> space in terms of the kernel of the Rarita–Schwinger operator and it also generalizes Bergman spaces to the higher spin cases.</p></div>","PeriodicalId":7330,"journal":{"name":"Advances in Applied Clifford Algebras","volume":"36 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2026-01-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145930692","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
Characterizations of Lipschitz Functions by Quaternion Linear Canonical Transform 用四元数线性正则变换刻画Lipschitz函数
IF 1.2 2区 数学
Advances in Applied Clifford Algebras Pub Date : 2026-01-03 DOI: 10.1007/s00006-025-01432-4
Monir Nadi, El Mostafa Sadek, Hassan Benlaajine
{"title":"Characterizations of Lipschitz Functions by Quaternion Linear Canonical Transform","authors":"Monir Nadi,&nbsp;El Mostafa Sadek,&nbsp;Hassan Benlaajine","doi":"10.1007/s00006-025-01432-4","DOIUrl":"10.1007/s00006-025-01432-4","url":null,"abstract":"<div><p>In this work, using the quaternion linear canonical transform, we establish an analogue of the classical Titchmarsh theorem and Younis’ theorem for higher-order differences of quaternion-valued functions satisfying certain Lipschitz conditions in the space <span>( L^{2}( {mathbb {R}}^{2},{mathbb {H}}),)</span> where <span>({mathbb {H}})</span> is a quaternion algebra.</p></div>","PeriodicalId":7330,"journal":{"name":"Advances in Applied Clifford Algebras","volume":"36 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2026-01-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145894477","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
Bedrosian Identities and Quaternion Hilbert Transforms: Advancing Color Image Pattern Recognition through Analytic Signal Processing Bedrosian恒等式和四元数Hilbert变换：通过分析信号处理推进彩色图像模式识别
IF 1.2 2区 数学
Advances in Applied Clifford Algebras Pub Date : 2025-12-24 DOI: 10.1007/s00006-025-01429-z
Xiaoxiao Hu, Zhifang Pan, Kit Ian Kou
{"title":"Bedrosian Identities and Quaternion Hilbert Transforms: Advancing Color Image Pattern Recognition through Analytic Signal Processing","authors":"Xiaoxiao Hu,&nbsp;Zhifang Pan,&nbsp;Kit Ian Kou","doi":"10.1007/s00006-025-01429-z","DOIUrl":"10.1007/s00006-025-01429-z","url":null,"abstract":"<div><p>This paper presents a significant extension of the classical Bedrosian identity to the quaternionic domain for functions of two variables. By leveraging the Quaternion Fourier transform, we develop a rigorous theoretical framework for the Quaternion Partial and Total Hilbert transforms. The core advantage of this Hilbert-based approach, as opposed to one using the rotational-invariant Riesz transform, is the simplicity of its Fourier multiplier. This property is fundamental and uniquely enables the derivation of Bedrosian-type identities, which are proven to be unattainable for the Riesz transform. We establish sufficient conditions for these identities to hold, providing a powerful multiplicative law for quaternionic signals under specific spectral conditions. Building upon this foundation, we delineate the necessary and sufficient conditions for the Quaternion Analytic Signal (QAS). Furthermore, as a key application of the Bedrosian theorems, we derive the precise criteria that ensure that the product of two holomorphic QASs remains a quaternion holomorphic function. The practical superiority of this framework is demonstrated through calculated examples and applications in two-dimensional image processing, where it offers a computationally effective and theoretically sound alternative to the monogenic signal, particularly for images with strong directional or lattice structures. This work provides essential theoretical tools for advancing hypercomplex signal processing and opens new avenues for sophisticated image analysis.</p></div>","PeriodicalId":7330,"journal":{"name":"Advances in Applied Clifford Algebras","volume":"36 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2025-12-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145829883","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
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