Subjects -> MATHEMATICS (Total: 1013 journals)
    - APPLIED MATHEMATICS (92 journals)
    - GEOMETRY AND TOPOLOGY (23 journals)
    - MATHEMATICS (714 journals)
    - MATHEMATICS (GENERAL) (45 journals)
    - NUMERICAL ANALYSIS (26 journals)
    - PROBABILITIES AND MATH STATISTICS (113 journals)

MATHEMATICS (714 journals)                  1 2 3 4 | Last

Showing 1 - 200 of 538 Journals sorted alphabetically
Abhandlungen aus dem Mathematischen Seminar der Universitat Hamburg     Hybrid Journal   (Followers: 2)
Accounting Perspectives     Full-text available via subscription   (Followers: 4)
ACM Transactions on Algorithms (TALG)     Hybrid Journal   (Followers: 14)
ACM Transactions on Mathematical Software (TOMS)     Hybrid Journal   (Followers: 6)
ACS Applied Materials & Interfaces     Hybrid Journal   (Followers: 49)
Acta Applicandae Mathematicae     Hybrid Journal   (Followers: 2)
Acta Mathematica Hungarica     Hybrid Journal   (Followers: 4)
Acta Mathematica Sinica, English Series     Hybrid Journal   (Followers: 5)
Acta Mathematica Vietnamica     Hybrid Journal  
Acta Mathematicae Applicatae Sinica, English Series     Hybrid Journal  
Advanced Science Letters     Full-text available via subscription   (Followers: 10)
Advances in Applied Clifford Algebras     Hybrid Journal   (Followers: 6)
Advances in Catalysis     Full-text available via subscription   (Followers: 7)
Advances in Complex Systems     Hybrid Journal   (Followers: 10)
Advances in Computational Mathematics     Hybrid Journal   (Followers: 21)
Advances in Difference Equations     Open Access   (Followers: 4)
Advances in Geosciences (ADGEO)     Open Access   (Followers: 20)
Advances in Linear Algebra & Matrix Theory     Open Access   (Followers: 6)
Advances in Materials Science     Open Access   (Followers: 24)
Advances in Mathematical Physics     Open Access   (Followers: 7)
Advances in Mathematics     Full-text available via subscription   (Followers: 21)
Advances in Numerical Analysis     Open Access   (Followers: 5)
Advances in Operations Research     Open Access   (Followers: 13)
Advances in Operator Theory     Hybrid Journal  
Advances in Pure Mathematics     Open Access   (Followers: 11)
Advances in Science and Research (ASR)     Open Access   (Followers: 9)
Aequationes Mathematicae     Hybrid Journal   (Followers: 2)
African Journal of Educational Studies in Mathematics and Sciences     Full-text available via subscription   (Followers: 10)
African Journal of Mathematics and Computer Science Research     Open Access   (Followers: 8)
Afrika Matematika     Hybrid Journal   (Followers: 2)
Air, Soil & Water Research     Open Access   (Followers: 9)
Al-Qadisiyah Journal for Computer Science and Mathematics     Open Access   (Followers: 5)
AL-Rafidain Journal of Computer Sciences and Mathematics     Open Access   (Followers: 4)
Algebra and Logic     Hybrid Journal   (Followers: 10)
Algebra Colloquium     Hybrid Journal   (Followers: 3)
Algebra Universalis     Hybrid Journal   (Followers: 3)
Algorithmic Operations Research     Open Access   (Followers: 7)
Algorithms     Open Access   (Followers: 15)
Algorithms Research     Open Access   (Followers: 1)
American Journal of Computational and Applied Mathematics     Open Access   (Followers: 4)
American Journal of Mathematical and Management Sciences     Hybrid Journal  
American Journal of Mathematics     Full-text available via subscription   (Followers: 9)
American Journal of Operations Research     Open Access   (Followers: 7)
American Mathematical Monthly     Full-text available via subscription   (Followers: 5)
An International Journal of Optimization and Control: Theories & Applications     Open Access   (Followers: 12)
Analele Universitatii Ovidius Constanta - Seria Matematica     Open Access  
Analysis and Applications     Hybrid Journal   (Followers: 2)
Analysis and Mathematical Physics     Hybrid Journal   (Followers: 7)
Annales Mathematicae Silesianae     Open Access  
Annales mathématiques du Québec     Hybrid Journal   (Followers: 3)
Annales Universitatis Mariae Curie-Sklodowska, sectio A – Mathematica     Open Access   (Followers: 1)
Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica     Open Access  
Annali di Matematica Pura ed Applicata     Hybrid Journal   (Followers: 1)
Annals of Combinatorics     Hybrid Journal   (Followers: 4)
Annals of Data Science     Hybrid Journal   (Followers: 15)
Annals of Functional Analysis     Hybrid Journal   (Followers: 2)
Annals of Mathematics     Full-text available via subscription   (Followers: 8)
Annals of Mathematics and Artificial Intelligence     Hybrid Journal   (Followers: 13)
Annals of PDE     Hybrid Journal   (Followers: 1)
Annals of Pure and Applied Logic     Open Access   (Followers: 5)
Annals of the Institute of Statistical Mathematics     Hybrid Journal   (Followers: 1)
Annals of West University of Timisoara - Mathematics     Open Access   (Followers: 1)
Annals of West University of Timisoara - Mathematics and Computer Science     Open Access   (Followers: 2)
Annuaire du Collège de France     Open Access   (Followers: 6)
ANZIAM Journal     Open Access   (Followers: 1)
Applicable Algebra in Engineering, Communication and Computing     Hybrid Journal   (Followers: 3)
Applications of Mathematics     Hybrid Journal   (Followers: 4)
Applied Categorical Structures     Hybrid Journal   (Followers: 5)
Applied Computational Intelligence and Soft Computing     Open Access   (Followers: 16)
Applied Mathematics     Open Access   (Followers: 6)
Applied Mathematics     Open Access   (Followers: 5)
Applied Mathematics & Optimization     Hybrid Journal   (Followers: 7)
Applied Mathematics - A Journal of Chinese Universities     Hybrid Journal   (Followers: 1)
Applied Mathematics and Nonlinear Sciences     Open Access   (Followers: 2)
Applied Mathematics Letters     Full-text available via subscription   (Followers: 4)
Applied Mathematics Research eXpress     Hybrid Journal   (Followers: 1)
Applied Network Science     Open Access   (Followers: 3)
Applied Numerical Mathematics     Hybrid Journal   (Followers: 4)
Applied Spatial Analysis and Policy     Hybrid Journal   (Followers: 5)
Arab Journal of Mathematical Sciences     Open Access   (Followers: 3)
Arabian Journal of Mathematics     Open Access   (Followers: 1)
Archive for Mathematical Logic     Hybrid Journal   (Followers: 3)
Archive of Applied Mechanics     Hybrid Journal   (Followers: 4)
Archive of Numerical Software     Open Access  
Archives of Computational Methods in Engineering     Hybrid Journal   (Followers: 5)
Arnold Mathematical Journal     Hybrid Journal   (Followers: 2)
Artificial Satellites     Open Access   (Followers: 22)
Asia-Pacific Journal of Operational Research     Hybrid Journal   (Followers: 4)
Asian Journal of Algebra     Open Access   (Followers: 1)
Asian Research Journal of Mathematics     Open Access  
Asian-European Journal of Mathematics     Hybrid Journal   (Followers: 2)
Australian Mathematics Teacher, The     Full-text available via subscription   (Followers: 7)
Australian Primary Mathematics Classroom     Full-text available via subscription   (Followers: 5)
Australian Senior Mathematics Journal     Full-text available via subscription   (Followers: 1)
Automatic Documentation and Mathematical Linguistics     Hybrid Journal   (Followers: 4)
Axioms     Open Access   (Followers: 1)
Banach Journal of Mathematical Analysis     Hybrid Journal  
Basin Research     Hybrid Journal   (Followers: 6)
Biomath     Open Access  
BIT Numerical Mathematics     Hybrid Journal  
Boletim Cearense de Educação e História da Matemática     Open Access  
Boletín de la Sociedad Matemática Mexicana     Hybrid Journal  
Bollettino dell'Unione Matematica Italiana     Full-text available via subscription  
British Journal for the History of Mathematics     Hybrid Journal   (Followers: 3)
Bulletin des Sciences Mathamatiques     Full-text available via subscription   (Followers: 3)
Bulletin of Dnipropetrovsk University. Series : Communications in Mathematical Modeling and Differential Equations Theory     Open Access   (Followers: 3)
Bulletin of Mathematical Sciences     Open Access   (Followers: 2)
Bulletin of Symbolic Logic     Full-text available via subscription   (Followers: 4)
Bulletin of the Australian Mathematical Society     Full-text available via subscription   (Followers: 2)
Bulletin of the Brazilian Mathematical Society, New Series     Hybrid Journal  
Bulletin of the Iranian Mathematical Society     Hybrid Journal  
Bulletin of the London Mathematical Society     Hybrid Journal   (Followers: 3)
Bulletin of the Malaysian Mathematical Sciences Society     Hybrid Journal  
Calculus of Variations and Partial Differential Equations     Hybrid Journal   (Followers: 2)
Canadian Journal of Mathematics / Journal canadien de mathématiques     Hybrid Journal  
Canadian Journal of Science, Mathematics and Technology Education     Hybrid Journal   (Followers: 20)
Canadian Mathematical Bulletin     Hybrid Journal  
Carpathian Mathematical Publications     Open Access  
Catalysis in Industry     Hybrid Journal  
CAUCHY     Open Access   (Followers: 1)
CEAS Space Journal     Hybrid Journal   (Followers: 5)
CHANCE     Hybrid Journal   (Followers: 5)
Chaos, Solitons & Fractals     Hybrid Journal   (Followers: 2)
Chaos, Solitons & Fractals : X     Open Access   (Followers: 1)
ChemSusChem     Hybrid Journal   (Followers: 8)
Chinese Annals of Mathematics, Series B     Hybrid Journal  
Chinese Journal of Catalysis     Full-text available via subscription   (Followers: 2)
Chinese Journal of Mathematics     Open Access  
Ciencia     Open Access  
CODEE Journal     Open Access  
Cogent Mathematics     Open Access   (Followers: 2)
Cognitive Computation     Hybrid Journal   (Followers: 3)
Collectanea Mathematica     Hybrid Journal  
College Mathematics Journal     Hybrid Journal   (Followers: 3)
COMBINATORICA     Hybrid Journal  
Combinatorics, Probability and Computing     Hybrid Journal   (Followers: 5)
Combustion Theory and Modelling     Hybrid Journal   (Followers: 21)
Commentarii Mathematici Helvetici     Hybrid Journal   (Followers: 1)
Communications in Combinatorics and Optimization     Open Access  
Communications in Contemporary Mathematics     Hybrid Journal  
Communications in Mathematical Physics     Hybrid Journal   (Followers: 4)
Communications On Pure & Applied Mathematics     Hybrid Journal   (Followers: 7)
Complex Analysis and its Synergies     Open Access   (Followers: 1)
Complex Variables and Elliptic Equations: An International Journal     Hybrid Journal  
Compositio Mathematica     Full-text available via subscription   (Followers: 2)
Comptes Rendus : Mathematique     Open Access  
Computational and Applied Mathematics     Hybrid Journal   (Followers: 4)
Computational and Mathematical Methods     Hybrid Journal  
Computational and Mathematical Methods in Medicine     Open Access   (Followers: 2)
Computational and Mathematical Organization Theory     Hybrid Journal   (Followers: 2)
Computational Complexity     Hybrid Journal   (Followers: 5)
Computational Mathematics and Modeling     Hybrid Journal   (Followers: 8)
Computational Mechanics     Hybrid Journal   (Followers: 14)
Computational Methods and Function Theory     Hybrid Journal  
Computational Optimization and Applications     Hybrid Journal   (Followers: 10)
Computers & Mathematics with Applications     Full-text available via subscription   (Followers: 11)
Confluentes Mathematici     Hybrid Journal  
Constructive Mathematical Analysis     Open Access   (Followers: 1)
Contributions to Game Theory and Management     Open Access   (Followers: 1)
COSMOS     Hybrid Journal   (Followers: 1)
Cross Section     Full-text available via subscription   (Followers: 1)
Cryptography and Communications     Hybrid Journal   (Followers: 12)
Cuadernos de Investigación y Formación en Educación Matemática     Open Access  
Cubo. A Mathematical Journal     Open Access  
Current Research in Biostatistics     Open Access   (Followers: 9)
Czechoslovak Mathematical Journal     Hybrid Journal  
Demographic Research     Open Access   (Followers: 15)
Design Journal : An International Journal for All Aspects of Design     Hybrid Journal   (Followers: 39)
Dhaka University Journal of Science     Open Access  
Differential Equations and Dynamical Systems     Hybrid Journal   (Followers: 4)
Digital Experiences in Mathematics Education     Hybrid Journal   (Followers: 3)
Discrete Mathematics     Hybrid Journal   (Followers: 7)
Discrete Mathematics & Theoretical Computer Science     Open Access   (Followers: 1)
Discrete Mathematics, Algorithms and Applications     Hybrid Journal   (Followers: 3)
Doklady Mathematics     Hybrid Journal  
Eco Matemático     Open Access  
Econometrics     Open Access   (Followers: 2)
Educação Matemática Debate     Open Access  
Emergent Scientist     Open Access  
Energy for Sustainable Development     Hybrid Journal   (Followers: 14)
Enseñanza de las Ciencias : Revista de Investigación y Experiencias Didácticas     Open Access  
Entropy     Open Access   (Followers: 5)
ESAIM: Control Optimisation and Calculus of Variations     Open Access   (Followers: 3)
European Journal of Applied Mathematics     Hybrid Journal  
European Journal of Combinatorics     Full-text available via subscription   (Followers: 3)
European Journal of Mathematics     Hybrid Journal   (Followers: 1)
European Scientific Journal     Open Access   (Followers: 11)
Examples and Counterexamples     Open Access   (Followers: 5)
Experimental Mathematics     Hybrid Journal   (Followers: 5)
Expositiones Mathematicae     Hybrid Journal   (Followers: 2)
Facta Universitatis, Series : Mathematics and Informatics     Open Access  
Finite Fields and Their Applications     Full-text available via subscription   (Followers: 6)
Formalized Mathematics     Open Access  
Forum of Mathematics, Pi     Open Access   (Followers: 1)
Forum of Mathematics, Sigma     Open Access   (Followers: 1)
Foundations and Trends® in Econometrics     Full-text available via subscription   (Followers: 6)
Foundations and Trends® in Networking     Full-text available via subscription   (Followers: 1)
Foundations and Trends® in Stochastic Systems     Full-text available via subscription   (Followers: 1)
Foundations and Trends® in Theoretical Computer Science     Full-text available via subscription   (Followers: 1)
Foundations of Computational Mathematics     Hybrid Journal   (Followers: 1)

        1 2 3 4 | Last

Similar Journals
Journal Cover
Advances in Applied Clifford Algebras
Journal Prestige (SJR): 0.698
Citation Impact (citeScore): 1
Number of Followers: 6  
 
  Hybrid Journal Hybrid journal (It can contain Open Access articles)
ISSN (Print) 1661-4909 - ISSN (Online) 0188-7009
Published by Springer-Verlag Homepage  [2468 journals]
  • Branching of Weil Representation for $$G_2$$

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      Abstract: Abstract This paper presents a discussion on the branching problem that arises in the Weil representation of the exceptional Lie group of type \(G_2\) . The focus is on its decomposition under the threefold cover of \(SL(2,\, {\mathbb {R}})\) associated with the short root of \(G_2\) .
      PubDate: 2025-01-29
      DOI: 10.1007/s00006-025-01370-1
       
  • Cubic Dirac operator for $$U_q({\mathfrak {sl}}_2)$$

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      Abstract: Abstract We construct the q-deformed Clifford algebra of  \(\mathfrak {sl}_2\) and study its properties. This allows us to define the q-deformed noncommutative Weil algebra  \(\mathcal {W}_q(\mathfrak {sl}_2)\) for  \(U_q(\mathfrak {sl}_2)\) and the corresponding cubic Dirac operator  \(D_q\) . In the classical case this was done by Alekseev and Meinrenken in 2000. We show that the cubic Dirac operator  \(D_q\) is invariant with respect to the \(U_q({\mathfrak {sl}}_2)\) -action and \(*\) -structures on  \(\mathcal {W}_q(\mathfrak {sl}_2)\) , moreover, the square of  \(D_q\) is central in  \(\mathcal {W}_q(\mathfrak {sl}_2)\) . We compute the spectrum of the cubic element on finite-dimensional and Verma modules of  \(U_q(\mathfrak {sl}_2)\) and the corresponding Dirac cohomology.
      PubDate: 2025-01-22
      DOI: 10.1007/s00006-025-01372-z
       
  • The Wigner Little Group for Photons is a Projective Subalgebra

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      Abstract: Abstract 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.
      PubDate: 2025-01-21
      DOI: 10.1007/s00006-025-01369-8
       
  • H-B Theorems of Cauchy Integral Operators in Clifford Analysis

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      Abstract: Abstract In this article, we verify the boundedness of the Cauchy type integral operators under the generalized Hölder norm in Clifford analysis, which are called H-B theorems of the Cauchy integral operators in Clifford analysis. We first demonstrate the generalized 2P theorems and the generalized Muskhelishvili theorem in Clifford analysis by Du’s method derived from Du (J Math (PRC) 2(2):115–12, 1982) and Lu (Boundary value problems of analytic functions. World Scientific, Singapore, 1993), which greatly refines the coefficients estimate of inequality in Du et al. (Acta Math Sci 29B(1):210–224, 2009) and Zhang (Complex Var Elliptic Equ 52(6):455–473, 2007). Then, we obtain the H-B theorems which extend and improve the corresponding results in Du et al. (2009) and Wang and Du (Z Anal Anwend, 2024).
      PubDate: 2025-01-18
      DOI: 10.1007/s00006-025-01371-0
       
  • Multicomplex Ideals, Modules and Hilbert Spaces

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      Abstract: Abstract In this article we study some algebraic aspects of multicomplex numbers \({\mathbb {M}}_n\) . For \(n\ge 2\) a canonical representation is defined in terms of the multiplication of \(n-1\) idempotent elements. This representation facilitates computations in this algebra and makes it possible to introduce a generalized conjugacy \(\Lambda _n\) , i.e. a composition of the n multicomplex conjugates \(\Lambda _n:=\dagger _1\cdots \dagger _n\) , as well as a multicomplex norm. The ideals of the ring of multicomplex numbers are then studied in details, free \({\mathbb {M}}_n\) -modules and their linear operators are considered and, finally, we develop Hilbert spaces on the multicomplex algebra.
      PubDate: 2025-01-17
      DOI: 10.1007/s00006-025-01373-y
       
  • MiTopos

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      Abstract: Abstract In the present article, the research work of many years is summarized in an interim report. This concerns the connection between logic, space, time and matter. The author always had in mind two things, namely 1. The discovery/construction of an interface between matter and mind, and 2. some entry points for the topos view that concern graphs, grade rotations and contravariant involutions in geometric Boolean lattices. In this part of the MiTopos theme I follow the historic approach to mathematical physics and remain with the Clifford algebra of the Minkowski space. It turns out that this interface is a basic morphogenetic structure inherent in both matter and thought. It resides in both oriented spaces and logic, and most surprisingly is closely linked to the symmetries of elementary particle physics.
      PubDate: 2024-12-19
      DOI: 10.1007/s00006-024-01362-7
       
  • Self-Dual Maxwell Fields from Clifford Analysis

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      Abstract: Abstract The study of complex functions is based around the study of holomorphic functions, satisfying the Cauchy-Riemann equations. The relatively recent field of Clifford Analysis lets us extend many results from Complex Analysis to higher dimensions. In this paper, I decompose the Cauchy-Riemann equations for a general Clifford algebra into grades using the Geometric Algebra formalism, and show that for the Spacetime Algebra Cl(3, 1) these equations are the equations for a self-dual source free Maxwell field, and for a massless uncharged Spinor. This shows a deep link between fundamental physics and the Clifford geometry of Spacetime.
      PubDate: 2024-12-11
      DOI: 10.1007/s00006-024-01368-1
       
  • STP Method for Solving the Least Squares Special Solutions of Quaternion
           Matrix Equations

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      Abstract: Abstract In this paper, we apply the semi-tensor product of matrices and the real vector representation of a quaternion matrix to find the least squares lower (upper) triangular Toeplitz solution of \(AX-XB=C\) , \(AXB-CX^{T}D=E\) and (anti)centrosymmetric solution of \(AXB-CYD=E\) . And the expressions of the least squares lower (upper) triangular Toeplitz and (anti)centrosymmetric solution for the studied equations are derived. Additionally, the necessary and sufficient conditions for the existence of solutions and general expression of the studied equations are given. Eventually, some numerical examples are provided for showing the validity and superiority of our method.
      PubDate: 2024-12-02
      DOI: 10.1007/s00006-024-01367-2
       
  • Construction of an Infinite-Dimensional Family of Exact Solutions of a
           Three-Dimensional Biharmonic Equation by the Hypercomplex Method

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      Abstract: Abstract An infinite-dimensional family of exact solutions of a three-dimensional biharmonic equation was constructed by the hypercomplex method.
      PubDate: 2024-11-25
      DOI: 10.1007/s00006-024-01365-4
       
  • Eigenvalues of Quaternion Tensors: Properties, Algorithms and Applications

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      Abstract: Abstract In this paper, we investigate the eigenvalues of quaternion tensors under Einstein Product and their applications in color video processing. We present the Ger \(\check{s}\) gorin theorem for quaternion tensors. Furthermore, we have executed some experiments to validate the efficacy of our proposed theoretical framework and algorithms. Finally, we contemplate the application of this methodology in color video compression, in which the reconstruction of an approximate original image is achieved by computing a limited number of the largest eigenvalues, yielding a favorable outcome. In summary, by utilizing block tensors in its iterations, this method converges more rapidly to the desired eigenvalues and eigentensors, which significantly reduces the time required for videos compression.
      PubDate: 2024-11-22
      DOI: 10.1007/s00006-024-01366-3
       
  • Geometric Product of Two Oriented Points in Conformal Geometric Algebra

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      Abstract: Abstract We compute and explore the full geometric product of two oriented points in conformal geometric algebra Cl(4, 1) of three-dimensional Euclidean space. We comment on the symmetry of the various components, and state for all expressions also a representation in terms of point pair center and radius vectors.
      PubDate: 2024-11-15
      DOI: 10.1007/s00006-024-01363-6
       
  • Riemann–Hilbert Problems for Biaxially Symmetric Monogenic Functions
           in $$\mathbb {R}^{n}$$

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      Abstract: Abstract We are dedicated to addressing Riemann–Hilbert boundary value problems (RHBVPs) with variable coefficients, where the solutions are valued in the Clifford algebra of \(\mathbb {R}_{0,n}\) , for biaxially monogenic functions defined in the biaxially symmetric domains of the Euclidean space \(\mathbb {R}^{n}\) . Our research establishes the equivalence between RHBVPs for biaxially monogenic functions defined in biaxially domains and RHBVPs for generalized analytic functions on the complex plane. We derive explicit solutions and conditions for solvability of RHBVPs for biaxially monogenic functions. Additionally, we explore related Schwarz problems and RHBVPs for biaxially meta-monogenic functions.
      PubDate: 2024-11-13
      DOI: 10.1007/s00006-024-01364-5
       
  • Conics, Their Pencils and Intersections in Geometric Algebra

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      Abstract: Abstract This paper presents an approach for extracting points from conic intersections by using the concept of pencils. This method is based on QC2GA—the two-dimensional version of QCGA (Quadric Conformal Geometric Algebra)—that is demonstrated to be equivalent to GAC (Geometric Algebra for Conics). A new interpretation of QC2GA and its objects based on pencils of conics and point space elements is presented, enabling the creation, constraining, and exploitation of pencils of conics. A Geometric Algebra method for computing the discriminants and center point of a conic will also be presented, enabling the proposition of an algorithm for extracting points from a conic intersection object.
      PubDate: 2024-11-05
      DOI: 10.1007/s00006-024-01356-5
       
  • Fueter’s Theorem for One Class of Pseudoanalytic Functions

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      Abstract: Abstract In this paper, we extend Fueter’s theorem in hypercomplex function theory to encompass a class of pseudoanalytic functions associated with the main Vekua equation. This class includes Duffin’s \(\mu \) -regular functions as special cases, which correspond to the Yukawa equation. As the parameter \(\mu \rightarrow 0\) , we recover the classical Fueter’s theorem.
      PubDate: 2024-10-26
      DOI: 10.1007/s00006-024-01361-8
       
  • Multivector Contractions Revisited, Part I

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      Abstract: Abstract We reorganize, simplify and expand the theory of contractions or interior products of multivectors, and related topics like Hodge star duality. Many results are generalized and new ones are given, like: geometric characterizations of blade contractions and regressive products, higher-order graded Leibniz rules, determinant formulas, improved complex star operators, etc. Different contractions found in the literature are discussed and compared, in special those of Clifford Geometric Algebra. Applications of the theory are developed in a follow-up paper.
      PubDate: 2024-10-24
      DOI: 10.1007/s00006-024-01357-4
       
  • The Plemelj-Sokhotski Formulas Associated to the k-Cauchy-Fueter Operator

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      Abstract: Abstract The Plemelj-Sokhotski formulas, which deal with limiting values of the Bochner-Martinelli type integral, are powerful tools for analyzing boundary value problems. This article aims to study the boundary behavior of the Bochner-Martinelli type integral formula for the k-Cauchy-Fueter operator. Specifically, we consider the Plemelj-Sokhotski formulas, which will extend the corresponding results in the complex analysis of several variables.
      PubDate: 2024-10-21
      DOI: 10.1007/s00006-024-01359-2
       
  • Multivector Contractions Revisited, Part II

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      Abstract: Abstract The theory of contractions of multivectors, and star duality, was reorganized in a previous article, and here we present some applications. First, we study inner and outer spaces associated to a general multivector M via the equations \(v \wedge M = 0\) and \(v \mathbin {\lrcorner }M=0\) . They are then used to analyze special decompositions, factorizations and ‘carvings’ of M, to define generalized grades, and to obtain new simplicity criteria, including a reduced set of Plücker-like relations. We also discuss how contractions are related to supersymmetry, and give formulas for supercommutators of multi-fermion creation and annihilation operators.
      PubDate: 2024-10-19
      DOI: 10.1007/s00006-024-01358-3
       
  • Scaled Global Operators and Fueter Variables on Non-zero Scaled
           Hypercomplex Numbers

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      Abstract: Abstract In this paper we describe the rise of global operators in the scaled quaternionic case, an important extension from the quaternionic case to the family of scaled hypercomplex numbers \(\mathbb {H}_t,\, t\in \mathbb {R}^*\) , of which the \(\mathbb {H}_{-1}=\mathbb {H}\) is the space of quaternions and \(\mathbb {H}_{1}\) is the space of split quaternions. We also describe the scaled Fueter-type variables associated to these operators, developing a coherent theory in this field. We use these types of variables to build different types of function spaces on \(\mathbb {H}_t\) . Counterparts of the Hardy space and of the Arveson space are also introduced and studied in the present setting. The two different adjoints in the scaled hypercomplex numbers lead to two parallel cases in each instance. Finally we introduce and study the notion of rational function.
      PubDate: 2024-10-15
      DOI: 10.1007/s00006-024-01347-6
       
  • The Radon–Penrose Transformation for Quaternionic k-Regular
           Functions on Right-Type Groups

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      Abstract: Abstract The right-type groups are nilpotent Lie groups of step two having a pair of anticommutative operators, and many aspects of quaternionic analysis can be generalized to this kind of groups. In this paper, we use the twistor transformation to study the tangential k-Cauchy–Fueter equations and quaternionic k-regular functions on these groups. We introduce the twistor space over the \((4n+r)\) -dimensional complex right-type groups and use twistor transformation to construct an explicit Radon–Penrose type integral formula to solve the holomorphic tangential k-Cauchy–Fueter equation on these groups. When restricted to the real right-type group, this formula provides solutions to tangential k-Cauchy–Fueter equations. In particular, it gives us many k-regular polynomials.
      PubDate: 2024-10-12
      DOI: 10.1007/s00006-024-01360-9
       
  • A Classical System of Matrix Equations Over the Split Quaternion Algebra

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      Abstract: Abstract We design several real representations of split quaternion matrices with the primary objective of establishing both necessary and sufficient conditions for the existence of solutions within a system of split quaternion matrix equations. This includes conditions for the general solution without any constraints, as well as \(X=\pm X^{\eta }\) solutions and \(\eta \) -(anti-)Hermitian solutions. Furthermore, we derive the expressions for the general solutions when it is solvable. As an application, we investigate the solutions to a system of five split quaternion matrix equations involving \(X^\star \) . Finally, we present several algorithms and numerical examples to demonstrate the results of this paper.
      PubDate: 2024-09-27
      DOI: 10.1007/s00006-024-01348-5
       
 
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  Subjects -> MATHEMATICS (Total: 1013 journals)
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School of Mathematical and Computer Sciences
Heriot-Watt University
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Email: journaltocs@hw.ac.uk
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