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  Subjects -> MATHEMATICS (Total: 968 journals)
    - APPLIED MATHEMATICS (81 journals)
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    - MATHEMATICS (714 journals)
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MATHEMATICS (714 journals)                  1 2 3 4 | Last

Showing 1 - 200 of 538 Journals sorted alphabetically
Abakós     Open Access   (Followers: 4)
Abhandlungen aus dem Mathematischen Seminar der Universitat Hamburg     Hybrid Journal   (Followers: 4)
Academic Voices : A Multidisciplinary Journal     Open Access   (Followers: 2)
Accounting Perspectives     Full-text available via subscription   (Followers: 7)
ACM Transactions on Algorithms (TALG)     Hybrid Journal   (Followers: 15)
ACM Transactions on Computational Logic (TOCL)     Hybrid Journal   (Followers: 3)
ACM Transactions on Mathematical Software (TOMS)     Hybrid Journal   (Followers: 6)
ACS Applied Materials & Interfaces     Hybrid Journal   (Followers: 29)
Acta Applicandae Mathematicae     Hybrid Journal   (Followers: 1)
Acta Mathematica     Hybrid Journal   (Followers: 12)
Acta Mathematica Hungarica     Hybrid Journal   (Followers: 2)
Acta Mathematica Scientia     Full-text available via subscription   (Followers: 5)
Acta Mathematica Sinica, English Series     Hybrid Journal   (Followers: 6)
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: 4)
Advances in Calculus of Variations     Hybrid Journal   (Followers: 3)
Advances in Catalysis     Full-text available via subscription   (Followers: 5)
Advances in Complex Systems     Hybrid Journal   (Followers: 7)
Advances in Computational Mathematics     Hybrid Journal   (Followers: 19)
Advances in Decision Sciences     Open Access   (Followers: 3)
Advances in Difference Equations     Open Access   (Followers: 3)
Advances in Fixed Point Theory     Open Access   (Followers: 5)
Advances in Geosciences (ADGEO)     Open Access   (Followers: 13)
Advances in Linear Algebra & Matrix Theory     Open Access   (Followers: 3)
Advances in Materials Science     Open Access   (Followers: 14)
Advances in Mathematical Physics     Open Access   (Followers: 4)
Advances in Mathematics     Full-text available via subscription   (Followers: 11)
Advances in Numerical Analysis     Open Access   (Followers: 5)
Advances in Operations Research     Open Access   (Followers: 12)
Advances in Porous Media     Full-text available via subscription   (Followers: 5)
Advances in Pure and Applied Mathematics     Hybrid Journal   (Followers: 6)
Advances in Pure Mathematics     Open Access   (Followers: 6)
Advances in Science and Research (ASR)     Open Access   (Followers: 6)
Aequationes Mathematicae     Hybrid Journal   (Followers: 2)
African Journal of Educational Studies in Mathematics and Sciences     Full-text available via subscription   (Followers: 5)
African Journal of Mathematics and Computer Science Research     Open Access   (Followers: 4)
Afrika Matematika     Hybrid Journal   (Followers: 1)
Air, Soil & Water Research     Open Access   (Followers: 11)
AKSIOMA Journal of Mathematics Education     Open Access   (Followers: 1)
Al-Jabar : Jurnal Pendidikan Matematika     Open Access   (Followers: 1)
Algebra and Logic     Hybrid Journal   (Followers: 6)
Algebra Colloquium     Hybrid Journal   (Followers: 4)
Algebra Universalis     Hybrid Journal   (Followers: 2)
Algorithmic Operations Research     Full-text available via subscription   (Followers: 5)
Algorithms     Open Access   (Followers: 11)
Algorithms Research     Open Access   (Followers: 1)
American Journal of Computational and Applied Mathematics     Open Access   (Followers: 5)
American Journal of Mathematical Analysis     Open Access  
American Journal of Mathematics     Full-text available via subscription   (Followers: 6)
American Journal of Operations Research     Open Access   (Followers: 5)
An International Journal of Optimization and Control: Theories & Applications     Open Access   (Followers: 8)
Analele Universitatii Ovidius Constanta - Seria Matematica     Open Access   (Followers: 1)
Analysis and Applications     Hybrid Journal   (Followers: 1)
Analysis and Mathematical Physics     Hybrid Journal   (Followers: 5)
Analysis Mathematica     Full-text available via subscription  
Analysis. International mathematical journal of analysis and its applications     Hybrid Journal   (Followers: 2)
Annales Mathematicae Silesianae     Open Access  
Annales mathématiques du Québec     Hybrid Journal   (Followers: 4)
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: 12)
Annals of Discrete Mathematics     Full-text available via subscription   (Followers: 6)
Annals of Mathematics     Full-text available via subscription   (Followers: 1)
Annals of Mathematics and Artificial Intelligence     Hybrid Journal   (Followers: 12)
Annals of Pure and Applied Logic     Open Access   (Followers: 3)
Annals of the Alexandru Ioan Cuza University - Mathematics     Open Access  
Annals of the Institute of Statistical Mathematics     Hybrid Journal   (Followers: 1)
Annals of West University of Timisoara - Mathematics     Open Access  
Annuaire du Collège de France     Open Access   (Followers: 5)
ANZIAM Journal     Open Access   (Followers: 1)
Applicable Algebra in Engineering, Communication and Computing     Hybrid Journal   (Followers: 2)
Applications of Mathematics     Hybrid Journal   (Followers: 2)
Applied Categorical Structures     Hybrid Journal   (Followers: 2)
Applied Computational Intelligence and Soft Computing     Open Access   (Followers: 11)
Applied Mathematics     Open Access   (Followers: 3)
Applied Mathematics     Open Access   (Followers: 7)
Applied Mathematics & Optimization     Hybrid Journal   (Followers: 6)
Applied Mathematics - A Journal of Chinese Universities     Hybrid Journal  
Applied Mathematics Letters     Full-text available via subscription   (Followers: 2)
Applied Mathematics Research eXpress     Hybrid Journal   (Followers: 1)
Applied Network Science     Open Access   (Followers: 3)
Applied Numerical Mathematics     Hybrid Journal   (Followers: 5)
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: 2)
Archive for Mathematical Logic     Hybrid Journal   (Followers: 3)
Archive of Applied Mechanics     Hybrid Journal   (Followers: 5)
Archive of Numerical Software     Open Access  
Archives of Computational Methods in Engineering     Hybrid Journal   (Followers: 5)
Arkiv för Matematik     Hybrid Journal   (Followers: 1)
Armenian Journal of Mathematics     Open Access  
Arnold Mathematical Journal     Hybrid Journal   (Followers: 1)
Artificial Satellites     Open Access   (Followers: 20)
Asia-Pacific Journal of Operational Research     Hybrid Journal   (Followers: 3)
Asian Journal of Algebra     Open Access   (Followers: 1)
Asian Journal of Current Engineering & Maths     Open Access  
Asian-European Journal of Mathematics     Hybrid Journal   (Followers: 2)
Australian Mathematics Teacher, The     Full-text available via subscription   (Followers: 6)
Australian Primary Mathematics Classroom     Full-text available via subscription   (Followers: 4)
Australian Senior Mathematics Journal     Full-text available via subscription   (Followers: 1)
Automatic Documentation and Mathematical Linguistics     Hybrid Journal   (Followers: 5)
Axioms     Open Access   (Followers: 1)
Baltic International Yearbook of Cognition, Logic and Communication     Open Access   (Followers: 1)
Basin Research     Hybrid Journal   (Followers: 5)
BIBECHANA     Open Access   (Followers: 2)
BIT Numerical Mathematics     Hybrid Journal  
BoEM - Boletim online de Educação Matemática     Open Access  
Boletim Cearense de Educação e História da Matemática     Open Access  
Boletim de Educação Matemática     Open Access  
Boletín de la Sociedad Matemática Mexicana     Hybrid Journal  
Bollettino dell'Unione Matematica Italiana     Full-text available via subscription   (Followers: 1)
British Journal of Mathematical and Statistical Psychology     Full-text available via subscription   (Followers: 20)
Bruno Pini Mathematical Analysis Seminar     Open Access  
Buletinul Academiei de Stiinte a Republicii Moldova. Matematica     Open Access   (Followers: 12)
Bulletin des Sciences Mathamatiques     Full-text available via subscription   (Followers: 4)
Bulletin of Dnipropetrovsk University. Series : Communications in Mathematical Modeling and Differential Equations Theory     Open Access   (Followers: 1)
Bulletin of Mathematical Sciences     Open Access   (Followers: 1)
Bulletin of Symbolic Logic     Full-text available via subscription   (Followers: 2)
Bulletin of the Australian Mathematical Society     Full-text available via subscription   (Followers: 1)
Bulletin of the Brazilian Mathematical Society, New Series     Hybrid Journal  
Bulletin of the London Mathematical Society     Hybrid Journal   (Followers: 4)
Bulletin of the Malaysian Mathematical Sciences Society     Hybrid Journal  
Calculus of Variations and Partial Differential Equations     Hybrid Journal  
Canadian Journal of Science, Mathematics and Technology Education     Hybrid Journal   (Followers: 19)
Carpathian Mathematical Publications     Open Access   (Followers: 1)
Catalysis in Industry     Hybrid Journal   (Followers: 1)
CEAS Space Journal     Hybrid Journal   (Followers: 2)
CHANCE     Hybrid Journal   (Followers: 5)
Chaos, Solitons & Fractals     Hybrid Journal   (Followers: 3)
ChemSusChem     Hybrid Journal   (Followers: 7)
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  
Clean Air Journal     Full-text available via subscription   (Followers: 1)
Cogent Mathematics     Open Access   (Followers: 2)
Cognitive Computation     Hybrid Journal   (Followers: 4)
Collectanea Mathematica     Hybrid Journal  
COMBINATORICA     Hybrid Journal  
Combinatorics, Probability and Computing     Hybrid Journal   (Followers: 4)
Combustion Theory and Modelling     Hybrid Journal   (Followers: 14)
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: 2)
Communications On Pure & Applied Mathematics     Hybrid Journal   (Followers: 3)
Complex Analysis and its Synergies     Open Access   (Followers: 2)
Complex Variables and Elliptic Equations: An International Journal     Hybrid Journal  
Complexus     Full-text available via subscription  
Composite Materials Series     Full-text available via subscription   (Followers: 8)
Compositio Mathematica     Full-text available via subscription   (Followers: 1)
Comptes Rendus Mathematique     Full-text available via subscription   (Followers: 1)
Computational and Applied Mathematics     Hybrid Journal   (Followers: 2)
Computational and Mathematical Methods in Medicine     Open Access   (Followers: 2)
Computational and Mathematical Organization Theory     Hybrid Journal   (Followers: 2)
Computational Complexity     Hybrid Journal   (Followers: 4)
Computational Mathematics and Modeling     Hybrid Journal   (Followers: 8)
Computational Mechanics     Hybrid Journal   (Followers: 5)
Computational Methods and Function Theory     Hybrid Journal  
Computational Optimization and Applications     Hybrid Journal   (Followers: 7)
Computers & Mathematics with Applications     Full-text available via subscription   (Followers: 8)
Concrete Operators     Open Access   (Followers: 5)
Confluentes Mathematici     Hybrid Journal  
Contributions to Game Theory and Management     Open Access  
COSMOS     Hybrid Journal  
Cryptography and Communications     Hybrid Journal   (Followers: 13)
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   (Followers: 1)
Demographic Research     Open Access   (Followers: 11)
Demonstratio Mathematica     Open Access  
Dependence Modeling     Open Access  
Design Journal : An International Journal for All Aspects of Design     Hybrid Journal   (Followers: 29)
Developments in Clay Science     Full-text available via subscription   (Followers: 1)
Developments in Mineral Processing     Full-text available via subscription   (Followers: 3)
Dhaka University Journal of Science     Open Access  
Differential Equations and Dynamical Systems     Hybrid Journal   (Followers: 3)
Differentsial'nye Uravneniya     Open Access  
Discrete Mathematics     Hybrid Journal   (Followers: 8)
Discrete Mathematics & Theoretical Computer Science     Open Access  
Discrete Mathematics, Algorithms and Applications     Hybrid Journal   (Followers: 2)
Discussiones Mathematicae - General Algebra and Applications     Open Access  
Discussiones Mathematicae Graph Theory     Open Access   (Followers: 1)
Diskretnaya Matematika     Full-text available via subscription  
Dnipropetrovsk University Mathematics Bulletin     Open Access  
Doklady Akademii Nauk     Open Access  
Doklady Mathematics     Hybrid Journal  
Duke Mathematical Journal     Full-text available via subscription   (Followers: 1)
Eco Matemático     Open Access  
Edited Series on Advances in Nonlinear Science and Complexity     Full-text available via subscription  
Electronic Journal of Combinatorics     Open Access  
Electronic Journal of Differential Equations     Open Access  
Electronic Journal of Graph Theory and Applications     Open Access   (Followers: 2)
Electronic Notes in Discrete Mathematics     Full-text available via subscription   (Followers: 2)
Elemente der Mathematik     Full-text available via subscription   (Followers: 4)
Energy for Sustainable Development     Hybrid Journal   (Followers: 9)
Enseñanza de las Ciencias : Revista de Investigación y Experiencias Didácticas     Open Access  

        1 2 3 4 | Last

Journal Cover
Advances in Applied Clifford Algebras
Journal Prestige (SJR): 0.698
Citation Impact (citeScore): 1
Number of Followers: 4  
 
  Hybrid Journal Hybrid journal (It can contain Open Access articles)
ISSN (Print) 1661-4909 - ISSN (Online) 0188-7009
Published by Springer-Verlag Homepage  [2348 journals]
  • Discrete Wavelets with Quaternion and Clifford Coefficients
    • Authors: Peter Fletcher
      Abstract: In this paper we use matrix representations of quaternions and Clifford algebras and solve the same matrix equations in each case to find Daubechies quaternion and Clifford scaling filters. We use paraunitary completion of the polyphase matrix to find corresponding quaternion and Clifford wavelet filters. We then use the cascade algorithm on our filters to find quaternion and Clifford scaling and wavelet functions, which we illustrate using all possible projections onto two and three dimensions: to our knowledge, this is the first time that this has been done. We discuss the shapes of these functions and conclude with a consideration of what we could actually do with our filters.
      PubDate: 2018-06-05
      DOI: 10.1007/s00006-018-0876-5
      Issue No: Vol. 28, No. 3 (2018)
       
  • Hybrid Complex Numbers: The Matrix Version
    • Authors: G. Dattoli; S. Licciardi; R. M. Pidatella; E. Sabia
      Abstract: In this paper we review the notion of hybrid complex numbers, recently introduced to provide a comprehensive conceptual and formal framework to deal with circular, hyperbolic and dual complex. We exploit the established isomorphism between complex numbers as abstract entities and as two dimensional matrices in order to derive the associated algebraic properties. Within such a respect we derive generalized forms of Euler exponential formula and explore the usefulness and relevance of operator ordering procedure of the Wei-Norman type. We also discuss the properties of dual numbers in terms of Pauli matrices. Finally we explore generalized forms of Dirac-like factorization, emerging from the properties of these numbers.
      PubDate: 2018-06-04
      DOI: 10.1007/s00006-018-0870-y
      Issue No: Vol. 28, No. 3 (2018)
       
  • The Graf Product: A Clifford Structure Framework on the Exterior Bundle
    • Authors: R. Lopes; R. da Rocha
      Abstract: The geometric product, defined by Graf on the space of differential forms, endows the sections of the exterior bundle by a structure that is necessary to construct a Clifford algebra. The Graf product is introduced and revisited with a suitable underlying framework that naturally encompasses a coframe in the cotangent bundle, besides the volume element centrality, the Hodge operator and the so called truncated subalgebra as well.
      PubDate: 2018-06-02
      DOI: 10.1007/s00006-018-0875-6
      Issue No: Vol. 28, No. 3 (2018)
       
  • Special Classes of Monogenic Functions in $$\mathbb {H}$$ H
    • Authors: Sebastian Bock
      Abstract: Recently, the classical orthogonal function systems of inner and outer monogenic Appell functions were used to find a new class of monogenic functions with (logarithmic) line singularities, which naturally extends the class of outer monogenic Appell functions. Based on these results, this article constructs another novel class of monogenic functions with line singularities, which now also relates the class of inner monogenic Appell functions and thus complements the previously known function classes. It is shown that a subset of the constructed functions are rational monogenic functions of the form \(\varvec{p}_{k}^{l}(\varvec{x})\,\varvec{q}^{l}(\overline{\varvec{\zeta }})^{-1}\) , where \(\varvec{p}_{k}^{l}(\varvec{x})\) and \(\varvec{q}^{l}(\overline{\varvec{\zeta }})\) are homogeneous polynomials in the respective variables. Finally, the classical and special classes of monogenic functions are brought together in a unified schematic representation and essential features of the individual function classes and their relationships to each other are shown.
      PubDate: 2018-06-02
      DOI: 10.1007/s00006-018-0874-7
      Issue No: Vol. 28, No. 3 (2018)
       
  • A Few Comments on Ado’s Theorem and Non-Linear Lie Groups
    • Authors: Pierre Anglès
      Abstract: There are claims in the literature on Clifford algebras that every Lie group can be represented as a spin group. In a letter, Pertti Lounesto emphasized, by explicit counter-examples, that this statement is false. This self-contained short paper intends to present a survey of publications of well-known scientists where explicitly developed counter-examples prove the importance of Lounesto’s letter.
      PubDate: 2018-05-31
      DOI: 10.1007/s00006-018-0871-x
      Issue No: Vol. 28, No. 3 (2018)
       
  • A Framework for Assumption-Free Assessment of Imperfect Geometry of a
           Linac C-Arms
    • Authors: R. A. Kycia; Z. Tabor; A. Woszczyna; D. Kabat; M. Tulik; Z. Latała
      Abstract: In the present paper a general setup for the determination of imperfect geometry of radiotherapeutic devices has been proposed that is based on a geometric algebra framework. To account for this imperfect geometry, two methods of a calibration were presented, consisting of determining for each angular position of a gantry a correction shift which must be applied to the origin of a laboratory frame of reference to place it along a radiation axis for this angular position. Closed form solutions for these corrections are provided.
      PubDate: 2018-05-24
      DOI: 10.1007/s00006-018-0873-8
      Issue No: Vol. 28, No. 3 (2018)
       
  • Covariantly Constant Solutions of the Yang–Mills Equations
    • Authors: Dmitry Shirokov
      Abstract: We present a new class of covariantly constant solutions of the Yang–Mills equations. These solutions correspond to the solution of the field equation for the spin connection of the general form.
      PubDate: 2018-05-05
      DOI: 10.1007/s00006-018-0868-5
      Issue No: Vol. 28, No. 3 (2018)
       
  • Leptons, Quarks, and Gauge from the Complex Clifford Algebra $$\mathbb
           {C}\ell _6$$ C ℓ 6
    • Authors: Ovidiu Cristinel Stoica
      Abstract: A simple geometric algebra is shown to contain automatically the leptons and quarks of a family of the Standard Model, and the electroweak and color gauge symmetries, without predicting extra particles and symmetries. The algebra is already naturally present in the Standard Model, in two instances of the Clifford algebra \(\mathbb {C}\ell _6\) , one being algebraically generated by the Dirac algebra and the weak symmetry generators, and the other by a complex three-dimensional representation of the color symmetry, which generates a Witt decomposition which leads to the decomposition of the algebra into ideals representing leptons and quarks. The two instances being isomorphic, the minimal approach is to identify them, resulting in the model proposed here. The Dirac and Lorentz algebras appear naturally as subalgebras acting on the ideals representing leptons and quarks. The resulting representations on the ideals are invariant to the electromagnetic and color symmetries, which are generated by the bivectors of the algebra. The electroweak symmetry is also present, and it is already broken by the geometry of the algebra. The model predicts a bare Weinberg angle \(\theta _W\) given by \(\sin ^2\theta _W=0.25\) . The model shares common ideas with previously known models, particularly with Chisholm and Farwell (Clifford (Geometric) algebras: with applications to physics, mathematics, and engineering. Birkhäuser Boston, Boston, pp 365–388, 1996), Trayling and Baylis (Clifford Algebras: applications to mathematics, physics, and engineering. Birkhäuser Boston, Boston, pp 547–558, 1996), and Furey (Standard Model Physics from an Algebra' Preprint arXiv:1611.09182, 2016).
      PubDate: 2018-05-05
      DOI: 10.1007/s00006-018-0869-4
      Issue No: Vol. 28, No. 3 (2018)
       
  • A Curvature-Based Descriptor for Point Cloud Alignment Using Conformal
           Geometric Algebra
    • Authors: Adam Leon Kleppe; Olav Egeland
      Abstract: This paper presents a descriptor for course alignment of point clouds using conformal geometric algebra. The method is based on selecting keypoints depending on shape factors to identify distinct features of the object represented by the point cloud, and a descriptor is then calculated for each keypoint by fitting two spheres that describe the local curvature. The method for estimating the point correspondences is to a larger extent based on geometric arguments than the method of Kleppe et al. (IEEE Trans Autom Sci Eng, 2017), which results in improved performance. The accuracy of the curvature-based descriptor is validated in experiments, and is shown to compare favorably to state-of-the-art methods in an experiment on course alignment of industrial parts to be assembled with robots.
      PubDate: 2018-05-03
      DOI: 10.1007/s00006-018-0864-9
      Issue No: Vol. 28, No. 2 (2018)
       
  • Spinor Modules of Clifford Algebras in Classes $$N_{2k-1}$$ N 2 k - 1 and
           $$\Omega _{2k-1}$$ Ω 2 k - 1 are Determined by Irreducible Nonlinear
           Characters of Corresponding Salingaros Vee Groups
    • Authors: Rafał Abłamowicz
      Abstract: Clifford algebras \(C \ell _{2,0}\) and \(C \ell _{1,1}\) are isomorphic simple algebras whose Salingaros vee groups belong to a class \(N_1\) . The algebras are isomorphic to the quotient algebra \(\mathbb {R}[D_8]/\mathcal {J}\) of the group algebra of the dihedral group \(D_8\) modulo an ideal \(\mathcal {J}=(1+\tau )\) where \(\tau \) is a central involution in \(D_8\) . Since all irreducible characters of \(D_8\) , including a single nonlinear character of degree 2, can be realized over  \(\mathbb {R}\) , spinor representations of the Clifford algebras can be realized over \(\mathbb {R}\) and so \(C \ell _{2,0} \cong C \ell _{1,1} \cong \mathbb {R}(2)\) . Spinor modules in \(C \ell _{2,0}\) and \(C \ell _{1,1}\) are isomorphic to irreducible \(\mathbb {R}D_8\) -submodules of dimension 2 of the regular module \(\mathbb {R}D_8\) . As such, they are uniquely determined by the nonlinear character of degree 2. These results are generalized to the vee groups in classes \(N_{2k-1}\) and \(\Omega _{2k-1}\) ( \(1 \le k \le 4\) ). It is proven that each irreducible character of \(G_{p,q}\) in these classes can be realized over \(\mathbb {R}.\) Consequently, every nonlinear character of \(G_{p,q}\) uniquely determines a spinor module of \(C \ell _{p,q}\) which is faithful (resp. unfaithful) when \(G_{p,q}\) is in the class \(N_{2k-1}\) (resp. \(\Omega _{2k-1})\) . This paper is a continuation of [1].
      PubDate: 2018-05-03
      DOI: 10.1007/s00006-018-0867-6
      Issue No: Vol. 28, No. 2 (2018)
       
  • Modified Spherical Harmonics in Four Dimensions
    • Authors: Heinz Leutwiler
      Abstract: The classical theory of spherical harmonics on the unit sphere S is well-known. In an earlier paper, entitled “Modified Spherical Harmonics”, we dealt with a modification of this theory, adapted to the half-sphere \(S_{+}\) , in case of three dimensions. In the present paper we extend these results to the four-dimensional case. Although the results look quite similar, their proofs are not. In \(\mathbb {R}^4 =\left\{ (x,y,t,s) \right\} \) the Laplace equation \(\Delta h=0\) will be replaced by the equation \(s\Delta u+2\,\frac{\partial u}{\partial s}=0\) . Homogeneous polynomial solutions of this equation, if restricted to the half-sphere \(S_{+}=\left\{ (x,y,t,s): x^2 + y^2 + t^2 + s^2=1, s > 0 \right\} \) are called modified spherical harmonics. Endowed with a non-Euclidean scalar product on \(S_{+}\) , these functions behave like the classical spherical harmonics on the full sphere in \(\mathbb {R}^4\) . We shall give an explicit expression for the corresponding zonal harmonics and dwell on their connection with the Poisson-type kernel, adapted to the above differential equation. Finally we shall give an explicit orthonormal system of modified spherical harmonics.
      PubDate: 2018-04-27
      DOI: 10.1007/s00006-018-0861-z
      Issue No: Vol. 28, No. 2 (2018)
       
  • About a Theorem of Hyman Bass and some other Topics
    • Authors: Jacques Helmstetter
      Abstract: Let V be a vector space of finite dimension over a field K, and \(V^*\) the dual space; there is a canonical quadratic form on \(V\oplus V^*\) , and there is a well known group morphism from \(\mathrm {GL}(V)\) into \(\mathrm {O}(V\oplus V^{*})\) . This morphism can be factored through the Clifford-Lipschitz group \(\mathrm {GLip}(V \oplus V^{*})\) that lies over \(\mathrm {O}(V\oplus V^*)\) ; but when K is the field \(\mathbb {R}\) or \(\mathbb {C}\) , it is not possible to factor it through the smaller group \(\mathrm {Spin}(V\oplus V^*)\) ; this follows from a theorem published by H. Bass in 1974. It is worth recalling this theorem, and comparing it with an article published by Doran, Hestenes, Sommen and Van Acker in 1993, which asserts that every Lie group can be embedded in a spinorial group. The falseness of this assertion is explained at the end of this article.
      PubDate: 2018-04-27
      DOI: 10.1007/s00006-018-0863-x
      Issue No: Vol. 28, No. 2 (2018)
       
  • Classical Field Theories from Hamiltonian Constraint: Local Symmetries and
           Static Gauge Fields
    • Authors: Václav Zatloukal
      Abstract: We consider the Hamiltonian constraint formulation of classical field theories, which treats spacetime and the space of fields symmetrically, and utilizes the concept of momentum multivector. The gauge field is introduced to compensate for non-invariance of the Hamiltonian under local transformations. It is a position-dependent linear mapping, which couples to the Hamiltonian by acting on the momentum multivector. We investigate symmetries of the ensuing gauged Hamiltonian, and propose a generic form of the gauge field strength. In examples we show how a generic gauge field can be specialized in order to realize gravitational and/or Yang–Mills interaction. Gauge field dynamics is not discussed in this article. Throughout, we employ the mathematical language of geometric algebra and calculus.
      PubDate: 2018-04-27
      DOI: 10.1007/s00006-018-0865-8
      Issue No: Vol. 28, No. 2 (2018)
       
  • On Weighted Dirac Operators and Their Fundamental Solutions for
           Anisotropic Media
    • Authors: Judith Vanegas; Franklin Vargas
      Abstract: The heat transfer problem in isotropic media has been studied extensively in Clifford analysis, but very little in the anisotropic case for this setting. As a first step in this way, we introduce in this work Dirac operators with weights belonging to the Clifford algebra \({\mathcal {A}}_n\) , which factor the second order elliptic differential operator \( {\tilde{\Delta }}_n= div (B \,\nabla ), \) where \(B \in \mathbb {R}^{n \times n}\) is a symmetric and positive definite matrix. For these weighted Dirac operators we construct fundamental solutions and get a Borel–Pompeiu and Cauchy integral formula.
      PubDate: 2018-04-26
      DOI: 10.1007/s00006-018-0860-0
      Issue No: Vol. 28, No. 2 (2018)
       
  • An Iterative Method to Compute the Dominant Zero of a Quaternionic
           Unilateral Polynomial
    • Authors: Rogério Serôdio; José Augusto Ferreira; José Vitória
      Abstract: The aim of this paper is to propose an iterative method to compute the dominant zero of a quaternionic unilateral polynomial. We prove that the method is convergent in the sense that it generates a sequence of quaternions that converges to the dominant zero of the polynomial. The idea subjacent to this method is the well known Sebastião e Silva’s method, proposed in “Sur une méthode d’approximation semblable à celle de Gräffe”, Portugaliae Mathematica, 1941, to approximate the dominant zero of complex polynomials.
      PubDate: 2018-04-26
      DOI: 10.1007/s00006-018-0866-7
      Issue No: Vol. 28, No. 2 (2018)
       
  • Gleason’s Problem Associated to a Real Ternary Algebra and
           Applications
    • Authors: D. Alpay; A. Vajiac; M. B. Vajiac
      Abstract: This paper is an introduction of a new class of analytic functions defined on a ternary algebra, a three dimensional structure different from \({{\mathbb {C}}}\times {{\mathbb {R}}}\) , i.e. a real commutative algebra given by the linear span of \(\{1,\mathbf{e},\mathbf{e}^2\}\) , where \(\mathbf{e}\not \in {{\mathbb {C}}}\) is a generating unit. We define a single ternary conjugate and we build a new analytic function theory, different from previous approaches, on the basis of this single conjugation (akin to the quaternionic case). We give the solution to the Gleason problem which gives rise to Fueter-type variables and study the space of rational functions in this case.
      PubDate: 2018-04-26
      DOI: 10.1007/s00006-018-0857-8
      Issue No: Vol. 28, No. 2 (2018)
       
  • Immersion in $$\mathbb {R}^n$$ R n by Complex Spinors
    • Authors: Rafael de Freitas Leão; Samuel Augusto Wainer
      Abstract: A beautiful solution to the problem of isometric immersions in \(\mathbb {R}^n\) using spinors was found by Bayard et al. (Pac J Math, arXiv:1505.02935v4 [math-ph], 2016). However to use spinors one must assume that the manifold carries a \(\text{ Spin }\) -structure and, especially for complex manifolds where is more natural to consider \(\text{ Spin }^{\mathbb {C}}\) -structures, this hypothesis is somewhat restrictive. In the present work we show how the above solution can be adapted to \(\text{ Spin }^{\mathbb {C}}\) -structures.
      PubDate: 2018-04-26
      DOI: 10.1007/s00006-018-0856-9
      Issue No: Vol. 28, No. 2 (2018)
       
  • Clifford Algebras as Twisted Group Algebras and the Arf Invariant
    • Authors: Alberto Elduque; Adrián Rodrigo-Escudero
      Abstract: Some connections between quadratic forms over the field of two elements, Clifford algebras of quadratic forms over the real numbers, real graded division algebras, and twisted group algebras will be highlighted. This allows to revisit real Clifford algebras in terms of the Arf invariant of the associated quadratic forms over the field of two elements, and give new proofs of some classical results.
      PubDate: 2018-04-23
      DOI: 10.1007/s00006-018-0862-y
      Issue No: Vol. 28, No. 2 (2018)
       
  • Subalgebras of the Split Octonions
    • Authors: Lida Bentz; Tevian Dray
      Abstract: We classify the subalgebras of the split octonions, paying particular attention to the null subalgebras and their extensions.
      PubDate: 2018-04-23
      DOI: 10.1007/s00006-018-0859-6
      Issue No: Vol. 28, No. 2 (2018)
       
  • First and Second Fundamental Solutions of the Time-Fractional Telegraph
           Equation with Laplace or Dirac Operators
    • Authors: M. Ferreira; M. M. Rodrigues; N. Vieira
      Abstract: In this work we obtain the first and second fundamental solutions (FS) of the multidimensional time-fractional equation with Laplace or Dirac operators, where the two time-fractional derivatives of orders \(\alpha \in ]0,1]\) and \(\beta \in ]1,2]\) are in the Caputo sense. We obtain representations of the FS in terms of Hankel transform, double Mellin-Barnes integrals, and H-functions of two variables. As an application, the FS are used to solve Cauchy problems of Laplace and Dirac type.
      PubDate: 2018-04-23
      DOI: 10.1007/s00006-018-0858-7
      Issue No: Vol. 28, No. 2 (2018)
       
 
 
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