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MATHEMATICS (646 journals)                  1 2 3 4 | Last

Showing 1 - 200 of 538 Journals sorted alphabetically
Abakós     Open Access   (Followers: 3)
Abhandlungen aus dem Mathematischen Seminar der Universitat Hamburg     Hybrid Journal   (Followers: 2)
Academic Voices : A Multidisciplinary Journal     Open Access   (Followers: 2)
Accounting Perspectives     Full-text available via subscription   (Followers: 6)
ACM Transactions on Algorithms (TALG)     Hybrid Journal   (Followers: 16)
ACM Transactions on Computational Logic (TOCL)     Hybrid Journal   (Followers: 4)
ACM Transactions on Mathematical Software (TOMS)     Hybrid Journal   (Followers: 6)
ACS Applied Materials & Interfaces     Full-text available via subscription   (Followers: 20)
Acta Applicandae Mathematicae     Hybrid Journal   (Followers: 1)
Acta Mathematica     Hybrid Journal   (Followers: 9)
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: 5)
Acta Mathematica Vietnamica     Hybrid Journal  
Acta Mathematicae Applicatae Sinica, English Series     Hybrid Journal  
Advanced Science Letters     Full-text available via subscription   (Followers: 4)
Advances in Applied Clifford Algebras     Hybrid Journal   (Followers: 3)
Advances in Calculus of Variations     Hybrid Journal   (Followers: 2)
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: 15)
Advances in Decision Sciences     Open Access   (Followers: 4)
Advances in Difference Equations     Open Access   (Followers: 1)
Advances in Fixed Point Theory     Open Access   (Followers: 5)
Advances in Geosciences (ADGEO)     Open Access   (Followers: 9)
Advances in Linear Algebra & Matrix Theory     Open Access   (Followers: 1)
Advances in Materials Sciences     Open Access   (Followers: 15)
Advances in Mathematical Physics     Open Access   (Followers: 6)
Advances in Mathematics     Full-text available via subscription   (Followers: 10)
Advances in Numerical Analysis     Open Access   (Followers: 3)
Advances in Operations Research     Open Access   (Followers: 11)
Advances in Porous Media     Full-text available via subscription   (Followers: 4)
Advances in Pure and Applied Mathematics     Hybrid Journal   (Followers: 5)
Advances in Pure Mathematics     Open Access   (Followers: 4)
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: 7)
AKSIOMA Journal of Mathematics Education     Open Access   (Followers: 1)
Algebra and Logic     Hybrid Journal   (Followers: 2)
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: 9)
Algorithms Research     Open Access  
American Journal of Biostatistics     Open Access   (Followers: 9)
American Journal of Computational and Applied Mathematics     Open Access   (Followers: 3)
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)
American Mathematical Monthly     Full-text available via subscription   (Followers: 5)
An International Journal of Optimization and Control: Theories & Applications     Open Access   (Followers: 7)
Analele Universitatii Ovidius Constanta - Seria Matematica     Open Access   (Followers: 1)
Analysis     Hybrid Journal   (Followers: 2)
Analysis and Applications     Hybrid Journal   (Followers: 1)
Analysis and Mathematical Physics     Hybrid Journal   (Followers: 4)
Analysis Mathematica     Full-text available via subscription  
Annales Mathematicae Silesianae     Open Access  
Annales mathématiques du Québec     Hybrid Journal   (Followers: 4)
Annales UMCS, 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: 3)
Annals of Data Science     Hybrid Journal   (Followers: 8)
Annals of Discrete Mathematics     Full-text available via subscription   (Followers: 6)
Annals of Mathematics     Full-text available via subscription  
Annals of Mathematics and Artificial Intelligence     Hybrid Journal   (Followers: 6)
Annals of Pure and Applied Logic     Open Access   (Followers: 2)
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)
Applicable Algebra in Engineering, Communication and Computing     Hybrid Journal   (Followers: 2)
Applications of Mathematics     Hybrid Journal   (Followers: 1)
Applied Categorical Structures     Hybrid Journal   (Followers: 2)
Applied Computational Intelligence and Soft Computing     Open Access   (Followers: 12)
Applied Mathematics     Open Access   (Followers: 3)
Applied Mathematics     Open Access   (Followers: 4)
Applied Mathematics & Optimization     Hybrid Journal   (Followers: 4)
Applied Mathematics - A Journal of Chinese Universities     Hybrid Journal  
Applied Mathematics Letters     Full-text available via subscription   (Followers: 1)
Applied Mathematics Research eXpress     Hybrid Journal   (Followers: 1)
Applied Numerical Analysis & Computational Mathematics     Hybrid Journal   (Followers: 5)
Applied Numerical Mathematics     Hybrid Journal   (Followers: 5)
Applied Spatial Analysis and Policy     Hybrid Journal   (Followers: 4)
Arab Journal of Mathematical Sciences     Open Access   (Followers: 2)
Arabian Journal of Mathematics     Open Access   (Followers: 2)
Archive for Mathematical Logic     Hybrid Journal   (Followers: 1)
Archive of Applied Mechanics     Hybrid Journal   (Followers: 4)
Archive of Numerical Software     Open Access  
Archives of Computational Methods in Engineering     Hybrid Journal   (Followers: 4)
Arkiv för Matematik     Hybrid Journal  
Arnold Mathematical Journal     Hybrid Journal   (Followers: 1)
Artificial Satellites : The Journal of Space Research Centre of Polish Academy of Sciences     Open Access   (Followers: 17)
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: 1)
Australian Senior Mathematics Journal     Full-text available via subscription   (Followers: 1)
Automatic Documentation and Mathematical Linguistics     Hybrid Journal   (Followers: 5)
Axioms     Open Access  
Baltic International Yearbook of Cognition, Logic and Communication     Open Access  
Basin Research     Hybrid Journal   (Followers: 3)
BIBECHANA     Open Access  
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: 19)
Bruno Pini Mathematical Analysis Seminar     Open Access  
Buletinul Academiei de Stiinte a Republicii Moldova. Matematica     Open Access   (Followers: 5)
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: 2)
Bulletin of the Brazilian Mathematical Society, New Series     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  
Canadian Journal of Science, Mathematics and Technology Education     Hybrid Journal   (Followers: 18)
Carpathian Mathematical Publications     Open Access   (Followers: 1)
Catalysis in Industry     Hybrid Journal   (Followers: 1)
CAUCHY     Open Access   (Followers: 1)
CEAS Space Journal     Hybrid Journal  
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: 2)
Cogent Mathematics     Open Access   (Followers: 2)
Cognitive Computation     Hybrid Journal   (Followers: 4)
Collectanea Mathematica     Hybrid Journal  
College Mathematics Journal     Full-text available via subscription   (Followers: 1)
COMBINATORICA     Hybrid Journal  
Combustion Theory and Modelling     Hybrid Journal   (Followers: 13)
Commentarii Mathematici Helvetici     Hybrid Journal   (Followers: 1)
Communications in Contemporary Mathematics     Hybrid Journal  
Communications in Mathematical Physics     Hybrid Journal   (Followers: 1)
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: 9)
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: 4)
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: 5)
Concrete Operators     Open Access   (Followers: 4)
Confluentes Mathematici     Hybrid Journal  
COSMOS     Hybrid Journal  
Cryptography and Communications     Hybrid Journal   (Followers: 12)
Cuadernos de Investigación y Formación en Educación Matemática     Open Access  
Cubo. A Mathematical Journal     Open Access  
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: 28)
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: 2)
Discrete Mathematics     Hybrid Journal   (Followers: 7)
Discrete Mathematics & Theoretical Computer Science     Open Access  
Discrete Mathematics, Algorithms and Applications     Hybrid Journal   (Followers: 2)
Discussiones Mathematicae Graph Theory     Open Access   (Followers: 1)
Doklady Mathematics     Hybrid Journal  
Duke Mathematical Journal     Full-text available via subscription   (Followers: 1)
Edited Series on Advances in Nonlinear Science and Complexity     Full-text available via subscription  
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: 3)
Energy for Sustainable Development     Hybrid Journal   (Followers: 9)
Enseñanza de las Ciencias : Revista de Investigación y Experiencias Didácticas     Open Access  
Ensino da Matemática em Debate     Open Access  
Entropy     Open Access   (Followers: 4)
ESAIM: Control Optimisation and Calculus of Variations     Full-text available via subscription   (Followers: 1)
European Journal of Combinatorics     Full-text available via subscription   (Followers: 4)
European Journal of Mathematics     Hybrid Journal   (Followers: 1)
European Scientific Journal     Open Access   (Followers: 2)
Experimental Mathematics     Hybrid Journal   (Followers: 3)
Expositiones Mathematicae     Hybrid Journal   (Followers: 2)
Facta Universitatis, Series : Mathematics and Informatics     Open Access  
Fasciculi Mathematici     Open Access  
Finite Fields and Their Applications     Full-text available via subscription   (Followers: 4)
Fixed Point Theory and Applications     Open Access   (Followers: 1)
Formalized Mathematics     Open Access   (Followers: 2)

        1 2 3 4 | Last

Journal Cover Advances in Applied Clifford Algebras
  [SJR: 0.319]   [H-I: 15]   [3 followers]  Follow
   Hybrid Journal Hybrid journal (It can contain Open Access articles)
   ISSN (Print) 1661-4909 - ISSN (Online) 0188-7009
   Published by Springer-Verlag Homepage  [2335 journals]
  • Super 3-Lie Algebras Induced by Super Lie Algebras
    • Authors: Viktor Abramov
      Pages: 9 - 16
      Abstract: Abstract We propose a notion of a super n-Lie algebra and construct a super n-Lie algebra with the help of a given binary super Lie algebra which is equipped with an analog of a supertrace. We apply this approach to the super Lie algebra of a Clifford algebra with even number of generators and making use of a matrix representation of this super Lie algebra given by a supermodule of spinors we construct a series of super 3-Lie algebras labeled by positive even integers.
      PubDate: 2017-03-01
      DOI: 10.1007/s00006-015-0604-3
      Issue No: Vol. 27, No. 1 (2017)
  • Noncommutative Galois Extensions and Ternary Clifford Analysis
    • Authors: Alexandre Trovon; Osamu Suzuki
      Pages: 59 - 70
      Abstract: Abstract In this paper we introduce the idea of Galois extension for a class of associative algebras and discuss binary and ternary Clifford algebras by such an algebraic construction. Nonion algebra is characterized by Galois extensions and a ternary structure is proposed for \({\mathfrak{su}(3)}\) leading to a duality for certain binary and ternary differential operators.
      PubDate: 2017-03-01
      DOI: 10.1007/s00006-015-0565-6
      Issue No: Vol. 27, No. 1 (2017)
  • Three-Term Recurrence Relations for Systems of Clifford Algebra-Valued
           Orthogonal Polynomials
    • Authors: I. Cação; M. I. Falcão; H. R. Malonek
      Pages: 71 - 85
      Abstract: Abstract Recently, systems of Clifford algebra-valued orthogonal polynomials have been studied from different points of view. We prove in this paper that for their building blocks there exist some three-term recurrence relations, similar to that for orthogonal polynomials of one real variable. As a surprising byproduct of own interest we found out that the whole construction process of Clifford algebra-valued orthogonal polynomials via Gelfand–Tsetlin basis or otherwise relies only on one and the same basic Appell sequence of polynomials.
      PubDate: 2017-03-01
      DOI: 10.1007/s00006-015-0596-z
      Issue No: Vol. 27, No. 1 (2017)
  • General Integral Formulas for k -hyper-mono-genic Functions
    • Authors: Sirkka-Liisa Eriksson; Heikki Orelma
      Pages: 99 - 110
      Abstract: Abstract We are studying a function theory of k-hypermonogenic functions connected to k-hyperbolic harmonic functions that are harmonic with respect to the hyperbolic Riemannian metric $$ds_{k}^{2} = x_{n}^{\frac{2k}{1-n}} \left(dx_{0}^{2} + \cdots + dx_{n}^{2} \right)$$ in the upper half space \({\mathbb{R}_{+}^{n+1} = \left\{\left(x_{0}, \ldots,x_{n}\right)\, \,x_{i} \in \mathbb{R}, x_{n} > 0\right\}}\) . The function theory based on this metric is important, since in case \({k = n-1}\) , the metric is the hyperbolic metric of the Poincaré upper half space and Leutwiler noticed that the power function \({x^{m}\,(m \in \mathbb{N}_{0})}\) , calculated using Clifford algebras, is a conjugate gradient of a hyperbolic harmonic function. We find a fundamental \({k}\) -hyperbolic harmonic function. Using this function we are able to find kernels and integral formulas for k-hypermonogenic functions. Earlier these results have been verified for hypermonogenic functions ( \({k = n-1}\) ) and for k-hyperbolic harmonic functions in odd dimensional spaces.
      PubDate: 2017-03-01
      DOI: 10.1007/s00006-015-0629-7
      Issue No: Vol. 27, No. 1 (2017)
  • Method of Averaging in Clifford Algebras
    • Authors: D. S. Shirokov
      Pages: 149 - 163
      Abstract: Abstract In this paper we consider different operators acting on Clifford algebras. We consider Reynolds operator of Salingaros’ vee group. This operator “average” an action of Salingaros’ vee group on Clifford algebra. We consider conjugate action on Clifford algebra. We present a relation between these operators and projection operators onto fixed subspaces of Clifford algebras. Using method of averaging we present solutions of system of commutator equations.
      PubDate: 2017-03-01
      DOI: 10.1007/s00006-015-0630-1
      Issue No: Vol. 27, No. 1 (2017)
  • Erratum to: Concept of Lie Derivative of Spinor Fields A Geometric
           Motivated Approach
    • Authors: Rafael F. Leão; Waldyr Alves Rodrigues; Samuel A. Wainer
      Pages: 229 - 230
      PubDate: 2017-03-01
      DOI: 10.1007/s00006-015-0632-z
      Issue No: Vol. 27, No. 1 (2017)
  • Using the Symmetries of the Cube and Tetrahedron as a Vehicle for
           Introducing Some Clifford Algebra to High School Students and
           Undergraduate College Students
    • Authors: John Snygg
      Pages: 231 - 239
      Abstract: Abstract This paper outlines how Clifford Algebra can be presented to high school or college students to deal with the symmetries of the Platonic solids. I concentrate on the cube but all five solids are discussed.
      PubDate: 2017-03-01
      DOI: 10.1007/s00006-015-0607-0
      Issue No: Vol. 27, No. 1 (2017)
  • Calculation of Quantum Eigens with Geometrical Algebra Rotors
    • Authors: A. Dargys; A. Acus
      Pages: 241 - 253
      Abstract: Abstract A practical computational method to find the eigenvalues and eigenspinors of quantum mechanical Hamiltonian is presented. The method is based on reduction of the eigenvalue equation to well known geometrical algebra rotor equation and, therefore, allows to replace the usual det (H − E) =  0 quantization condition by much simple vector norm preserving requirement. In order to show how it works in practice a number of examples are worked out in Cl 3,0 (monolayer graphene and spin in the quantum well) and in Cl 3,1 (two coupled two-level atoms and bilayer graphene) algebras.
      PubDate: 2017-03-01
      DOI: 10.1007/s00006-015-0549-6
      Issue No: Vol. 27, No. 1 (2017)
  • Could Elko Spinor Fields Induce VSR Symmetry in the DKP (Meson)
    • Authors: R. T. Cavalcanti; R. da Rocha; J. M. Hoff da Silva
      Pages: 267 - 277
      Abstract: Abstract It is shown that the meson algebra can be faced as the tensor product of Clifford algebras and, then, by constructing the DKP field by means of Elko spinors, we demonstrate that the symmetries of the so called very special relativity are inherited by the DKP field.
      PubDate: 2017-03-01
      DOI: 10.1007/s00006-015-0563-8
      Issue No: Vol. 27, No. 1 (2017)
  • Geometric Algebra to Model Uncertainties in the Discretizable Molecular
           Distance Geometry Problem
    • Authors: Rafael Alves; Carlile Lavor
      Pages: 439 - 452
      Abstract: Abstract The discretizable molecular distance geometry problem (DMDGP) is related to the determination of 3D protein structure using distance information detected by nuclear magnetic resonance (NMR) experiments. The chemistry of proteins and the NMR distance information allow us to define an atomic order \({v_{1},\ldots,v_{n}}\) such that the distances related to the pairs \({\{v_{i-3},v_{i}\},\{v_{i-2},v_{i}\},\{v_{i-1},v_{i}\}}\) , for \({i > 3}\) , are available, which implies that the search space can be represented by a tree. A DMDGP solution can be represented by a path from the root to a leaf node of this tree, found by an exact method, called branch-and-prune (BP). Because of uncertainty in NMR data, some of the distances related to the pairs \({\{v_{i-3},v_{i}\}}\) may not be precise values, being represented by intervals of real numbers \({[\underline{d}_{i-3,i},\overline{d}_{i-3,i}]}\) . In order to apply BP algorithm in this context, sample values from those intervals should be taken. The main problem of this approach is that if we sample many values, the search space increases drastically, and for small samples, no solution can be found. We explain how geometric algebra can be used to model uncertainties in the DMDGP, avoiding sample values from intervals \({[\underline{d}_{i-3,i},\overline{d}_{i-3,i}]}\) and eliminating the heuristic characteristics of BP when dealing with interval distances.
      PubDate: 2017-03-01
      DOI: 10.1007/s00006-016-0653-2
      Issue No: Vol. 27, No. 1 (2017)
  • Matrices of SL $${(4, \mathbb{R})}$$ ( 4 , R ) that are the Product of Two
           Skew-Symmetric Matrices
    • Authors: Lei Dong; Lei Huang; Changpeng Shao; Yong Wen
      Pages: 475 - 489
      Abstract: Abstract The Jordan forms of matrices that are the product of two skew-symmetric matrices over a field of characteristic \({\neq 2}\) have been a research topic in linear algebra since the early twentieth century. For such a matrix, its Jordan form is not necessarily real, nor does the matrix similarity transformation change the matrix into the Jordan form. In 3-D oriented projective geometry, orientation-preserving projective transformations are matrices of \({SL(4, \mathbb{R})}\) , and those matrices of \({SL(4, \mathbb{R})}\) that are the product of two skew-symmetric matrices are the generators of the group \({SL(4, \mathbb{R})}\) . The canonical forms of orientation-preserving projective transformations under the group action of \({SL(4, \mathbb{R})}\) -similarity transformations, called \({SL(4, \mathbb{R})}\) -Jordan forms, are more useful in geometric applications than complex-valued Jordan forms. In this paper, we find all the \({SL(4, \mathbb{R})}\) -Jordan forms of the matrices of \({SL(4, \mathbb{R})}\) that are the product of two skew-symmetric matrices, and divide them into six classes, so that each class has an unambiguous geometric interpretation in 3-D oriented projective geometry. We then consider the lifts of these transformations to SO(3, 3) by extending the action of \({SL(4, \mathbb{R})}\) from points to lines in space, so that in the vector space \({\mathbb{R}^{3, 3}}\) spanned by the Plücker coordinates of lines these projective transformations become special orthogonal transformations, and the six classes are lifted to six different rotations in 2-D planes of \({\mathbb{R}^{3, 3}}\) .
      PubDate: 2017-03-01
      DOI: 10.1007/s00006-016-0701-y
      Issue No: Vol. 27, No. 1 (2017)
  • Inverse Kinematics for a 6-DOF Walking Humanoid Robot Leg
    • Authors: L. Campos-Macías; O. Carbajal-Espinosa; A. Loukianov; E. Bayro-Corrochano
      Pages: 581 - 597
      Abstract: Abstract This paper describes a novel method for solving the inverse kinematics of a humanoid robot leg anthropomorphically configured with 6 degrees of freedom using conformal geometric algebra. We have used different geometric entities such as lines, planes, and spheres in order to achieve the desired position and orientation of the body and the foot, individually reconfiguring the amount of rotation for each joint. The proposed method can be used in a future work to design obstacle avoidance and self collision algorithms. The effectiveness of the proposed algorithm is proved via practical experiments. Results indicate that the proposed algorithm achieves the expected behavior.
      PubDate: 2017-03-01
      DOI: 10.1007/s00006-016-0705-7
      Issue No: Vol. 27, No. 1 (2017)
  • Parallel Clifford Support Vector Machines Using the Gaussian Kernel
    • Authors: Gehová López-González; Nancy Arana-Daniel; Eduardo Bayro-Corrochano
      Pages: 647 - 660
      Abstract: Abstract This work presents a parallelization method for the Clifford support vector machines, based in two characteristics of the Gaussian Kernel. The pure real-valued result and its commutativity allows us to separate the multivector data in its defining subspaces. These subspaces are independent from each other, so we can solve the problem using parallelism. The motivation is to present an easy approach that can be explained using the more common known concepts of complex numbers and quaternions, because in general there exists a lack of familiarity with geometric algebra.
      PubDate: 2017-03-01
      DOI: 10.1007/s00006-016-0726-2
      Issue No: Vol. 27, No. 1 (2017)
  • Bicomplex Harmonic and Isotonic Oscillators: The Excited States
    • Authors: Abhijit Banerjee
      Abstract: Abstract We investigate the complete analytical solutions of quantum mechanical harmonic and isotonic oscillators formulated in the commutative ring of bicomplex numbers. We obtain the explicit closed form expressions for the excited eigenstates and corresponding energy eigenvalues associated with the harmonic and isotonic oscillator potentials by extending the formalism adopted in Banerjee (Ann Phys 377:493, 2017) recently to find the analytical closed form solutions for ground states.
      PubDate: 2017-03-16
      DOI: 10.1007/s00006-017-0772-4
  • A Geometric Algebra Implementation using Binary Tree
    • Authors: Stéphane Breuils; Vincent Nozick; Laurent Fuchs
      Abstract: Abstract This paper presents an efficient implementation of geometric algebra, based on a recursive representation of the algebra elements using binary trees. The proposed approach consists in restructuring a state of the art recursive algorithm to handle parallel optimizations. The resulting algorithm is described for the outer product and the geometric product. The proposed implementation is usable for any dimensions, including high dimension (e.g. algebra of dimension 15). The method is compared with the main state of the art geometric algebra implementations, with a time complexity study as well as a practical benchmark. The tests show that our implementation is at least as fast as the main geometric algebra implementations.
      PubDate: 2017-03-16
      DOI: 10.1007/s00006-017-0770-6
  • Rotations on a Lightcone in Minkowski 3-Space
    • Authors: Hakan Simsek; Mustafa Özdemir
      Abstract: Abstract In this paper the generalization of the rotations on any lightcone in Minkowski 3-space \({\mathbb {R}}_{g}^{1,2}\) is given. The rotation motion on the lightcone is examined by means of a bilinear form and Lorentzian notions. We use the corresponding Rodrigues and Cayley formulas and benefit from the hyperbolic split quaternion product to obtain the corresponding rotation matrix.
      PubDate: 2017-03-16
      DOI: 10.1007/s00006-017-0771-5
  • Pseudo-bundles of Exterior Algebras as Diffeological Clifford Modules
    • Authors: Ekaterina Pervova
      Abstract: Abstract We consider the diffeological pseudo-bundles of exterior algebras, and the Clifford action of the corresponding Clifford algebras, associated to a given finite-dimensional and locally trivial diffeological vector pseudo-bundle, as well as the behavior of the former three constructions (exterior algebra, Clifford action, Clifford algebra) under the diffeological gluing of pseudo-bundles. Despite these being our main object of interest, we dedicate significant attention to the issues of compatibility of pseudo-metrics, and the gluing-dual commutativity condition, that is, the condition ensuring that the dual of the result of gluing together two pseudo-bundles can equivalently be obtained by gluing together their duals, which is not automatic in the diffeological context. We show that, assuming that the dual of the gluing map, which itself does not have to be a diffeomorphism, on the total space is one, the commutativity condition is satisfied, via a natural map, which in addition turns out to be an isometry for the natural pseudo-metrics on the pseudo-bundles involved.
      PubDate: 2017-03-14
      DOI: 10.1007/s00006-017-0769-z
  • Quaternionic Aharonov–Bohm Effect
    • Authors: Sergio Giardino
      Abstract: Abstract A quaternionic analog of the Aharonov–Bohm effect is developed without the usual anti-hermitian operators in quaternionic quantum mechanics. A quaternionic phase links the solutions obtained to ordinary complex wave functions, and new theoretical studies and experimental tests are possible for them.
      PubDate: 2017-03-07
      DOI: 10.1007/s00006-017-0766-2
  • The Relativistic Hamilton–Jacobi Equation for a Massive, Charged and
           Spinning Particle, its Equivalent Dirac Equation and the de Broglie–Bohm
    • Authors: Waldyr Alves Rodrigues; Samuel A. Wainer
      Abstract: Abstract Using Clifford and Spin–Clifford formalisms we prove that the classical relativistic Hamilton Jacobi equation for a charged massive (and spinning) particle interacting with an external electromagnetic field is equivalent to Dirac–Hestenes equation satisfied by a class of spinor fields that we call classical spinor fields. These spinor fields are characterized by having the Takabayashi angle function constant (equal to 0 or \(\pi \) ). We also investigate a nonlinear Dirac–Hestenes like equation that comes from a class of generalized classical spinor fields. Finally, we show that a general Dirac–Hestenes equation (which is a representative in the Clifford bundle of the usual Dirac equation) gives a generalized Hamilton–Jacobi equation where the quantum potential satisfies a severe constraint and the “mass of the particle” becomes a variable. Our results can then eventually explain experimental discrepancies found between prediction for the de Broglie–Bohm theory and recent experiments. We briefly discuss de Broglie’s double solution theory in view of our results showing that it can be realized, at least in the case of spinning free particles.The paper contains several appendices where notation and proofs of some results of the text are presented.
      PubDate: 2017-03-07
      DOI: 10.1007/s00006-017-0768-0
  • Derivations and Linear Connections on Clifford Vector Bundles
    • Authors: Mircea Martin
      Abstract: Abstract The goal of this article is to introduce a concept of Clifford structures on vector bundles as natural extensions of the standard complex and quaternionic structures, and to determine the derivations and linear connections on smooth Clifford vector bundles compatible with their Clifford structures. The basic object used to get such descriptions is an involution on the space of derivations of a Clifford vector bundle explicitly defined in terms of the specific Clifford structure. That involution is actually derived from an operation called the Clifford conjugation relative to a Clifford structure, which is defined in a purely algebraic setting as an involution on the space of derivations of a Euclidean Clifford algebra. Its definition essentially relies on the use and a complete description of the geometric concept of tangent Clifford structures of a Euclidean Clifford algebra.
      PubDate: 2017-03-03
      DOI: 10.1007/s00006-017-0767-1
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