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MATHEMATICS (651 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: 8)
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: 21)
Acta Applicandae Mathematicae     Hybrid Journal   (Followers: 1)
Acta Mathematica     Hybrid Journal   (Followers: 11)
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: 7)
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: 10)
Advances in Linear Algebra & Matrix Theory     Open Access   (Followers: 1)
Advances in Materials Sciences     Open Access   (Followers: 16)
Advances in Mathematical Physics     Open Access   (Followers: 5)
Advances in Mathematics     Full-text available via subscription   (Followers: 10)
Advances in Numerical Analysis     Open Access   (Followers: 4)
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: 3)
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: 10)
Algorithms Research     Open Access   (Followers: 1)
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: 7)
American Journal of Operations Research     Open Access   (Followers: 5)
American Mathematical Monthly     Full-text available via subscription   (Followers: 6)
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: 3)
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 Network Science     Open Access  
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   (Followers: 1)
Arnold Mathematical Journal     Hybrid Journal   (Followers: 1)
Artificial Satellites : The Journal of Space Research Centre of Polish Academy of Sciences     Open Access   (Followers: 19)
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: 7)
Australian Primary Mathematics Classroom     Full-text available via subscription   (Followers: 2)
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: 4)
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: 21)
Bruno Pini Mathematical Analysis Seminar     Open Access  
Buletinul Academiei de Stiinte a Republicii Moldova. Matematica     Open Access   (Followers: 7)
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 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)
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: 2)
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: 14)
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: 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: 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: 5)
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: 4)
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)
Foundations and Trends® in Econometrics     Full-text available via subscription   (Followers: 4)

        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  [2355 journals]
  • A Note on Standard Composition Algebras of Types II and III
    • Authors: P. D. Beites; A. P. Nicolás
      Pages: 955 - 964
      Abstract: Some identities satisfied by certain standard composition algebras, of types II and III, are studied and become candidates for the characterization of the mentioned types. Composition algebras of arbitrary dimension, over a field F with char \({(F) \neq 2}\) and satisfying the identity \({x^{2}y = n(x)y}\) are shown to be standard composition algebras of type II. As a consequence, the identity \({yx^{2} = n(x)y}\) characterizes the type III.
      PubDate: 2017-06-01
      DOI: 10.1007/s00006-016-0668-8
      Issue No: Vol. 27, No. 2 (2017)
  • Standard Polynomial Equations Over Division Algebras
    • Authors: Adam Chapman; Casey Machen
      Pages: 1065 - 1072
      Abstract: Given a central division algebra D of degree d over a field F, we associate to any standard polynomial \(\phi (z)=z^n+c_{n-1} z^{n-1}+\cdots +c_0\) over D a “companion polynomial” \(\Phi (z)\) of degree nd with coefficients in F. The roots of \(\Phi (z)\) in D are exactly the set of conjugacy classes of the roots of \(\phi (z)\) . When D is a quaternion algebra, we explain how all the roots of \(\phi (z)\) can be recovered from the roots of \(\Phi (z)\) . Along the way, we are able to generalize a few known facts from \(\mathbb {H}\) to any division algebra. The first is the connection between the right eigenvalues of a matrix and the roots of its characteristic polynomial. The second is the connection between the roots of a standard polynomial and left eigenvalues of the companion matrix.
      PubDate: 2017-06-01
      DOI: 10.1007/s00006-016-0740-4
      Issue No: Vol. 27, No. 2 (2017)
  • A Cauchy Integral Formula for Inframonogenic Functions in Clifford
    • Authors: Arsenio Moreno García; Tania Moreno García; Ricardo Abreu Blaya; Juan Bory Reyes
      Pages: 1147 - 1159
      Abstract: In this paper we derive a Cauchy integral representation formula for the solutions of the sandwich equation \(\partial _{\underline{x}}f\partial _{\underline{x}}=0\) , where \(\partial _{\underline{x}}\) stands for the first-order vector-valued rotation invariant differential operator in the Euclidean space \({\mathbb R}^m\) , called Dirac operator. Such a solutions are referred in the literature as inframonogenic functions and represent an extension of the monogenic functions, i.e., null solutions of \(\partial _{\underline{x}}\) , which represent higher-dimensional generalizations of the classic Cauchy–Riemann operator.
      PubDate: 2017-06-01
      DOI: 10.1007/s00006-016-0745-z
      Issue No: Vol. 27, No. 2 (2017)
  • Similarity and Semi-similarity Relations on the Degenerate Quaternions,
           Pseudodegenerate Quaternions and Doubly Degenerate Quaternions
    • Authors: Abdullah Inalcik
      Pages: 1329 - 1341
      Abstract: In this paper, we establish the concept of similarity and semi-similarity for elements of set of degenerate quaternions, pseudodegenerate quaternions and doubly degenerate quaternions by solving \({ax=xb}\) and \({xay=b, ybx=a}\) , respectively.
      PubDate: 2017-06-01
      DOI: 10.1007/s00006-016-0674-x
      Issue No: Vol. 27, No. 2 (2017)
  • On the Geometry of the Hyperbolic Scator Space in 1+2 Dimensions
    • Authors: Artur Kobus; Jan L. Cieśliński
      Pages: 1369 - 1386
      Abstract: We consider the scator space in 1+2 dimensions—a hypercomplex, non-distributive hyperbolic algebra introduced by Fernández-Guasti and Zaldívar. We find a method for treating scators algebraically by embedding them into a distributive and commutative algebra. A notion of dual scators is introduced and discussed. We also study isometries of the scator space. It turns out that zero divisors cannot be avoided while dealing with these isometries. The scator algebra may be endowed with a nice physical interpretation, although it suffers from lack of some physically demanded important features. Despite that, there arise some open questions, e.g., whether hypothetical tachyons can be considered as usual particles possessing time-like trajectories.
      PubDate: 2017-06-01
      DOI: 10.1007/s00006-016-0658-x
      Issue No: Vol. 27, No. 2 (2017)
  • Linear Spectral Sets and Their Extremal Varieties
    • Authors: John Leventides; George Petroulakis
      Pages: 1503 - 1515
      Abstract: In this article we define a number of varieties and sets in the projective space \({\mathbb{P} \left(\wedge^{2}\mathbb{R}^{n}\right)}\) , which are obtained from the spectral analysis of a 2-tensor in \({\wedge^2\mathbb{R}^n}\) . We refer to these sets as \({\mathcal{G}_{\mathcal{V}}}\) , special cases of which are the Grassmannian and its extremal variety, as well as other sets. We study the problem of finding the projective variety whose 2-tensors in \({\wedge^{2}\mathbb{R}^{n}}\) have the maximum distance from these varieties, via the use of a special mapping which we call Extr \({(\cdot)}\) . It is shown that successive applications of this mapping lead either to the Grassmannian or its Extremal variety.
      PubDate: 2017-06-01
      DOI: 10.1007/s00006-016-0721-7
      Issue No: Vol. 27, No. 2 (2017)
  • Some P-properties of the Quadratic Representations and Automorphism
           Invariance in Euclidean Jordan Algebras
    • Authors: Yuan-Min Li
      Pages: 1517 - 1530
      Abstract: Quadratic representations are very useful in the study of Euclidean Jordan algebras and complementarity problems. In this paper, we provide some characterizations of the complementarity properties for the quadratic representation P a . For example, P a has the E0-property; P a is monotone iff \({\pm a \in {\mathcal K}}\) . In addition, the algebra and cone automorphism invariance of some E-properties are studied. By use of the quadratic representations, the Jordan quad E-property is proved to keep cone automorphism invariant in simple Jordan algebras. The pseudomonotone property is shown to be cone automorphism invariant.
      PubDate: 2017-06-01
      DOI: 10.1007/s00006-016-0678-6
      Issue No: Vol. 27, No. 2 (2017)
  • On $$({\varvec{p,q}})$$ ( p , q ) Baskakov–Durrmeyer–Stancu Operators
    • Authors: Vishnu Narayan Mishra; Shikha Pandey
      Pages: 1633 - 1646
      Abstract: In the present paper, we introduce the generalized form of (p, q) Baskakov–Durrmeyer Operators with Stancu type parameters. We derived the local and global approximation properties of these operators and obtained the convergence rate and behaviour for the Lipschitz functions. Moreover, we give comparisons and some illustrative graphics for the convergence of operators to some function.
      PubDate: 2017-06-01
      DOI: 10.1007/s00006-016-0738-y
      Issue No: Vol. 27, No. 2 (2017)
  • Fourier Multipliers and Dirac Operators
    • Authors: Craig A. Nolder; Guanghong Wang
      Pages: 1647 - 1657
      Abstract: We use Fourier multipliers of the Dirac operator and Cauchy transform to obtain composition theorems and integral representations. In particular we calculate the multiplier of the \(\Pi \) -operator. This operator is the hypercomplex version of the Beurling-Ahlfors transform in the plane. The hypercomplex Beurling-Ahlfors transform is a direct generalization of the Beurling-Ahlfors transform and reduces to this operator in the plane. We give an integral representation for iterations of the hypercomplex Buerling-Ahlfors transform and we present here a bound for the \(L^p\) -norm. Such \(L^p\) -bounds are essential for applications of the Beurling-Ahlfors transformation in the plane. The upper bound presented here is \(m(p^*-1)\) where m is the dimension of the Euclidean space on which the functions are defined, \(1<p<\infty \) and \(p^*=\max (p,p/(p-1))\) . We use recent estimates on second order Riesz transforms to obtain this result. Using the Fourier multiplier of the \(\Pi \) -operator we express this operator as a hypercomplex linear combination of second order Riesz transforms.
      PubDate: 2017-06-01
      DOI: 10.1007/s00006-016-0752-0
      Issue No: Vol. 27, No. 2 (2017)
  • Erratum to: Centrohermitian and Skew-Centrohermitian Solutions to the
           Minimum Residual and Matrix Nearness Problems of the Quaternion Matrix
           Equation $$(AXB,DXE)=(C,F)$$ ( A X B , D X E ) = ( C , F )
    • Authors: S. Şimşek; M. Sarduvan; H. Özdemir
      Pages: 1939 - 1940
      PubDate: 2017-06-01
      DOI: 10.1007/s00006-016-0733-3
      Issue No: Vol. 27, No. 2 (2017)
  • Modeling 3D Geometry in the Clifford Algebra R (4, 4)
    • Authors: Juan Du; Ron Goldman; Stephen Mann
      Abstract: We flesh out the affine geometry of \({{\mathbb {R}}^3}\) represented inside the Clifford algebra \({\mathbb {R}}(4,4)\) . We show how lines and planes as well as conic sections and quadric surfaces are represented in this model. We also investigate duality between different representations of points, lines, and planes, and we show how to represent intersections between these geometric elements. Formulas for lengths, areas, and volumes are also provided.
      PubDate: 2017-07-20
      DOI: 10.1007/s00006-017-0798-7
  • $$\varvec{\sigma }$$ σ -PBW Extensions of Skew Armendariz Rings
    • Authors: Armando Reyes; Héctor Suárez
      Abstract: The aim of this paper is to investigate a general notion of \(\sigma \) -PBW extensions over Armendariz rings. As an application, the properties of Baer, quasi-Baer, p.p., and p.q.-Baer are established for these extensions. We generalize several results in the literature for Ore extensions of injective type and skew PBW extensions.
      PubDate: 2017-07-17
      DOI: 10.1007/s00006-017-0800-4
  • Preface for Special Issue on Geometric Algebra in Computer Science and
    • Authors: Dietmar Hildenbrand; Eckhard Hitzer; George Papagiannakis
      PubDate: 2017-07-15
      DOI: 10.1007/s00006-017-0799-6
  • 3-ary Hom-Lie Superalgebras Induced By Hom-Lie Superalgebras
    • Authors: Baoling Guan; Liangyun Chen; Bing Sun
      Abstract: The purpose of this paper is to study the relationships between a Hom-Lie superalgebra and its induced 3-ary-Hom-Lie superalgebra. We provide an overview of the theory and explore the structure properties such as ideals, center, derived series, solvability, nilpotency, central extensions, and the cohomology.
      PubDate: 2017-07-15
      DOI: 10.1007/s00006-017-0801-3
  • A New Polar Representation for Split and Dual Split Quaternions
    • Authors: Ali Atasoy; Erhan Ata; Yusuf Yayli; Yasemin Kemer
      Abstract: We present a new different polar representation of split and dual split quaternions inspired by the Cayley–Dickson representation. In this new polar form representation, a split quaternion is represented by a pair of complex numbers, and a dual split quaternion is represented by a pair of dual complex numbers as in the Cayley–Dickson form. Here, in a split quaternion these two complex numbers are a complex modulus and a complex argument while in a dual split quaternion two dual complex numbers are a dual complex modulus and a dual complex argument. The modulus and argument are calculated from an arbitrary split quaternion in Cayley–Dickson form. Also, the dual modulus and dual argument are calculated from an arbitrary dual split quaternion in Cayley–Dickson form. By the help of polar representation for a dual split quaternion, we show that a Lorentzian screw operator can be written as product of two Lorentzian screw operators. One of these operators is in the two-dimensional space produced by 1 and i vectors. The other is in the three-dimensional space generated by 1, j and k vectors. Thus, an operator in a four-dimensional space is expressed by means of two operators in two and three-dimensional spaces. Here, vector 1 is in the intersection of these spaces.
      PubDate: 2017-07-03
      DOI: 10.1007/s00006-017-0797-8
  • Intersection of a Double Cone and a Line in the Split-Quaternions Context
    • Authors: R. Serôdio; P. D. Beites; José Vitória
      Abstract: This is a work on an application of the real split-quaternions to Spatial Analytic Geometry. Concretely, the intersection of a double cone and a line, which can be the empty set, a point, two points or a line, is studied in the real split-quaternions setting.
      PubDate: 2017-06-16
      DOI: 10.1007/s00006-017-0796-9
  • Niven’s Algorithm Applied to the Roots of the Companion Polynomial Over
           $${{\mathbb {R}}}^4$$ R 4 Algebras
    • Authors: Gerhard Opfer
      Abstract: This paper will contain an extension of Niven’s algorithm of 1941, which in its original form is designed for finding zeros of unilateral polynomials p over quaternions \({\mathbb {H}}\) . The extensions will cover the algebra \({{\mathbb {H}}_{\mathrm{coq}}}\) of coquaternions, the algebra \({{\mathbb {H}}_{\mathrm{nec}}}\) of nectarines and the algebra \({{\mathbb {H}}_{\mathrm{con}}}\) of conectarines. These are nondivision algebras in \({{\mathbb {R}}}^4\) . In addition, it is also shown that in all algebras the most difficult part of Niven’s algorithm can easily be solved by inserting the roots of the companion polynomial c of p, with the result, that all zeros of all unilateral polynomials over all noncommutative \({{\mathbb {R}}}^4\) algebras can be found. In addition, for all four algebras the maximal number of zeros can be given. For the three nondivision algebras besides the known types of zeros: isolated, spherical, hyperbolic, a new type of zero will appear, which will be called unexpected zero of p.
      PubDate: 2017-06-13
      DOI: 10.1007/s00006-017-0786-y
  • Graded Clifford Algebras and Graded Skew Clifford Algebras and Their Role
           in the Classification of Artin–Schelter Regular Algebras
    • Authors: Padmini Veerapen
      Abstract: This paper is a survey of work done on \(\mathbb {Z}\) -graded Clifford algebras (GCAs) and \(\mathbb {Z}\) -graded skew Clifford algebras (GSCAs) by Vancliff et al. (Commun Algebra 26(4): 1193–1208, 1998), Stephenson and Vancliff (J Algebra 312(1): 86–110, 2007), Cassidy and Vancliff (J Lond Math Soc 81:91–112, 2010), Nafari et al. (J Algebra 346(1): 152–164, 2011), Vancliff and Veerapen (Contemp Math 592: 241–250, 2013), (J Algebra 420:54–64, 2014). In particular, we discuss the hypotheses necessary for these algebras to be Artin Schelter-regular (Adv Math 66:171–216, 1987), (The Grothendieck Festschrift. Birkhäuser, Boston, 1990) and show how certain ‘points’ called, point modules, can be associated to them. We may view an AS-regular algebra as a noncommutative analog of the polynomial ring. We begin our survey with a fundamental result in Vancliff et al. (Commun Algebra 26(4): 1193–1208, 1998) that is essential to subsequent results discussed here: the connection between point modules and rank-two quadrics. Using, in part, this connection the authors in Stephenson and Vancliff (J Algebra 312(1): 86–110, 2007) provide a method to construct GCAs with finitely many distinct isomorphism classes of point modules. In Cassidy and Vancliff (J Lond Math Soc 81:91–112, 2010), Cassidy and Vancliff introduce a quantized analog of a GCA, called a graded skew Clifford algebra and Nafari et al. (J Algebra 346(1): 152–164, 2011) show that most Artin Schelter-regular algebras of global dimension three are either twists of graded skew Clifford algebras of global dimension three or Ore extensions of graded Clifford algebras of global dimension two. Vancliff and Veerapen (Contemp Math 592: 241–250, 2013), (J Algebra 420:54–64, 2014) go a step further and generalize the result of Vancliff et al. (Commun Algebra 26(4): 1193–1208, 1998), between point modules and rank-two quadrics, by showing that point modules over GSCAs are determined by (noncommutative) quadrics of \(\mu \) -rank at most two.
      PubDate: 2017-06-12
      DOI: 10.1007/s00006-017-0795-x
  • Obituary: Professor Waldyr Alves Rodrigues Jr (1946–2017)
    • PubDate: 2017-04-26
      DOI: 10.1007/s00006-017-0785-z
  • Erratum to: The Genesis of Geometric Algebra: A Personal Retrospective
    • Authors: David Hestenes
      PubDate: 2017-03-25
      DOI: 10.1007/s00006-017-0776-0
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