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MATHEMATICS (751 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: 35)
Acta Applicandae Mathematicae     Hybrid Journal   (Followers: 1)
Acta Mathematica     Hybrid Journal   (Followers: 13)
Acta Mathematica Hungarica     Hybrid Journal   (Followers: 2)
Acta Mathematica Scientia     Full-text available via subscription   (Followers: 6)
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: 11)
Advances in Applied Clifford Algebras     Hybrid Journal   (Followers: 4)
Advances in Calculus of Variations     Hybrid Journal   (Followers: 6)
Advances in Catalysis     Full-text available via subscription   (Followers: 5)
Advances in Complex Systems     Hybrid Journal   (Followers: 9)
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: 17)
Advances in Linear Algebra & Matrix Theory     Open Access   (Followers: 6)
Advances in Materials Science     Open Access   (Followers: 15)
Advances in Mathematical Physics     Open Access   (Followers: 5)
Advances in Mathematics     Full-text available via subscription   (Followers: 11)
Advances in Nonlinear Analysis     Open Access  
Advances in Numerical Analysis     Open Access   (Followers: 7)
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: 7)
Advances in Pure Mathematics     Open Access   (Followers: 7)
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: 6)
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: 14)
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     Open Access   (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: 11)
Anadol University Journal of Science and Technology B : Theoritical Sciences     Open Access  
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   (Followers: 1)
Annales mathématiques du Québec     Hybrid Journal   (Followers: 4)
Annales Universitatis Mariae Curie-Sklodowska, sectio A – Mathematica     Open Access   (Followers: 1)
Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica     Open Access  
Annali di Matematica Pura ed Applicata     Hybrid Journal   (Followers: 1)
Annals of Combinatorics     Hybrid Journal   (Followers: 4)
Annals of Data Science     Hybrid Journal   (Followers: 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: 4)
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  
Annals of West University of Timisoara - Mathematics and Computer Science     Open Access  
Annuaire du Collège de France     Open Access   (Followers: 6)
ANZIAM Journal     Open Access   (Followers: 1)
Applicable Algebra in Engineering, Communication and Computing     Hybrid Journal   (Followers: 2)
Applications of Mathematics     Hybrid Journal   (Followers: 2)
Applied Categorical Structures     Hybrid Journal   (Followers: 4)
Applied Computational Intelligence and Soft Computing     Open Access   (Followers: 14)
Applied Mathematics     Open Access   (Followers: 3)
Applied Mathematics     Open Access   (Followers: 7)
Applied Mathematics & Optimization     Hybrid Journal   (Followers: 8)
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: 7)
Arab Journal of Mathematical Sciences     Open Access   (Followers: 4)
Arabian Journal of Mathematics     Open Access   (Followers: 2)
Archive for Mathematical Logic     Hybrid Journal   (Followers: 3)
Archive of Applied Mechanics     Hybrid Journal   (Followers: 6)
Archive of Numerical Software     Open Access  
Archives of Computational Methods in Engineering     Hybrid Journal   (Followers: 6)
Arkiv för Matematik     Hybrid Journal   (Followers: 2)
Armenian Journal of Mathematics     Open Access  
Arnold Mathematical Journal     Hybrid Journal   (Followers: 1)
Artificial Satellites     Open Access   (Followers: 21)
Asia-Pacific Journal of Operational Research     Hybrid Journal   (Followers: 3)
Asian Journal of Algebra     Open Access   (Followers: 1)
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)
Biomath     Open Access  
BIT Numerical Mathematics     Hybrid Journal  
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: 13)
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: 3)
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: 3)
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 Advanced Mathematical Sciences     Open Access  
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  
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: 3)
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: 9)
Computational Mechanics     Hybrid Journal   (Followers: 5)
Computational Methods and Function Theory     Hybrid Journal  
Computational Optimization and Applications     Hybrid Journal   (Followers: 8)
Computers & Mathematics with Applications     Full-text available via subscription   (Followers: 9)
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: 8)
Czechoslovak Mathematical Journal     Hybrid Journal   (Followers: 1)
Demographic Research     Open Access   (Followers: 14)
Demonstratio Mathematica     Open Access  
Dependence Modeling     Open Access  
Design Journal : An International Journal for All Aspects of Design     Hybrid Journal   (Followers: 31)
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: 4)
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  
Econometrics     Open Access   (Followers: 2)
Edited Series on Advances in Nonlinear Science and Complexity     Full-text available via subscription  
Educação Matemática Debate     Open Access  
EduMatSains     Open Access  
Electronic Journal of Combinatorics     Open Access  

        1 2 3 4 | Last

Similar Journals
Journal Cover
Advances in Applied Clifford Algebras
Journal Prestige (SJR): 0.698
Citation Impact (citeScore): 1
Number of Followers: 4  
  Hybrid Journal Hybrid journal (It can contain Open Access articles)
ISSN (Print) 1661-4909 - ISSN (Online) 0188-7009
Published by Springer-Verlag Homepage  [2351 journals]
  • Drinfeld Codoubles of Hom–Hopf Algebras
    • Abstract: The main purpose of the present paper is to develop the theory of center constructions on Hom–Hopf algebras. Let H be a Hom–Hopf algebra, we first introduce the notions of nth Yetter–Drinfeld modules and mth Drinfeld codouble for H. Also we prove that the category \({\mathcal {YD}}_H^H(n)\) of nth Yetter–Drinfeld modules of H is a braided autonomous category. Finally, we show that \({\mathcal {YD}}_H^H(n)\) and \(Corep^{i,j}(CD_m(H))\) (i.e., the corepresentation category of the Drinfeld codouble of H) are braided isomorphic as the full subcategories of \(Corep^{i,j}(H)\) .
      PubDate: 2019-03-16
  • Correction to: Some New Quaternionic Quadratics with Zeros in Terms of
           Second Order Quaternion Recurrences
    • Abstract: Unfortunately, the communicating editor was wrongly published as Dr. Cristina Elena Flaut instead of Prof. Rafał Abłamowicz
      PubDate: 2019-03-04
  • $${2\times 2}$$ 2 × 2 Matrix Representation Forms and Inner Relationships
           of Split Quaternions
    • Abstract: This paper proposes a \({2\times 2}\) real matrix isomorphic representation form of split quaternions and a \({2m\times 2n}\) real matrix isomorphic representation form of \({m\times n}\) split quaternion matrices. In particular, we highlighted the inner relationships among the existing different \({2\times 2}\) matrix representation forms of split quaternions. Furthermore, we studied the inner relationships among different \({2\times 2}\) matrix representation forms of Hamilton quaternions as an application. The forms and relationships discussed in this paper can simplify the computation and make split quaternions get extensive applications.
      PubDate: 2019-03-01
  • On Paravectors and Their Associated Algebras
    • Abstract: Some algebraic structures that can be defined on the spaces of paravectors and k-paravectors are studied. Firstly, a version of the exterior and interior products resembling those in the exterior algebra of k-vectors but according to the k-paravector grading is defined. Secondly, a new Clifford algebra is constructed from the operations of exterior and interior products of paravectors and k-paravectors such that if the original vector space has a metric of signature (n, 0), then the metric of this new Clifford algebras has a metric of signature (1, n). The noticeable difference between this new Clifford algebra and usual ones is the necessity of the conjugation operation in its definition. Thirdly, since the space of k-paravectors is not an invariant space under the Clifford product by a paravector, another product is defined in such a way to make the space of k-paravectors invariant under this product by a paravector. The algebra defined by this product is shown to be a DKP algebra.
      PubDate: 2019-02-26
  • L1-Norm Minimization for Multi-dimensional Signals Based on Geometric
    • Abstract: We address the \(\ell _1 \) -norm minimization problem, which plays an important role in the compressed sensing (CS) theory. While most previous approaches are designed for signals of low dimensions, we present in this paper an algorithm using geometric algebra (GA) for solving the problem of \(\ell _1 \) -norm minimization for multi-dimensional signals with and without noise contamination by converting it to second-order cone programming. The algorithm represents the multi-dimensional signal as a multivector in the GA form to process it in a holistic way without losing the correlation among different dimensions of the multi-dimensional signal. Numerical experiments are provided to demonstrate the effectiveness of the proposed algorithm and its robustness to noise. The proposed algorithm can also be used to guide perfect recovery of multi-dimensional signals, and may find potential applications when CS theory meets the multi-dimensional signal processing.
      PubDate: 2019-02-26
  • Correction to: Poincaré–Bertrand and Hilbert formulas for the
           Cauchy–Cimmino Singular Integrals
    • Abstract: Unfortunately, the name of the communicating editor has been published incorrectly. The correct name is Rafał Abłamowicz
      PubDate: 2019-02-19
  • Characteristic Polynomials in Clifford Algebras and in More General
    • Abstract: This article combines two independent theories: firstly, the algorithm of Faddeev–Leverrier which calculates characteristic polynomials of matrices; secondly, the Descent Theory which, in particular, lets many properties of matrix algebras descend down to Azumaya algebras, especially the characteristic polynomials. The algorithm of Faddeev–Leverrier is completely revisited. The details of the descent are explained as far as they are needed for Clifford algebras over fields.
      PubDate: 2019-02-19
  • Construction of Multivector Inverse for Clifford Algebras Over $$2m+1$$ 2
           m + 1 -Dimensional Vector Spaces from Multivector Inverse for Clifford
           Algebras Over 2 m -Dimensional Vector Spaces
    • Abstract: Assuming known algebraic expressions for multivector inverses in any Clifford algebra over an even dimensional vector space \(\mathbb {R}^{p',q'}\) , \(n'=p'+q'=2m\) , we derive a closed algebraic expression for the multivector inverse over vector spaces one dimension higher, namely over \(\mathbb {R}^{p,q}\) , \(n=p+q=p'+q'+1=2m+1\) . Explicit examples are provided for dimensions \(n'=2,4,6\) , and the resulting inverses for \(n=n'+1=3,5,7\) . The general result for \(n=7\) appears to be the first ever reported closed algebraic expression for a multivector inverse in Clifford algebras Cl(p, q), \(n=p+q=7\) , only involving a single addition of multivector products in forming the determinant.
      PubDate: 2019-02-19
  • Quaternion-Valued Smooth Compactly Supported Orthogonal Wavelets with
    • Abstract: We construct two novel quaternion-valued smooth compactly supported symmetric orthogonal wavelet (QSCSW) filters of length greater than existing ones. In order to obtain their filter coefficients, we propose an optimization-based method for solving a specific kind of multivariate quadratic equations. This method provides a new idea for solving multivariate quadratic equations and could be applied to construct much longer QSCSW filters.
      PubDate: 2019-02-18
  • Solutions of Inhomogeneous Generalized Moisil–Teodorescu Systems in
           Euclidean Space
    • Abstract: Let \(\mathbb R_{0, m+1}^{(s)}\) be the space of s-vectors ( \(0\le s\le m+1\) ) in the Clifford algebra \(\mathbb R_{0, m+1}\) constructed over the quadratic vector space \(\mathbb R^{0, m+1}\) , let \(r, p, q\in \mathbb N\) with \(0\le r\le m+1\) , \(0\le p\le q\) and \(r+2q\le m+1\) and let \(\mathbb R_{0, m+1}^{(r,p,q)}=\sum _{j=p}^q\bigoplus \mathbb R_{0, m+1}^{(r+2j)}\) . Then a \(\mathbb R_{0, m+1}^{(r,p,q)}\) -valued smooth function F defined in an open subset \(\Omega \subset \mathbb R^{m+1}\) is said to satisfy the generalized Moisil–Teodorescu system of type (r, p, q) if \(\partial _x F=0\) in \(\Omega \) , where \(\partial _x\) is the Dirac operator in \(\mathbb R^{m+1}\) . To deal with the inhomogeneous generalized Moisil–Teodorescu systems \(\partial _x F=G\) , with a \(\sum _{j=p}^{q} \bigoplus {\mathbb {R}}^{(r+2j-1)}_{0,m+1}\) -valued continuous function G as a right-hand side, we embed the systems in an appropriate Clifford analysis setting. Necessary and sufficient conditions for the solvability of inhomogeneous systems are provided and its general solution described.
      PubDate: 2019-02-14
  • Monte Carlo Geometry Modeling for Particle Transport Using Conformal
           Geometric Algebra
    • Abstract: The Monte Carlo (MC) simulations are considered the gold-standard method for calculating the transport and interaction of radiation with the matter. A fundamental component of any MC simulation is the geometrical modeling. Current implementations of the geometrical modeling are based only on the Euclidean representations. However, Euclidean representations may not be the best option for speed up the geometric debugging-modeling computations of radiation transport, due to the number of operations involved in the estimation of position and direction of particles within each geometry shape. In this work, it is proposed for the first time, the use of Conformal Geometric Algebra (CGA), for geometric modeling in MC simulation for radiation transport. In this context, we present some elemental CGA equations for the microscopic modeling of positions and rotations of a radiation particle and the macroscopic modeling of geometrical shapes. It is shown that it is possible to take advantage of the expression power of CGA to create and debug geometry modeling with a triboelectric X-ray application. Additionally, some advantages of the CGA for the microscopic geometric computations are explored.
      PubDate: 2019-02-08
  • Differential Calculus of Zeon Functions
    • Abstract: Analogous to real functions, zeon functions are defined as zeon-valued functions of a zeon variable. In this paper, formal criteria for continuity and differentiability of zeon functions are put on a rigorous footing and the “usual” differentiation rules are formally established. As special cases, zeon extensions of real functions and zeon functions of one real variable are considered.
      PubDate: 2019-02-08
  • Born–Infeld Gravity from the MacDowell–Mansouri Action and Its
           Associated $${\varvec{\beta }}$$ β -Term
    • Abstract: In this work a generalization of a Born–Infeld theory of gravity with a topological \(\beta \) -term is proposed. These type of Born–Infeld actions were found from the theory introduced by MacDowell and Mansouri. This theory known as MacDowell–Mansouri (MM) gravity was one of the first attempts to construct a gauge theory of gravitation, and within this framework it was introduced in the action a topological \(\beta \) -term relevant for quantization purposes in an analogous way as in Yang–Mills theory. By the use of the self-dual and antiself-dual actions of MM gravity, we further define a Born–Infeld gravity generalization corresponding to MM gravity with the \(\beta \) -term.
      PubDate: 2019-02-05
  • A Hardware Implementation for Colour Edge Detection Using Prewitt-Inspired
           Filters Based on Geometric Algebra
    • Abstract: Geometric algebra (GA) is a powerful mathematical tool that offers intuitive solutions for image-processing problems, including colour edge detection. Rotor-based and Prewitt-inspired Sangwine (RBS and PIS) filters are amongst the efficient algorithms based on GA operators for solving colour edge detection problem. Algorithms in GA framework have enormous computational load that limits the general-purpose processors’ ability to execute them in reasonable time. Recently, some specialized hardware architectures, called full-hardware implementations, are proposed. These architectures, such as ConformalALU co-processor, are able to execute GA algorithms in acceptable time with the moderate use of computational resources. So far, all colour edge detection hardwares in GA framework exploited RBS filters. Nevertheless, this novel work presents a full-hardware architecture for efficient execution of PIS filters. PIS filters consume less computational resources and are faster to execute. For comparison, the hardware obtained by Gaalop pre-compiler uses twice as much resources with the same speed as the proposed hardware. As an evidence of faster operation, the proposed hardware is able to execute the edge detection algorithm almost 315 times faster than a GA co-processor, with only 2.5 times of its resources.
      PubDate: 2019-02-05
  • Zeros of Zeon Polynomials and the Zeon Quadratic Formula
    • Abstract: Zeon algebras arise as commutative subalgebras of fermions, and can be constructed as subalgebras of Clifford algebras of appropriate signature. Their combinatorial properties have been applied to graph enumeration problems, stochastic integrals, and even routing problems in communication networks. Analogous to real polynomial functions, zeon polynomial functions are defined as zeon-valued polynomial functions of a zeon variable. In this paper, properties of zeon polynomials and their zeros are considered. Nilpotent and invertible zeon zeros of polynomials with real coefficients are characterized, and necessary conditions are established for the existence of zeros of polynomials with zeon coefficients. Quadratic polynomials with zeon coefficients are considered in detail. A “zeon quadratic formula” is developed, and solutions of \(ax^2+bx+c=0\) are characterized with respect to the “zeon discriminant” of the equation.
      PubDate: 2019-01-22
  • R $$\otimes $$ ⊗ C $$\otimes $$ ⊗ H $$\otimes $$ ⊗ O-Valued Gravity
           as a Grand Unified Field Theory
    • Abstract: It is argued how R \(\otimes \) C \(\otimes \) H \(\otimes \) O-valued Gravity (real-complex-quaterno-octonionic Gravity) naturally can describe a Grand Unified Field theory of Einstein’s gravity with a Yang-Mills theory containing the Standard Model group \(SU(3) \times SU(2) \times U(1)\) . In particular, it leads to a \([SU(4)]^4\) symmetry group revealing the possibility of extending the standard model by introducing additional gauge bosons, heavy quarks and leptons, and an extra fourth family of fermions. We finalize by displaying the analog of the Einstein–Hilbert action for \(\mathbf{R} \otimes \mathbf{C} \otimes \mathbf{H} \otimes \mathbf{O}\) -valued gravity via the use of matrices, and which is based on “coloring” the graviton; i.e. by attaching internal indices to the metric \(g_{\mu \nu }\) . In the most general case, U(16) arises as the isometry group, while U(8) is the isometry group in the split-octonion case.
      PubDate: 2019-01-22
  • On a Microscopic Representation of Space-Time III
    • Abstract: Using the Dirac (Clifford) algebra \(\gamma ^{\mu }\) as initial stage of our discussion, we summarize previous work with respect to the isomorphic 15 dimensional Lie algebra su*(4) as complex embedding of sl(2, \(\mathbb {H}\) ), the relation to the compact group SU(4) as well as subgroups and group chains. The main subject, however, is to relate these technical procedures to the geometrical (and physical) background which we see in projective and especially in line geometry of \(\mathbb {R}^{3}\) . This line geometrical description, however, leads to applications and identifications of line Complexe and the discussion of technicalities versus identifications of classical line geometrical concepts, Dirac’s ‘square root of \(p^{2}\) ’, the discussion of dynamics and the association of physical concepts like electromagnetism and relativity. We outline a generalizable framework and concept, and we close with a short summary and outlook.
      PubDate: 2019-01-08
  • Consistently Oriented Dart-based 3D Modelling by Means of Geometric
           Algebra and Combinatorial Maps
    • Abstract: The modelling of real world objects is not a straightforward subject. There are many different schemes; constructive solid geometry (CSG), cell decomposition, boundary representation, etcetera. Obviously, somehow, any scheme will be related to any other since they have a common goal. The paper shows how to model general polyhedra as an unordered discrete and finite set of geometric numbers of a projective Clifford Algebra or Geometric Algebra (GA). Clearly, not any randomly generated finite set of geometric numbers will have the structure of an object, this set must have some well defined properties. The topological properties extracted from this set are mapped to a boundary representation scheme based on a type of combinatorial map called generalised map or n-gmap. The n-gmaps have different types of orbits (in the mathematical sense) to which an attribute can be attached. When the attribute has a geometrical meaning, it is said that it is the geometrical embedding of the n-gmap. In this way the n-gmap holds explicitly the topology or structure already defined by the discrete geometry. In our proposal, each single element of a n-gmap is consistently embedded into a geometrical number also known as multi-vector. The scheme has been implemented by modifying an open source code [46] of n-gmaps. This representation has interesting properties. GA and n-gmaps complement and reinforce each other. For instance; it improves the robustness when computing the structure from the geometrical information. It is capable of computing lengths, areas and volumes of any polyhedral complex (with or without holes) using the orbits of the n-gmap (some examples are given). Finally the paper gives hints about other potentialities.
      PubDate: 2019-01-08
  • On Super Yangian Covariance of the Triple Product System
    • Abstract: We investigate the relation between a triple product system and the super Yangian \(Y(\mathfrak {gl}(2 1))\) . We present the super Yangian covariance structure for a triple product system associated with a rational R-matrix. Moreover, we obtain the ternary Hopf algebraic structure of the super Yangian \(Y(\mathfrak {gl}(2 1))\) .
      PubDate: 2019-01-02
  • Some New Quaternionic Quadratics with Zeros in Terms of Second Order
           Quaternion Recurrences
    • Abstract: In this paper a comprehensive analysis of the Horadam quaternion zeros for some new types of bivariate quadratic quaternion polynomial equations is presented.
      PubDate: 2019-01-02
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