Subjects -> MATHEMATICS (Total: 1013 journals)
    - APPLIED MATHEMATICS (92 journals)
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    - MATHEMATICS (714 journals)
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MATHEMATICS (714 journals)                  1 2 3 4 | Last

Showing 1 - 200 of 538 Journals sorted alphabetically
Abakós     Open Access   (Followers: 3)
Abhandlungen aus dem Mathematischen Seminar der Universitat Hamburg     Hybrid Journal   (Followers: 2)
Accounting Perspectives     Full-text available via subscription   (Followers: 4)
ACM Transactions on Algorithms (TALG)     Hybrid Journal   (Followers: 13)
ACM Transactions on Computational Logic (TOCL)     Hybrid Journal   (Followers: 5)
ACM Transactions on Mathematical Software (TOMS)     Hybrid Journal   (Followers: 6)
ACS Applied Materials & Interfaces     Hybrid Journal   (Followers: 39)
Acta Applicandae Mathematicae     Hybrid Journal   (Followers: 2)
Acta Mathematica Hungarica     Hybrid Journal   (Followers: 3)
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: 9)
Advances in Applied Clifford Algebras     Hybrid Journal   (Followers: 5)
Advances in Catalysis     Full-text available via subscription   (Followers: 7)
Advances in Complex Systems     Hybrid Journal   (Followers: 10)
Advances in Computational Mathematics     Hybrid Journal   (Followers: 20)
Advances in Decision Sciences     Open Access   (Followers: 4)
Advances in Difference Equations     Open Access   (Followers: 2)
Advances in Fixed Point Theory     Open Access  
Advances in Geosciences (ADGEO)     Open Access   (Followers: 19)
Advances in Linear Algebra & Matrix Theory     Open Access   (Followers: 9)
Advances in Materials Science     Open Access   (Followers: 19)
Advances in Mathematical Physics     Open Access   (Followers: 5)
Advances in Mathematics     Full-text available via subscription   (Followers: 19)
Advances in Numerical Analysis     Open Access   (Followers: 4)
Advances in Operations Research     Open Access   (Followers: 13)
Advances in Operator Theory     Hybrid Journal  
Advances in Pure Mathematics     Open Access   (Followers: 8)
Advances in Science and Research (ASR)     Open Access   (Followers: 8)
Aequationes Mathematicae     Hybrid Journal   (Followers: 2)
African Journal of Educational Studies in Mathematics and Sciences     Full-text available via subscription   (Followers: 7)
African Journal of Mathematics and Computer Science Research     Open Access   (Followers: 5)
Afrika Matematika     Hybrid Journal   (Followers: 2)
Air, Soil & Water Research     Open Access   (Followers: 6)
AKSIOMATIK : Jurnal Penelitian Pendidikan dan Pembelajaran Matematika     Open Access  
Al-Jabar : Jurnal Pendidikan Matematika     Open Access  
Al-Qadisiyah Journal for Computer Science and Mathematics     Open Access   (Followers: 2)
AL-Rafidain Journal of Computer Sciences and Mathematics     Open Access   (Followers: 3)
Algebra and Logic     Hybrid Journal   (Followers: 7)
Algebra Colloquium     Hybrid Journal   (Followers: 1)
Algebra Universalis     Hybrid Journal   (Followers: 2)
Algorithmic Operations Research     Open Access   (Followers: 5)
Algorithms     Open Access   (Followers: 13)
Algorithms Research     Open Access   (Followers: 1)
American Journal of Computational and Applied Mathematics     Open Access   (Followers: 8)
American Journal of Mathematical Analysis     Open Access   (Followers: 1)
American Journal of Mathematical and Management Sciences     Hybrid Journal  
American Journal of Mathematics     Full-text available via subscription   (Followers: 8)
American Journal of Operations Research     Open Access   (Followers: 6)
American Mathematical Monthly     Full-text available via subscription   (Followers: 3)
An International Journal of Optimization and Control: Theories & Applications     Open Access   (Followers: 12)
Analele Universitatii Ovidius Constanta - Seria Matematica     Open Access  
Analysis and Applications     Hybrid Journal   (Followers: 2)
Analysis and Mathematical Physics     Hybrid Journal   (Followers: 9)
Anargya : Jurnal Ilmiah Pendidikan Matematika     Open Access  
Annales Mathematicae Silesianae     Open Access  
Annales mathématiques du Québec     Hybrid Journal   (Followers: 3)
Annales Universitatis Mariae Curie-Sklodowska, sectio A – Mathematica     Open Access   (Followers: 1)
Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica     Open Access  
Annali di Matematica Pura ed Applicata     Hybrid Journal   (Followers: 1)
Annals of Combinatorics     Hybrid Journal   (Followers: 3)
Annals of Data Science     Hybrid Journal   (Followers: 14)
Annals of Functional Analysis     Hybrid Journal   (Followers: 2)
Annals of Mathematics     Full-text available via subscription   (Followers: 4)
Annals of Mathematics and Artificial Intelligence     Hybrid Journal   (Followers: 16)
Annals of PDE     Hybrid Journal  
Annals of Pure and Applied Logic     Open Access   (Followers: 4)
Annals of the Alexandru Ioan Cuza University - Mathematics     Open Access   (Followers: 1)
Annals of the Institute of Statistical Mathematics     Hybrid Journal   (Followers: 1)
Annals of West University of Timisoara - Mathematics     Open Access   (Followers: 1)
Annuaire du Collège de France     Open Access   (Followers: 6)
ANZIAM Journal     Open Access   (Followers: 1)
Applicable Algebra in Engineering, Communication and Computing     Hybrid Journal   (Followers: 3)
Applications of Mathematics     Hybrid Journal   (Followers: 2)
Applied Categorical Structures     Hybrid Journal   (Followers: 4)
Applied Computational Intelligence and Soft Computing     Open Access   (Followers: 16)
Applied Mathematics     Open Access   (Followers: 7)
Applied Mathematics     Open Access   (Followers: 6)
Applied Mathematics & Optimization     Hybrid Journal   (Followers: 11)
Applied Mathematics - A Journal of Chinese Universities     Hybrid Journal   (Followers: 1)
Applied Mathematics and Nonlinear Sciences     Open Access  
Applied Mathematics Letters     Full-text available via subscription   (Followers: 1)
Applied Mathematics Research eXpress     Hybrid Journal   (Followers: 1)
Applied Network Science     Open Access   (Followers: 2)
Applied Numerical Mathematics     Hybrid Journal   (Followers: 4)
Applied Spatial Analysis and Policy     Hybrid Journal   (Followers: 5)
Arab Journal of Mathematical Sciences     Open Access   (Followers: 3)
Arabian Journal of Mathematics     Open Access   (Followers: 1)
Archive for Mathematical Logic     Hybrid Journal   (Followers: 3)
Archive of Applied Mechanics     Hybrid Journal   (Followers: 4)
Archive of Numerical Software     Open Access  
Archives of Computational Methods in Engineering     Hybrid Journal   (Followers: 5)
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 Research Journal of Mathematics     Open Access  
Asian-European Journal of Mathematics     Hybrid Journal   (Followers: 2)
Australian Mathematics Teacher, The     Full-text available via subscription   (Followers: 7)
Australian Primary Mathematics Classroom     Full-text available via subscription   (Followers: 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: 2)
Banach Journal of Mathematical Analysis     Hybrid Journal  
Basin Research     Hybrid Journal   (Followers: 7)
BIBECHANA     Open Access  
Biomath     Open Access  
BIT Numerical Mathematics     Hybrid Journal  
Boletim Cearense de Educação e História da Matemática     Open Access  
Boletín de la Sociedad Matemática Mexicana     Hybrid Journal  
Bollettino dell'Unione Matematica Italiana     Full-text available via subscription  
British Journal for the History of Mathematics     Hybrid Journal   (Followers: 1)
British Journal of Mathematical and Statistical Psychology     Full-text available via subscription   (Followers: 17)
Buletinul Academiei de Stiinte a Republicii Moldova. Matematica     Open Access   (Followers: 1)
Bulletin des Sciences Mathamatiques     Full-text available via subscription   (Followers: 3)
Bulletin of Dnipropetrovsk University. Series : Communications in Mathematical Modeling and Differential Equations Theory     Open Access   (Followers: 2)
Bulletin of Mathematical Sciences     Open Access   (Followers: 1)
Bulletin of Symbolic Logic     Full-text available via subscription   (Followers: 4)
Bulletin of Taras Shevchenko National University of Kyiv. Series: Physics and Mathematics     Open Access  
Bulletin of the Australian Mathematical Society     Full-text available via subscription   (Followers: 2)
Bulletin of the Brazilian Mathematical Society, New Series     Hybrid Journal  
Bulletin of the Iranian Mathematical Society     Hybrid Journal  
Bulletin of the London Mathematical Society     Hybrid Journal   (Followers: 3)
Bulletin of the Malaysian Mathematical Sciences Society     Hybrid Journal  
Cadernos do IME : Série Matemática     Open Access  
Calculus of Variations and Partial Differential Equations     Hybrid Journal  
Canadian Journal of Mathematics / Journal canadien de mathématiques     Hybrid Journal  
Canadian Journal of Science, Mathematics and Technology Education     Hybrid Journal   (Followers: 20)
Canadian Mathematical Bulletin     Hybrid Journal  
Carpathian Mathematical Publications     Open Access  
Catalysis in Industry     Hybrid Journal  
CAUCHY     Open Access   (Followers: 1)
CEAS Space Journal     Hybrid Journal   (Followers: 6)
CHANCE     Hybrid Journal   (Followers: 5)
Chaos, Solitons & Fractals     Hybrid Journal   (Followers: 1)
Chaos, Solitons & Fractals : X     Open Access   (Followers: 1)
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  
Ciencia     Open Access  
CODEE Journal     Open Access  
Cogent Mathematics     Open Access   (Followers: 2)
Cognitive Computation     Hybrid Journal   (Followers: 2)
Collectanea Mathematica     Hybrid Journal  
College Mathematics Journal     Hybrid Journal   (Followers: 3)
COMBINATORICA     Hybrid Journal  
Combinatorics, Probability and Computing     Hybrid Journal   (Followers: 4)
Combustion Theory and Modelling     Hybrid Journal   (Followers: 18)
Commentarii Mathematici Helvetici     Hybrid Journal   (Followers: 1)
Communications in Combinatorics and Optimization     Open Access  
Communications in Contemporary Mathematics     Hybrid Journal  
Communications in Mathematical Physics     Hybrid Journal   (Followers: 2)
Communications On Pure & Applied Mathematics     Hybrid Journal   (Followers: 6)
Complex Analysis and its Synergies     Open Access   (Followers: 2)
Complex Variables and Elliptic Equations: An International Journal     Hybrid Journal  
Compositio Mathematica     Full-text available via subscription   (Followers: 1)
Comptes Rendus : Mathematique     Open Access  
Computational and Applied Mathematics     Hybrid Journal   (Followers: 3)
Computational and Mathematical Methods     Hybrid Journal  
Computational and Mathematical Methods in Medicine     Open Access   (Followers: 2)
Computational and Mathematical Organization Theory     Hybrid Journal   (Followers: 1)
Computational Complexity     Hybrid Journal   (Followers: 5)
Computational Mathematics and Modeling     Hybrid Journal   (Followers: 8)
Computational Mechanics     Hybrid Journal   (Followers: 11)
Computational Methods and Function Theory     Hybrid Journal  
Computational Optimization and Applications     Hybrid Journal   (Followers: 9)
Computers & Mathematics with Applications     Full-text available via subscription   (Followers: 9)
Confluentes Mathematici     Hybrid Journal  
Constructive Mathematical Analysis     Open Access  
Contributions to Discrete Mathematics     Open Access  
Contributions to Game Theory and Management     Open Access  
COSMOS     Hybrid Journal   (Followers: 1)
Cross Section     Full-text available via subscription   (Followers: 1)
Cryptography and Communications     Hybrid Journal   (Followers: 11)
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  
Daya Matematis : Jurnal Inovasi Pendidikan Matematika     Open Access  
Demographic Research     Open Access   (Followers: 14)
Design Journal : An International Journal for All Aspects of Design     Hybrid Journal   (Followers: 33)
Desimal : Jurnal Matematika     Open Access  
Dhaka University Journal of Science     Open Access  
Differential Equations and Dynamical Systems     Hybrid Journal   (Followers: 2)
Differentsial'nye Uravneniya     Open Access  
Digital Experiences in Mathematics Education     Hybrid Journal   (Followers: 2)
Discrete Mathematics     Hybrid Journal   (Followers: 8)
Discrete Mathematics & Theoretical Computer Science     Open Access   (Followers: 1)
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  
Doklady Akademii Nauk     Open Access  
Doklady Mathematics     Hybrid Journal  
Eco Matemático     Open Access  
Econometrics     Open Access   (Followers: 2)

        1 2 3 4 | Last

Similar Journals
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Advances in Applied Clifford Algebras
Journal Prestige (SJR): 0.698
Citation Impact (citeScore): 1
Number of Followers: 5  
 
  Hybrid Journal Hybrid journal (It can contain Open Access articles)
ISSN (Print) 1661-4909 - ISSN (Online) 0188-7009
Published by Springer-Verlag Homepage  [2469 journals]
  • Extensions and Crossed Modules of $$\varvec{n}$$ n -Lie–Rinehart
           Algebras

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      Abstract: Abstract We introduce a notion of n-Lie–Rinehart algebras as a generalization of Lie–Rinehart algebras to n-ary case. This notion is also an algebraic analogue of n-Lie algebroids. We develop representation theory and describe a cohomology complex of n-Lie–Rinehart algebras. Furthermore, we investigate extension theory of n-Lie–Rinehart algebras by means of 2-cocycles. Finally, we introduce crossed modules of n-Lie–Rinehart algebras to gain a better understanding of their third cohomology groups.
      PubDate: 2022-05-19
       
  • Cameras Seeing Cameras Geometry

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      Abstract: Abstract We study several theoretical aspects of both 2D and 3D intra multi-view geometry of calibrated cameras when all that they can reliably recognize is each other. Starting with minimal reconstructable configurations, we propose a method for obtaining the position-orientation structure of such camera ensembles, up to a global similarity. In the 3D setting we base our analysis on Rodrigues’ vector techniques familiar from mechanics and robotics. We also examine the average number of visible cameras and discuss some kinematic aspects of the problem.
      PubDate: 2022-04-29
       
  • Riemann Boundary Value Problems for Monogenic Functions on the Hyperplane

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      Abstract: Abstract In this paper we systematically study the Riemann boundary value problems on the hyperplane for monogenic functions in Clifford analysis. The concept of the principal part of a sectionally regular function with the hyperplane as its jump surface is first introduced. Based on this concept the general forms of the Riemann boundary value problems on the hyperplane for monogenic functions are formulated. Then, the explicit expressions and explicit solvable conditions for solutions with any finite integer order at infinity are obtained.
      PubDate: 2022-04-20
       
  • Formalizing Geometric Algebra in Lean

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      Abstract: Abstract This paper explores formalizing Geometric (or Clifford) algebras into the Lean 3 theorem prover, building upon the substantial body of work that is the Lean mathematics library, mathlib. As we use Lean source code to demonstrate many of our ideas, we include a brief introduction to the Lean language targeted at a reader with no prior experience with Lean or theorem provers in general. We formalize the multivectors as the quotient of the tensor algebra by a suitable relation, which provides the ring structure automatically, then go on to establish the universal property of the Clifford algebra. We show that this is quite different to the approach taken by existing formalizations of Geometric algebra in other theorem provers; most notably, our approach does not require a choice of basis. We go on to show how operations and structure such as involutions, versors, and the \(\mathbb {Z}_2\) -grading can be defined using the universal property alone, and how to recover an induction principle from the universal property suitable for proving statements about these definitions. We outline the steps needed to formalize the wedge product and \(\mathbb {N}\) -grading, and some of the gaps in mathlib that currently make this challenging.
      PubDate: 2022-04-18
       
  • Brownian Motion, Martingales and Itô Formula in Clifford Analysis

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      Abstract: Abstract Clifford analysis has been the field of active research for several decades resulting in various methods to solve problems in pure and applied mathematics. However, the area of stochastic analysis has not been addressed in its full generality in the Clifford setting, since only a few contributions have been presented so far. Considering that the tools of stochastic analysis play an important role in the study of objects, such as positive definite functions, reproducing kernels and partial differential equations, it is important to develop tools for the study of these objects in the context of Clifford analysis. Therefore, in this work-in-progress paper, we present further steps towards stochastic Clifford analysis by studying random variables, martingales, Brownian motion, and Itô formula in the Clifford setting, as well as their applications in Clifford analysis.
      PubDate: 2022-04-05
       
  • Lyapunov Stability: A Geometric Algebra Approach

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      Abstract: Abstract Lyapunov stability theory for smooth nonlinear autonomous dynamical systems is presented in terms of Geometric Algebra. The system is described by a smooth nonlinear state vector differential equation, driven by a vector field in \(\mathbb {R}^n\) . The level sets of the scalar Lyapunov function candidate are assumed to be compact smooth vector manifolds in \(\mathbb {R}^n\) . The level sets induce an associated global foliation of the state space. On any leaf of this foliation, a geometric subalgebra is naturally attached to the corresponding tangent vector space of the smooth vector manifold. The pseudoscalar (field) of this subalgebra completely characterizes the tangent space. Asymptotic stability of the system equilibria is described in terms of equilibria of, easily computable, rejection vector fields with respect to the pseudoscalar field. Nonexistence of invariant sets of the Lyapunov function directional derivative, along the defining vector field, are also tested using a simple tangency condition. Several illustrative examples are presented.
      PubDate: 2022-03-19
       
  • Clifford-Valued Stockwell Transform and the Associated Uncertainty
           Principles

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      Abstract: Abstract In the framework of higher-dimensional time-frequency analysis, we propose a novel Clifford-valued Stockwell transform for an effective and directional representation of Clifford-valued functions. The proposed transform rectifies the windowed Fourier and wavelet transformations by employing an angular, scalable and localized window, which offers directional flexibility in the multi-scale signal analysis in Clifford domains. The basic properties of the proposed transform such as inner product relation, reconstruction formula, and the range theorem are investigated using the machinery of operator theory and Clifford Fourier transforms. Moreover, several extensions of the well-known Heisenberg-type inequalities are derived for the proposed transform in the Clifford Fourier domain. We culminate our investigation by deriving the directional uncertainty principles for the Clifford-valued Stockwell transform. To validate the acquired results, illustrative examples are given.
      PubDate: 2022-03-19
       
  • Deep Learning Gauss–Manin Connections

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      Abstract: Abstract The Gauss–Manin connection of a family of hypersurfaces governs the change of the period matrix along the family. This connection can be complicated even when the equations defining the family look simple. When this is the case, it is expensive to compute the period matrices of varieties in the family via homotopy continuation. We train neural networks that can quickly and reliably guess the complexity of the Gauss–Manin connection of pencils of hypersurfaces. As an application, we compute the periods of \(96\%\) of smooth quartic surfaces in projective 3-space whose defining equation is a sum of five monomials; from the periods of these quartic surfaces, we extract their Picard lattices and the endomorphism fields of their transcendental lattices.
      PubDate: 2022-02-22
      DOI: 10.1007/s00006-022-01207-1
       
  • Clifford Algebraic Approach to the De Donder–Weyl Hamiltonian Theory

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      Abstract: Abstract The Clifford algebraic formulation of the Duffin–Kemmer–Petiau (DKP) algebras is applied to recast the De Donder–Weyl Hamiltonian (DWH) theory as an algebraic description independent of the matrix representation of the DKP algebra. We show that the DWH equations for antisymmetric fields arise out of the action of the DKP algebra on certain invariant subspaces of the Clifford algebra which carry the representations of the fields. The matrix representation-free formula for the bracket associated with the DKP form of the DWH equations is also derived. This bracket satisfies a generalization of the standard properties of the Poisson bracket.
      PubDate: 2022-02-22
      DOI: 10.1007/s00006-022-01202-6
       
  • Spinorial Representation of Surfaces in Lorentzian Homogeneous Spaces of
           Dimension $$\varvec{3}$$ 3

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      Abstract: Abstract We find a spinorial representation of a Riemannian or Lorentzian surface in a Lorentzian homogeneous space of dimension 3. We in particular obtain a representation theorem for surfaces in \(\mathbb {L}(\kappa ,\tau )\) spaces. We then recover the Calabi correspondence between minimal surfaces in \(\mathbb {R}^3\) and maximal surfaces in \(\mathbb {R}_1^3\) , and obtain a new Lawson type correspondence between CMC surfaces in \(\mathbb {R}_1^3\) and in the 3-dimensional pseudo-hyperbolic space \(\mathbb {H}_1^{3}.\)
      PubDate: 2022-02-21
      DOI: 10.1007/s00006-022-01205-3
       
  • A Use of Elliptic Complex Numbers in Newtonian Gravity

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      Abstract: Abstract In this study, we used the fact that unit circle for elliptic numbers is an ellipse to model motion of a planet around a star. For that purpose we first have given a standard derivation of elliptic orbits in Newtonian two-body problem. Then we translated the variables found in the coordinates where the origin is at the focus of the ellipse to elliptic number parameters where the origin is at the center of the ellipse. We noted that a similar argument may be used to model hyperbolic orbits in Newtonian gravity with hyperbolic numbers. However it seems that modelling parabolic orbits is not possible within the context of p-complex numbers.
      PubDate: 2022-02-21
      DOI: 10.1007/s00006-022-01208-0
       
  • An Operator Related to the Sub-Laplacian on the Quaternionic Heisenberg
           Group

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      Abstract: Abstract We study an operator related to the sub-Laplacian on the non-isotropic quaternionic Heisenberg group and construct the fundamental solution for this operator. For the isotropic case, we derive the closed form of this solution. The techniques we used can be applied to the standard Heisenberg group. We also give the connection between this operator and the Heisenberg sub-Laplacian.
      PubDate: 2022-02-21
      DOI: 10.1007/s00006-022-01206-2
       
  • Multi-modal Medical Image Fusion Based on Geometric Algebra Discrete
           Cosine Transform

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      Abstract: Abstract Multi-modal medical image fusion refers to the combination of patient area images obtained under diverse or identical imaging modalities, which improves the clinical applicability and provides more specific disease information for diagnosis. However, most of the existing image fusion algorithms usually divided color images into three channels of R, G, B for processing separately, which ignores the correlation between the channels and easily causes image information loss and blurring. This paper proposes a multi-modal color medical image fusion algorithm based on geometric algebra discrete cosine transform (GA-DCT). The GA-DCT algorithm combines the character of GA, which represents the multi-vector signal as a whole, can improve the quality of the fusion image and avoid a large number of complex operations related to encoding and decoding. Firstly, the source images are divided into several image blocks and expressed in GA multi-vector form; Secondly, we extend the traditional DCT to GA space and propose GA-DCT; Thirdly, we use GA-DCT to decompose the image to obtain AC and DC coefficients and finally a fusion algorithm are used to fuse the images. The experimental results show that the proposed algorithm can get clear and comprehensive fusion image, which also has great advantages under different compression ratios.
      PubDate: 2022-02-20
      DOI: 10.1007/s00006-021-01197-6
       
  • M, The Power Definition in Geometric Algebra that Unveils the Shortcomings
           of the Nonsinusoidal Apparent Power S

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      Abstract: Abstract The circuit analysis approach based on geometric algebra and \(\varvec{M}\) , the power definition based on the geometric product between the voltage and the current multivectors, are used here to demonstrate the shortcomings of the traditional definition of the non-sinusoidal apparent power S. The shortcomings of S are illustrated in three ways. Firstly, by showing an example of how the norm of \(\varvec{M}\) contains S. Secondly, through six experiments that involve compliance with: Kirchhoff’s circuit laws, Tellegen’s theorem, the principle of conservation of energy, the equivalency of two terminal networks and the concept of reactive power compensation. Lastly, by showing how the use of S leads the current’s physical component power theory astray. The experiments show contradictions between the aforementioned circuit theory fundamentals and the results attained with S but a compelling harmony with the results attained with \(\varvec{M}\) . The evidence reveals two unprecedented discoveries: (1) that mathematical models aimed at explaining energy flow in non-sinusoidal circuits shouldn’t be based on the decomposition of S—as traditionally done— and, (2) the inappropriateness of extrapolating definitions from sinusoidal conditions to non-sinusoidal settings.
      PubDate: 2022-02-18
      DOI: 10.1007/s00006-022-01200-8
       
  • New Applications of Clifford’s Geometric Algebra

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      Abstract: Abstract The new applications of Clifford’s geometric algebra surveyed in this paper include kinematics and robotics, computer graphics and animation, neural networks and pattern recognition, signal and image processing, applications of versors and orthogonal transformations, spinors and matrices, applied geometric calculus, physics, geometric algebra software and implementations, applications to discrete mathematics and topology, geometry and geographic information systems, encryption, and the representation of higher order curves and surfaces.
      PubDate: 2022-02-14
      DOI: 10.1007/s00006-021-01196-7
       
  • MPCEP- $$*$$ ∗ CEPMP-Solutions of Some Restricted Quaternion Matrix
           Equations

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      Abstract: Abstract The notions of the MPCEP inverse and \(*\) CEPMP inverse are expanded to quaternion matrices and their determinantal representations are developed in terms of minors of appropriate matrices. Solvability of novel quaternion restricted matrix equations (QRME) is investigated and their solutions are obtained in terms of the corresponding MPCEP and \(*\) CEPMP inverses. Generalized Cramer’s rules for obtained solutions to new QRME are developed. A numerical example is presented to illustrate the derived results.
      PubDate: 2022-02-02
      DOI: 10.1007/s00006-021-01192-x
       
  • Ellipticity of Some Higher Order Conformally Invariant Differential
           Operators

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      Abstract: Abstract In this article, we prove the ellipticity of higher order conformally invariant differential operators in the higher spin spaces, where functions take values in certain irreducible representations of the spin group in the Euclidean space. We introduce the product formulas for these operators obtained in our previous work to greatly simplify our proofs. In both the bosonic cases and fermionic cases, our product formula enables us to use similar methods as for the higher spin Laplace operator, exploiting the structure of the conformal Lie algebra and branching rules.
      PubDate: 2022-01-31
      DOI: 10.1007/s00006-022-01198-z
       
  • Properties of Clifford-Legendre Polynomials

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      Abstract: Abstract Clifford-Legendre and Clifford–Gegenbauer polynomials are eigenfunctions of certain differential operators acting on functions defined on m-dimensional euclidean space \({\mathbb R}^m\) and taking values in the associated Clifford algebra \({\mathbb R}_m\) . New recurrence and Bonnet-type formulae for these polynomials are provided, and their Fourier transforms are computed. Explicit representations in terms of spherical monogenics and Jacobi polynomials are given, with consequences including the interlacing of zeros. In the case \(m=2\) we describe a degeneracy between the even- and odd-indexed polynomials.
      PubDate: 2022-01-31
      DOI: 10.1007/s00006-021-01179-8
       
  • Twistor Operators in Symplectic Geometry

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      Abstract: Abstract On a symplectic manifold equipped with a symplectic connection and a metaplectic structure, we define two families of sequences of differential operators, called the symplectic twistor operators. We prove that if the connection is torsion-free and Weyl-flat, the sequences in these families form complexes.
      PubDate: 2022-01-31
      DOI: 10.1007/s00006-022-01199-y
       
  • Some Estimates Over Spacelike Spin Hypersurfaces of Lorentzian Manifold

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      Abstract: Abstract We generalized the lower bound estimates for eigenvalues of the Dirac operator on spacelike hypersurfaces of Lorentzian manifolds obtained by Yongfa Chen in (Sci China Ser A Math 52(11):2459–2468, 2009) based on the constraint between the scalar curvature of the manifold, energy–momentum tensor and the mean curvature of the manifold. Afterwards, we examined the geometric data in the case of estimation satisfies equality condition.
      PubDate: 2022-01-31
      DOI: 10.1007/s00006-022-01201-7
       
 
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School of Mathematical and Computer Sciences
Heriot-Watt University
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