Advances in Mathematics, ISSN 0001-8708, 06/2019, Volume 349, pp. 1036 - 1116

We introduce and study the algebras of generalized quaternion type, being natural generalizations of algebras which occurred in the study of blocks of group...

Periodic algebra | Symmetric algebra | Tame algebra | Cohen-Macaulay module | Generalized quaternion type | Weighted surface algebra | QUIVERS | POTENTIALS | MATHEMATICS | FINITE | BLOCKS | PERIODIC RESOLUTIONS | CATEGORY | SELF-INJECTIVE ALGEBRAS

Periodic algebra | Symmetric algebra | Tame algebra | Cohen-Macaulay module | Generalized quaternion type | Weighted surface algebra | QUIVERS | POTENTIALS | MATHEMATICS | FINITE | BLOCKS | PERIODIC RESOLUTIONS | CATEGORY | SELF-INJECTIVE ALGEBRAS

Journal Article

Automatica, ISSN 0005-1098, 03/2019, Volume 101, pp. 207 - 213

In this paper, we consider the solvability of a system of constrained two-sided coupled generalized Sylvester quaternion matrix equations. Some necessary and...

Sylvester matrix equations | General solution | Quaternion | Solvability | SINGULAR-VALUE DECOMPOSITION | SYSTEMS | GENERALIZED SYLVESTER | AUTOMATION & CONTROL SYSTEMS | ENGINEERING, ELECTRICAL & ELECTRONIC

Sylvester matrix equations | General solution | Quaternion | Solvability | SINGULAR-VALUE DECOMPOSITION | SYSTEMS | GENERALIZED SYLVESTER | AUTOMATION & CONTROL SYSTEMS | ENGINEERING, ELECTRICAL & ELECTRONIC

Journal Article

Journal of Algebra and its Applications, ISSN 0219-4988, 08/2018, Volume 17, Issue 8

For a symmetric algebra A over a field K of characteristic p > 0 Kulshammer constructed a descending sequence of ideals of the center of A. If K is perfect,...

socle deformation | Derived equivalences | algebras of quaternion type | tame blocks | Külshammer ideals | stable equivalences of Morita type | MATHEMATICS, APPLIED | SYMMETRIC ALGEBRAS | CATEGORIES | EQUIVALENCE CLASSIFICATION | MATHEMATICS | DOMESTIC TYPE | GENERALIZED REYNOLDS IDEALS | CARTAN INVARIANTS | Kulshammer ideals

socle deformation | Derived equivalences | algebras of quaternion type | tame blocks | Külshammer ideals | stable equivalences of Morita type | MATHEMATICS, APPLIED | SYMMETRIC ALGEBRAS | CATEGORIES | EQUIVALENCE CLASSIFICATION | MATHEMATICS | DOMESTIC TYPE | GENERALIZED REYNOLDS IDEALS | CARTAN INVARIANTS | Kulshammer ideals

Journal Article

Mathematical Methods in the Applied Sciences, ISSN 0170-4214, 12/2018, Volume 41, Issue 18, pp. 9477 - 9484

This article aims to discuss a class of quaternion Fourier integral operators on certain set of generalized functions, leading to a method of discussing...

Boehmian space | generalized quaterion space | quaternion fourier | quaternion | MATHEMATICS, APPLIED | TRANSFORMS | Operators (mathematics) | Convolution | Quaternions | Integrals

Boehmian space | generalized quaterion space | quaternion fourier | quaternion | MATHEMATICS, APPLIED | TRANSFORMS | Operators (mathematics) | Convolution | Quaternions | Integrals

Journal Article

Multiscale Modeling and Simulation, ISSN 1540-3459, 2018, Volume 16, Issue 1, pp. 28 - 77

We introduce a model of multiagent dynamics for self-organized motion; individuals travel at a constant speed while trying to adopt the averaged body attitude...

Vicsek model | Quaternions | Dry active matter | Nematic alignment | Q-tensor | Generalized collision invariant | Body attitude coordination | Self-organized hydrodynamics | Collective motion | generalized collision invariant | quaternions | LIMIT | dry active matter | MODEL | PHYSICS, MATHEMATICAL | CORPORA | self-organized hydrodynamics | SELF-DRIVEN PARTICLES | SUPPLY CHAINS | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MOTION | SYSTEMS | body attitude coordination | collective motion | nematic alignment | EQUATION | FLOCKING | Mathematical Physics | Analysis of PDEs | Mathematics

Vicsek model | Quaternions | Dry active matter | Nematic alignment | Q-tensor | Generalized collision invariant | Body attitude coordination | Self-organized hydrodynamics | Collective motion | generalized collision invariant | quaternions | LIMIT | dry active matter | MODEL | PHYSICS, MATHEMATICAL | CORPORA | self-organized hydrodynamics | SELF-DRIVEN PARTICLES | SUPPLY CHAINS | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MOTION | SYSTEMS | body attitude coordination | collective motion | nematic alignment | EQUATION | FLOCKING | Mathematical Physics | Analysis of PDEs | Mathematics

Journal Article

Circuits, Systems, and Signal Processing, ISSN 0278-081X, 12/2018, Volume 37, Issue 12, pp. 5486 - 5506

In this paper, we introduce the quaternion Fourier number transform (QFNT), which corresponds to a quaternionic version of the well-known number-theoretic...

Engineering | Signal,Image and Speech Processing | Image processing | Electronics and Microelectronics, Instrumentation | Circuits and Systems | Number-theoretic transform | Generalized quaternions | Electrical Engineering | Quaternion Fourier transform | ENCRYPTION | THEORETIC TRANSFORMS | ENGINEERING, ELECTRICAL & ELECTRONIC | Algebra | Digital imaging | Quaternions | Rounding

Engineering | Signal,Image and Speech Processing | Image processing | Electronics and Microelectronics, Instrumentation | Circuits and Systems | Number-theoretic transform | Generalized quaternions | Electrical Engineering | Quaternion Fourier transform | ENCRYPTION | THEORETIC TRANSFORMS | ENGINEERING, ELECTRICAL & ELECTRONIC | Algebra | Digital imaging | Quaternions | Rounding

Journal Article

Optics and Laser Technology, ISSN 0030-3992, 10/2018, Volume 106, pp. 234 - 250

•Two quaternion generalized orthogonal rotation invariant moments are proposed.•The effect of parameter α is analysed for image reconstruction and...

Moment invariants | Object recognition | Image reconstruction | Generalized pseudo-Jacobi-Fourier moments | Generalized Chebyshev-Fourier moments | PHYSICS, APPLIED | MELLIN MOMENTS | IMAGE-ANALYSIS | INVARIANT | TRANSFORM | OPTICS | ZERNIKE MOMENTS | Computer science | Equipment and supplies | Algebra | Image processing | Analysis

Moment invariants | Object recognition | Image reconstruction | Generalized pseudo-Jacobi-Fourier moments | Generalized Chebyshev-Fourier moments | PHYSICS, APPLIED | MELLIN MOMENTS | IMAGE-ANALYSIS | INVARIANT | TRANSFORM | OPTICS | ZERNIKE MOMENTS | Computer science | Equipment and supplies | Algebra | Image processing | Analysis

Journal Article

Advances in Applied Clifford Algebras, ISSN 0188-7009, 3/2018, Volume 28, Issue 1, pp. 1 - 16

Within the framework of the theory of quaternion column–row determinants and using determinantal representations of the Moore–Penrose inverse previously...

Quaternion matrix | Theoretical, Mathematical and Computational Physics | Cramer rule | 15A15 | Secondary 15A09 | System matrix equations | Physics | Mathematical Methods in Physics | Primary 15A33 | 15A24 | Moore–Penrose inverse | Applications of Mathematics | Physics, general | MATHEMATICS, APPLIED | ALGEBRA | SKEW FIELD | LEAST-SQUARES SOLUTIONS | PHYSICS, MATHEMATICAL | Moore-Penrose inverse | GENERALIZED INVERSES | ETA-HERMICITY | WEIGHTED DRAZIN INVERSE | RULE

Quaternion matrix | Theoretical, Mathematical and Computational Physics | Cramer rule | 15A15 | Secondary 15A09 | System matrix equations | Physics | Mathematical Methods in Physics | Primary 15A33 | 15A24 | Moore–Penrose inverse | Applications of Mathematics | Physics, general | MATHEMATICS, APPLIED | ALGEBRA | SKEW FIELD | LEAST-SQUARES SOLUTIONS | PHYSICS, MATHEMATICAL | Moore-Penrose inverse | GENERALIZED INVERSES | ETA-HERMICITY | WEIGHTED DRAZIN INVERSE | RULE

Journal Article

Mathematical Methods in the Applied Sciences, ISSN 0170-4214, 07/2018, Volume 41, Issue 11, pp. 4021 - 4032

Quaternion‐valued signals along with quaternion Fourier transforms (QFT) provide an effective framework for vector‐valued signal and image processing. However,...

convolution theorem | generalized sampling expansions | quaternion Fourier transform | generalized translation | Quaternion‐valued signals | quaternion linear canonical transform | Quaternion-valued signals | MATHEMATICS, APPLIED | THEOREM | COLOR IMAGES | STURM-LIOUVILLE PROBLEMS | HYPERCOMPLEX | MATRICES | LAGRANGE INTERPOLATION | BAND-LIMITED SIGNALS | Linear systems | Fourier transforms | Convolution | Image processing | Quaternions | Signal processing | Sampling

convolution theorem | generalized sampling expansions | quaternion Fourier transform | generalized translation | Quaternion‐valued signals | quaternion linear canonical transform | Quaternion-valued signals | MATHEMATICS, APPLIED | THEOREM | COLOR IMAGES | STURM-LIOUVILLE PROBLEMS | HYPERCOMPLEX | MATRICES | LAGRANGE INTERPOLATION | BAND-LIMITED SIGNALS | Linear systems | Fourier transforms | Convolution | Image processing | Quaternions | Signal processing | Sampling

Journal Article

Advances in Applied Clifford Algebras, ISSN 0188-7009, 9/2013, Volume 23, Issue 3, pp. 673 - 688

In this paper, we investigate some properties of generalized Fibonacci quaternions and Fibonacci-Narayana quaternions in a generalized quaternion algebra.

Mathematical Methods in Physics | Fibonacci quaternions | Theoretical, Mathematical and Computational Physics | Fibonacci-Narayana quaternions | Applications of Mathematics | Physics, general | Physics | generalized Fibonacci quaternions | MATHEMATICS, APPLIED | NUMBERS | PHYSICS, MATHEMATICAL | Computer science | Analysis

Mathematical Methods in Physics | Fibonacci quaternions | Theoretical, Mathematical and Computational Physics | Fibonacci-Narayana quaternions | Applications of Mathematics | Physics, general | Physics | generalized Fibonacci quaternions | MATHEMATICS, APPLIED | NUMBERS | PHYSICS, MATHEMATICAL | Computer science | Analysis

Journal Article

Advances in Applied Clifford Algebras, ISSN 0188-7009, 9/2017, Volume 27, Issue 3, pp. 2201 - 2214

It is established that the precise solutions on the minimum residual and matrix nearness problems of the quaternion matrix equation $${(AXB,DXE)=(C,F)}$$ ( A X...

Theoretical, Mathematical and Computational Physics | 15A06 | Matrix nearness problem | Quaternion matrices | Moore–Penrose generalized inverse | Physics | The minimum residual problem | Mathematical Methods in Physics | 15A24 | Applications of Mathematics | Physics, general | 65F35 | Matrix equation | Moore-Penrose generalized inverse | SYSTEM | MATHEMATICS, APPLIED | GENERAL-SOLUTION | LEAST-NORM | PHYSICS, MATHEMATICAL | Algorithms

Theoretical, Mathematical and Computational Physics | 15A06 | Matrix nearness problem | Quaternion matrices | Moore–Penrose generalized inverse | Physics | The minimum residual problem | Mathematical Methods in Physics | 15A24 | Applications of Mathematics | Physics, general | 65F35 | Matrix equation | Moore-Penrose generalized inverse | SYSTEM | MATHEMATICS, APPLIED | GENERAL-SOLUTION | LEAST-NORM | PHYSICS, MATHEMATICAL | Algorithms

Journal Article

12.
Full Text
Generalized Likelihood Ratios for Testing the Properness of Quaternion Gaussian Vectors

IEEE Transactions on Signal Processing, ISSN 1053-587X, 04/2011, Volume 59, Issue 4, pp. 1356 - 1370

In a recent paper, the second-order statistical analysis of quaternion random vectors has shown that there exist two different kinds of quaternion widely...

propriety | Quaternions | Estimation | Signal processing algorithms | Generalized likelihood ratio test (GLRT) | principal {\BBC} -properness direction | Vectors | Loss measurement | properness | second-order circularity | Testing | Convergence | principal BBC-properness direction | quaternions | SIGNAL | ALGORITHM | COMPLEX RANDOM VECTORS | principal C-properness direction | IMPROPRIETY | CIRCULARITY | ENGINEERING, ELECTRICAL & ELECTRONIC | Technology application | Usage | Mathematical statistics | Analysis | Gaussian processes | Innovations | Signal processing | Likelihood functions | Simulation methods | Studies | BBC | Approximation | Mathematical analysis | Likelihood ratio | Entropy | Gaussian | Vectors (mathematics) | Statistics

propriety | Quaternions | Estimation | Signal processing algorithms | Generalized likelihood ratio test (GLRT) | principal {\BBC} -properness direction | Vectors | Loss measurement | properness | second-order circularity | Testing | Convergence | principal BBC-properness direction | quaternions | SIGNAL | ALGORITHM | COMPLEX RANDOM VECTORS | principal C-properness direction | IMPROPRIETY | CIRCULARITY | ENGINEERING, ELECTRICAL & ELECTRONIC | Technology application | Usage | Mathematical statistics | Analysis | Gaussian processes | Innovations | Signal processing | Likelihood functions | Simulation methods | Studies | BBC | Approximation | Mathematical analysis | Likelihood ratio | Entropy | Gaussian | Vectors (mathematics) | Statistics

Journal Article

Mathematics, ISSN 2227-7390, 01/2019, Volume 7, Issue 1, p. 80

In this paper, we introduce the bicomplex generalized tribonacci quaternions. Furthermore, Binet's formula, generating functions, and the summation formula for...

Bicomplex number | Generalized tribonacci sequence | Bicomplex generalized tribonacci quaternion | MATHEMATICS | bicomplex number | generalized tribonacci sequence | bicomplex generalized tribonacci quaternion

Bicomplex number | Generalized tribonacci sequence | Bicomplex generalized tribonacci quaternion | MATHEMATICS | bicomplex number | generalized tribonacci sequence | bicomplex generalized tribonacci quaternion

Journal Article

Advances in Applied Clifford Algebras, ISSN 0188-7009, 12/2017, Volume 27, Issue 4, pp. 3183 - 3196

By keeping in mind the great number of applications of generalized Sylvester matrix equations in systems and control theory, in this paper we establish some...

11R52 | Quaternion | Theoretical, Mathematical and Computational Physics | Rank | 15A03 | 15B57 | 15A09 | Physics | Mathematical Methods in Physics | 15A24 | Moore–Penrose inverse | 15B33 | Generalized Sylvester matrix equation | Applications of Mathematics | Physics, general | Exclusive solution | CONSISTENCY | MATHEMATICS, APPLIED | PHYSICS, MATHEMATICAL | Moore-Penrose inverse | Control systems | Rankings | Algebra | Algorithms

11R52 | Quaternion | Theoretical, Mathematical and Computational Physics | Rank | 15A03 | 15B57 | 15A09 | Physics | Mathematical Methods in Physics | 15A24 | Moore–Penrose inverse | 15B33 | Generalized Sylvester matrix equation | Applications of Mathematics | Physics, general | Exclusive solution | CONSISTENCY | MATHEMATICS, APPLIED | PHYSICS, MATHEMATICAL | Moore-Penrose inverse | Control systems | Rankings | Algebra | Algorithms

Journal Article

Journal of Theoretical Probability, ISSN 0894-9840, 9/2016, Volume 29, Issue 3, pp. 1100 - 1120

It is well known that the Gaussian symplectic ensemble is defined on the space of $$n\times n$$ n × n quaternion self-dual Hermitian matrices with Gaussian...

Primary 15B52 | Semicircular law | 62E20 | GSE | Probability Theory and Stochastic Processes | Quaternion matrices | Mathematics | Secondary 60F17 | Statistics, general | 60F15 | STATISTICS & PROBABILITY | GENERALIZED WIGNER MATRICES | BULK UNIVERSALITY

Primary 15B52 | Semicircular law | 62E20 | GSE | Probability Theory and Stochastic Processes | Quaternion matrices | Mathematics | Secondary 60F17 | Statistics, general | 60F15 | STATISTICS & PROBABILITY | GENERALIZED WIGNER MATRICES | BULK UNIVERSALITY

Journal Article

Iranian Journal of Science and Technology, Transactions A: Science, ISSN 1028-6276, 6/2019, Volume 43, Issue 3, pp. 1071 - 1080

In this paper, we derive some necessary and sufficient conditions for two, three and four quaternion matrices to be block independent in the least squares...

System of quaternion matrix equations | Materials Science, general | Earth Sciences, general | 15A03 | Generalized inverse | 15A09 | Engineering | Life Sciences, general | 15A24 | Chemistry/Food Science, general | 15A33 | Engineering, general | Physics, general | Block matrix | MULTIDISCIPLINARY SCIENCES

System of quaternion matrix equations | Materials Science, general | Earth Sciences, general | 15A03 | Generalized inverse | 15A09 | Engineering | Life Sciences, general | 15A24 | Chemistry/Food Science, general | 15A33 | Engineering, general | Physics, general | Block matrix | MULTIDISCIPLINARY SCIENCES

Journal Article

Advances in Difference Equations, ISSN 1687-1839, 12/2015, Volume 2015, Issue 1, pp. 1 - 8

In this paper, we give the exponential generating functions for the generalized Fibonacci and generalized Lucas quaternions, respectively. Moreover, we give...

11B39 | Ordinary Differential Equations | Functional Analysis | generalized Lucas quaternions | Analysis | Difference and Functional Equations | Mathematics, general | Mathematics | Partial Differential Equations | generalized Fibonacci quaternions | MATHEMATICS | MATHEMATICS, APPLIED | SUMS | Fibonacci numbers | Usage | Binomial theorem | Difference equations | Quaternions | Binomials | Formulas (mathematics) | Sums

11B39 | Ordinary Differential Equations | Functional Analysis | generalized Lucas quaternions | Analysis | Difference and Functional Equations | Mathematics, general | Mathematics | Partial Differential Equations | generalized Fibonacci quaternions | MATHEMATICS | MATHEMATICS, APPLIED | SUMS | Fibonacci numbers | Usage | Binomial theorem | Difference equations | Quaternions | Binomials | Formulas (mathematics) | Sums

Journal Article

Mediterranean Journal of Mathematics, ISSN 1660-5446, 12/2017, Volume 14, Issue 6, pp. 1 - 12

Let $$V_{n}$$ V n denote the third order linear recursive sequence defined by the initial values $$V_{0}$$ V 0 , $$V_{1}$$ V 1 and $$V_{2}$$ V 2 and the...

11B39 | third order Jacobsthal sequence | 11B83 | 11R52 | Quaternion | generalized Tribonacci sequence | Mathematics, general | Mathematics | Narayana sequence | 11B37 | FIBONACCI QUATERNIONS | MATHEMATICS | MATHEMATICS, APPLIED | IDENTITIES

11B39 | third order Jacobsthal sequence | 11B83 | 11R52 | Quaternion | generalized Tribonacci sequence | Mathematics, general | Mathematics | Narayana sequence | 11B37 | FIBONACCI QUATERNIONS | MATHEMATICS | MATHEMATICS, APPLIED | IDENTITIES

Journal Article

Algebra Colloquium, ISSN 1005-3867, 03/2017, Volume 24, Issue 1, pp. 169 - 180

We in this paper derive necessary and sufficient conditions for the system of the periodic discrete-time coupled Sylvester matrix equations A(k)X(k) + YkBk =...

generalized inverse | rank | quaternion algebra | Sylvester matrix equation | periodic discrete-time equation | POLE ASSIGNMENT | SOLVING TRIANGULAR SYSTEMS | MATHEMATICS, APPLIED | HERMITIAN SOLUTIONS | MATHEMATICS | RECURSIVE BLOCKED ALGORITHMS | CONSISTENCY | OPERATOR-EQUATIONS | INVARIANT SYSTEMS | OUTPUT-FEEDBACK | GENERALIZED SYLVESTER | SIMULTANEOUS DECOMPOSITION

generalized inverse | rank | quaternion algebra | Sylvester matrix equation | periodic discrete-time equation | POLE ASSIGNMENT | SOLVING TRIANGULAR SYSTEMS | MATHEMATICS, APPLIED | HERMITIAN SOLUTIONS | MATHEMATICS | RECURSIVE BLOCKED ALGORITHMS | CONSISTENCY | OPERATOR-EQUATIONS | INVARIANT SYSTEMS | OUTPUT-FEEDBACK | GENERALIZED SYLVESTER | SIMULTANEOUS DECOMPOSITION

Journal Article

20.
Full Text
Augmentation Quotients for Complex Representation Rings of Generalized Quaternion Groups

数学年刊：B辑英文版, ISSN 0252-9599, 2016, Volume 37, Issue 4, pp. 571 - 584

Abstract Denote by Qm the generalized quaternion group of order 4m. Let R（Qm） be its complex representation ring, and △（Qm） its augmentation ideal. In this...

复表示 | 正整数 | 同构类 | 量子力学 | 增广理想 | 广义四元数群 | Augmentation quotients | 16S34 | Generalized quaternion groups | Representation ring | Mathematics, general | Mathematics | Applications of Mathematics | 20C05 | MATHEMATICS

复表示 | 正整数 | 同构类 | 量子力学 | 增广理想 | 广义四元数群 | Augmentation quotients | 16S34 | Generalized quaternion groups | Representation ring | Mathematics, general | Mathematics | Applications of Mathematics | 20C05 | MATHEMATICS

Journal Article

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