Results 11 to 20 of about 542 (165)

Characteristic of Quaternion Algebra Over Fields

Cauchy: Jurnal Matematika Murni dan Aplikasi, 2023
Quaternion is an extension of the complex number system. Quaternion are discovered by formulating 4 points in 4-dimensional vector space using the cross product between two standard vectors. Quaternion algebra over a field is a 4-dimensional vector space
Muhammad Faldiyan, Ema Carnia, Asep K. Supriatna   +2 more
doaj   +1 more source

A novel color images security-based on SPN over the residue classes of quaternion integers [Formula: see text]. [PDF]

Sci Rep
The exponential growth of multimedia data transmission has intensified the demand for advanced image encryption systems capable of resisting contemporary cryptanalytic attacks while maintaining computational efficiency.
Sajjad M, Alqwaifly NA.
europepmc   +2 more sources

RSVD for Three Quaternion Tensors with Applications in Color Video Watermark Processing

Axioms, 2023
In this paper, we study the restricted singular-value decomposition (RSVD) for three quaternion tensors under the Einstein product, and give higher-order RSVD over the quaternion algebra, which can achieve simultaneous singular value decomposition of ...
Wen-Juan Chen, Shao-Wen Yu
doaj   +1 more source

Quaternion and Split Quaternion Neural Networks for Low-Light Color Image Enhancement

IEEE Access, 2023
In this study, two models of multilayer quaternionic feedforward neural networks are presented. Whereas the first model is based on quaternion algebra, the second model uses split quaternion algebra.
Eduardo Jesus De Davila-Meza, Eduardo Jose Bayro-Corrochano   +1 more
doaj   +1 more source

One-dimensional quaternion Laplace transform: Properties and its application to quaternion-valued differential equations

Partial Differential Equations in Applied Mathematics, 2023
This paper is devoted to the study of the quaternion Laplace transform, which is a natural generalization of the classical Laplace transform using the quaternion algebra. We find that some of its properties such as derivative, convolution and correlation
Muhammad Afdal Bau, Mawardi Bahri, Nasrullah Bachtiar, St. Nurhilmah Busrah, Muh. Nur   +4 more
doaj   +1 more source

Existence of Split Property in Quaternion Algebra Over Composite of Quadratic Fields

Cauchy: Jurnal Matematika Murni dan Aplikasi, 2023
Quaternions are extensions of complex numbers that are four-dimensional objects. Quaternion consists of one real number and three complex numbers, commonly denoted by the standard vectors  and .
Muhammad Faldiyan, Ema Carnia, Asep Kuswandi Supriatna   +2 more
doaj   +1 more source

RKHS Representations for Augmented Quaternion Random Signals: Application to Detection Problems

Mathematics, 2022
The reproducing kernel Hilbert space (RKHS) methodology has shown to be a suitable tool for the resolution of a wide range of problems in statistical signal processing both in the real and complex domains.
Antonia Oya
doaj   +1 more source

A Comparative Study of Three Inverse Kinematic Methods of Serial Industrial Robot Manipulators in the Screw Theory Framework

International Journal of Advanced Robotic Systems, 2011
In this paper, we compare three inverse kinematic formulation methods for the serial industrial robot manipulators. All formulation methods are based on screw theory.
Emre Sariyildiz, Eray Cakiray, Hakan Temeltas   +2 more
doaj   +2 more sources

Algebraic Techniques for Canonical Forms and Applications in Split Quaternionic Mechanics

Journal of Mathematics, 2023
The algebra of split quaternions is a recently increasing topic in the study of theory and numerical computation in split quaternionic mechanics. This paper, by means of a real representation of a split quaternion matrix, studies the problem of canonical
Tongsong Jiang, Dong Zhang, Zhenwei Guo, Gang Wang, V. I. Vasil’ev   +4 more
doaj   +1 more source

Unitary Diagonalization of the Generalized Complementary Covariance Quaternion Matrices with Application in Signal Processing

Mathematics, 2023
Let H denote the quaternion algebra. This paper investigates the generalized complementary covariance, which is the ϕ-Hermitian quaternion matrix. We give the properties of the generalized complementary covariance matrices.
Zhuo-Heng He, Xiao-Na Zhang, Xiaojing Chen   +2 more
doaj   +1 more source