Results 61 to 70 of about 18,831 (324)

A Variation on Uncertainty Principle and Logarithmic Uncertainty Principle for Continuous Quaternion Wavelet Transforms

Abstract and Applied Analysis, 2017
The continuous quaternion wavelet transform (CQWT) is a generalization of the classical continuous wavelet transform within the context of quaternion algebra.
Mawardi Bahri, Ryuichi Ashino
doaj   +1 more source

Contractions on ranks and quaternion types in clifford algebras

Vestnik Samarskogo Gosudarstvennogo Tehničeskogo Universiteta. Seriâ: Fiziko-Matematičeskie Nauki, 2015
In this paper we consider expressions in real and complex Clifford algebras, which we call contractions or averaging. We consider contractions of arbitrary Clifford algebra element.
Dmitry S Shirokov
doaj   +1 more source

Counting problems for geodesics on arithmetic hyperbolic surfaces

, 2017
It is a longstanding problem to determine the precise relationship between the geodesic length spectrum of a hyperbolic manifold and its commensurability class.
Linowitz, Benjamin
core   +1 more source

Graph Attention Neural Networks for Interpretable and Generalizable Prediction of Janus III–Vi Van Der Waals Heterostructures

Advanced Intelligent Discovery, EarlyView.
A crystal graph neural network based on the attention mechanism is proposed in this work. The model dynamically weights features through the attention mechanism, enabling precise prediction of properties of material from structural features. Here, taking Janus III–VI van der Waals heterostructures as a representative case, the properties have been ...
Yudong Shi, Zhao Zheng, Yinggan Zhang, Zhou Cui, Peng Lin, Cuilian Wen, Baisheng Sa, Zhimei Sun   +7 more
wiley   +1 more source

Quadratic Equation in Split Quaternions

Axioms, 2022
Split quaternions are noncommutative and contain nontrivial zero divisors. Generally speaking, it is difficult to solve equations in such an algebra. In this paper, by using the roots of any split quaternions and two real nonlinear systems, we derive ...
Wensheng Cao
doaj   +1 more source

Hypercomplex quantum mechanics

, 1995
The fundamental axioms of the quantum theory do not explicitly identify the algebraic structure of the linear space for which orthogonal subspaces correspond to the propositions (equivalence classes of physical questions).
A. A. Albert, A. Razon, A. Razon, B. Misra, C. Flesia, D. Finkelstein, E. Eisenberg, H. H. Goldstine, H. H. Goldstine, H. Taber, J. W. Gibbs, L. P. Horwitz, L. P. Horwitz, L. P. Horwitz, L. P. Horwitz, L. P. Horwitz, L. P. Howitz, M. B. Green, M. Günaydin, M. Jammer, P. Jordan, S. L. Adler, T. D. Lee, W. R. Hamilton   +23 more
core   +2 more sources

Free Subgroups of Quaternion Algebras [PDF]

Proceedings of the American Mathematical Society, 1993
Using the theory of group actions on trees, we shall prove that if a quaternion algebra over Laurant polynomials is not split then a certain congruence subgroup of the group of norm one elements is a free group. This generalizes and gives an easy, conceptually simpler proof than that given by Pollen for the field of real numbers.
openaire   +2 more sources

Quaternion algebras over local fields [PDF]

, 2021
John Voight
openalex   +1 more source

Interpretability and Representability of Commutative Algebra, Algebraic Topology, and Topological Spectral Theory for Real‐World Data

Advanced Intelligent Discovery, EarlyView.
This article investigates how persistent homology, persistent Laplacians, and persistent commutative algebra reveal complementary geometric, topological, and algebraic invariants or signatures of real‐world data. By analyzing shapes, synthetic complexes, fullerenes, and biomolecules, the article shows how these mathematical frameworks enhance ...
Yiming Ren, Guo‐Wei Wei
wiley   +1 more source

Universal approach to derivation of quaternion rotation formulas [PDF]

MATEC Web of Conferences, 2019
This paper introduces and defines the quaternion with a brief insight into its properties and algebra. The main part of this paper is devoted to the derivation of basic equations of the vector rotation around each rotational x, y, z axis.
Chudá Hana
doaj   +1 more source