Related papers: RBF Solver for Quaternions Interpolation
We provide a sufficient condition for avoiding squared propagators in the intermediate stages of setting up differential equations for loop integrals. This condition is satisfied in a large class of two- and three-loop diagrams. For these…
Let A be a modular abelian variety over \Q of arbitrary even dimension. We establish criteria to prevent a given quaternion algebra over a totally real number field to be the endomorphism algebra of A over \bar\Q. We accomplish this by…
Over the split-octonion algebra defined over an arbitrary field, we solve all polynomial equations whose coefficients are scalar except for the constant term. As an application, we determine the square and cubic roots of an octonion.
Realizations of four dimensional Lie algebras as vector fields in the plane are explicitly constructed. Fourth order ordinary differential equations which admit such Lie symmetry algebras are derived. The route to their integration is…
We determine endomorphism algebras of abelian surfaces with quaternion multiplication.
Neville's algorithm is known to provide an efficient and numerically stable solution for polynomial interpolations. In this paper, an extension of this algorithm is presented which includes the derivatives of the interpolating polynomial.
Many common methods for data analysis rely on linear algebra. We provide new results connecting data analysis error to numerical accuracy, which leads to the first meaningful stopping criterion for two way spectral partitioning. More…
Solving a quadratic equation $P(x)=ax^2+bx+c=0$ with real coefficients is known to middle school students. Solving the equation over the quaternions is not straightforward. Huang and So \cite{Huang} give a complete set of formulas, breaking…
In this article, we introduce balance equations over commutative rings $R$ and associate $R$-weighted graphs to them so that solving balance equations corresponds to a consistent labeling of vertices of the associated graph. Our primary…
Neural Networks have been widely used to solve Partial Differential Equations. These methods require to approximate definite integrals using quadrature rules. Here, we illustrate via 1D numerical examples the quadrature problems that may…
Over the past century, a correlation has been an essential mathematical technique utilized in engineering sciences, including practically every signal/image processing field. This paper describes an effective method of calculating the…
In this paper, we propose novel quaternion activation functions where we modify either the quaternion magnitude or the phase, as an alternative to the commonly used split activation functions. We define criteria that are relevant for…
We introduce the Segal-Bargmann transform associated to the Mittag Leffler Fock space and study how it will be connected to the Fourier transform. We will discuss also the counterpart of the creation and annihilation operator in this…
We construct r-matrices for simple Lie superalgebras with non-degenerate Killing forms using Belavin-Drinfeld type triples. This construction gives us the standard r-matrices and some nonstandard ones.
We obtain rapidly convergent series expansions of resolvents of operators taking the form ${\bf A}=\Gamma_1{\bf B}\Gamma_1$ where $\Gamma_1({\bf k})$ is a projection that acts locally in Fourier space and ${\bf B}({\bf x})$ is an operator…
Regarding quaternions as normal matrices, we first characterize the $2\times 2$ matrix-valued functions, defined on subsets of quaternions, whose values are quaternions. Then we investigate the regularity of quaternionic-valued functions,…
Dual quaternions and dual quaternion matrices have garnered widespread applications in robotic research, and its spectral theory has been extensively studied in recent years. This paper introduces the novel concept of the dual complex…
There is a commutative algebra of differential-difference operators, acting on polynomials on R_2, associated with the reflection group B2. This paper presents an integral transform which intertwines this algebra, allowing one free…
In this paper, we propose a new approach for fast processing of SPARQL queries on large RDF datasets containing RDF quadruples (or quads). Our approach called RIQ employs a decrease-and-conquer strategy: Rather than indexing the entire RDF…
This paper applies the quadtree structure for image coding. The goal is to adapt the block size and thus to increase the compression ratio (without reducing SNR). Also, the computational time is not significatively increased. It has been…