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Functions of several quaternion variables are investigated and integral representation theorems for them are proved. With the help of them solutions of the $\tilde \partial $-equations are studied. Moreover, quaternion Stein manifolds are…
Already for bivariate tropical polynomials, factorization is an NP-Complete problem. In this paper, we give an efficient algorithm for factorization and rational factorization of a rich class of tropical polynomials in $n$ variables.…
We study polynomial iterative roots of polynomials and describe the locus of complex polynomials of degree 4 admitting a polynomial iterative square root.
We consider a new class of quaternionic mappings, associated with the spatial partial differential equations. We describe all mappings from this class using four analytic functions of the complex variable.
Locating the zeros of quaternionic polynomials is a fundamental problem with significant implications across scientific and engineering disciplines, yet the noncommutative nature of quaternion multiplication makes it fundamentally more…
This paper discusses the split feasibility problem with polynomials. The sets are semi-algebraic, defined by polynomial inequalities. They can be either convex or nonconvex, either feasible or infeasible. We give semidefinite relaxations…
This paper is concerned with the factorization and equivalence problems of multivariate polynomial matrices. We present some new criteria for the existence of matrix factorizations for a class of multivariate polynomial matrices, and obtain…
We study the factorization of the PT symmetric Hamiltonian. The general expression for the superpotential corresponding to the PT symmetric potential is obtained and explicit examples are presented.
Let $L$ be a separable quadratic extension of either $\mathbb{Q}$ or $\mathbb{F}_q(t)$. We propose efficient algorithms for finding isomorphisms between quaternion algebras over $L$. Our techniques are based on computing maximal one-sided…
We study systems of quadratic forms over fields and their isotropy over 2-extensions. We apply this to obtain particular splitting fields for quaternion algebras defined over a finite field extension. As a consequence, we obtain that every…
The satisfactory development of Quaternionic Analysis has indicated new solutions for physical and mathematical problems. It is worth mentioning the fact that quaternions possess four dimensions, and in this way they may be considered as…
Motion polynomials are a specific type of polynomial over a Clifford algebra that can conveniently describe rational motions. There exists an algorithm for the factorization of motion polynomials that works in generic cases. It hinges on…
This paper investigates some univariate and bivariate constrained interpolation problems using rational quartic fractal interpolation functions, which has been submitted long back in a reputed journal and revised as per the journal…
Schroedinger's famous quadruple of factorizations of the hypergeometric equation is archived here
We discuss an unusual phenomenon in (integral) positive ternary quadratic forms. We also describe an interesting pairing of genera of ternary forms.
Multidimensional factorization method is formulated in arbitrary curvilinear coordinates. Particular cases of polar and spherical coordinates are considered and matrix potentials with separating variables are constructed. A new class of…
We formulate and prove a criterion for reducibility of a quadratic polynomial over the integers. The main theorem was suggested by the teaching experience with the concrete material called "the polynomial box". Through the corollaries we…
We treat the quaternionic Fourier transform (QFT) applied to quaternion fields and investigate QFT properties useful for applications. Different forms of the QFT lead us to different Plancherel theorems. We relate the QFT computation for…
We show some elementary facts about the semantical analogue of Parikh's Splitting, which we call Factorization.
We briefly introduce several problems: (1) a generalization of the convex fair partition conjecture, (2) on non-trivial invariants among polyhedrons that can be formed from the same set of face polygons, (3) two questions on assembling…