Related papers: A new shift operator-based polynomial method in ad…

In this paper, for a generalised shift operator introduced earlier, we prove theorem of coincidence of classes of functions defined by the order of best approximation by algebraical polynomials and the generalised Lipschitz classes defined…

Real Nullstellensatz is a classical result from Real Algebraic Geometry. It has recently been extended to quaternionic polynomials by Alon and Paran. The aim of this paper is to extend their Quaternionic Nullstellensatz to matrix…

The Koopman operator approach provides a powerful linear description of nonlinear dynamical systems in terms of the evolution of observables. While the operator is typically infinite-dimensional, it is crucial to develop finite-dimensional…

We study distribution of zeros of a complex polynomial whose coefficients has been modified. We give a new proof of the theorem of Rubinstein, and with similar method we prove a new theorem that is not generalization of the previous…

The aim of this article is to define some new families of the special numbers. These numbers provide some further motivation for computation of combinatorial sums involving binomial coefficients and the Euler kind numbers of negative order.…

A novel polynomial expansion method of symmetric Boolean functions is described. The method is efficient for symmetric Boolean function with small set of valued numbers and has the linear complexity for elementary symmetric Boolean…

We give several new algorithms for dense polynomial multiplication based on the Kronecker substitution method. For moderately sized input polynomials, the new algorithms improve on the performance of the standard Kronecker substitution by a…

A new method of algebraic nature is proposed for the study of the asymptotic properties of special polynomials. The technique we foresee is based on the use of umbral operators, allowing a unified treatment of a large body of polynomial…

Many applied time-dependent problems are characterized by an additive representation of the problem operator. Additive schemes are constructed using such a splitting and associated with the transition to a new time level on the basis of the…

A new family of polynomials, called cumulant polynomial sequence, and its extensions to the multivariate case is introduced relied on a purely symbolic combinatorial method. The coefficients of these polynomials are cumulants, but depending…

We study an action of the skew divided difference operators on the Schubert polynomials and give an explicit formula for structural constants for the Schubert polynomials in terms of certain weighted paths in the Bruhat order on the…

Combinatorial methods (or methods of elementary transformations) came to group theory from low-dimensional topology in the beginning of the century. Soon after that, combinatorial group theory became an independent area with its own…

The convergence of a new general variable metric algorithm based on compositions of averaged operators is established. Applications to monotone operator splitting are presented.

Motivated by existing blend-to-zero techniques, a formal framework is developed for defining and constructing blend-to-zero operators on closed intervals for the generation of sufficiently smooth transitions between functions. Such…

Elementary techniques from operational calculus, differential algebra, and noncommutative algebra lead to a new approach for change-point detection, which is an important field of investigation in various areas of applied sciences and…

We discuss a new approach to realization of the well-known Weierstrass's programme on efficient continuation of an analytic element corresponding to a~multivalued analytic function with finite number of branch points. Our approach is based…

In this paper we introduce a new algebraic method in tilings. Combining this method with Hilbert's Nullstellensatz we obtain a necessary condition for tiling $n$-space by translates of a cluster of cubes. Further, the polynomial method will…

We present new polynomial-based methods for discrete-time quaternionic systems, highlighting how noncommutative multiplication modifies classical control approaches. Defining quaternionic polynomials via a backward-shift operator, we…

Schubert polynomials were introduced in the context of the geometry of flag varieties. This paper investigates some of the connections not yet understood between several combinatorial structures for the construction of Schubert polynomials;…

We introduce braided Dunkl operators that are acting on a q-polynomial algebra and q-commute. Generalizing the approach of Etingof and Ginzburg, we explain the q-commutation phenomenon by constructing braided Cherednik algebras for which…