Methods approaching the problem of the Hermite Birkhoff interpolation of scattered data by combining Shepard operators with local interpolating polynomials are not new in literature [1–4]. In [3] combinations of Shepard operators with bivariate Hermite-Birkhoff local interpolating polynomials are introduced to increase the algebraic degree of precision (polynomial reproduction degree) of Shepar...

We consider the class of polynomial differential equations ẋ = λx + Pn(x, y), ẏ = μy + Qn(x, y) in R where Pn(x, y) and Qn(x, y) are homogeneous polynomials of degree n > 1 and λ 6= μ, i.e. the class of polynomial differential systems with a linear node with different eigenvalues and homogeneous nonlinearities. For this class of polynomial differential equations we study the existence and non–e...

in this paper we establish several polynomials similar to bernstein's polynomials and several refinements of  hermite-hadamard inequality for convex functions.

This paper considers parallel Gröbner bases al-gorithms on distributed memory parallel comput-ers with multi-core compute nodes. We summa-rize three different Gröbner bases implementations:shared memory parallel, pure distributed memoryparallel and distributed memory combined withshared memory parallelism. The last algorithm,called distributed hybrid, uses only one c...

We describe a fast method for the evaluation of an arbitrary high-dimensional multivariate algebraic polynomial in Chebyshev form at the nodes of an arbitrary rank-1 Chebyshev lattice. Our main focus is on conditions on rank-1 Chebyshev lattices allowing for the exact reconstruction of such polynomials from samples along such lattices and we present an algorithm for constructing suitable rank-1...

In Cyber-Physical System (CPS), attackers could inject false measurements to the controller through compromised sensor nodes, which not only threaten the security of the system, but also consumes significant network resources. To deal with this issue, a number of en-route filtering schemes have been designed for wireless sensor networks. However, these schemes either lack resilience to the numb...

The study of iterations of functions over a finite field and the corresponding functional graphs is a growing area of research with connections to cryptography. The behaviour of such iterations is frequently approximated by what is know as the Brent-Pollard heuristic, where one treats functions as random mappings. We aim at understanding this heuristic and focus on the expected rho length of a ...

General technical problems of obtaining coefficients of reliability polynomials for different reliability indices, such as all-terminal reliability, average pairwise reliability and average size of a connected sub-graph containing a special node are discussed in the paper. It is shown that one of possible forms of a reliability polynomial presentation helps in considerable speeding up of its ob...

In the large rank limit, for any nonexceptional affine algebra, the graded branching multiplicities known as one-dimensional sums, are conjectured to have a simple relationship with those of type A, which are known as generalized Kostka polynomials. This is called the X = M = K conjecture. It is proved for tensor products of the “symmetric power” Kirillov-Reshetikhin modules for all nonexceptio...