Related papers: Constructing permutations of finite fields via lin…
A finitely generated shift invariant space $V$ is a closed subspace of $L^2(\R^d)$ that is generated by the integer translates of a finite number of functions. A set of frame generators for $V$ is a set of functions whose integer translates…
By using the piecewise method, Lagrange interpolation formula and Lucas' theorem, we determine explicit expressions of the inverses of a class of reversed Dickson permutation polynomials and some classes of generalized cyclotomic mapping…
Representations of polynomial covariance commutation relations by pairs of linear integral and differential operators are constructed in the space of infinitely continuously differentiable functions. Representations of polynomial covariance…
We consider an arbitrary representation of the additive group over a field of characteristic zero and give an explicit description of a finite separating set in the corresponding ring of invariants.
A method for constructing Lagrangians for the Lie transformation groups is explained. As examples, the Lagrangians for real plane rotations and affine transformations of the real line are constructed.
We present a framework for the construction of linearizations for scalar and matrix polynomials based on dual bases which, in the case of orthogonal polynomials, can be described by the associated recurrence relations. The framework…
This work is divided into three parts. The first part concerns polynomials in one variable with all real roots. We consider linear transformations that preserve real rootedness, as well as matrices that preserve interlacing. The second part…
We prove that generating subspaces of matrix rings over finite fields are counted by polynomials. We use this result to define and study two-variable versions of polynomials counting isomorphism classes of absolutely irreducible…
We give criteria for finite dimensionality or infinite dimensionality of the polynomial centralizer of the Lie algebra of a linear Lie group, in terms of invariants and relative invariants of the group. In the finite dimensional scenario…
The new method for obtaining a variety of extensions of Hermite polynomials is given. As a first example a family of orthogonal polynomial systems which includes the generalized Hermite polynomials is considered. Apparently, either these…
We give new characterizations of the algebra $\mathscr{L}_n(\mathbb{F}_{q^n})$ formed by all linearized polynomials over the finite field $\mathbb{F}_{q^n}$ after briefly surveying some known ones. One isomorphism we construct is between…
A large family of linear, usually overdetermined, systems of partial differential equations that admit a multiplication of solutions, i.e, a bi-linear and commutative mapping on the solution space, is studied. This family of PDE's contains…
We consider chaining multiplicative-inverse operations in finite fields under alternating polynomial bases. When using two distinct polynomial bases to alternate the inverse operation we obtain a partition of $\mathbb F_{p^n}\setminus…
We prove the existence of common hypercyclic, entire functions for certain uncountable families of traslation type operators with relative large gaps.
Finite field transforms have many applications and, in many cases, can be implemented with a low computational complexity. In this paper, the Z Transform over a finite field is introduced and some of its properties are presented.
We survey new results on finite groups of birational transformations of algebraic varieties.
Finite groups with given systems of permuteral and strongly permuteral subgroups are studied. New characterizations of w-supersoluble and supersoluble groups are received.
Tensor transpose is a higher order generalization of matrix transpose. In this paper, we use permutations and symmetry group to define? the tensor transpose. Then we discuss the classification and composition of tensor transposes.…
In this paper we show an alternative way of defining Fourier Series and Transform by using the concept of convolution with exponential signals. This approach has the advantage of simplifying proofs of transforms properties and, in our view,…
It is well known that there exists a significant equivalence between the vector space $\mathbb{F}_{q}^n$ and the finite fields $\mathbb{F}_{q^n}$, and many scholars often view them as the same in most contexts. However, the precise…