Related papers: Forms of Nice Functions
We consider several classes of complete intersection numerical semigroups, aris- ing from many different contexts like algebraic geometry, commutative algebra, coding theory and factorization theory. In particular, we determine all the…
Imposing some conditions on derivatives of the known functions, using the Fiber Contraction Theorem we prove the existence of $C^1$ solutions of a class of iterative functional equations which involves iterates of the unknown functions and…
Let G be a finite group of order n and V an irreducible representation over the complex numbers of dimension d. For some nonnegative number e, we have n=d(d+e). If e is small, then the character of V has unusually large degree. We fix e and…
We consider sequences of integers defined by a system of linear inequalities with integer coefficients. We show that when the constraints are strong enough to guarantee that all the entries are nonnegative, the generating function for the…
Inspired by Quantum Mechanics, we reformulate Hilbert's tenth problem in the domain of integer arithmetics into problems involving either a set of infinitely-coupled non-linear differential equations or a class of linear Schr\"odinger…
Using tools from computable analysis we develop a notion of effectiveness for general dynamical systems as those group actions on arbitrary spaces that contain a computable representative in their topological conjugacy class. Most natural…
We begin by defining general hypergeometric functions over finite fields and obtaining a finite field analogue of a classical symmetry in their complex counterparts. We give a geometric proof for the symmetry by constructing isomorphisms…
We study the continuous solutions of several classical functional equations by using the properties of the spaces of continuous functions which are invariant under some elementary linear trans-formations. Concretely, we use that the sets of…
Finite group theorists have established many formulas that express interesting properties of a finite group in terms of sums of characters of the group. An obstacle to applying these formulas is lack of control over the dimensions of…
Given $k\in\mathbb N$, we define a class of continuous piecewise functions $f$ having abrupt but controlled magnitude changes so that the problem $$\Delta u +f(u)=0,\quad x\in \mathbb R^N, N> 2, $$ has at least $k$ radially symmetric ground…
We study the geometry of functions from the plane to the plane. For a large special class we are able to count preimages and compute them. Both numerical and theoretical aspects are discussed. Some of the tools used are Whitney's…
Making use of nonabelian harmonic analysis and representation theory, we solve the functional equation $$f_1(xy)+f_2(yx)+f_3(xy^{-1})+f_4(y^{-1}x)=f_5(x)f_6(y)$$ on arbitrary compact groups. The structure of its general solution is…
The fundamental importance of functional differential equations has been recognized in many areas of mathematical physics, such as fluid dynamics (Hopf characteristic functional equation), quantum field theory (Schwinger-Dyson equations)…
The basic concepts of classical mechanics are given in the operator form. The dynamical equation for a hybrid system, consisting of quantum and classical subsystems, is introduced and analyzed in the case of an ideal nonselective…
In this paper, two new classes of perfect nonlinear functions over $\mathbb{F}_{p^{2m}}$ are proposed, where $p$ is an odd prime. Furthermore, we investigate the nucleus of the corresponding semifields of these functions and show that the…
We consider the problem of classifying gradings by groups on a finite-dimensional algebra $A$ (with any number of multilinear operations) over an algebraically closed field. We introduce a class of gradings, which we call almost fine, such…
We develop a novel formal theory of finite structures, based on a view of finite structures as a fundamental artifact of computing and programming, forming a common platform for computing both within particular finite structures, and in the…
An appropriate diagram is a required element of a solution building process in physics problem solving and it can transform a given problem into a representation that is easier to exploit for solving the problem. A major focus while helping…
For certain problems involving vector fields, it is possible to find an associated imaginary field that, in conjunction with the first, forms a complex field for which the equation can be solved. This result is generalized to arbitrary…
The object of this lecture is to propose a series of conjectures and problems in different fields of analysis. They have been formulated with the aim of introducing some innovative methods in the study of classical topics, as open mappings,…