Related papers: Algebraically Constructible Functions and Signs of…

Nash and Tognoli show that smooth closed manifolds can be the zero sets of some real polynomial maps and non-singular. The canonical projections of spheres naturally embedded in the $1$-dimensional higher Euclidean spaces and some natural…

Alesker's theory of generalized valuations unifies smooth measures and constructible functions on real analytic manifolds, extending classical operations on functions and measures. Alesker showed that these operations agree with the…

We study the algebraic and geometric properties of the integral closure of different rings of functions on a real algebraic variety : the regular functions and the continuous rational functions.

The analysis of solutions to algebraic equations is further simplified. A couple of functions and their analytic continuation or root findings are required.

In the paper we prove for every finite algebra A that either it has the polynomially generated powers (PGP) property, or it has the exponentially generated powers (EGP) property. For idempotent algebras we give a simple criteria for the…

In this paper we define a class of polynomial functors suited for constructing coalgebras representing processes in which uncertainty plays an important role. In these polynomial functors we include upper and lower probability measures,…

Let A be the integral closure of the ring of polynomials CC[t], within the field of algebraic functions in one variable. We show that A interprets the ring of integers. This contrasts with the analogue for finite fields, proved to have a…

In this technical report, certain interesting classification of arithmetical functions is proposed. The notion of additively decomposable and multiplicatively decomposable arithmetical functions is proposed. The concepts of arithmetical…

We prove the existence of Hall polynomials for prinjective representations of finite partially ordered sets of finite prinjective type. In Section 4 we shortly discuss consequences of the existence of Hall polynomials, in particular, we are…

We give a short proof of polynomial recurrence with large intersection for additive actions of finite-dimensional vector spaces over countable fields on probability spaces, improving upon the known size and structure of the set of strong…

In this paper we give an effective characterization of Hilbert functions and polynomials of standard algebras over an Artinian equicharacteristic local ring; the cohomological properties of such algebras are also studied. We describe…

Given finitely many consecutive terms of an infinite sequence, we discuss the construction of a polynomial difference equation that the sequence may satisfy. We also present a method to seek a candidate polynomial differential equation for…

We define antidomain operations for algebras of multiplace partial functions. For all signatures containing composition, the antidomain operations and any subset of intersection, preferential union and fixset, we give finite equational or…

Finite trigonometric sums appear in various branches of Physics, Mathematics and their applications. For p; q to coprime positive integers and r we consider the finite trigonometric sums involving the product of three trigonometric…

There are two kinds of polynomial functions on matrix algebras over commutative rings: those induced by polynomials with coefficients in the algebra itself and those induced by polynomials with scalar coefficients. In the case of algebras…

We study symmetries enjoyed by the polynomials enumerating non-degenerate flags in finite vector spaces, equipped with a non-degenerate alternating bilinear, hermitian or quadratic form. To this end we introduce Igusa-type rational…

A hypergeometric type equation satisfying certain conditions defines either a finite or an infinite system of orthogonal polynomials. We present in a unified and explicit way all these systems of orthogonal polynomials, the associated…

We present a new probabilistic algorithm to find a finite set of points intersecting the closure of each connected component of the realization of every sign condition over a family of real polynomials defining regular hypersurfaces that…

In this note, we establish some new results on some special types of function algebras and also give new proofs to some existing ones

In this thesis quadratic and cubic algebras, which are extensions of SU(1,1) and SU(2) are studied in detail, with particular attention being given to their construction, their finite and infinite dimensional irreducible representations and…