Related papers: Normality through partial sharing of sets with dif…

In this note, we provide a simple derivation of expressions for the restricted partition function and its polynomial part. Our proof relies on elementary algebra on rational functions and a lemma that expresses the polynomial part as an…

The probability content of a convex polyhedron with a multivariate normal distribution can be regarded as a real analytic function. We give a system of linear partial differential equations with polynomial coefficients for the function and…

In this article, we define a matrix multinomial distribution. We prove some properties of the matrix multinomial distribution. We prove that the matrix Poisson distribution can be used as an approximation to the matrix multinomial…

This article offers a comprehensive treatment of polynomial functional regression, culminating in the establishment of a novel finite sample bound. This bound encompasses various aspects, including general smoothness conditions, capacity…

In this paper, we first generalize a value distribution result of Lahiri and Dewan [4] and as an application of this result we prove a normality criterion using partial sharing of small functions. Further, in sequel normality criteria of Hu…

Some Dirichlet-like functions, attached to a pair (periodic function, polynomial) are introduced and studied. These functions generalize the standard Dirichlet L-functions of Dirichlet characters. They have similar properties, being…

This paper is devoted to the specific class of pseudoconformal mappings of quaternion and octonion variables. Normal families of functions are defined and investigated. Four criteria of a family being normal are proven. Then groups of…

Let X be an analytic set defined by polynomials whose coefficients a_1,...,a_s are holomorphic functions. We formulate conditions such that for all sequences {a_(1,n)},...,{a_(s,n)} of holomorphic functions converging locally uniformly to…

Observed clusters should be modelled by considering the distribution function to be a random variable that quantifies the degree of excitation of the system's normal modes. A system of canonical coordinates for the space of DFs is…

In this paper we study the problem of deciding whether two disjoint semialgebraic sets of an algebraic variety over R are separable by a polynomial. For that we isolate a dense subfamily of Spaces of Orderings, named Geometric, which…

This paper discusses the split feasibility problem with polynomials. The sets are semi-algebraic, defined by polynomial inequalities. They can be either convex or nonconvex, either feasible or infeasible. We give semidefinite relaxations…

We consider sequences of polynomials that satisfy differential-difference recurrences. Polynomials satisfying such recurrences frequently appear as generating polynomials of integer valued random variables that are of interest in discrete…

This paper investigates certain classes of entire functions in C^n that, together with their partial derivatives, share a finite set consisting of three elements. By employing normality criteria, we study the behaviour of such functions and…

In two previous papers we showed that any analytically integrable vector field admits a local analytic Poincar\'e-Birkhoff normalization in the neighborhood of a singular point. The aim of this paper is to extend this analytic normalization…

The purpose of this work is to analyse a family of mutually orthogonal polynomials on the unit ball with respect to an inner product which includes an additional term on the sphere. First, we will get connection formulas relating classical…

In this paper we prove a number of results concerning uniqueness of a meromorphic function as well as its derivative sharing one or two sets. In particular, we deal with the specific question raised in [18], [19], [20] and ultimately…

It is well known that the real and imaginary parts of any holomorphic function are harmonic functions of two variables. In this paper we generalize this property to finite-dimensional commutative algebras. We prove that if some basis of a…

We establish regularity for functions satisfying a dynamic programming equation, which may arise for example from stochastic games or discretization schemes. Our results can also be utilized in obtaining regularity and existence results for…

The paper addresses questions of existence and regularity of solutions to linear partial differential equations whose coefficients are generalized functions or generalized constants in the sense of Colombeau. We introduce various new…

The aim of this paper is a quantitative analysis of the solution set of a system of polynomial nonlinear differential equations, both in the ordinary and partial case. Therefore, we introduce the differential counting polynomial, a common…