In this paper, we investigate a composition of entire function several complex variables and analytic in the unit ball. We modified early known results with conditions providing equivalence boundedness $L$-index direction for such $l$-index initial one variable, where continuous $L:\mathbb{B}^n\to \mathbb{R}_+$ is constructed by $l: \mathbb{C}^m\to \mathbb{R}_+.$ Taking into account new ideas f...

A time sequence is a discrete sequence of values, e.g. temperature measurements, varying over time. By applying an interpolation function a discrete time sequence can be coerced into a continues function over time, F(t), which we call an interpolated time sequence. Many applications need to deal with querying interpolated time sequences. Simple queries involve finding F(t’) for a given time poi...

We provide an index formula for solutions of variational inequality problems defined by a continuously differentiable function F over a convex set M represented by a finite number of inequality constraints. Our index formula can be applied when the solutions are non-singular and possibly degenerate, as long as they also satisfy the injective normal map (INM) property, which is implied by strong...

Theorem 1. Let L be a locally compact, nondiscrete topological field. a) Then L is a finite extension of one of the following fields: (i) K = R. (ii) K = Qp. (iii) K = Fp((t)). b) In case (i) L = R or L = C. c) In case (ii) the ramification index e(L/Qp) and residual degree f(L/Qp) are uniquely determined by the abstract field L, and for any given e, f ∈ Z, the number of finite extensions L/Qp ...

The convolution of regularly varying probability densities is proved asymptotic to their sum, and hence is also regularly varying. Extensions to rapid variation, O-regular variation, and other types of asymptotic decay are also given. Regularly varying distribution functions have long been used in probability theory; see e.g. Feller [7, VIII.8], Bingham, Goldie and Teugels [5, Ch. 8]. This note...

The Lovász extension of a pseudo-Boolean function f : {0, 1}n → R is defined on each simplex of the standard triangulation of [0, 1]n as the unique affine function f̂ : [0, 1]n → R that interpolates f at the n+1 vertices of the simplex. Its degree is that of the unique multilinear polynomial that expresses f . In this paper we investigate the least squares approximation problem of an arbitrary L...

Let X be a uniform space; that is to say, let X be a space provided with a system of indexed neighborhoods Ua(x) (x(EX, a=index), subject to the conditions (A. Weil) : (1) If xÇzX and if a is an index, then xÇzUa(x)\ (2) If a and /? are indices, then there exists an index y such that xÇzX implies U7(x)ÇZUa(x)r\Up(x); (3) If a is an index, then there exists an index /? such that x, y, zÇzX with ...

Inspired by the chemical applications of higher-order connectivity index (or Randic index), we consider here the higher-order first Zagreb index of a molecular graph. In this paper, we study the linear regression analysis of the second order first Zagreb index with the entropy and acentric factor of an octane isomers. The linear model, based on the second order first Zag...