Here we study cohomological and geometrical properties of the general zero-dimensional section of a nonreduced curve C P n and (in positive characteristic) of an integral variety. 0. Introduction The main actors in this paper will be zero-dimensional subschemes of a projective space P r. This paper consists of three parts. The link between the three parts is given by the common main actors. The...

We consider a modiication of moment functionals for the Hahn classical polynomials of a discrete variable by adding two mass points at the ends of the interval, i.e., in x = 0 and x = N 1. We obtain the resulting orthogonal polynomials and identify them as hypergeometric functions. The corresponding three term recurrence relation and tridiagonal matrices are also studied. x1 Introduction. The s...

Secure sets were introduced by Brigham, Dutton, and Hedetniemi [1] as an extension of defensive alliances in a graph. Members of a defensive alliance have agreed to come to the aid of their neighbors in the alliance for mutual protection from attack by nonmembers. Alliances can occur, for example, between nations, biological sequences, and business cartels, and also have been used to model a va...

and Applied Analysis 3 (3) The Brouwer degree deg{JQN,Ω∩Ker L, 0} ̸ = 0, where J : ImQ → Ker L is an isomorphism. Then equation Lx = Nx has at least one solution onD(L)∩Ω. 3. Main Results In this section, we will use the continuation theorem introduced in Section 2 to prove the existence of periodic solutions of (1). To this end, we first quote some notations and definitions. Let X and Y be two ...

We study linear torsional Alfvén waves in a magnetic flux tube with an arbitrary cross-section. assume that the equilibrium field is propagating z-direction Cartesian coordinates x,y, and z. The cross-section bounded by smooth closed curve. Both plasma are homogeneous outside this magnitude function of x y, while density product two functions: one dependent on z other y. As result, speed also e...

HE male determining influence of the autosomes on sex differentiation T in Drosophila melanogaster was proven by BRIDGES in 1921 with the discovery of triploid intersexes. He found that individuals with two X chromosomes, as in diploid females, and three of each autosome (3A) develop intersexually. BRIDGES concluded that sex is determined by an interplay of female determining genes located prin...

The equivalent kernel [1] is a way of understanding how Gaussian process regression works for large sample sizes based on a continuum limit. In this paper we show (1) how to approximate the equivalent kernel of the widely-used squared exponential (or Gaussian) kernel and related kernels, and (2) how analysis using the equivalent kernel helps to understand the learning curves for Gaussian proces...

Projective spaces and hyperquadrics are the simplest projective algebraic varieties, and they can be characterized in many ways. The aim of this paper is to provide a new characterization of them in terms of positivity properties of the tangent bundle (Theorem 1.1). The first result in this direction was Mori’s proof of the Hartshorne conjecture in [Mor79] (see also Siu and Yau [SY80]), that ch...

In particular they proved that for x > 0 and α = 0 the function [Γ(1 + 1/x)]x decreases with x, while when α=1 the function x[Γ(1+1/x)]x increases.Moreover they also showed that the values α= 0 and α= 1, in the properties mentioned above, cannot be improved if x ∈ (0,+∞). In this paper we continue the investigation on the monotonicity properties for the gamma function proving, in Section 2, the...