Note on Multiplicity

A Note on Authentication Accuracy with Multiplicity of Biometric Images

This project cum paper we have implemented basically deals with authentication and the various improvements that can be brought about by integrating them with real time scenarios. Our basic aim of it to implement is to develop a secure environment that cannot be breached easily. There are many applications or algorithms that provide authentication at the finest level but we are a step ahead I b...

A Note on the Multiplicity of Determinantal Ideals

Abstract. Herzog, Huneke, and Srinivasan have conjectured that for any homogeneous k-algebra, the multiplicity is bounded above by a function of the maximal degrees of the syzygies and below by a function of the minimal degrees of the syzygies. The goal of this paper is to establish the multiplicity conjecture of Herzog, Huneke, and Srinivasan about the multiplicity of graded Cohen-Macaulay alg...

A note on the existence and multiplicity of solutions for sublinear fractional problems

On Covering Multiplicity

Let A = {as +nsZ}s=1 be a system of arithmetic sequences which forms an m-cover of Z (i.e. every integer belongs at least to m members of A). In this paper we show the following surprising properties of A: (a) For each J ⊆ {1, · · · , k} there exist at least m subsets I of {1, · · · , k} with I 6= J such that ∑ s∈I 1/ns − ∑ s∈J 1/ns ∈ Z. (b) If A forms a minimal m-cover of Z, then for any t = 1...

Intersection Multiplicity on Blow-ups

A conjecture on vanishing and non-negativity of intersection multiplicity on the blow-up of a regular local ring at its closed point has been proposed. Proofs of vanishing, several special cases of non-negativity and a sufficient condition for non-negativity of this conjecture are described. The topic on intersection multiplicity on vector bundles is also addressed. Introduction. Let X be a reg...