In this paper we present an improved version of HF-hash [DMS] viz., GB-hash: Hash Functions Using Groebner Basis. In case of HF-hash, the compression function consists of 32 polynomials with 64 variables, which were taken from the first 32 polynomials of hidden field equations challenge-1 by forcing last 16 variables as 0. In GB-hash we have designed the compression function in such way that th...

We present combinatorial Gray codes and explicit designs of efficient algorithms for lexicographical combinatorial generation of the sets of nonnesting and sparse nonnesting set partitions of length n. AMS Subject Classification (2000): 05A18, 68R05, 68W99, 94B25.

Since mathematical morphology is based on complete lattice theory, a vector ordering method becomes indispensable for its extension to multivariate images. Among the several approaches developed with this purpose, lexicographical orderings are by far the most frequent, as they possess certain desirable theoretical properties. However, their main drawback consists of the excessive priority attri...

Abstract. General Schrödinger equation is considered with a central polynomial potential depending on 2q arbitrary coupling constants. Its exceptional solutions of the so called Magyari type (i.e., exact bound states proportional to a polynomial of degree N) are sought. In any spatial dimension D ≥ 1, this problem leads to the Magyari’s system of coupled polynomial constraints, and only purely ...

In this paper, the problem of measuring the degree of inclusion and similarity measure for two   interval-valued intuitionistic  fuzzy sets is considered. We propose inclusion and similarity measure by using  order on interval-valued intuitionistic fuzzy sets connected with lexicographical order. Moreover, some properties of inclusion and similarity measure and some correlation, between them an...

The aim of this article is to contribute to the development of the modern theory of lexicographical functions by offering a critical examination of the following concepts associated with it: primary needs, primary data, secondary needs, secondary data, function-related needs, and functionrelated data. By way of introduction, a presentation of the basic tenets of the theory is offered, followed ...