When Zharkov and Blinkov ([ZB93]) applied the classical ideas of involutive systems originating from the theory of partial dierential equations (c.f. [Ja29],[Po78]) to the computation of Gr obner bases (c.f. [Bu65],[BW93]) their theory seemed to be a rather marginal concept. But due to the opportunity of gaining a faster version for one of the most frequently applied algorithms the method came...

In this paper, we first present a new class of code based public key cryptosystem(PKC) based on ReedSolomon code over extension field of less than m=9, referred to as K(XVI)SE(1)PKC. We then present a new class of quadratic multivariate PKC, K(XVI)SE(2)PKC, based on binary cyclic code. We show that both K(XVI)SE(1)PKC and K(XVI)SE(2)PKC can be secure against the various linear transformation at...

Many problems in kinematic synthesis of mechanisms and robots lead naturally to systems of bilinear equations in design parameters. Such systems are typically solved using well-known methods for solutions of systems of polynomial equations, e.g., Dialytic Elimination, Grobner bases, and Polynomial Continuation. This paper presents a new nullspace analysis method for solving a system of bilinear...

Algebraic cryptanalysis usually requires to recover the secret key by solving polynomial equations. Gröbner bases algorithm is a well-known method to solve this problem. However, a serious drawback exists in the Gröbner bases based algebraic attacks, namely, any information won’t be got if we couldn’t work out the Gröbner bases of the polynomial equations system. In this paper, firstly, a gener...

In this paper, we propose the concept of involutive direction ss a vector representation for the concept of involutive division proposed by Gerdt and hi co-workers. With this representation, most of the properties of involutive divisions such as Noetherity, Artinity, and constructivity, can be greatly simplified. A new algorithm to compute the involutive completion is also given. Based on the v...

Abstract: This is the first of two articles devoted to a exposition of the generatingfunction method for computing fusion rules in affine Lie algebras. The present paper is entirely devoted to the study of the tensor-product (infinite-level) limit of fusions rules. We start by reviewing Sharp’s character method. An alternative approach to the construction of tensor-product generating functions ...

We present a new method that addresses the various deficiencies of the state-ofthe-art non-linear invariant generation methods for hybrid systems. Present approaches for non-linear invariant generation are limited to linear systems, or they relay on non scalable methods which have high complexity. Moreover, for hybrid systems with discrete transitions, differential rules, and local conditions t...

Mixed-integer polynomial programming (MIPP) problems are one class of mixed-integer nonlinear programming (MINLP) problems where objective function and constraints are restricted to the polynomial functions. Although the MINLP problem is NP-hard, in special cases such as MIPP problems, an efficient algorithm can be extended to solve it. In this research, we propose an algorit...

This paper addresses the critical issue of the development of intelligent or assisting tools for the scientist who is working in the initial problem formulation and mathematical model representation stage of research. In particular, examples of that representation in fluid dynamics and instability theory are discussed. The creation of a mathematical model that is ready for application of certai...