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...

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...

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...

It is well-known that one of open problems in the theory Leibniz algebras to find asuitable generalization Lie’s third theorem which associates a (local) Lie group any Liealgebra, real or complex. turns out, this related finding an appropriate analogue Liegroup for algebras. Using notion digroup, Kinyon obtained partial solution ofthis problem, namely, class so-called split Leibnizalgebras. A d...

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, it is proved that any algehraicgeometr ic code can be expressed as a cross section of an extended multidimensional cyclic code. Both algebraic-geometric codes and multidimensional cyclic codes are descr ibed by a unified theory of l inear block codes def ined over point sets: algebraic-geometric codes are def ined over the points of an algebraic curve, and an m-dimensional cyclic...

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...