We consider the following NP optimization problem: Given a set of polynomials Pi(x), i = 1 : : : s of degree at most 2 over GF [p] in n variables, nd a root common to as many as possible of the polynomials Pi(x). We prove that in the case when the polynomials do not contain any squares as monomials, it is always possible to approximate this problem within a factor of p 2 p 1 in polynomial time ...

The topic in the PI’s current grant1 is: Given a linear homogeneous linear differential equation with polynomial coefficients, decide if it can be solved in terms of special functions, and if so, find such solutions. Much progress on his topic has been made by the PI and his graduate students (Sections 2 and 6). Numerous algorithms were developed that turned out to be very effective. The PI tes...

Let Ratk(CP) denote the space of based holomorphic maps of degree k from the Riemannian sphere S2 = C ∪∞ to the complex projective space CPn . The basepoint condition we assume is that f (∞) = [1, . . . , 1]. Such holomorphic maps are given by rational functions: Ratk(CP) = {(p0(z), . . . , pn(z)) : each pi(z) is a monic polynomial over C of degree k and such that there are no roots common to a...

In this paper, a design method for a robust PI/PID controller for fuzzy parametric uncertain systems is proposed. An uncertain Linear Time Invariant (LTI) system with fuzzy coefficients is referred as fuzzy parametric uncertain system. The fuzzy coefficients are approximated by intervals (crisp sets) using the nearest interval approximation approach to obtain an interval system. Further, a robu...

We consider the problem of solving systems of equations Pi(x) 0 (mod ni) i = 1 : : : k where Pi are polynomials of degree d and the ni are distinct relatively prime numbers and x < min(ni). We prove that if k > d(d+1) 2 we can recover x in polynomial time provided min(ni) > 2 d . As a consequence the RSA cryptosystem used with a small exponent is not a good choice to use as a public key cryptos...

We consider a setting where we are given a graph G = (R, E), where R = {R1, . . . , Rn} is a set of polygonal regions in the plane. Placing a point pi inside each region Ri turns G into an edge-weighted graph Gp , p = {p1, . . . , pn}, where the cost of (Ri, Rj) ∈ E is the distance between pi and pj . The Shortest Path Problem with Neighborhoods asks, for given Rs and Rt, to find a placement p ...

The aim of this work is to improve the dynamics and overcome limitation conventional fixed parameters PI controller used in induction motor (IM) field-oriented control (FOC). This study presents implements a RST an adaptive fuzzy (AFC) enhance variable speed control. Theoretical background theses controllers outlined then experimental results are presented. Practical implementation has been rea...

In this paper, we study the problem of efficiently mining frequent partite episodes that satisfy partwise constraints from an input event sequence. Through our constraints, we can extract episodes related to events and their precedent-subsequent relations, on which we focus, in a short time. This improves the efficiency of data mining using trial and error processes. A partite episode of length...

This paper considers the variance minimization problem with job-dependent weights. We show that an optimal job sequence must be V-shaped in terms of weighted processing time when the problem is agreeably weighted, in the sense that Pi <(Pj implies w i > wj, where Pi and w i are the processing time and the weight of job i, respectively. An O(nWP) algorithm is proposed to find an optimal solution...

We consider the problem of finding, for two pairs (s1, t1) and (s2, t2) of vertices in an undirected graphs, an (s1, t1)-path P1 and an (s2, t2)-path P2 such that P1 and P2 share no edges and the length of each Pi satisfies Li, where Li ∈ {≤ ki, = ki, ≥ ki, ≤ ∞}. We regard k1 and k2 as parameters and investigate the parameterized complexity of the above problem when at least one of P1 and P2 ha...