W 2 h 2 is an asymptotic upper bound for the VC-dimension of a large class of neural networks including sigmoidal, radial basis functions, and sigma-pi networks, where h is the number of hidden units and W is the number of adjustable parameters, which extends Karpinski and Macintyre's resent results.* The class is characterized by polynomial input functions and activation functions that are sol...

The k-IN-A-PATH problem is to test whether a graph contains an induced path spanning k given vertices. This problem is NP-complete in general graphs, already when k = 3. We show how to solve it in polynomial time on claw-free graphs, when k is an arbitrary fixed integer not part of the input. As a consequence, also the k-INDUCED DISJOINT PATHS and the k-IN-A-CYCLE problem are solvable in polyno...

Let P = {p1, . . . , pr} ⊂ Q[n1, . . . , nm] be a family of polynomials such that pi(Z) ⊆ Z, i = 1, . . . , r. We say that the family P has the PSZ property if for any set E ⊆ Z with d∗(E) = lim supN−M→∞ |E∩[M,N−1]| N−M > 0 there exist infinitely many n ∈ Zm such that E contains a polynomial progression of the form {a, a + p1(n), . . . , a + pr(n)}. We prove that a polynomial family P = {p1, . ...

h our previous paper [l], we observed that generalized Vandermonde determinants of the form vn;~(ll,. , G) = \q” / I 1 5 i, k 5 n, where the 2, are distinct points belonging to an interval [a, b] of the real line, the index n stands for the order, the sequence p consists of ordered integers 0 5 pi < ~2 < ... < pLn, can be factored as a product of the classical Vandermonde determinant and a Schu...

We study the situation where a set of n jobs with release dates and equal processing times have to be scheduled on m identical parallel machines. We show that, if the objective function can be expressed as the sum of n functions fi of the completion time Ci of each job Ji, the problem can be solved in polynomial time for any fixed value of m. The only restriction is that functions fi have to be...

Proportional-integral-derivative (PID) controllers are described in most automatic control textbooks. The application of PID controllers is widely spread in automation of mechanical processes where control of motors is of concern. This paper focuses on implementation of the PID control when used for regulation of dc motors. Two basic PID structures for position regulation of armature-controlled...

In this work we propose a general procedure for estimating the global minima of mathematical programs given in the general form as follows: min P0 (t) s.t. Pi (t) ≤ 0 for i = 1, . . . , k (Π) , where the functions Pi : R n → R are n-dimensional polynomials which are supposed to be non convex. The theory behind the Method of Moments guarantees that all global minima of the non convex program (Π)...

Our main result is that every ro-dimensional polytope can be described by at most (2n — 1) polynomial inequalities and, moreover, these polynomials can explicitly be constructed. For an n-dimensional pointed polyhedral cone we prove the bound 2n — 2 and for arbitrary polyhedra we get a constructible representation by 2n polynomial inequalities. 1. I N T R O D U C T I O N By a striking result of...

r is called commuting regular ring (resp. semigroup) if for each x,y $in$ r thereexists a $in$ r such that xy = yxayx. in this paper, we introduce the concept of commuting$pi$-regular rings (resp. semigroups) and study various properties of them.

It is well known that Euclid's algorithm for computing the greatest common divisor (gcd) of two integer numbers is more than two thousand years old and, as it turns out, it is the oldest known algorithm. Interest in computing a gcd of two polynomials first appeared only in the sixteenth century and the problem was solved by Simon Stevin [13] simply by applying Euclid's algorithm (for integers) ...