We study linear subspaces L ⊆ Mn (over an algebraically closed field F of characteristic zero) and their singular sets S(L) defined by S(L) = {A ∈ Mn : χ(A+ L) is not dense in Fn}, where χ : Mn −→ F n is the characteristic map. We give a complete characterization of the subspaces L ⊂ M2 such that ∅ 6= S(L) 6= M2. We also provide a complete characterization of the singular sets S(L) in the case ...

We express the Euler-Poincaré characteristic of a semi-algebraic set, which is the intersection of a non-singular complete intersection with two polynomial inequalities, in terms of the signatures of appropriate bilinear symmetric forms.

In this paper we show that every finite-player game in characteristic function form obeying an innocuous condition (that the set of individually rational pay-off vectors are bounded) possesses a farsighted von-Neumann-Morgenstern stable set. JEL Classification No.: C71, D71.

In this work we summarize some recent results, to be included in a forthcoming paper [1]. We define μ-density as a characteristic of quality for the kind of coverings codes called multiple coverings of the farthest-off points (MCF). A concept of multiple saturating sets ((ρ, μ)-saturating sets) in projective spaces PG(N, q) is introduced. A fundamental relationship of these sets with MCF is sho...

The main purpose of this work is to characterize computably enumerable (c.e.) sets and generalized c.e. sets according to Kolmogorov complexity hierarchy. Given a set A, we consider A m, the initial segment of length m of the characteristic sequence of A. We show that the characteristic sequence of a 2 x-c.e. set can be random in the sense of Martin-LL of. We show that for x n-c.e. sets A, the ...

In this paper, we deal with second-order conic programming (SOCP) duals for a robust convex quadratic optimization problem uncertain data in the constraints. We first introduce SOCP dual polytopic sets. Then, obtain zero duality gap result between and its terms of new type characteristic cone constraint qualification. also construct norm-constrained sets corresponding them. Moreover, some numer...

A tree pattern p is a first-order term in formal logic, and the language of p is the set of all the tree patterns obtainable by replacing each variable in p with a tree pattern containing no variables. We consider the inductive inference of the unions of these languages from positive examples using strategies that guarantee some forms of minimality during the learning process. By a result in ou...

There is polynomial function Xq in the entries of an m×m(q− 1) matrix over a field of prime characteristic p, where q = p is a power of p, that has very similar properties to the determinant of a square matrix. It is invariant under multiplication on the left by a non-singular matrix, and under permutations of the columns. This gives a way to extend the invariant theory of sets of points in pro...

This paper presents a novel idea to the problem of learning concept descriptions from examples. Whereas most existing approaches rely on a large number of classiied examples, the approach presented in the paper is aimed at being applicable when only a few examples are classiied as positive (and negative) instances of a concept. The approach tries to take advantage of the information which can b...

Different ensemble voting approaches have been successfully applied for reverse-engineering of gene regulatory networks. They are based on the assumption that a good approximation of true network structure can be derived by considering the frequencies of individual interactions in a large number of predicted networks. Such approximations are typically superior in terms of prediction quality and...