In this paper, we prove that the most important concept of supervisory control of discrete-event systems, the controllability property, is undecidable for two deterministic context-free languages K and L, where L is prefix-closed, even though K is a subset of L. If K is not a subset of L, the undecidability follows from the work by Sreenivas. However, the case where K is a subset of L does not ...

Given a set L of non-parallel lines in the plane and a nonempty subset L′ ⊆ L, a guarding tree for L′ is a tree contained in the union of the lines in L such that if a mobile guard (agent) runs on the edges of the tree, all lines in L′ are visited by the guard. Similarly, given a connected arrangement S of line segments in the plane and a nonempty subset S ′ ⊆ S, we define a guarding tree for S...

Let M denote the class of infinite product probability l:leaSUres J-1=J-1 1 xJ-l 2 x • • • defined on an infinite product of replications of a given measurable space (X~A), and let H denote the subset of fl for which J-1(A)=O or 1 for each permutation invariant event A. Previous works (referenced in the paper) discuss very restrictive sufficient conditions under which a given member J-I of M be...

In the transformation semigroup (X, S) we introduce the height of a closed nonempty invariant subset of X, define the transformed dimension of nonempty subset S of X and obtain some results and relations.

A bstract: The seeding technique became central in the theory of sequence alignment and there are several efficient tools applying seeds to D N A homology search. Recently, a concept of subset seeds has been proposed for similarity search in protein sequences. We experimentally evaluate the applicability of subset seeds to protein homology search. We advocate the use of multiple subset seeds de...

A subset A of a group G is called (k, l)-sumset, if A = kB−lB for some B ⊆ G, where kB − lB = {x1 + · · · + xk − xk+1 − · · · − xk+l : x1, . . . , xk+l ∈ B}. Upper and lower bounds for the number (k, l)-sumsets in groups of prime order are provided.

In this paper we show the weak Banach-Saks property of the Banach vector space (L p µ) m generated by m L p µ-spaces for 1 ≤ p < +∞, where m is any given natural number. When m = 1, this is the famous Banach-Saks-Szlenk theorem. By use of this property, we also present inequalities for integrals of functions that are the composition of nonnegative continuous convex functions on a convex set of ...

Let n-2&lt;\lambda&lt;n , f be a function in Morrey spaces L^{1,\lambda}(\Omega) and the equation&#x0D; Lu=f&#x0D; u \in W^{1,2}(\Omega)&#x0D; Dirichlet problem, where \Omega is bounded open subset of R^{n} n \ge 3 L divergent elliptic operator. In this paper, we prove existence uniqueness problem by directly using Lax-Milgram Lemma weighted estimation

Let G be a group. A subset X of G is a set of pairwise noncommuting elements if xy ̸= yx for any two distinct elements x and y in X. If |X| ≥ |Y | for any other set of pairwise non-commuting elements Y in G, then X is said to be a maximal subset of pairwise non-commuting elements. In this paper we determine the cardinality of a maximal subset of pairwise non-commuting elements in any non-abelian...