In this paper we study a two-phase free boundary problem for a semilinear elliptic equation on a bounded domain $Dsubset mathbb{R}^{n}$ with smooth boundary‎. ‎We give some results on the growth of solutions and characterize the free boundary points in terms of homogeneous harmonic polynomials using a fundamental result of Caffarelli and Friedman regarding the representation of functions whose ...

Let G be a simple graph with vertex set {v1, v2, … , vn}. The common neighborhood graph of G, denoted by con(G), is a graph with vertex set {v1, v2, … , vn}, in which two vertices are adjacent if and only if they have at least one common neighbor in the graph G. In this paper, we compute the common neighborhood of some composite graphs. In continue, we investigate the relation between hamiltoni...

The set of all bounded linear functional operations on a given vector spacej plays an important role in the consideration of linear functional operations. For the sake of greater definiteness it is desirable to know the form of such operations and a space determined thereby. This problem has been solved for a number of spaces, for instance, all continuous functions on a bounded closed interval,...

The problem of simultaneous Chebyshev approximation of a set F of uniformly bounded, real-valued functions on a compact interval / by a set P of continuous functions is equivalent to the problem of simultaneous approximation of two real-valued functions F+ (x), F~ (x), with F~ (x) ¿ F+ (x), for all x in I, where F~ is lower semicontinuous and F+ is upper semicontinuous. 1. Formulation of the Ap...

An irreversible k-threshold process (also a k-neighbor bootstrap percolation) is a dynamic process on a graph where vertices change color from white to black if they have at least k black neighbors. An irreversible k-conversion set of a graph G is a subset S of vertices of G such that the irreversible k-threshold process starting with S black eventually changes all vertices of G to black. We sh...

In this paper we consider the problem of uniication of bounded simple set terms in the eld of deductive databases. Simple set terms are of the form fe 1 ; : : : ; e n g, where e i is a constant or a variable and are much used in deductive database systems such as LDL and Coral. In this paper we consider a restricted form of uniication, called \weak uniication", which is mainly used in the eld o...

Motivated by applications in sociology, economy and medicine, we study variants of the Target Set Selection problem, first proposed by Kempe, Kleinberg and Tardos. In our scenario one is given a graph G = (V,E), integer values t(v) for each vertex v (thresholds), and the objective is to determine a small set of vertices (target set) that activates a given number (or a given subset) of vertices ...

AlWlmet--ln the context of bounded-error estimation, one is interested in characterizing the set of all the values of the parameters to be estimated that are consistent with the data in the sense that the errors between the data and model outputs fall within prior bounds. While the problem can be considered as solved when the model output is linear in the parameters, the situation is far less a...

We analyze the bounded reachability problem of programs that use abstract data types and set comprehensions. Such programs are common as high-level executable specifications of complex protocols. We prove decidability and undecidability results of restricted cases of the problem and extend the Satisfiability Modulo Theories approach to support analysis of set comprehensions over tuples and bag ...