In this paper, we investigate the local and global stability and the period two solutions of all nonnegative solutions of the difference equation, xn+1 = axn + bxn−k A + Bxn−k where a, b, A, B are all positive real numbers, k ≥ 1 is a positive integer, and the initial conditions x−k, x−k+1, ..., x0 are nonnegative real numbers. It is shown that the zero equilibrium point is globally asymptotica...

In this talk K be a global field and GK := Gal(K/K) the absolute Galois group over K. We let V be a p-adic representation of GK (finite-dimensional over Qp), and Σ a finite set of places of K containing p and ∞, outside which V is unramified. So we can and will view V as a representation of GK,Σ for technical reasons, it is at times important to work with that rather than the full GK ! We are g...

We show that when X = P 1 k , the projective line over the eld k, with the open covering fX 0 = Spec(kx]); X 1 = Spec(ky])g, the Mayer-Vietoris sequence of the K-theory of the schemes with endo-morphisms for the covering is not exact for all K i when i = 2n + 1 and n 1. This leads to the conclusion that the K-theory of schemes with endomorphisms is a global theory.

A clique in a graph is a set of vertices, each of which is adjacent to every other vertex in this set. A k-clique relaxes this requirement, requiring vertices to be within a distance k of each other, rather than directly adjacent. In theory, a maximum clique algorithm can easily be adapted to solve the maximum k-clique problem, although large sparse k-clique graphs reduce to large dense clique ...

In this paper we study global bifurcation phenomena for a class of nonlinear elliptic equations governed by the h-Hessian operator. The bifurcation phenomena considered provide new methods for establishing existence results concerning fully nonlinear elliptic equations. Applications to the theory of critical exponents and the geometry of k-convex functions are considered. In addition, a related...

The structure of real-world complex networks has long been an area of interest, and one common way to describe the structure of a network has been with the k-core decomposition. The core number of a node can be thought of as a measure of its centrality and importance, and is used by applications such as community detection, understanding viral spreads, and detecting fraudsters. However, we obse...

In today’s world, governmental, public, and private institutions systematically release data which describes individual entities (commonly referred as microdata). Those institutions are increasingly concerned with possible misuses of the data that might lead to disclosure of confidential information. Moreover, confidentiality regulation requires that privacy of individuals represented in the re...

  The clustering problem under the criterion of minimum sum of squares is a non-convex and non-linear program, which possesses many locally optimal values, resulting that its solution often falls into these trap and therefore cannot converge to global optima solution. In this paper, an efficient hybrid optimization algorithm is developed for solving this problem, called Tabu-KM. It gathers the ...

Our aim in this paper is to investigate the global attractivity of all positive solutions of the higher order nonlinear difference equation xn+1 = a+ bxn A−∑k i=0 bixn−i , n = 0, 1, . . . , where A, b, bk ∈ (0,∞), a, b0, . . . , bk−1 ∈ [0,∞), k ∈ {1, 2, . . .} and the initial conditions x−k, . . . , x0 are arbitrary. We show that one positive equilibrium of the equation is a global attractor wi...

Global schema generation is the problem of generating a unified schema based on existing heterogeneous local schemas and a set of correspondences which are generated by a schema matching algorithm. The current schema integration approaches cannot satisfy users' requirements due to several reasons. The existing approaches cannot handle hierarchical schema structure, cannot solve conflicts proble...