Consider an elliptic curve E without complex multiplication defined over the rationals. The absolute Galois group of Q acts on the group of torsion points of E, and this action can be expressed in terms of a Galois representation ρE : Gal(Q/Q) → GL2(b Z). A renowned theorem of Serre says that the image of ρE is open, and hence has finite index, in GL2(b Z). We give the first general bounds of t...

In current era, the involvement of technologies like virtualization, consolidation and cloud computing, and adoption of free and open source software in designing and deploying e-governance that can reduce the total cost associated with and hence the financial burden abide by the state and central governments. The success of any egovernance project depends upon its utilization by the intended g...

This paper applies an evolutionary algorithm, the particle swarm optimization (PSO), to design the optimum open channel section. Depth, channel side slope and bottom width are considered as the variables for rectangular, triangular and trapezoidal channels, respectively. The objective function is minimizing the construction cost of the channel section. MATLAB software is used for programming an...

Abstract: A 2-rainbow domination function of a graph G = (V, E) is a function f mapping each vertex v to a subset of {1, 2} such that ⋃ u∈N(v) f (u) = {1, 2} when f (v) = �, where N(v) is the open neighborhood of v. The weight of f is denoted by wf (G) = ∑ v∈V �f (v)�. The 2-rainbow domination number, denoted by r2(G), is the smallest wf (G) among all 2-rainbow domination functions f of G. The ...

The chromatic symmetric function of a graph is a symmetric function that generalizes the chromatic polynomial. Its investigation has largely been motivated by the existence of an open problem, the poset-chain conjecture, which is equivalent to the assertion that for certain graphs, the coefficients in the expansion of the chromatic symmetric function in terms of elementary symmetric functions, ...

Let G = (V,E) be a locally finite graph, i.e. a graph in which every vertex has finitely many adjacent vertices. In this paper, we associate a topology to G, called graphic topology of G and we show that it is an Alexandroff topology, i.e. a topology in which intersec- tion of every family of open sets is open. Then we investigate some properties of this topology. Our motivation is to give an e...

The operators min·, max·, and #· translate classes of the polynomial-time hierarchy to function classes. Although the inclusion relationships between these function classes have been studied in depth, some questions concerning separations remained open. We provide oracle constructions that answer most of these open questions in the relativized case. As a typical instance for the type of results...

Open-source software (OSS) is one of the hottest trends in terms of the software development in the current days. It is highly discussed if this is the best model for software creation when compared to non-open-source alternatives, and most of the times this discussion is mostly driven by passion than by facts. The main rational behind this paper is to discuss the opportunities and challenges t...

Technologies and approaches in the field of Electronic Commerce are not mature enough in order to allow for their broad successful commercial application. Neither existing, successful approaches that are very much restricted to large companies, specific branches, and business domains, nor approaches just merging new technologies like Internet, WWW, and XML allow for scaling up electronic commer...