• INDEPENDENT -SET = {[G, k] : G is an undirected graph with an independent set of vertices I ⊆ V (G) of size ≥ k} where a subset I is independent iff it contains no edges of G. – Guess a set I of size k. Verify that it contains no edges of G. • CLIQUE = {[G, k] : G is an undirected graph with an independent set of vertices C ⊆ V (G) of size ≥ k} where a subset C is a clique iff every edge on t...

let $r$ be a commutative ring with identity. let $g(r)$ denote the maximal graph associated to $r$, i.e., $g(r)$ is a graph with vertices as the elements of $r$, where two distinct vertices $a$ and $b$ are adjacent if and only if there is a maximal ideal of $r$ containing both. let $gamma(r)$ denote the restriction of $g(r)$ to non-unit elements of $r$. in this paper we study the various graphi...

LetHWR be the path on 3 vertices with a loop at each vertex. D. Galvin [4, 5] conjectured, and E. Cohen, W. Perkins and P. Tetali [2] proved that for any d-regular simple graph G on n vertices we have hom(G,HWR) ≤ hom(Kd+1, HWR) . In this paper we give a short proof of this theorem together with the proof of a conjecture of Cohen, Perkins and Tetali [2]. Our main tool is a simple bijection betw...

The purpose of this study was to evaluate the individual contraction force during polymerization of a composite resin (Z-250), a flowable composite (Filtek Flow, FF) and a resin-modified glass ionomer cement (Vitrebond, VB), and the transmission of Z-250 composite resin polymerization contraction force through different thicknesses of FF and VB. The experiment setup consisted of two identical p...

The issue of graph recognition has been not always investigated until today though the subjects on the document image understanding are very interest and have proposed many methods/systems. This is partly because the graph reading is not yet sufficiently recognized in the practical applications, and partly because the graph recognition is more difficult than the ordinary document analysis/recog...

In contrast with knots, whose properties depend only on their extrinsic topology in S3, there is a rich interplay between the intrinsic structure of a graph and the extrinsic topology of all embeddings of the graph in S3. For example, it was shown in [2] that every embedding of the complete graph K7 in S 3 contains a non-trivial knot. Later in [3] it was shown that for every m ∈ N, there is a c...

Web processes are made up of services as their units of functionality. The services are represented as a graph and compose a synergy of service. The composite service is prone to failure due to various causes. However, the end-user should receive a smooth and non-interrupted execution. Atomic replacement of a failed Web service to recover the system is a straightforward approach. Nevertheless, ...

This paper shows how the modular structure of composite systems can guide the state-space exploration in explicit-state linear-time model-checking and make it more efficient in practice. Given a composite system where every module has input and output variables — and variables of different modules can be connected — a total ordering according to which variables are generated is determined, thro...

The Unified Modeling Language (UML) has been widely accepted as a standard for modeling software systems from various perspectives. The intuitive notations of UML diagrams greatly improve the communication among developers. However, the lack of a formal semantics makes it difficult to automate analysis and verification. This paper offers a graphical yet formal approach to specifying the behavio...

the aim of this work was to develop a new and simple coacervative extraction method for the preconcentration and spectrophotometric determination of cu(ii) in water samples. dithizone was used as the chelating agent while an anionic surfactant, namely sodium dodecyl sulfate (sds), was used as extracting agent at room temperature. central composite design (ccd) based on response surface methodol...