A Steiner tree for a set S of vertices in a connected graph G is a connected subgraph of G with a smallest number of edges that contains S. The Steiner interval I (S) of S is the union of all the vertices of G that belong to some Steiner tree for S. If S = {u, v}, then I (S) = I [u, v] is called the interval between u and v and consists of all vertices that lie on some shortest u–v path in G. T...

Space geodetic estimates of the rate of Nazca-South America convergence and Nazca-Pacific spreading averaging over several years show that present day rates are significantly slower than the 3 million year average NUVEL-1A model. The implied rates of deceleration are consistent with longer term trends extending back to at least 20 Ma, about the time of initiation of Andes growth, and may reflec...

Three-dimensional (3-D) video compression using wavelets decomposition along the temporal axis dictates that a number of video frames must be buffered to allow for the temporal decomposition. Buffering of frames allows for the temporal correlation to be made use of, and the larger the buffer the more effective the decomposition. One problem inherent in such a set up in interactive applications ...

This paper analyzes the edge-reflection problem of obliquely incident guided waves in a plate. The generalized guided-wave theories in a plate, including the orthogonality of modes and the mode-decomposition method are summarized. The edge-reflection problem is solved on the basis of the mode-decomposition method. Some numerical results are presented and compared to experimental results. [doi:1...

Coupling methods for continuum models with molecular models are developed. Two methods are studied here: an overlapping domain decomposition method, which has overlapping domain, and an edge-to-edge decomposition method, which has an interface between two models. These two methods enforce the compatibility on the overlapping domain or interface nodes/atoms by the Lagrange multiplier method or t...

Let $G$ be a finite group and $pi(G)$ be the set of all prime divisors of $|G|$. The prime graph of $G$ is a simple graph $Gamma(G)$ with vertex set $pi(G)$ and two distinct vertices $p$ and $q$ in $pi(G)$ are adjacent by an edge if an only if $G$ has an element of order $pq$. In this case, we write $psim q$. Let $|G= p_1^{alpha_1}cdot p_2^{alpha_2}cdots p_k^{alpha_k}$, where $p_1

In this paper we consider the problem of finding the smallest number  such that any graph G of order n admits a decomposition into edge disjoint copies of C4 and single edges with at most  elements. We solve this problem for n sufficiently large.