Traditional Adomian decomposition method (ADM) usually fails to solve singular initial value problems of Emden-Fowler type. To overcome this shortcoming, a new and effective modification of ADM that only requires calculation of the first Adomian polynomial is formally proposed in the present paper. Three singular initial value problems of Emden-Fowler type with , 1 α  , 2 and , 2  and have be...

The anti-Kekul\'{e} number of a connected graph $G$ is the smallest edges whose deletion results in subgraph having no Kekul\'{e} structures (perfect matchings). As common generalization (conditional) matching preclusion and $G$, we introduce $s$-restricted as without perfect matchings such that each component has at least $s+1$ vertices. In this paper, first show conditional problem are NP-com...

As an extension of orthogonal matching pursuit (OMP) improving the recovery performance of sparse signals, generalized OMP (gOMP) has recently been studied in the literature. In this paper, we present a new analysis of the gOMP algorithm using restricted isometry property (RIP). We show that if the measurement matrix Φ ∈ R satisfies the RIP with δmax{9,S+1}K ≤ 1 8 , then gOMP performs stable re...

Generalized Orthogonal Matching Pursuit (gOMP) is a natural extension of OMP algorithm where unlike OMP, it may select N(≥ 1) atoms in each iteration. In this paper, we demonstrate that gOMP can successfully reconstruct a K-sparse signal from a compressed measurement y = Φx by K iteration if the sensing matrix Φ satisfies restricted isometry property (RIP) of order NK where δNK < √ N √ K+2 √ N ...

In this letter, we first construct a counter example to show that for any given positive integer K ≥ 2 and for any 1 √ K+1 ≤ t < 1, there always exist a K−sparse x and a matrix A with the restricted isometry constant δK+1 = t such that the OMP algorithm fails in K iterations. Secondly, we show that even when δK+1 = 1 √ K+1 , the OMP algorithm can also perfectly recover every K−sparse vector x f...

A simple 2-matching in a graph is a subgraph all of whose nodes have degree 1 or 2. A simple 2-matching is called k-restricted if every connected component has > k edges. We consider the problem of finding a k-restricted simple 2-matching with a maximum number of edges, which is a relaxation of the problem of finding a Hamilton cycle in a graph. Our main result is a min-max theorem for the maxi...