In this article the nonlinear mixed Volterra-Fredholm integral equations are investigated by means of the modied three-dimensional block-pulse functions (M3D-BFs). This method converts the nonlinear mixed Volterra-Fredholm integral equations into a nonlinear system of algebraic equations. The illustrative   examples are provided to demonstrate the applicability and simplicity of our   scheme.    

In this paper, we revisit two fundamental results of the self-stabilizing literature about silent BFS spanning tree constructions: the Dolev et al algorithm and the Huang and Chen’s algorithm. More precisely, we propose in the composite atomicity model three straightforward adaptations inspired from those algorithms. We then present a deep study of these three algorithms. Our results are relate...

We provide the first non-trivial result on dynamic breadth-first search (BFS) in external-memory: For general sparse undirected graphs of initially n nodes and O(n) edges and monotone update sequences of either Θ(n) edge insertions or Θ(n) edge deletions, we prove an amortized high-probability bound of O(n/B + sort(n) · log B) I/Os per update. In contrast, the currently best approach for static...

We propose a unique few-mode fiber (FMF)-based multi-parameter optical-fiber sensor for distributed measurement of temperature and strain. We launch a pump and a probe signal through specific linearly polarized modes into a FMF, and monitor the Brillouin frequency shift (BFS) in each mode. By analyzing the temperature and strain coefficients of the BFS of the two lowest order (LP(01), LP(11)) m...

In this chapter, we study the problem of traversing large graphs. A traversal, a systematic method of exploring all the vertices and edges in a graph, can be done in many different orders. A traversal in “breadth-first” order, a breadth-first search (BFS), is important because it serves as a building block for many graph algorithms. Parallel graph algorithms increasingly rely on BFS for explori...

In this work, we address the problem of locally estimating the size of a Peerto-Peer (P2P) network using local information. We present a novel approach for estimating the size of a peer-to-peer (P2P) network, fitting the sum of new neighbors discovered at each iteration of a breadth-first search (BFS) with a logarithmic function, and then using Lambert’s W function to solve a root of a ln(n)+b−...

A fault-tolerant structure for a network is required to continue functioning following the failure of some of the network’s edges or vertices. This paper addresses the problem of designing a fault-tolerant (α, β) approximate BFS structure (or FT-ABFS structure for short), namely, a subgraph H of the network G such that subsequent to the failure of some subset F of edges or vertices, the survivi...

The degree distribution of the Internet topology is considered as one of its main properties. However, it is only known through a measurement procedure which gives a biased estimate. This measurement may in first approximation be modeled by a BFS (Breadth-First Search) tree. We explore here our ability to infer the type (Poisson or power-law) of the degree distribution from such a limited knowl...