Many embedded systems have high safety and dependability requirements, which makes ensuring software robustness a top priority in these systems. As embedded computer systems become more complex and incorporate increasing functionality, their software systems become increasingly more difficult to design, build, and maintain. One approach to achieving software robustness is graceful degradation. ...

We discuss an inflationary scenario based on Lovelock terms. These higher order curvature terms can lead to inflation when there are more than three spatial dimensions. Inflation will end if the extra dimensions are stabilised, so that at most three dimensions are free to expand. This relates graceful exit to the number of large dimensions.

In this Letter, we describe how a spectrum of entropic perturbations generated during period slow contraction can source nearly scale-invariant curvature on length scales larger than the Hubble radius transition from to classical non-singular bounce (the `graceful exit' phase). The sourcing occurs naturally through higher-order scalar field kinetic terms common (non-singular) mechanisms. We pre...

A digraph D with p vertices and q arcs is labeled by assigning a distinct integer value g(v) from {0, 1, ..., q} to each vertex v. The vertex values, in turn, induce a value g(u, v) on each arc (u, v) where g(u, v) = (g(v)− g(u))(mod q + 1). If the arc values are all distinct then the labeling is called a graceful labeling of a digraph. In this paper, we prove a general result on graceful digra...

The ladder graph plays an important role in many applications as Electronics, Electrical and Wireless communication areas. The aim of this work is to present a new class of odd graceful labeling for the ladder graph. In particular, we show that the ladder graph Ln with m-pendant Ln mk1 is odd graceful. We also show that the subdivision of ladder graph Ln with m-pendant S(Ln)  mk1 is odd grace...

We show that to each graceful labelling of a path on 2s + 1 vertices, s ≥ 2, there corresponds a current assignment on a 3-valent graph which generates at least 22s cyclic oriented triangular embeddings of a complete graph on 12s + 7 vertices. We also show that in this correspondence, two distinct graceful labellings never give isomorphic oriented embeddings. Since the number of graceful labell...

A function f is called an odd-even graceful labeling of a graph G if f: V(G) → {0,1,2,...,q} is injective and the induced function f : E(G) → { { 0,2,4,...,2q+2i/i= 1 to n} such that when each edge uv is assigned the label |f(u) – f(v)| the resulting edge labels are {2,4,6,...,2q}. A graph which admits an odd-even graceful labeling is called an odd-even graceful graph. In this paper, the odd-ev...