Byzantine Vector Consensus in Complete Graphs

Consider a network of n processes each of which has a d-dimensional vector of reals as its input. Each process can communicate directly with all the processes in the system; thus the communication network is a complete graph. All the communication channels are reliable and FIFO (first-in-first-out). The problem of Byzantine vector consensus (BVC) requires agreement on a d-dimensional vector that is in the convex hull of the d-dimensional input vectors at the non-faulty processes. We obtain the following results for Byzantine vector consensus in complete graphs while tolerating up to f Byzantine failures: * We prove that in a synchronous system, n >= max(3f+1, (d+1)f+1) is necessary and sufficient for achieving Byzantine vector consensus. * In an asynchronous system, it is known that exact consensus is impossible in presence of faulty processes. For an asynchronous system, we prove that n >= (d+2)f+1 is necessary and sufficient to achieve approximate Byzantine vector consensus. Our sufficiency proofs are constructive. We show sufficiency by providing explicit algorithms that solve exact BVC in synchronous systems, and approximate BVC in asynchronous systems. We also obtain tight bounds on the number of processes for achieving BVC using algorithms that are restricted to a simpler communication pattern

A radiating dyon solution

We give a non-static exact solution of the Einstein-Maxwell equations (with null fluid), which is a non-static magnetic charge generalization to the Bonnor-Vaidya solution and describes the gravitational and electromagnetic fields of a nonrotating massive radiating dyon. In addition, using the energy-momentum pseudotensors of Einstein and Landau and Lifshitz we obtain the energy, momentum, and power output of the radiating dyon and find that both prescriptions give the same result.Comment: 9 pages, LaTe

Propagation of high amplitude higher order sounds in slightly soft rectangular ducts, carrying mean flow

The resonance expansion method, developed to study the propagation of sound in rigid rectangular ducts is applied to the case of slightly soft ducts. Expressions for the generation and decay of various harmonics are obtained. The effect of wall admittance is seen through a dissipation function in the system of nonlinear differential equations, governing the generation of harmonics. As the wall admittance increases, the resonance is reduced. For a given wall admittance this phenomenon is stronger at higher input intensities. Both the first and second order solutions are obtained and the results are extended to the case of ducts having mean flow

Fibonacci and Super Fibonacci Graceful Labeling of Some Graphs

Abstract: In the present work we discuss the existence and non-existence of Fibonacci and super Fibonacci graceful labeling for certain graphs. We also show that the graph obtained by switching a vertex in cycle Cn, (where n >= 6 ) is not super Fibonacci graceful but it can be embedded as an induced subgraph of a super Fibonacci graceful graph. Key words: Graceful Labeling; Fibonacci Graceful Labeling; Super Fibonacci Graceful Labelin

No news for Kerr-Schild fields

Algebraically special fields with no gravitational radiation are described. Kerr-Schild fields, which include as a concrete case the Kinnersley photon rocket, form an important subclass of them.Comment: 4 pages, Revtex

Site and species selection criteria for cage culture

Site selection is the most important factor which determines the commercial viability of mariculture systems. Cage culture can be made possible only when the site for cage culture operation is located, designed and operated to provide optimum water quality and to avoid stress conditions. In addition to water and sediment quality of the site some biological and natural distribution information for the species should also be known before a site is selected for cage culture. The selection of fish for cage culture should be based on biological criteria, such as physiological, behavioural characteristics and level of domestication; marketing criteria and environmental criteria, distribution and habitat of sit

E-cordial Labeling for Cartesian Product of Some Graphs

We investigate E-cordial labeling for some cartesian product of graphs. We prove that the graphs Kn × P2 and Pn × P2 are E-cordial for n even while Wn × P2 andK1,n × P2 are E-cordial for n odd. Key words: E-Cordial labeling; Edge graceful labeling; Cartesian produc