Mathematical Journal of Interdisciplinary Sciences
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Collapsible and Spiky Wave for Dust Acoustic Waves in Dusty Plasmas
Get PDFIn multicomponent dusty plasma, the Sagdeev Potential (SP) approach is employed to formulate the Energy Equation for arbitrary amplitude dust acoustic waves (DAWs), where an amount of electrons is trapped in potential well. The dependence of amplitude and width of the solitons of Sagdeev Potential on plasma parameters is widely discussed. The range of Mach number has determined for solitary waves (SWs) with the help of critical Mach number. The solution of the Energy Equation obtained, has been discussed by expanding the expression for SP in the higher terms of φ . The different solutions of Energy Equation give us SWs, breakable waves, collapsible waves and SWs with spiky and explosive nature. The role of temperature ratio on the transformation of SWs to collapsible waves is discussed. With the help of standard values of plasma parameters relevant to such plasma environment, the results so obtained, are discussed. These results may help us to explain the nature of SWs in different astrophysical situations
Prime Coloring of Crossing Number Zero Graphs
Get PDFIn this paper, prime coloring and its chromatic number of some crossing number zero graphs are depicted and its results are vali-dated with few theorems. Prime Coloring is defined as G be a loop less and Without multiple edges with n distinct Vertices on Color class C={c1,c2,c3,…..cn} a bijection ψ:V {c1,c2,c3,…..cn} if for each edge e = cicj ,i≠j , gcd{ ψ (ci), ψ (cj)}=1, ψ (ci) and ψ (cj) receive distinct Colors. The Chromatic number of Prime coloring is minimum cardinality taken by all the Prime colors. It is denoted by η (G)
Stochastic Reliability Analysis of Two Identical Cold Standby Units with Geometric Failure & Repair Rates
Get PDFThe present paper is based on the analysis of an two identical unit system wherein initially one unit is in operative state and other is in cold standby and total failure of the unit is via partial failure mode. Single repairman is always available with the system for any repair of failed unit (partially/ completely). Failure/repair time is considered to be a Geometric distribution. Measures of system effectiveness had also been calculated for the system
Radial Basis Neural Network for Availability Analysis
Get PDFThe appliance of radial basis neural network is demostrated in this paper. The method applies failure and repair rate signals to learn the hidden relationship presented into the input pattern. Statistics of availability of several years is considered and collected from the management of concern plant. This data is considered to train and calidate the radial basis neural network (RBNN). Subsequently validated RBNN is used to estimate the availability of concern plant. The main objective of using neural network approach is that it’s not require assumption, nor explicit coding of the problem and also not require the complete knowledge of interdependencies, only requirement is raw data of system functioning
Bounds For The Complex Part of Phase Velocity
Get PDFWe study incompressible, inviscid, density stratified fluid with variable cross section in this present paper. For this problem, we have obtained a bound for the complex part of phase velocity. Furthermore, we have obtained an instability region which depends on number of parameters
Binet – Type Formula For The Sequence of Tetranacci Numbers by Alternate Methods
Get PDFThe sequence {Tn} of Tetranacci numbers is defined by recurrence relation Tn= Tn-1 + Tn-2 + Tn-3 + Tn-4; n≥4 with initial condition T0=T1=T2=0 and T3=1. In this Paper, we obtain the explicit formulla-Binet-type formula for Tn by two different methods. We use the concept of Eigen decomposition as well as of generating functions to obtain the result
On Some Special Property of The Farey Sequence
Get PDFIn this paper, some special property of the Farey sequence is discussed. We prove in each term of the Farey sequence, the sum of elements in the denominator is two times of the sum of elements in the numerator. We also prove that the Farey sequence contains a palindrome structure
Characteristic Graph vs Benzenoid Graph
Get PDFA characteristic graph is a tree representative of its corresponding benzenoid (cyclic) graph. It may contain necessary information of several properties of benzenoids. The PI-index of benzenoids and their characteristic graphs are compared by correlating it to a structural property (π-electron energy) of the benzenoids using MLR analysis. PI index being applicable to both trees and cyclic graphs, yielded required results for benzenoid and their characteristic graph
On Color Energy of Few Classes of Bipartite Graphs and Corresponding Color Complements
Get PDFFor a given colored graph G, the color energy is defined as Ec(G) = Σλi, for i = 1, 2,…., n; where λi is a color eigenvalue of the color matrix of G, Ac (G) with entries as 1, if both the corresponding vertices are neighbors and have different colors; -1, if both the corresponding vertices are not neighbors and have same colors and 0, otherwise. In this article, we study color energy of graphs with proper coloring and L (h, k)-coloring. Further, we examine the relation between Ec(G) with the corresponding color complement of a given graph G and other graph parameters such as chromatic number and domination number.
AMS Subject Classification: 05C15, 05C5