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Exact and Explicit Solutions of Whitham-Broer-Kaup Equations in Shallow Water
Issue:
Volume 5, Issue 6, December 2016
Pages:
174-180
Received:
2 September 2016
Accepted:
18 September 2016
Published:
17 October 2016
Abstract: In this paper, a simple direct method is presented to find equivalence transformation of a nonlinear Whitham- Broer-Kaup equations. Applying this equivalence transformation, we can obtain the symmetry group theorem of the Whitham-Broer-Kaup equations and then derive series of new exact and explicit solutions of the Whitham-Broer-Kaup equations according to solutions of the previous references.
Abstract: In this paper, a simple direct method is presented to find equivalence transformation of a nonlinear Whitham- Broer-Kaup equations. Applying this equivalence transformation, we can obtain the symmetry group theorem of the Whitham-Broer-Kaup equations and then derive series of new exact and explicit solutions of the Whitham-Broer-Kaup equations acco...
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Bayesian Test for Lifetime Performance Index of Ailamujia Distribution Under Squared Error Loss Function
Issue:
Volume 5, Issue 6, December 2016
Pages:
181-185
Received:
5 October 2016
Accepted:
14 October 2016
Published:
7 November 2016
Abstract: The aim of this paper is to estimate the lifetime performance index of Ailamujia distribution. A Bayesian test procedure is developed under squared error loss function. Firstly, Bayes estimation of life performance index is derived, then a Bayesian test procedure for lifetime performance index using posteriori probability ratio test method. Finally, an example is used to illustrate the effectiveness and feasibility of the method.
Abstract: The aim of this paper is to estimate the lifetime performance index of Ailamujia distribution. A Bayesian test procedure is developed under squared error loss function. Firstly, Bayes estimation of life performance index is derived, then a Bayesian test procedure for lifetime performance index using posteriori probability ratio test method. Finally...
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Admissibility Estimation of Pareto Distribution Under Entropy Loss Function Based on Progressive Type-II Censored Sample
Issue:
Volume 5, Issue 6, December 2016
Pages:
186-191
Received:
5 October 2016
Accepted:
14 October 2016
Published:
7 November 2016
Abstract: The aim of this paper is to study the estimation of Pareto distribution on the basis of progressive type-II censored sample. First, the maximum likelihood estimator (MLE) is derived. Then the Bayes estimator of the unknown parameter of Pareto distribution is derived on the basis of Gamma prior distribution under entropy loss function. Further the empirical Bayes estimator also obtained by using maximum likelihood on the basis of Bayes estimator. Finally, the admissibility of a class of inverse linear estimators are discussed under suitable conditions.
Abstract: The aim of this paper is to study the estimation of Pareto distribution on the basis of progressive type-II censored sample. First, the maximum likelihood estimator (MLE) is derived. Then the Bayes estimator of the unknown parameter of Pareto distribution is derived on the basis of Gamma prior distribution under entropy loss function. Further the e...
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The Singular Function Boundary Integral Method for the 2-D and 3-D Laplace Equation Problems in Mechanics, with a Boundary Singularity
Issue:
Volume 5, Issue 6, December 2016
Pages:
192-204
Received:
3 October 2016
Accepted:
15 October 2016
Published:
10 November 2016
Abstract: In this study the Singular Function Boundary Integral Method (SFBIM) is implemented in the case of a planar elliptic boundary value problem in Mechanics, with a point boundary singularity. The method is also extended in the case of a typical problem of Solid Mechanics, concerning the Laplace equation problem in three dimensions, defined in a domain with a straight edge singularity on the surface boundary. In both the 2-D and 3-D cases, the general solution of the Laplace equation is approximated by the leading terms (which contain the singular functions) of the local asymptotic solution expansion. The singular functions are used to weight the governing equation in the Galerkin sense. For the 2-D Laplacian model problem of this study, which is defined over a domain with a re-entrant corner, the resulting discretized equations are reduced to boundary integrals by means of Green’s second identity. For the 3-D model problem of this work, the volume integrals of the discretized equations are reduced to surface integrals by implementing Gauss’ divergence theorem. The Dirichlet boundary conditions are then weakly enforced by means of Lagrange multipliers. The values of the latter are calculated together with the singular coefficients, in the 2-D case or the Edge Flux Intensity Functions (EFIFs), in the 3-D model problem, which appear in the local solution expansion. For the planar problem, the numerical results are favorably compared with the analytic solution. Especially for the extension of the method in three dimensions, the preliminary numerical results compare favorably with available post-processed finite element results.
Abstract: In this study the Singular Function Boundary Integral Method (SFBIM) is implemented in the case of a planar elliptic boundary value problem in Mechanics, with a point boundary singularity. The method is also extended in the case of a typical problem of Solid Mechanics, concerning the Laplace equation problem in three dimensions, defined in a domain...
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On a Consumer Problem
Issue:
Volume 5, Issue 6, December 2016
Pages:
205-210
Received:
10 February 2015
Accepted:
20 October 2016
Published:
15 November 2016
Abstract: The model of economic dynamics of the Leontief type is considered. The problem of determining the equilibrium state of the model with a fixed budget is investigated. It is proved that the state of equilibrium exists, if the trajectory model is a solution to the consumer problem.
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The Method of Successive Approximations (Neumann’s Series) of Volterra Integral Equation of the Second Kind
Teshome Bayleyegn Matebie
Issue:
Volume 5, Issue 6, December 2016
Pages:
211-219
Received:
12 October 2016
Accepted:
28 October 2016
Published:
23 December 2016
Abstract: In this paper, the solving of a class of both linear and nonlinear Volterra integral equations of the first kind is investigated. Here, by converting integral equation of the first kind to a linear equation of the second kind and the ordinary differential equation to integral equation we are going to solve the equation easily. The method of successive approximations (Neumann’s series) is applied to solve linear and nonlinear Volterra integral equation of the second kind. Some examples are presented to illustrate methods.
Abstract: In this paper, the solving of a class of both linear and nonlinear Volterra integral equations of the first kind is investigated. Here, by converting integral equation of the first kind to a linear equation of the second kind and the ordinary differential equation to integral equation we are going to solve the equation easily. The method of success...
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Error Detection and Correction Using Hamming and Cyclic Codes in a Communication Channel
Irene Ndanu John,
Peter Waweru Kamaku,
Dishon Kahuthu Macharia,
Nicholas Muthama Mutua
Issue:
Volume 5, Issue 6, December 2016
Pages:
220-231
Received:
1 December 2016
Accepted:
28 December 2016
Published:
20 January 2017
Abstract: This paper provides an overview of two types of linear block codes: Hamming and cyclic codes. We have generated, encoded and decoded these codes as well as schemes and/or algorithms of error-detecting and error-correcting of these codes. We have managed to detect and correct errors in a communication channel using error detection and correction schemes of hamming and cyclic codes.
Abstract: This paper provides an overview of two types of linear block codes: Hamming and cyclic codes. We have generated, encoded and decoded these codes as well as schemes and/or algorithms of error-detecting and error-correcting of these codes. We have managed to detect and correct errors in a communication channel using error detection and correction sch...
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