Modern Scientific Press

ABSTRACT: In this paper, we construct an approximate analytic solution of (2+1) dimensional Zakhorov-Kuznetsov equations using Homotopy iteration method with hyperbolic & periodic initial conditions and the result is compared with the exact solutions obtained by sine-cosine method.

ABSTRACT: Mathematical modeling of numerous physical phenomena often leads to high-dimensional partial differential equations and thus the higher dimensional nonlinear evolution equations come into further attractive in many branches of physical sciences. In this paper, we apply (G´/G,1/G)-expansion method to construct more general and abundant new exact traveling wave solutions of nonlinear Second extended model of shallow water waves equation, ZK-MEW. When the parameters take special values, solitary waves are derived from the traveling waves. The present method more reliable to constructs more general traveling wave solution of nonlinear physical models. The method appears to be easier and more convenient by means of a symbolic computation system.

ABSTRACT: In this paper, a new class of size-biased Generalized Gamma Distribution is considered. A Size-biased Generalized Gamma Distribution; a particular case of Weighted Generalized Gamma Distribution, taking the weights as the variety values have been defined. The important statistical properties of a new model have been defined. The estimation of parameter of a new model is obtained by employing the Bayesian method of estimation. The Bayes’ estimators of Size biased Generalized Gamma distribution (SBGGMD), that stems from an extension of Jeffery’s prior (Al-Kutubi) with a squared error loss function and new loss function (Al-Bayyati). We propose four different types of estimator. Under squared error loss function, there are two estimators formed by using Jaffrey prior and an extension of Jaffrey’s prior. The other two remaining estimators are derived using the same Jeffrey’s prior and extension of Jeffrey’s prior under a new loss function. We are also deriving the survival functions of the size biased Generalized Gamma distribution under Jaffrey and extension of Jaffrey’s prior. These methods are compared by using mean square error through simulation study with varying sample sizes.

ABSTRACT: In this work, the reliability optimization problem of the redundant system in fuzzy environment is developed and the results are discussed. The numerical solutions of crisp reliability optimization problems are compared and the fuzzy solution and its effectiveness are presented and discussed. The penalty function method has be developed and mixed with Nelder and Mend’s algorithm of direct optimization problems solution are used together to solve this mixed-integer programming problem.

ABSTRACT: Some new representations of the supersymmetric transformations are derived, and the supermultiplets are introduced. Based on these representations, Graded Lie Algebras and various formulations (equations, commutation relations, propagators, Jacobi identities, etc.) of bosons and fermions may be unified. On the one hand, the mathematical characteristic of particles is proposed: bosons correspond to real number, and fermions correspond to imaginary number, respectively. Such fermions of even (or odd) number form bosons (or fermions), which is just consistent with a relation between imaginary and real number. The imaginary number is only included in the equations, forms, and matrixes of fermions. It is connected with relativity. On the other hand, the unified forms of supersymmetry are also connected with the statistics unifying Bose-Einstein and Fermi-Dirac statistics, and with the possible violation of Pauli exclusion principle; and a unified partition function is obtained. Moreover, three quarks may be described by the Borromean rings. Some unifications in particle physics are discussed. The quantum statistics is unified by the nonlinear equations. Based on the gauge groups, various unifications of interactions are researched. A developed direction of particle physics and modern science is possibly the higher dimensional complex space.