This paper presents a simple and efficient method for determining the solution of Riccati differential equation with coefficients rational. In case the differential Galois group of the differential equation (E l) : y = ry, r ∈ C(x) is reducible, we look for the rational solutions of Riccati differential equation θ + θ 2 = r, by reducing the number of check to be made and by accelerating the sea...

Bethe-Salpeter equation for the massive particles with spin 1 is considered. The scattering amplitude decomposition of the particles with spin 1 by relativistic tensors is derived. The transformation coefficients from helicity amplitudes to invariant functions is found. The integral equations system for invariant functions is obtained and partial decomposition of this system is performed. Equiv...

Abstract: In this article, we develop a method to obtain approximate solutions of nonlinear coupled partial differential equations with the help of Laplace Decomposition Method (LDM). The technique is based on the application of Laplace transform to nonlinear coupled partial differential equations. The nonlinear term can easily be handled with the help of Adomian polynomials. We illustrate this...

Algorithms for Blind Audio Source Separation (BASS) in time domain can be categories as based on complete decomposition or based on complete decomposition. Partial decomposition of observation space leads to additional computational complexity and burden, to minimize resource requirement complete decomposition technique is preferred. In this script an optimized divergence based ICA technique is...

Decomposition is a technique to obtain complete solutions by assembling independently obtained partial solutions. In particular, constraint decomposition plays an important role in distributed databases, distributed scheduling and violation detection: It enables conflictfree local decision making, while avoiding communication overloading. One of the main issues in decomposition is the loss of f...

Domain decomposition methods are widely used to solve the parabolic partial differential equations with Dirichlet, Neumann, or mixed boundary conditions. Modified implicit prediction (MIP) algorithm is unconditionally stable domain decomposition method. In this paper, the SOR iterative technique is applied to the MIP algorithm and the optimum over-relaxation parameter is provided.

Two numerical algorithms based on variational iteration and decomposition methods are developed to solve a linear partial integro-differential equation with a weakly singular kernel arising from viscoelasticity. In addition, analytic solution is re-derived by using the variational iteration method and decomposition method.

An optimal decomposition formula for the norm in the Orlicz space L(log L) is given. New proofs of some results involving L(log L) spaces are given and the decomposition is applied to apriori estimates for elliptic partial differential equations with the right-hand side in Zygmund classes. 2000 Mathematics Subject Classification: 46E35, 46E39, 35J05.

No general algorithm is known for the functional decomposition of wild polynomials over a finite field. However partial solutions exist. In particular, a fast functional decomposition algorithm for linearised polynomials has been developed using factoring methods in skew-polynomial rings. This algorithm is extended to a related class of wild polynomials, which are sub-linearised polynomials.

In this paper we study the partial Brauer C-algebras Rn(δ, δ ), where n ∈ N and δ, δ ∈ C. We show that these algebras are generically semisimple, construct the Specht modules and determine the Specht module restriction rules for the restriction Rn−1 →֒ Rn. We also determine the corresponding decomposition matrix, and the Cartan decomposition matrix.