In this paper, analytic solutions of two-dimensional coupled Burgers’ equations are obtained by the HOMOTOPY analysis and the HOMOTOPY Pade methods. The obtained approximation by using HOMOTOPY method contains an auxiliary parameter which is a simple way to control and adjust the convergence region and rate of solution series. The approximation solutions by [m,m] HOMOTOPY Pade technique is often independent of auxiliary parameter and this technique accelerate the convergence of the related series.

We construct a q-model structure, an h-model structure and an m-model structure on multipointed d-spaces and on flows. The two q-model structures are combinatorial and left determined and they coincide with the combinatorial model structures already known on these categories. The four other model structures (the two m-model structures and the two h-model structures) are accessible. We give an example of multipointed d-space and of flow which are not cofibrant in any of the model structures. We explain why the m-model structures, Quillen equivalent to the q-model structure of the same category, are better behaved than the q-model structures.

In this article, the HOMOTOPY Perturbation Method (HPM) is employed to approximate solutions of a modified Lotka–Volterra equation. HPM has been introduced by He to solve approximately linear or nonlinear differential equations. Approximate polynomials have also been constructed to find approximate solutions of a modified Lotka-Volterra system. Numerical comparisons are made between HPM and maple numerical results.

In this paper, analytic solutions of the modified Burgers-Korteweg-de Vries equation (mBKdVE) and the Newell -Whitehead equation are obtained by the Ho-motopy analysis method (HAM) and the HOMOTOPY Pade method (HPadeM). The obtained approximation by using HAM contains an auxiliary parameter which is a way to control and adjust the convergence region and rate of the solution series.The approximation solution by [m; m] HPadeM is often independent of auxiliary parameter`h and this technique accelerate the convergence of the related series.

In this paper, we introduce the notion of braiding crossed polymodule and 􀀀,equivariant braided crossed polymodule of polygroups and we give some of their properties. Further, we study the concept of , ber hyperproduct. Our results extend the classical results of crossed squares to crossed polysquares. Moreover, we study crossed polysquare version of HOMOTOPY kernels by using the fundamental relations.