We will pursue a way of building up an algebraic structure that involves, in a mathematical abstract way, the well known Grassmann variables. The problem arises when we tried to understand the grassmannian polynomial expansion on the scope of ring theory. The formalization of this kind of variables and its properties will help us to have a better idea of some algebraic structures and the way th...

We develop an effective Gauss-Bonnet extension of Loop Quantum Cosmology, by introducing holonomy corrections in modified F (G) theories of gravity. Within the context of our formalism, we provide a perturbative expansion in the critical density, a parameter characteristic of Loop Quantum Gravity theories, and we result in having leading order corrections to the classical F (G) theories of grav...

In the present paper we study a conformally flat generalized Ricci recurrent perfect fluid spacetime with constant scalar as solution of modified $F(R)$-gravity theory. We show that Robertson-Walker is Recurrent if and only it symmetric. The type matter shown to have EoS $\omega=-1$. Some energy conditions are analyzed couple popular toy models $F(R)$-gravity, like $F(R)= R+\alpha R^m $ where $...

in this paper, a boussinesq equation is solved by using the adomian's decomposition method, modified adomian's decomposition method and homotopy analysis method. the approximate solution of this equation is calculated in the form of series which its components are computed by applying a recursive relation. the existence and uniqueness of the solution and the convergence of the propose...

One of the possible potential candidates for describing universe's rapid expansion is modified gravity. In framework theory gravity $f(R,G)$, present work features materialization anisotropic matter, such as compact stars. Specifically, to learn more about physical behavior stars, radial, and tangential pressures well energy density six stars namely $Her X-1$, $SAXJ1808.4-3658$, $4U1820-30$, $P...

Background. The essential drawbacks of conventional tissue expansion, a technique widely used in reconstructive surgery, are its significant duration and the high complications rate. The experience of our clinic covers 329 patients treated with this method from 1987 to 2006. The mean time of expansion was previously 72 ± 2 days (± SD) and the rate of local complications was 38.6%. We applied ef...

Several types of solitary wave solutions (3 + 1)-dimensional nonlinear extended and modified quantum Zakharov–Kuznetsov equations are established successfully via the implantation three mathematical methods. The concerned models have many fruitful applications to describe waves in electron–positron–ion magnetoplasmas weakly ion-acoustic plasma. derived results MEAEM method, ESE F-expansion been...

As two-dimensional coupled system of nonlinear partial differential equations does not give enough smooth solutions, when approximated by linear, quadratic and cubic polynomials and gives poor convergence or no convergence. In such cases, approximation by zero degree polynomials like Haar wavelets (continuous functions with finite jumps) are most suitable and reliable. Therefore, modified numer...