The purpose of this paper is to give some results theorems , propositions and corollaries concerning new algebraic systems flower , garden and farm with accustomed algebraic systems groupoid , group and ring.

In this paper, the Decomposition method was used to find approximation solutions for a system of linear Fredholm integral equations of the second kind. In this method the solution of a functional equations is considered as the sum of an infinite series usually converging to the solution, and Adomian decomposition method for solving linear and nonlinear integral equations. Finally, numerical examples are prepared to illustrate these considerations.

In this paper the full stable Banach gamma-algebra modules, fully stable Banach gamma-algebra modules relative to ideal are introduced. Some properties and characterizations of these classes of full stability are studied.

A method for Approximated evaluation of linear functional differential equations is described. where a function approximation as a linear combination of a set of orthogonal basis functions which are chebyshev functions .The coefficients of the approximation are determined by (least square and Galerkin’s) methods. The property of chebyshev polynomials leads to good results , which are demonstrated with examples.

Dyspepsia is a significant public health issue that affects the entire world population. In this work, we formulate and analyze a deterministic model for the population dynamics of Gut bacteria in the presence of antibiotics and Probiotic supplements. All the possible equilibria and their local stability are obtained. The global stability around the positive equilibrium point is established. Numerical simulations back up our analytical findings and show the temporal dynamics of gut microorganisms.

An adaptive nonlinear neural controller to reduce the nonlinear flutter in 2-D wing is proposed in the paper. The nonlinearities in the system come from the quasi steady aerodynamic model and torsional spring in pitch direction. Time domain simulations are used to examine the dynamic aero elastic instabilities of the system (e.g. the onset of flutter and limit cycle oscillation, LCO). The structure of the controller consists of two models :the modified Elman neural network (MENN) and the feed forward multi-layer Perceptron (MLP). The MENN model is trained with off-line and on-line stages to guarantee that the outputs of the model accurately represent the plunge and pitch motion of the wing and this neural model acts as the identifier. Th

The stability and releasing profile of 2:1 core: wall ratio ibuprofen microcapsules prepared by aqueous coacervation (gelatin and acacia polymers coat) and an organic coacervation methods (ethyl cellulose and sodium alginate polymers coat) in weight equivalent to 300mg drug, were studied using different storage temperatures 40°C, 50°C ,60°C and refrigerator temperature 4°C in an opened and closed container for three months (releasing profile) and four months (stability study).It was found that, these ibuprofen microcapsules were stable with expiration dates of 4.1 and 3.1 years for aqueous and an organic method respectively.Aqueous prepared ibuprofen microcapsules were found more stable than those microcapsules prepared by or