Generalized random processes and Cauchy's problem for some partial differential systems

In this paper we consider a parabolic partial differential system of the form DtHt=L(t,x,D)Ht. The generalized stochastic solutions Ht, corresponding to the generalized stochastic initial conditions H0 are given. Some properties concerning these generalized stochastic solutions are also obtained

Solvability of an Infinite System of Singular Integral Equations

2000 Mathematics Subject Classification: 45G15, 26A33, 32A55, 46E15.Schauder's fixed point theorem is used to establish an existence result for an infinite system of singular integral equations in the form: (1) xi(t) = ai(t)+ ∫t0 (t − s)− α (s, x1(s), x2(s), …) ds, where i = 1,2,…, α ∈ (0,1) and t ∈ I = [0,T]. The result obtained is applied to show the solvability of an infinite system of differential equation of fractional orders

Synthesis of New Formyl Halo N-methylimidazole Derivatives

Bromo-formyl imidazoles 16-20 have been prepared by three different ways. The first consisted of conversion of bromo or iodo imidazoles 1-6 into diethyl acetals 13-15, and subsequent hydrolysis into formyl derivatives 7-9. In the second, bromination of. formyl imidazoles with NBS afforded compounds 16-18 in 45-70°/o yield. The third method used direct formylation of bromo imidazoles 10-12 with n-BuLi/DMF reagent into compounds 16, 19, and 20

On the solvability of a nonlinear functional integral equations via measure of noncompactness in

Using the technique of a suitable measure of non-compactness and the Darbo fixed point theorem, we investigate the existence of a nonlinear functional integral equation of Urysohn type in the space of Lebesgue integrable functions Lp(RN). In this space, we show that our functional-integral equation has at least one solution. Finally, an example is also discussed to indicate the natural realizations of our abstract result

AN ANALYSIS OF TWO DIMENSIONAL INTEGRAL EQUATIONS OF THE SECOND KIND

In this article, a numerical method is used to solve the two dimensionalFredholm integral equation of the second kind with weak singular kernel using the Toeplitz matrix and product Nystrom method. The numerical results given in this paper are computed using maple 8. The error, in each case, is computed.In this article, A numerical method is used to solve the two dimensionalFredholm integral equation of the second kind with weak singular kernel using the Toeplitz matrix and product Nystrom method. The numerical results given in this paper are computed using maple 8. The error, in each case, is computed

A Parabolic Transform and Averaging Methods for General Partial Differential Equations

Averaging method of the fractional general partial differential equations and a special case of these equations are studied, without any restrictions on the characteristic forms of the partial differential operators. We use the parabolic transform, existence and stability results can be obtained

On the correct formulation of a nonlinear differential equations in Banach space

We study, the existence and uniqueness of the initial value problems in a Banach space E for the abstract nonlinear differential equation (dn−1/dtn−1)(du/dt+Au)=B(t)u+f(t,W(t)), and consider the correct solution of this problem. We also give an application of the theory of partial differential equations

SULPHATED POLYSACCHARIDES (SPS) FROM THE GREEN ALGA ULVA FASCIATA EXTRACT MODULATES LIVER AND KIDNEY FUNCTION IN HIGH FAT DIET-INDUCED HYPERCHOLESTEROLEMIC RATS

Objective: Hypercholesterolemia (HC) was frequently associated with oxidative stress, and release of inflammatory cytokines is to determine the hypolipidemic effects of sulphated polysaccharides from seaweed Ulva fasciata algal extracts through measuring the activities of some parameters related to liver and kidney functions in the serum of hypercholesterolemic rats as compared to normal one.Methods: Different groups of rats were administered a high cholesterol diet. Liver and kidney functions, inflammatory cytokines (TNF-α, CRP, MPO and IL-10), oxidative stress (GSH, MDA and NO), in addition to cell adhesion molecules (ICAM-1 and VCAM-1) were assessed before and after treatment with the algal polysaccharides. In addition, histological examination of liver and kidney were performed to confirm the biochemical findings.Results: The obtained results showed that oxidative stress and inflammatory markers associated with hypercholesterolemia were significantly increased in HC-rats. The histopathological examination of liver and kidney demonstrated severe degeneration with diffuse vacuolar degeneration, necrosis and the presence of fatty droplets. In addition; nephron-histological examination revealed, mild glomerular injury with mild vascular and inflammatory changes. Treatment with the algal sulphated polysaccharides effectively improved these disorders and diminished the formation of fatty liver, as well as renal dysfunction more than the reference drug; fluvastatin. Conclusion: It could be concluded that the consumption of UFP (Ulva fasciata polysaccharides), may be associated with attenuation of inflammatory markers, amelioration of fatty liver and improvement of renal dysfunction, that in turn lead to counteract hypercholesterolemia and its related disorders; such as obesity, and heart disease.Keywords: Non-alcoholic fatty liver disease, Seaweed, Ulva fasciata, Hypercholesterolemia, Hypolipidemic activity, Sulphated polysaccharides (SPs