Most of the fundamental theories and mathematical models engineering physical sciences are expressed in terms partial differential equations (PDEs). Several studies were carried out for numerical approximation second order linear Klein-Gordon equation. This study constructed a new technique The scheme was based on employing non-polynomial cubic spline method (NPCSM). time derivatives involved e...

Among the many different definitions of fractional derivative, Riemann–Liouville and Gerasimov–Caputo derivatives are most commonly used. In this paper, we consider equations with Dzhrbashyan–Nersesyan which generalizes derivatives; it is transformed into such for two sets parameters that are, in a certain sense, symmetric. The issues unique solvability initial value problems some classes linea...

In a cosmological context, the electric and magnetic parts of the Weyl tensor, Eab and Hab, represent the locally free curvature – i.e. they are not pointwise determined by the matter fields. By performing a complete covariant decomposition of ∇cEab and ∇cHab, we show that the parts of the derivative of the curvature which are locally free (i.e. not pointwise determined by the matter via the Bi...

The paper studies a model of fluid flow in fractured porous medium which fractures are distributed uniformly over the volume. This includes nonlinear equation containing several terms with fractional derivatives sense Caputo order belonging to interval 1,2. relevance studying this problem is determined by its practical significance oil industry, since most world’s reserves these types reservoir...

An efficient protocol for post-functionalization of organo-imido polyoxometalates is developed via creating a remote tertiary “N” atom over the surface of organo-imido hexamolybdates and subsequently post-functionalizing it with the help of allyl or alkyl halides to afford stoichiometric, “in situ” crystalline products at moderate temperatures. The parent organo-imido product 2 and post-functio...

Microbial protein synthesis in the rumen would be optimized when dietary carbohydrates and proteins have synchronized rates and extent of degradation. The aim of this study was to evaluate the effect of varying ruminal degradation rate of energy and nitrogen sources on intake, nitrogen balance, microbial protein yield, and kinetics of nutrients in the rumen of growing kids. Eight Boer goats (38...

above. For example, does each carbon atom of the ring in phenol lack one electron of filling its eight "possible electron positions" or do three of the carbon atoms lack two electrons each while the remaining three carbon atoms have all their "possible electron positions" filled, or is there some other combination? In conclusion, the main purpose of presenting this detailed scale model of the b...

We present a method for estimating intrinsic images from a fixed-viewpoint image sequence captured under changing illumination directions. Previous work on this problem reduces the influence of shadows on reflectance images, but does not address shading effects which can significantly degrade reflectance image estimation under the typically biased sampling of illumination directions. In this pa...

Surface modification of nanocrystalline TiO(2) particles (45 A) with bidentate benzene derivatives (catechol, pyrogallol, and gallic acid) was found to alter optical properties of nanoparticles. The formation of the inner-sphere charge-transfer complexes results in a red shift of the semiconductor absorption compared to unmodified nanocrystallites. The binding structures were investigated by us...