In this work, the modified Lyapunov-Schmidt reduction is used to find a nonlinear Ritz approximation of Fredholm functional defined by the nonhomogeneous Camassa-Holm equation and Benjamin-Bona-Mahony. We introduced the modified Lyapunov-Schmidt reduction for nonhomogeneous problems when the dimension of the null space is equal to two.  The nonlinear Ritz approximation for the nonhomogeneous Camassa-Holm equation has been found as a function of codimension twenty-four.

The theory of Topological Space Fiber is a new and essential branch of mathematics, less than three decades old, which is created in forced topologies. It was a very useful tool and played a central role in the theory of symmetry. Furthermore, interdependence is one of the main things considered in topology fiber theory. In this regard, we present the concept of topological spaces α associated with them and study the most important results.

This research presents a new algorithm for classification the
shadow and water bodies for high-resolution satellite images (4-
meter) of Baghdad city, have been modulated the equations of the
color space components C1-C2-C3. Have been using the color space
component C3 (blue) for discriminating the shadow, and has been
used C1 (red) to detect the water bodies (river). The new technique
was successfully tested on many images of the Google earth and
Ikonos. Experimental results show that this algorithm effective to
detect all the types of the shadows with color, and also detects the
water bodies in another color. The benefit of this new technique to
discriminate between the shadows and water in fast Matlab pro

Background: The access cavity is a critical stage in root canal therapy and it may influence the subsequent steps of the treatment. The new minimally invasive endodontic access cavity preparation concept aims to preserve sound tooth structure by conserving as much intact dentine as possible including the pulp chamber's roof, to keep the teeth from fracturing during and after endodontic treatment. While there is great interest in such access opening designs in numerous publications, still there is a lack of scientific evidence to support the application of such modern access cavity designs in clinical practice. This review aims to critically examine the literature on minimal access cavity preparations, explain the effect of minimally inva

An optoelectronic flow-through detector for active ingredients determination in pharmaceutical formulations is explained. Two consecutive compact photodetector’s devices operating according to light-emitting diodes-solar cells concept where the LEDs acting as a light source and solar cells for measuring the attenuated light of the incident light at 180˚ have been developed. The turbidimetric detector, fabricated of ten light-emitting diodes and five solar cells only, integrated with a glass flow cell has been easily adapted in flow injection analysis manifold system. For active ingredients determination, the developed detector was successfully utilized for the development and validation of an analytical method for warfarin determination

Here, we found an estimation of best approximation of unbounded functions which satisfied weighted Lipschitz condition with respect to convex polynomial by means of weighted Totik-Ditzian modulus of continuity

Abstract: The M(II) complexes [M2(phen)2(L)(H2O)2Cl2] in (2:1:2 (M:L:phen) molar ratio, (where M(II) =Mn(II), Co(II), Cu(II), Ni(II) and Hg(II), phen = 1,10-phenanthroline; L = 2,2'-(1Z,1'Z)-(biphenyl-4,4'-diylbis(azan-1-yl-1-ylidene))bis(methan-1-yl-1- ylidene)diphenol] were synthesized. The mixed complexes have been prepared and characterized using 1H and13C NMR, UV/Visible, FTIR spectra methods and elemental microanalysis, as well as magnetic susceptibility and conductivity measurements. The metal complexes were tested in vitro against three types of pathogenic bacteria microorganisms: Staphylococcus aurous, Escherichia coli, Bacillussubtilis and Pseudomonasaeroginosa to assess their antimicrobial properties. From this study shows that a

Copper zinc tin sulfide selenide, Cu2 ZnSn(S1−x Se x)4 , absorbers are promising earth-abundant and environmentally benign materials for low-cost photovoltaic applications. This study investigates the structural and optical properties of Cu 2 ZnSn(S1−x Se x)4 nanostructured thin films prepared by pulsed laser deposition using melt-quenched targets with selenium compositions x = 0.0–1.0. X-ray diffraction revealed that films with low selenium content remained amorphous, whereas higher selenium incorporation promoted the formation of polycrystalline kesterite–stannite phases with preferred orientations along (112), (200), (220), and (312). The crystallite size increased from 12.3 to 17.9 nm as selenium reached x = 1.0, indicating enha