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.

   In this work, a novel technique to obtain an accurate solutions to nonlinear form by multi-step combination with Laplace-variational approach (MSLVIM) is introduced. Compared with the  traditional approach for variational it overcome all difficulties and enable to provide us more an accurate solutions with extended of the convergence region as well as covering to larger intervals which providing us a continuous representation of approximate analytic solution and it give more better information of the solution over the whole time interval. This technique is more easier for obtaining the general Lagrange multiplier with reduces the time and calculations. It converges rapidly to exact formula with simply computable terms wit

sanaa tareq, Baghdad Science Journal, - Cited by 1

Some physical properties enthalpy (?H), entropy (?s), free energy (?G),capacities(?cp?) and Pka values) for valine in dimethyl foramideover the temperature range 293.15-318.15K, were determined by direct conductance measurements. The acid dissociation at six temperature was examined at solvent composition x2) involving 0.141 of dimethyl foramide . As results, calculated values have been used to determine the dissociation constant and the associated thermodynamic function for the valine in the solvent mixture over temperatures in the range 293.15-318.15 k. The Pka1, and Pka2 were increased with increasing temperature.

The development of economic and environmentally friendly extractants to recover cobalt metal is required due to the increasing demand for this metal. In this study, solvent extraction of Co(II) from aqueous solution using a mixture of N,N0-carbonyl difatty amides (CDFAs) synthesised from palm oil as the extractant was carried out. The effects of various parameters such as acid, contact time, extractant concentration, metal ion concentration and stripping agent and the separation of Co(II) from other metal ions such as Fe(II), Ni(II), Zn(III) and Cd(II) were investigated. It was found that the extraction of Co(II) into the organic phase involved the formation of 1:1 complexes. Co(II) was successfully separated from commonly associated metal

The best proximity point is a generalization of a fixed point that is beneficial when the contraction map is not a self-map. On other hand, best approximation theorems offer an approximate solution to the fixed point equation . It is used to solve the problem in order to come up with a good approximation. This paper's main purpose is to introduce new types of proximal contraction for nonself mappings in fuzzy normed space and then proved the best proximity point theorem for these mappings. At first, the definition of fuzzy normed space is given. Then the notions of the best proximity point and - proximal admissible in the context of fuzzy normed space are presented. The notion of α ̃–ψ ̃- proximal contractive mapping is introduced.

This paper presents a hybrid energy resources (HER) system consisting of solar PV, storage, and utility grid. It is a challenge in real time to extract maximum power point (MPP) from the PV solar under variations of the irradiance strength.  This work addresses challenges in identifying global MPP, dynamic algorithm behavior, tracking speed, adaptability to changing conditions, and accuracy. Shallow Neural Networks using the deep learning NARMA-L2 controller have been proposed. It is modeled to predict the reference voltage under different irradiance. The dynamic PV solar and nonlinearity have been trained to track the maximum power drawn from the PV solar systems in real time.

Moreover, the proposed controller i

The objective of this research is to study experimentally and theoretically the girder vertical load share of the curved I-Girder bridges subjected to the point load in addition to the self-weigh and supper imposed dead loads. The experimental program consist of manufacturing and testing the five simply supported bridge models was scaled down by (1/10) from a prototype of 30m central span. The models carriageway central radii are 30 m, 15m or 10m. The girder spacing of the first two models is 175 mm with an overall carriageway width of 650mm. The girder spacing of the other three bridge models is 200mm with the overall carriageway width of 700 mm. The overall depth of the composite section was 164 mm. To investigate the effect of live load