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.

This research presents a particular designing strategy for a free form of surfaces, constructed by the lofting design method. The regarded surfaces were created by sliding a B-spline curves (profile curves), in addition to describing an automatic procedure for selective identification of sampling points in reverse engineering applications using Coordinate Measurement Machine. Two models have been implemented from (Ureol material) to represent the different cases of B-spline types to clarify its scope of application. The interior data of the desired surfaces was designed by MATLAB software, which then were transformed to UG-NX9 software for connecting the sections that were designed in MATLAB program and obtaining G-code programs for the

Water pollution as a result of contamination with dye-contaminating effluents is a severe issue for water reservoirs, which instigated the study of biodegradation of Reactive Red 195 and Reactive Blue dyes by E. coli and Bacillus sp. The effects of occupation time, solution pH, initial dyes concentrations, biomass loading, and temperature were investigated via batch-system experiments by using the Design of Experiment (DOE) for 2 levels and 5 factors response surface methodology (RSM). The operational conditions used for these factors were optimized using quadratic techniques by reducing the number of experiments. The results revealed that the two types of bacteria had a powerful effect on biodegradable dyes. The regression analysis reveale

The reducing of erosion and the solubility of irrigation canals soils which constructed on gypsum soil is important in civil and water resources engineering. The main problem of gypsum soils is the presence of gypsum which represents one of most complex engineering problems, especially when accompanied by the moving of water which represent dynamic load along the canal. There are several solutions to this problem, in this research “Poly urethane” is used to give the gypsum soil sufficient hardness to reduce the solubility and erosion, after compacting the soil in the canal, percentages of Poly urethane was used to making cover to the soil by mixing percent of soil with Poly urethane, and the ratio was as follows: (5 and 10) % an

This work deals with kinetics and chemical equilibrium studies of esterification reaction of ethanol with acetic acid. The esterification reaction was catalyzed by an acidic ion exchange resin (Amberlyst- 15) using a batch stirred tank reactor. The pseudo-homogenous and Eley-Rideal models were successfully fitted with experimental data. At first, Eley-Rideal model was examined for heterogeneous esterification of acetic acid and ethanol. The pseudo-homogenous model was investigated with a power-law model. The apparent reaction order was determined to be (0.88) for Ethanol and (0.92) for acetic acid with a correlation coefficient (R2) of 0.981 and 0.988, respectively. The reaction order was determined to be 4.1087x10-3 L0.8/(mol0.8.min) with

The present work is devoted to investigate the performance of a homemade Y-shape catalytic microreactor for degradation of dibenzothiophene (DBT), as a model of sulphur compounds including in gas oil, utilizing solar incident energy. The microchannel was coated with TiO2 nanoparticles which were used as a photocatalyst. Performance of the microreactor was investigated using different conditions (e.g., DBT concentration, LHSV, operating temperature, and (H₂O₂/DBT) ratio). Our experiments show that, in the absence of UV light, no reaction takes place. The results revealed that outlet concentration of DBT decreases as the mean residence time in the microreactor increases. Also, it was noted that operating temperature s

Information security is a crucial factor when communicating sensitive information between two parties. Steganography is one of the most techniques used for this purpose. This paper aims to enhance the capacity and robustness of hiding information by compressing image data to a small size while maintaining high quality so that the secret information remains invisible and only the sender and recipient can recognize the transmission. Three techniques are employed to conceal color and gray images, the Wavelet Color Process Technique (WCPT), Wavelet Gray Process Technique (WGPT), and Hybrid Gray Process Technique (HGPT). A comparison between the first and second techniques according to quality metrics, Root-Mean-Square Error (RMSE), Compression-

Fractal image compression depends on representing an image using affine transformations. The main concern for researches in the discipline of fractal image compression (FIC) algorithm is to decrease encoding time needed to compress image data. The basic technique is that each portion of the image is similar to other portions of the same image. In this process, there are many models that were developed. The presence of fractals was initially noticed and handled using Iterated Function System (IFS); that is used for encoding images. In this paper, a review of fractal image compression is discussed with its variants along with other techniques. A summarized review of contributions is achieved to determine the fulfillment of fractal ima