This paper aims to propose a hybrid approach of two powerful methods, namely the differential transform and finite difference methods, to obtain the solution of the coupled Whitham-Broer-Kaup-Like equations which arises in shallow-water wave theory. The capability of the method to such problems is verified by taking different parameters and initial conditions. The numerical simulations are depicted in 2D and 3D graphs. It is shown that the used approach returns accurate solutions for this type of problems in comparison with the analytic ones.

The sol-gel preparation technique of transparent silica monoliths containing up to 0.5 M of samarium have been described. The sol-gel processing parameters are: acid catalyzed hydrolysis and controlled drying. The prepared monoliths are analyzed by X-ray diffraction, pycnometer measurements, Fourier transformation infrared spectroscopy and optical spectroscopy. The oscillator strengths of the Sm3+ ions in the silica monoliths are calculated. The results show a linear concentration dependence of some Sm3+ transitions in UV/Vis absorption spectra and formation of Sm3+ clusters inside the pores structure of silica monoliths at high Sm3+ concentration

This paper discusses the problem of decoding codeword in Reed- Muller Codes. We will use the Hadamard matrices as a method to decode codeword in Reed- Muller codes.In addition Reed- Muller Codes are defined and encoding matrices are discussed. Finally, a method of decoding is explained and an example is given to clarify this method, as well as, this method is compared with the classical method which is called Hamming distance.

The main objective of this paper is to find the order and its exponent, the general form of all conjugacy classes, Artin characters table and Artin exponent for the group of lower unitriangular matrices L(3,? p ), where  p  is prime number.

<p>Daftardar Gejji and Hossein Jafari have proposed a new iterative method for solving many of the linear and nonlinear equations namely (DJM). This method proved already the effectiveness in solved many of the ordinary differential equations, partial differential equations and integral equations. The main aim from this paper is to propose the Daftardar-Jafari method (DJM) to solve the Duffing equations and to find the exact solution and numerical solutions. The proposed (DJM) is very effective and reliable, and the solution is obtained in the series form with easily computed components. The software used for the calculations in this study was MATHEMATICA^® 9.0.</p>

The method of operational matrices based on different types of polynomials such as Bernstein, shifted Legendre and Bernoulli polynomials will be presented and implemented to solve the nonlinear Blasius equations approximately. The nonlinear differential equation will be converted into a system of nonlinear algebraic equations that can be solved using Mathematica®12. The efficiency of these methods has been studied by calculating the maximum error remainder ( ), and it was found that their efficiency increases as the polynomial degree (n) increases, since the errors decrease. Moreover, the approximate solutions obtained by the proposed methods are compared with the solution of the 4th order Runge-Kutta method (RK4), which gives very

Biomass has been extensively investigated, because of its presence as clean energy source. Tars and particulates formation problems are still the major challenges in development especially in the implementation of gasification technologies into nowadays energy supply systems. Laser Induced Fluorescence spectroscopy (LIF) method is incorporated for determining aromatic and Polycyclic Aromatic Hydrocarbons (PAH) produced at high temperature gasification technology. The effect of tars deposition when the gases are cooled has been highly reduced by introducing a new concept of measurement cell. The samples of PAH components have been prepared with the standard constrictions of measured PAHs by using gas chromatograph (GC). OPO laser with tun

  There are many researches deals with constructing an efficient solutions for real problem having Multi - objective confronted with each others. In this paper we construct a decision for Multi – objectives based on building a mathematical model formulating a unique objective function by combining the confronted objectives functions. Also we are presented some theories concerning this problem. Areal application problem has been presented to show the efficiency of the performance of our model and the method. Finally we obtained some results by randomly generating some problems.