The problem of Bi-level programming is to reduce or maximize the function of the target by having another target function within the constraints. This problem has received a great deal of attention in the programming community due to the proliferation of applications and the use of evolutionary algorithms in addressing this kind of problem. Two non-linear bi-level programming methods are used in this paper. The goal is to achieve the optimal solution through the simulation method using the Monte Carlo method using different small and large sample sizes. The research reached the Branch Bound algorithm was preferred in solving the problem of non-linear two-level programming this is because the results were better.

        In this paper, the Magnetohydrodynamic (MHD) for Williamson fluid with varying temperature and concentration in an inclined channel with variable viscosity has been examined. The perturbation technique in terms of the Weissenberg number  to obtain explicit forms for the velocity field has been used. All the solutions of physical parameters of the Darcy parameter , Reynolds number , Peclet number  and Magnetic parameter  are discussed under the different values as shown in plots.

The Frequency-hopping Spread Spectrum (FHSS) systems and techniques are using in military and civilianradar recently and in the communication system for securing the information on wireless communications link channels, for example in the Wi-Fi 8.02.X IEEE using multiple number bandwidth and frequencies in the wireless channel in order to hopping on them for increasing the security level during the broadcast, but nowadays FHSS problem, which is, any Smart Software Defined Radio (S-SDR) can easily detect a wireless signal at the transmitter and the receiver for the hopping sequence in both of these, then duplicate this sequence in order to hack the signal on both transmitter and receiver messages using the order of the se

The corona virus epidemic outbreak has urged an extreme worldwide effort for re‐purposing obtainable approved medications for its treatment. In this review, we're focusing on the chemicals properties andpharmacologicaleffectiveness of medicationsofsmallmolecule that are presently being evaluated in clinical trials for the management of corona virus (COVID‐19). The current review sheds light on a number of drugs that have been diagnosed to treat COVID‐19 and their biological effects.

One of the important differences between multiwavelets and scalar wavelets is that each channel in the filter bank has a vector-valued input and a vector-valued output. A scalar-valued input signal must somehow be converted into a suitable vector-valued signal. This conversion is called preprocessing. Preprocessing is a mapping process which is done by a prefilter. A postfilter just does the opposite.

The most obvious way to get two input rows from a given signal is to repeat the signal. Two rows go into the multifilter bank. This procedure is called “Repeated Row” which introduces oversampling of the data by a factor of 2.

 For data compression, where one is trying to find compact transform representations for a

Theoretical spectroscopic study of  Beryllium Oxide has been carried out, Boltzmann distribution of P, Q and R branches in the range of (0<J<13) at temperature 4200K for (0-0) band for electronic transitions B¹Σ⁺-A¹Π and B¹Σ-X¹Σ. The Boltzmann distribution of these branches has a maximum values at equal J approximately while the values of relative population are different. For the B¹Σ⁺- X¹Σ⁺ transition the branch's lines extend towards lower wavenumber. This is because (B_v'-B_v") value is negative, i.e  B_v'< B_v" For B¹Σ⁺-A¹Π

The study is aimed at social support to the students of the College of Education for women (The research sample) and measuring the quality of life at students of the College of Education for women (The research sample) And to identify the relationship between social support and quality of life of students of the College Education for Women and research sample consisted of 200 students The adoption of the resolution as a tool for data collection and the most important results of the search results that the students of the College Education for Women have social support. In other words, parents and friends are supporting the students. The students have the quality of life any positive meaning to life and that when a person has a quality of

In this paper, the proposed phase fitted and amplification fitted of the Runge-Kutta-Fehlberg method were derived on the basis of existing method of 4(5) order to solve ordinary differential equations with oscillatory solutions. The recent method has null phase-lag and zero dissipation properties. The phase-lag or dispersion error is the angle between the real solution and the approximate solution. While the dissipation is the distance of the numerical solution from the basic periodic solution. Many of problems are tested over a long interval, and the numerical results have shown that the present method is more precise than the 4(5) Runge-Kutta-Fehlberg method.

     The problem in the design of a cam is the analyzing of the mechanisms and dynamic forces that effect on the family of parametric polynomials for describing the motion curve. In present method, two ways have been taken for optimization of the cam size, first the high dynamic loading (such that impact and elastic stress waves propagation) from marine machine tool which translate by the roller follower to the cam surface and varies with time causes large contact loads and second it must include the factors of kinematics features including the acceleration, velocity, boundary condition and the unsymmetrical curvature of the cam profile for the motion curve.

     In the theoretical solution

Comparative morphological study has been treated for two species of the genus Chaenorhinum (D.C.) Richb., These species were: 1. Chaenorhinum calycinum 2. Chaenorhinum rubrifolium (Robill. & cast. Ex Lam. & DC.) Fourr. The genus belong to the family Scorphulariaceae. Morphological characters has been studies for: root, stem, leaves, flowers (calyx, corolla, androcium including filaments and anthers, gynocium including ovary, style and stigma), fruits and seeds also has been characterized. Key for there two species presented using some quantitative characters. Other characters like shape of fruits and seeds were used too, and they were of a useful taxonomic value