This book includes three main chapters: 1. Functions & Their Derivatives. 2. Minimum, Maximum and Inflection points. 3. Partial Derivative. In addition to many examples and exercises for the purpose of acquiring the student's ability to think correctly in solving mathematical questions.

Several attempts have been made to modify the quasi-Newton condition in order to obtain rapid convergence with complete properties (symmetric and positive definite) of the inverse of  Hessian matrix (second derivative of the objective function). There are many unconstrained optimization methods that do not generate positive definiteness of the inverse of Hessian matrix. One of those methods is the symmetric rank 1( H-version) update (SR1 update), where this update satisfies the quasi-Newton condition and the symmetric property of inverse of Hessian matrix, but does not preserve the positive definite property of the inverse of Hessian matrix where the initial inverse of Hessian matrix is positive definiteness. The positive definite prope

Extension of bandwidth for high reflectance zone for the spectral region (8-14pm) was studied adapting the concept of contiguous and overlapping high reflectance stacks. Computations was carried out using the modified characteristic matrix theory restricted to near-normal incidence of light on dielectric , homogenous and isotropic symmetrical stack. Certain precautions must be taken in the choice of stacks to avoid deep —reflectance minima from developing within the extended high reflectance region. Results illustrate that the techniques of extending the high reflectance regions are applicable not only to mirrors , but also to short-and long-edge filter and to narrow band pass filters.

Charge multipole Coulomb scattering form factors in ⁴⁸Ca nucleus have been reproduced utilizing the theory of nuclear shell. The efficient two-body nuclear potential fpbm is considered to construct the-spin orbit term LS vectors with Harmonic Oscillator HO potential as a wave function of single particle in Fp shell. Discarded spaces ( core + higher configuration) are taken into account through the Core polarization effect by model space with accurate two-body potential of Gogny to  interact the LS operating particles with the discarded space pair ( particle-hole) with energy of excitation equal to 2ћω. Gogny interaction has been selected as it had succeeded in nuclear shell theory. The computed results were compared with th

Objective: To assess role of obesity in Covid-19 patients on antibodies production, diabetes development, and treatment of this disease. Methodology: This observational study included 200 Covid-19 patients in privet centers from January 1, 2021 to January 1, 2022. All patients had fasting blood sugars and anti-Covid-19 antibodies. Anthropometric parameters were measured in all participants. Results: The patients were divided into two groups according to body weight; normal body weight (50) and excess body weight (150). There was a significant difference between them regarding age. Diabetes mellitus developed in 20% of normal weight patients while 80% of excess weight patients had diabetes (p=0.0001). Antibodies production (IgM and

Objective: To assess role of obesity in Covid-19 patients on antibodies production, diabetes development, and treatment of this disease. Methodology: This observational study included 200 Covid-19 patients in privet centers from January 1, 2021 to January 1, 2022. All patients had fasting blood sugars and anti-Covid-19 antibodies. Anthropometric parameters were measured in all participants. Results: The patients were divided into two groups according to body weight; normal body weight (50) and excess body weight (150). There was a significant difference between them regarding age. Diabetes mellitus developed in 20% of normal weight patients while 80% of excess weight patients had diabetes (p=0.0001). Antibodies production (IgM and

The effect of different cutting fluids on surface roughness of brass alloy workpiece during turning operation was carried out in this research. This was performed with different cutting speed, while other cutting parameters had been regarded as constants(feeding rate , and depth of cut). Surface roughness of machined parts that will be tested by electronic surface roughness tester .The results show that the standard coolant gives the best values of surface roughness for fixed cutting speed ,followed by sun flower oil that has approximately the same effect, while the air stream as a coolant gave unsatisfied results for the evaluation of surface roughness.

In the other hand the best values of surface roughness were recorded for max

        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.