This paper including a gravitational lens time delays study for a general family of lensing potentials, the popular singular isothermal elliptical potential (SIEP), and singular isothermal elliptical density distribution (SIED) but allows general angular structure. At first section there is an introduction for the selected observations from the gravitationally lensed systems. Then section two shows that the time delays for singular isothermal elliptical potential (SIEP) and singular isothermal elliptical density distributions (SIED) have a remarkably simple and elegant form, and that the result for Hubble constant estimations actually holds for a general family of potentials by combining the analytic results with data for the time dela

Elastic magnetic M1 electron scattering form factor has been calculated for the ground state J,T=1/2-,1/2 of 13C. The single-particle model is used with harmonic oscillator wave function. The core-polarization effects are calculated in the first-order perturbation theory including excitations up to 5ħω, using the modified surface delta interaction (MSDI) as a residual interaction. No parameters are introduced in this work. The data are reasonably explained up to q~2.5fm-1 .

This research deals with the most important indicators used to measure the phenomenon of financial depth, beyond the traditional indicators, which are called quantitative indicators, which is shown to be inadequate to show the facts accurately, but it may come in the results of a counterfactual, although reliable in econometric studies done in this regard.

Therefore, this research has sought to put forward alternative indicators, is the structural indicators, and financial prices, and availability of financial instruments, and cost of transactions concluded, in order to measure the phenomenon of financial depth.

After using and analyzing data collected from countries the research

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     The paired sample t-test is a type of classical test statistics that is used to test the difference between two means in paired data, but it is not robust against the violation of the normality assumption. In this paper, some alternative robust tests are suggested by combining the Jackknife resampling with each of the Wilcoxon signed-rank test for small sample size and Wilcoxon signed-rank test for large sample size, using normal approximation. The Monte Carlo simulation experiments were employed to study the performance of the test statistics of each of these tests depending on the type one error rates and the power rates of the test statistics. All these tests were applied on different sa

We consider some nonlinear partial differential equations in higher dimensions, the negative order of the Calogero-Bogoyavelnskii-Schiff (nCBS) equationin (2+1) dimensions, the combined of the Calogero-Bogoyavelnskii-Schiff equation and the negative order of the Calogero-Bogoyavelnskii-Schiff equation (CBS-nCBS) in (2+1) dimensions, and two models of the negative order Korteweg de Vries (nKdV) equations in (3+1) dimensions. We show that these equations can be reduced to the  same class of ordinary differential equations via wave reduction variable. Solutions in terms of symmetrical Fibonacci and Lucas functions are presented by implementation of the modified Kudryashov method.

In this research, the mutual correlations between ionospheric parameters (MUF, OWF and LUF) have been suggested. The datasets of the MUF and OWF parameters have been generated using ASAPS international communication model, while the LUF parameter has been calculated using the REC533 model. The calculations have been made for the connection links between the capital Baghdad and many other locations that spread over the studied zone (Middle East region). The annual time of the years (2009 & 2014) of solar cycle 24 has been adopted to make the investigation in order to get the mutual correlation between ionospheric parameters. The test results of the annual correlation between ionospheric parameters showed that the mutual correlation be

Medical imaging is a technique that has been used for diagnosis and treatment of a large number of diseases. Therefore it has become necessary to conduct a good image processing to extract the finest desired result and information. In this study, genetic algorithm (GA)-based clustering technique (K-means and Fuzzy C Means (FCM)) were used to segment thyroid Computed Tomography (CT) images to an extraction thyroid tumor. Traditional GA, K-means and FCM algorithms were applied separately on the original images and on the enhanced image with Anisotropic Diffusion Filter (ADF). The resulting cluster centers from K-means and FCM were used as the initial population in GA for the implementation of GAK-Mean and GAFCM. Jaccard index was used to s

Ping message focused on highlighting the fact commodity trading in Iraq, and increased exposure to world merchandise trade imbalance, which dominate Iraq's foreign trade major commodity is oil, and therefore the inability of Iraq to control financial revenue as a result of the fluctuations in the international market, the shortage of commodity products will lead inevitably to the weakness in the ability of the local market to meet the internal demand and due to the lack of flexible production machine For agricultural, industrial and economic sectors are responding to changes in the domestic or external demand which will open the door to merchandise imports to invade these markets, since the adoption of the Iraq oil exports,

This paper has the interest of finding the approximate solution (APPS) of a nonlinear variable coefficients hyperbolic boundary value problem (NOLVCHBVP).  The given boundary value problem is written in its discrete weak form (WEFM) and proved  have a unique solution, which is obtained via the mixed Galerkin finite element with implicit method that reduces the problem to solve the Galerkin nonlinear algebraic system  (GNAS). In this part, the predictor and the corrector techniques (PT and CT, respectively) are proved at first convergence and then are used to transform  the obtained GNAS to a linear GLAS . Then the GLAS is solved using the Cholesky method (ChMe). The stability and the convergence of the method are stud