Nonlinear differential equation stability is a very important feature of applied mathematics, as it has a wide variety of applications in both practical and physical life problems. The major object of the manuscript is to discuss and apply several techniques using modify the Krasovskii's method and the modify variable gradient method which are used to check the stability for some kinds of linear or nonlinear differential equations. Lyapunov function is constructed using the variable gradient method and Krasovskii’s method to estimate the stability of nonlinear systems. If the function of Lyapunov is positive, it implies that the nonlinear system is asymptotically stable. For the nonlinear systems, stability is still difficult even though

Abstract:

Robust statistics Known as, resistance to errors caused by deviation from the stability hypotheses of the statistical operations (Reasonable, Approximately Met, Asymptotically Unbiased, Reasonably Small Bias, Efficient ) in the data selected in a wide range of probability distributions whether they follow a normal distribution or a mixture of other distributions deviations different standard .

power spectrum function lead to, President role in the analysis of Stationary random processes, form stable random variables organized according to time, may be discrete random variables or continuous. It can be described by measuring its total capacity as function in frequency.

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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

   In this paper, Mann-Kendall test was used to investigate the existence of possible deterministic and stochastic climatic trends in (Baghdad,Basrah,Mosul,Al-Qaim) stations. The statistical test was applied to annual monthly mean of temperatures for the period (19932009). The values of S-statistic were (62, 44, 52, 64) by comparing these values with the table of null probability values for S we get a probability of (0.002, 0.026, 0.010, 0.002) this result is less than α for the 95% confidence level (α = 0.05) indicating a significant result at this level of confidence. Concluded that an increasing trend in concentration is present at the 95% confidence level and the variance of the S-statistic is calculated and it is com

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

Sustainability is a major demand and need pursued by cities in all areas of life due to the environmental, social and economic gains they provide, especially in the field of city planning and urban renewal projects that aim to integrate the past, present and future.

The research aims to evaluate the Haifa Street renewal project, and Al-Shawaka district, one of the Baghdad districts located next to Al-Karkh, was elected by comparing the sustainability indicators of urban renewal with the reality of the situation through a field survey and questionnaire form and focusing on the social and economic impacts and environmental for the project on the study area. To reach the most important conclusions and recommendations

The Child is the first sedum for the human society performing, and we deal in our
research to explain the nature of the mutual relations in between the form and the medicine
social caring foundation. So the motherhood and the childhood nowadays become the most
dedicated in the researchers works, whom interesting in the social affairs, and that whom
work in the medicine field as scientists.
So the child is the future man and must be in wright body construction that need to great
care and interest to make him wright mind through capability of performing anything support
to him.
In our research we deal with the main factors in which lead to infect the child by the
creative malfunction, like the environmental and m

Abstract
             In this research will be treated with a healthy phenomenon has a significant impact on different age groups in the community, but a phenomenon tonsillitis where they will be first Tawfiq model slope self moving averages seasonal ARMA Seasonal through systematic Xbox Cengnzla counter with rheumatoid tonsils in the city of Mosul, and for the period 2004-2009 with prediction of these numbers coming twelve months, has found that the specimen is the best representation of the data model is the phenomenon SARMA (1,1) * (2,1) 12  from the other side and explanatory variables using a maximum temperature and minimum temperature, sol

In this paper, experimental study has been done for temperature distribution in space conditioned with Ventilation Hollow Core Slab (TermoDeck) system. The experiments were carried out on a model room with dimensions of (1m 1.2m 1m) that was built according to a suitable scale factor of (1/4). The temperature distributions was measured by 59 thermocouples fixed in several locations in the test room. Two cases were considered in this work,  the first one during unoccupied period at night time (without external load) and the other at day period with external load of 800W/m² according to solar heat gain calculations during summer season in Iraq. All results confirm the use of TermoDeck system for ventilation and cooling/heat

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