In this paper the modified trapezoidal rule is presented for solving Volterra linear Integral Equations (V.I.E) of the second kind and we noticed that this procedure is effective in solving the equations. Two examples are given with their comparison tables to answer the validity of the procedure.

This paper aims to find new analytical closed-forms to the  solutions of the nonhomogeneous functional differential equations of the n^th order with finite and constants delays and various initial delay conditions in terms of elementary functions using Laplace transform method. As well as, the definition of dynamical systems for ordinary differential equations is used to introduce the definition of dynamical systems for delay differential equations which contain multiple delays with a discussion of their dynamical properties: The exponential stability and strong stability

A new method based on the Touchard polynomials (TPs) was presented for the numerical solution of the linear Fredholm integro-differential equation (FIDE) of the first order and second kind with condition. The derivative and integration of the (TPs) were simply obtained. The convergence analysis of the presented method was given and the applicability was proved by some numerical examples. The results obtained in this method are compared with other known results.

The research aims to find approximate solutions for two dimensions Fredholm linear integral equation. Using the two-variables of the Bernstein polynomials we find a solution to the approximate linear integral equation of the type two dimensions. Two examples have been discussed in detail.

At present, the ability to promote national economy by adjusting to political, economic, and technological variables is one of the largest challenges faced by organization productivity. This challenge prompts changes in structure and line productivity, given that cash has not been invested. Thus, the management searches for investment opportunities that have achieved the optimum value of the annual increases in total output value of the production line workers in the laboratory. Therefore, the application of dynamic programming model is adopted in this study by addressing the division of investment expenditures to cope with market-dumping policy and to strive non-stop production at work.

 يدرس هذا البحث طرائق اختزال الابعاد التي تعمل على تجاوز مشكلة البعدية عندما تفشل الطرائق التقليدية في ايجاد تقدير جيد للمعلمات، لذلك يتوجب التعامل مع هذه المشكلة بشكل مباشر. ومن اجل ذلك، يجب التخلص من هذه المشكلة لذا تم استعمال اسلوبين لحل مشكلة البيانات ذات الابعاد العالية الاسلوب الاول طريقة الانحدار الشرائحي المعكوس SIR ) ) والتي تعتبر طريقة غير كلاسيكية  وكذلك طريقة ( WSIR ) المقترحة والاسلوب الثاني طري

As a star explode as a supernova its ejecta will directly interact with relativelylow density interstellar medium with high shock wave velocity, and due to thisinteraction many of forbidden emission lines will give a raise from both theexcitation and ionization of the atom in the region. So, the study of these emissionlines can reveal many physical properties of the region, in this case the remnant ofthe supernova, such as temperature, density, composition, and many other importantphysical processes. In this paper the optical spectrum of the young galacticsupernova remnant which is the Crab Nebula has used, in order to calculate it’selectron temperature (Te) and electron density (ne) by using the [OIII] and [SII]forbidden lines. From the

In the present work, lead silicate glasses have been prepared with
different amount of lead oxide content. Structure properties such as
X-ray diffraction, AFM, and FTIR analyses have been done. The
exceeding of PbO content more than 25wt% revealed a decreasing in
density. The X- ray revealed that the strongest peak related to
Hexagonal silica dioxide and the other crystal phases formed were
related to silica oxide (SiO2) and lead oxide (PbO). Growth and
decayed phases in X-ray have been observed with changing lead
oxide content. Homogeneous surface was obtained using AFM
analyzer with an average diameter around 100 nm. Infrared spectrum
is characterized by the presence of large absorption band between
120

Many cities suffer from the large spread of slums, especially the cities of the Middle East. The purpose of the paper is to study the reality of informal housing in Al-Barrakia and the most important problems that it suffers from. The paper also seeks to study the presence or absence of a correlation between urban safety indicators and urban containment indicators as one of the methods of developing and planning cities. This can be achieved through sustainable urban management. The slums are a source of many urban problems that threaten the security and safety of the residents and represent a focus for the concentration of crimes and drugs. The paper seeks to answer the following question: How can urban safety be improved through urban cont

Reliability analysis methods are used to evaluate the safety of reinforced concrete structures by evaluating the limit state function 𝑔(𝑋𝑖). For implicit limit state function and nonlinear analysis , an advanced reliability analysis methods are needed. Monte Carlo simulation (MCS) can be used in this case however, as the number of input variables increases, the time required for MCS also increases, making it a time consuming method especially for complex problems with implicit performance functions. In such cases, MCS-based FORM (First Order Reliability Method) and Artificial Neural Network-based FORM (ANN FORM) have been proposed as alternatives. However, it is important to note that both MCS-FORM and ANN-FORM can also be time-con