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.

Purpose: This research is to identify the most important challenges for the local investment commissions and to develop solutions and proposals to encourage local and foreign investment in local governments in Iraq (the Iraqi provinces are irregular in the region).   Theoretical Framework: This research suggests a conceptual framework for the local investment commissions in order to solve their problems, the most important of which was to identify the most critical challenges which are facing the Baghdad Investment Commission BIC and how to overcome them.   Design/The methodology approach: Research involved a mixed-methods approach through two stages. During the first stage, the researcher gathered quantitative data from all inves

This study explores the role of nanomaterials in the performance of asphalt binders and mixtures. Two commonly available nanomaterials, i.e., nanosilica (NS) and nanoalumina (NA), were used at contents of 0%, 2%, 4%, 6%, and 8% by weight of asphalt binder. A set of experiments was carried out at the binder level to investigate properties such as penetration, softening point, aging-related mass loss, nanomaterial dispersion (storage stability), and workability (rotational viscosity). In addition, the suitability of NS and NS was also assessed through the testing of nanomodified asphalt mixtures, which focused on Marshall properties, the resilient modulus, moisture susceptibility, permanent deformation, and fatigue resistance. The findings in

As an architectural philosophical concept, Islamic architecture cannot be considered arches, doors, domes and lighthouses, since Islamic architecture is based on a structural system of religious, mental, philosophical and logical origins and beliefs shared by the arts, technology and the requirements of the surrounding environment. Rather, the architectural designer's distance from it becomes as if it is for people not from this world, and Islamic architecture is not abbreviated on the heritage side as much as it is a renewed "modern" state, dealing with the concepts of Islam that are valid for every time and place. This can be seen through the mechanisms that produced heritage architecture and what was built on it, which is not a simula

The main objective of this research is to find out the effect of deviation in the aggregate gradients of asphalt mixtures from the Job Mix Formula (JMF) on the general mixture performance. Three road layers were worked on (wearing layer, binder layer, and base layer) and statistical analysis was performed for the data of completed projects in Baghdad city, and the sieve that carried the largest number of deviations for each layer was identified. No.8 sieve (2.36mm), No.50 sieve (0.3mm), and 3/8'' sieve (9.5mm) had the largest number of deviations in the wearing layer, the binder layer, and the base layer respectively. After that, a mixture called Mix 1, was made. This mixture was selected from a number of completed mixtures, and it

This paper describes theoretical modeling of electrostatic mirror based on two cylindrical electrodes, A computational investigation has been carried out on the design and properties of the electrostatic  mirror. we suggest a mathematical expression to represent the axial potential of an electrostatic mirror. The  beam path  by using the Bimurzaev technique have been investigated as a mirror trajectory with the aid of Runge – Kutta  method. the electrode shape of mirror two electrode has been determined by using package SIMION computer program . The spherical and chromatic aberrations coefficients of mirror has been computed and normalized in terms of the focal length. The choice of the mirror depends on the op

The physicochemical behaviour of dodecyltrimethylammonium bromide (DTAB) in water and ethanol-water mixture in the presence and absence of ZnSO₄ were studied by measuring the conductivity at 298.15 K. The pre-micellar (S₁) and post-micellar slopes (S₂) were obtained and calculated the degree of dissociation (α) and the critical micelle concentration (cmc). With an increase in ethanol content, the cmc and α of DTAB increased whereas, in the presence of ZnSO₄, the cmc and α decreased. By using cmc and α, thermodynamic properties as the standard free energy of micellization ( ) were evaluated. With an increase in ethanol content, the negative values of  are decreased indicating less spont