In this paper, a computational method for solving optimal problem is presented, using indirect method (spectral methodtechnique) which is based on Boubaker polynomial. By this method the state and the adjoint variables are approximated by Boubaker polynomial with unknown coefficients, thus an optimal control problem is transformed to algebraic equations which can be solved easily, and then the numerical value of the performance index is obtained. Also the operational matrices of differentiation and integration have been deduced for the same polynomial to help solving the problems easier. A numerical example was given to show the applicability and efficiency of the method. Some characteristics of this polynomial which can be used for solvin

In this paper we will investigate some Heuristic methods to solve travelling salesman problem. The discussed methods are Minimizing Distance Method (MDM), Branch and Bound Method (BABM), Tree Type Heuristic Method (TTHM) and Greedy Method (GRM).

The weak points of MDM are manipulated in this paper. The Improved MDM (IMDM) gives better results than classical MDM, and other discussed methods, while the GRM gives best time for 5≤ n ≤500, where n is the number of visited cities.

This paper derives the EDITRK4 technique, which is an exponentially fitted diagonally implicit RK method for solving ODEs . This approach is intended to integrate exactly initial value problems (IVPs), their solutions consist of linear combinations of the group functions  and  for exponentially fitting  problems, with  being the problem’s major frequency utilized to improve the precision of the method. The modified  method EDITRK4 is a new three-stage fourth-order exponentially-fitted diagonally implicit approach for solving IVPs with functions that are exponential as solutions. Different forms of -order ODEs must be derived using the modified system, and when the same issue is reduced to a  framework of equations that can be sol

Many numerical approaches have been suggested to solve nonlinear problems. In this paper, we suggest a new two-step iterative method for solving nonlinear equations. This iterative method has cubic convergence. Several numerical examples to illustrate the efficiency of this method by Comparison with other similar methods is given.

The Korteweg-de Vries equation plays an important role in fluid physics and applied mathematics. This equation is a fundamental within study of shallow water waves. Since these equations arise in many applications and physical phenomena, it is officially showed that this equation has solitary waves as solutions, The Korteweg-de Vries equation is utilized to characterize a long waves travelling in channels. The goal of this paper is to construct the new effective frequent relation to resolve these problems where the semi analytic iterative technique presents new enforcement to solve Korteweg-de Vries equations. The distinctive feature of this method is, it can be utilized to get approximate solution

Recent technological developments in the mass media a major paradigm shift in important segments of society, particularly among young people in particular social networking sites including (Facebook) .
it was able to link the sprawling parts of the world and paved the way for all the communities of convergence and exchange views, ideas and desires as provided by their ability to communicate through the use of video clips,pictures,share files, chat, communicate and direct interaction between the audience for this the means. Wondered problem Find the role that can be played using the university youth to the social networking site (Facebook ) to modify their attitudes or their interest in Iraqi society issues, With focused research objec

Background: The quantity and the quality of available bone, influence the clinical success of dental implants surgery. Cone beam Computed tomography is an established method for acquiring bone images before performing dental implant. Cone beam computed tomography is an essential tool for treatment planning and post-surgical procedure monitoring, by providing highly accurate 3-D images of the patient's anatomy from a single, low-radiation scan which yields high resolution images with favorable accuracy. The aim of study is the Measurement of alveolar bone (height and buccolingual width) and density in the mandible among Iraqi adult subject using CBCT for assessment of dental implant site dimensions. Material and method: The study sample in

Photonic crystal fiber interferometers are used in many sensing applications. In this work, an in-reflection photonic crystal fiber (PCF) based on Mach-Zehnder (micro-holes collapsing) (MZ) interferometer, which exhibits high sensitivity to different volatile organic compounds (VOCs), without the needing of any permeable material. The interferometer is robust, compact, and consists of a stub photonic crystal fiber of large-mode area, photonic crystal fiber spliced to standard single mode fiber (SMF) (corning-28), this splicing occurs with optimized splice loss 0.19 dB In the splice regions the voids of the holey fiber are completely collapsed, which allows the excitation and recombination of core and cladding modes. The device reflection