Scholars have inherited a tremendous wealth in all sciences and knowledge, especially jurisprudence; therefore, the students of forensic science had to execute this precious heritage, achieving a serious scientific investigation; So I opted for the realization of this part of the Book of Leasing for the small book of fatwas of Yusuf bin Ahmed al-Khasi.

The aim of this paper is to present the numerical method for solving linear system of Fredholm integral equations, based on the Haar wavelet approach. Many test problems, for which the exact solution is known, are considered. Compare the results of suggested method with the results of another method (Trapezoidal method). Algorithm and program is written by Matlab vergion 7.

Background: Imaging techniques play a very important role in the specialty of endodontic. The ultrasonographic technique is non-expensive procedure, safe, and reproducible. The aim of the study was to determine the sensitivity, specificity, and accuracy of ultrasound and color Doppler ultrasonography in evaluation of periapical lesions (cyst, granuloma, mixed lesion “cyst within graulomas mass”, and abscess. Subject, Material and method: The sample consists of prospective study for 64 Iraqi participants who attended Karbalaa Specialized Center for Dentistry (males & females). Those patients were diagnosed clinically and radiographically as having periapical lesions of dental origin. They were examined by real time ultrasound and color

<p>Daftardar Gejji and Hossein Jafari have proposed a new iterative method for solving many of the linear and nonlinear equations namely (DJM). This method proved already the effectiveness in solved many of the ordinary differential equations, partial differential equations and integral equations. The main aim from this paper is to propose the Daftardar-Jafari method (DJM) to solve the Duffing equations and to find the exact solution and numerical solutions. The proposed (DJM) is very effective and reliable, and the solution is obtained in the series form with easily computed components. The software used for the calculations in this study was MATHEMATICA^® 9.0.</p>

We present a reliable algorithm for solving, homogeneous or inhomogeneous, nonlinear ordinary delay differential equations with initial conditions. The form of the solution is calculated as a series with easily computable components. Four examples are considered for the numerical illustrations of this method. The results reveal that the semi analytic iterative method (SAIM) is very effective, simple and very close to the exact solution demonstrate reliability and efficiency of this method for such problems.

The researcher [1-10] proposed a method for computing the numerical solution to quasi-linear parabolic p.d.e.s using a Chebyshev method. The purpose of this paper is to extend the method to problems with mixed boundary conditions. An error analysis for the linear problem is given and a global element Chebyshev method is described. A comparison of various chebyshev methods is made by applying them to two-point eigenproblems. It is shown by analysis and numerical examples that the approach used to derive the generalized Chebyshev method is comparable, in terms of the accuracy obtained, with existing Chebyshev methods.

The Aim of this paper is to investigate numerically the simulation of ice melting in one and two dimension using the cell-centered finite volume method. The mathematical model is based on the heat conduction equation associated with a fixed grid, latent heat source approach. The fully implicit time scheme is selected to represent the time discretization. The ice conductivity is chosen
to be the value of the approximated conductivity at the interface between adjacent ice and water control volumes. The predicted temperature distribution, percentage melt fraction, interface location and its velocity is compared with those obtained from the exact analytical solution. A good agreement is obtained when comparing the numerical results of one

Since the Internet has been more widely used and more people have access to multimedia content, copyright hacking, and piracy have risen. By the use of watermarking techniques, security, asset protection, and authentication have all been made possible. In this paper, a comparison between fragile and robust watermarking techniques has been presented to benefit them in recent studies to increase the level of security of critical media. A new technique has been suggested when adding an embedded value (129) to each pixel of the cover image and representing it as a key to thwart the attacker, increase security, rise imperceptibility, and make the system faster in detecting the tamper from unauthorized users. Using the two watermarking ty

      Big data usually running in large-scale and centralized key management systems. However, the centralized key management systems are increasing the problems such as single point of failure, exchanging a secret key over insecure channels, third-party query, and key escrow problem. To avoid these problems, we propose an improved certificate-based encryption scheme that ensures data confidentiality by combining symmetric and asymmetric cryptography schemes. The combination can be implemented by using the Advanced Encryption Standard (AES) and Elliptic Curve Diffie-Hellman (ECDH). The proposed scheme is an enhanced version of the Certificate-Based Encryption (CBE) scheme and preserves all its advantages. However

This paper experimentally investigates the heating process of a hot water supply using a neural network implementation of a self-tuning PID controller on a microcontroller system. The Particle Swarm Optimization (PSO) algorithm employed in system tuning proved very effective, as it is simple and fast optimization algorithm. The PSO method for the PID parameters is executed on the Matlab platform in order to put these parameters in the real-time digital PID controller, which was experimented with in a pilot study on a microcontroller platform. Instead of the traditional phase angle power control (PAPC) method, the Cycle by Cycle Power Control (CBCPC) method is implemented because it yields better power factor and eliminates harmonics