In this paper, a new technique is offered for solving three types of linear integral equations of the 2nd kind including Volterra-Fredholm integral equations (LVFIE) (as a general case), Volterra integral equations (LVIE) and Fredholm integral equations (LFIE) (as special cases). The new technique depends on approximating the solution to a polynomial of degree and therefore reducing the problem to a linear programming problem(LPP), which will be solved to find the approximate solution of LVFIE. Moreover, quadrature methods including trapezoidal rule (TR), Simpson 1/3 rule (SR), Boole rule (BR), and Romberg integration formula (RI) are used to approximate the integrals that exist in LVFIE. Also, a comparison between those methods is produced. Finally, for more explanation, an algorithm is proposed and applied for testing examples to illustrate the effectiveness of the new technique.
* مشكلة البحث والحاجة اليه:
تأتي أهمية هذا العلم وقوته ومدى الحاجة اليه لكل الناس وخاصة اللذين يريدون أن يغيروا عاداتهم السيئة ويأثروا في غيرهم ، أذ اكد المفكرون والقادة والمصلحون ورجال التربية أنه يجب على الإنسان ان يكون مثابراً ومجتهداً ومتقناً لعمله ، ومنظماً لوقته الى اخر القائمة الطويلة من مفردات الجودة ولم يقولوا كيف يمكن للانسان ان يفعل ذلك ؟ أن علم الهندسة النفسية استطاع ان يجيب. 
... Show MoreA new class of higher derivatives for harmonic univalent functions defined by a generalized fractional integral operator inside an open unit disk E is the aim of this paper.
In this study, the modified size-strain plot (SSP) method was used to analyze the x-ray diffraction lines pattern of diffraction lines (1 0 1), (1 2 1), (2 0 2), (0 4 2), (2 4 2) for the calcium titanate(CaTiO3) nanoparticles, and to calculate lattice strain, crystallite size, stress, and energy density, using three models: uniform (USDM). With a lattice strain of (2.147201889), a stress of (0.267452615X10), and an energy density of (2.900651X10-3 KJ/m3), the crystallite was 32.29477611 nm in size, and to calculate lattice strain of Scherrer (4.1644598X10−3), and (1.509066023X10−6 KJ/m3), a stress of(6.403949183X10−4MPa) and (26.019894 nm).
The problems of modeling the signal and dispersion properties of a second order recursive section in the integer parameter space are considered. The formulation and solution of the section synthesis problem by selective and dispersive criteria using the methods of integer nonlinear mathematical programming are given. The availability of obtaining both positive and negative frequency dispersion of a signal in a recursive section, as well as the possibility of minimizing dispersion distortions in the system, is shown.
The objective of the present study is to verify the actual carious lesion depth by laser
fluorescence technique using 650 nm CW diode laser in comparison with the histopathological
investigation. Five permanent molar teeth were extracted from adult individuals for different reasons
(tooth impaction, periodontal diseases, and pulp infections); their ages were ranging from 20-25 years
old. Different carious teeth with varying clinical stages of caries progression were examined. An
experimental laser fluorescence set-up was built to perform the work regarding in vitro detection and
quantification of occlusal dental caries and the determination of its actual clinical carious lesion depth by
650 nm CW diode laser (excitat
A condense study was done to compare between the ordinary estimators. In particular the maximum likelihood estimator and the robust estimator, to estimate the parameters of the mixed model of order one, namely ARMA(1,1) model.
Simulation study was done for a varieties the model. using: small, moderate and large sample sizes, were some new results were obtained. MAPE was used as a statistical criterion for comparison.
This paper deals with a method called Statistical Energy Analysis that can be applied to the mechanical and acoustical systems like buildings, bridges and aircrafts …etc. S.E.A as a tool can be applied to the resonant systems in the circumstances of high frequency or/and complex structure». The parameters of S.E.A such as coupling loss factor, internal loss factor, modal density and input power are clarified in this work ; coupled plate sub-systems and explanations are presented for these parameters. The developed system is assumed to be resonant, conservative, linear and there is an equipartition of energy between all the resonant modes within a given frequency band in a given sub-system. The aim of th
... Show MoreWe have studied Bayesian method in this paper by using the modified exponential growth model, where this model is more using to represent the growth phenomena. We focus on three of prior functions (Informative, Natural Conjugate, and the function that depends on previous experiments) to use it in the Bayesian method. Where almost of observations for the growth phenomena are depended on one another, which in turn leads to a correlation between those observations, which calls to treat such this problem, called Autocorrelation, and to verified this has been used Bayesian method.
The goal of this study is to knowledge the effect of Autocorrelation on the estimation by using Bayesian method. F
... Show MoreThis study aims to find out the effectiveness of instructional scaffolding strategy in the development of academic achievement and critical thinking of female second grade secondary mathematics students. Semi-experimental and relational descriptive method was used. The sample of the study consisted of (50) students divided into an experimental group and a control group. The experimental group was taught using scaffolding strategy whereas the control group was taught using traditional method. Pre- and Post-tests were used to achieve the objective of the study. The results of the study revealed that there are statistically significant differences in the mean scores of the experimental and control groups in the posttest for both the academi
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