This paper presents a new transform method to solve partial differential equations, for finding suitable accurate solutions in a wider domain. It can be used to solve the problems without resorting to the frequency domain. The new transform is combined with the homotopy perturbation method in order to solve three dimensional second order partial differential equations with initial condition, and the convergence of the solution to the exact form is proved. The implementation of the suggested method demonstrates the usefulness in finding exact solutions. The practical implications show the effectiveness of approach and it is easily implemented in finding exact solutions.

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Necessary and sufficient conditions for the operator equation I AXAX n*, to have a real positive definite solution X are given. Based on these conditions, some properties of the operator A as well as relation between the solutions X andAare given.

The aim of this paper is to present a method for solving third order ordinary differential equations with two point boundary condition , we propose two-point osculatory interpolation to construct polynomial solution. The original problem is concerned using two-points osculatory interpolation with the fit equal numbers of derivatives at the end points of an interval [0 , 1] . Also, many examples are presented to demonstrate the applicability, accuracy and efficiency of the method by compared with conventional method .

Orthogonal polynomials and their moments serve as pivotal elements across various fields. Discrete Krawtchouk polynomials (DKraPs) are considered a versatile family of orthogonal polynomials and are widely used in different fields such as probability theory, signal processing, digital communications, and image processing. Various recurrence algorithms have been proposed so far to address the challenge of numerical instability for large values of orders and signal sizes. The computation of DKraP coefficients was typically computed using sequential algorithms, which are computationally extensive for large order values and polynomial sizes. To this end, this paper introduces a computationally efficient solution that utilizes the parall

The present study aimed to identify teaching problems which facing the teachers for first three grades classes, and if these problems different according to some variables teacher qualification, experience period, class grade). The study sample consist of (137 )

 female teachers who teach the first three grades in Braimy city in Oman, teachers spread in five government schools. Both researchers developed questionnaire to measure problems faced by the mentioned teachers, consist of 50 questions distributed into 4 dimensions (teacher, students, the curriculum, the evaluations), Also researchers checked questionnaire validity and stability. The results indicate to: The most common probl

The physical behavior for the energy distribution function (EDF) of the reactant particles depending upon the gases (fuel) temperature are completely described by a physical model covering the global formulas controlling the EDF profile. Results about the energy distribution for the reactant system indicate a standard EDF, in which it’s arrive a steady state form shape and intern lead to fix the optimum selected temperature.

Di Benzylidenes were prepared by condensation of 1,2-diamino benzene with o- hydroxy benzaldehyde. These dibenzylidenes when treated with one equivalent of malonic anhydride or 5-oxo-spiro[2,3]hexane-4,6-dione in dry benzene give 6-membered heterocyclic ring system of 3-{2-[(2-Hydroxy-benzylidene)-amino]-phenyl}-2-(2-hydroxy –phenyl)-[1,3]oxazinane-4,6-diones ( 1-3) or 7-{2-[(2-hydroxy-benzylidene)-amino]-phenyl}-6-(2-hydroxy-phenyl)-5-oxa-7-aza-spiro[2.5]octane-4,8-diones ( 7- 9 ) But when two equivalents of malonic anhydride or 5-oxo-spiro[2,3]hexane-4,6-dione were used and under sam conditions compounds (4-6 , 10-12 ) were obtained .