This study presents a practical method for solving fractional order delay variational problems. The fractional derivative is given in the Caputo sense. The suggested approach is based on the Laplace transform and the shifted Legendre polynomials by approximating the candidate function by the shifted Legendre series with unknown coefficients yet to be determined. The proposed method converts the fractional order delay variational problem into a set of (n ＋ 1) algebraic equations, where the solution to the resultant equation provides us the unknown coefficients of the terminated series that have been utilized to approximate the solution to the considered variational problem. Illustrative examples are given to show that the recommended appro

Isolated Bacteria from the roots of barley were studied; two stages of processes Isolated and screening were applied in order to find the best bacteria to remove kerosene from soil. The active bacteria are isolated for kerosene degradation process. It has been found that Klebsiella pneumoniae sp. have the highest kerosene degradation which is 88.5%. The optimum conditions of kerosene degradation by Klebsiella pneumonia sp. are pH5, 48hr incubation period, 35°C temperature and 10000ppm the best kerosene concentration. The results 10000ppm showed that the maximum kerosene degradation can reach 99.58% after 48 h of incubation. Higher Kerosene degradation which was 99.83% was obtained at pH5. Kerosene degradation was found to be maximum at 3

Under cyclic loading, aluminum alloys exhibit less fatigue life than steel alloys of similar strength and this is considered as Achilles's heel of such alloys. A nanosecond fiber laser was used to apply high speed laser shock peening process on thin aluminum plates in order to enhance the fatigue life by introducing compressive residual stresses. The effect of three working parameters namely the pulse repetition rate (PRR), spot size (ω) and scanning speed (v) on limiting the fatigue failure was investigated. The optimum results, represented by the longer fatigue life, were at PRR of 22.5 kHz, ω of 0.04 mm and at both v's of 200 and 500 mm/sec. The research yielded significant results represented by a maximum percentage increase in the fa

In this paper we use Bernstein polynomials for deriving the modified Simpson's 3/8 , and the composite modified Simpson's 3/8 to solve one dimensional linear Volterra integral equations of the second kind , and we find that the solution computed by this procedure is very close to exact solution.

In all applications and specially in real time applications, image processing and compression plays in modern life a very important part in both storage and transmission over internet for example, but finding orthogonal matrices as a filter or transform in different sizes is very complex and importance to using in different applications like image processing and communications systems, at present, new method to find orthogonal matrices as transform filter then used for Mixed Transforms Generated by using a technique so-called Tensor Product based for Data Processing, these techniques are developed and utilized. Our aims at this paper are to evaluate and analyze this new mixed technique in Image Compression using the Discrete Wavelet Transfo

Background: Painful elbow joint over the lateral epicondyle especially with resisted wrist extension are common signs of lateral epicondyle tendinopathy, also called tennis elbow. Objective: To evaluate the clinical outcome of local platelet rich plasma (PRP) injection in patients with chronic tennis elbow compared with a steroid (Depomedrol 40 mg) injection. Methods: A total of 88 patients with chronic tennis elbow were treated at Al-Kindy Teaching Hospital and private clinics. All patients had chronic pain for about 24 weeks or more and had failed first line treatment. The patients dividing into two groups, Group A injected with PRP (n = 44), and group B injected with depomedrol 40 mg (n = 44). A good clinical result w

Identifying phenolic compounds in some genera belonging in the Amaranthaceae family by HPLC technique

This paper is concerned with combining two different transforms to present a new joint transform FHET and its inverse transform IFHET. Also, the most important property of FHET was concluded and proved, which is called the finite Hankel – Elzaki transforms of the Bessel differential operator property, this property was discussed for two different boundary conditions, Dirichlet and Robin. Where the importance of this property is shown by solving axisymmetric partial differential equations and transitioning to an algebraic equation directly. Also, the joint Finite Hankel-Elzaki transform method was applied in solving a mathematical-physical problem, which is the Hotdog Problem. A steady state which does not depend on time was discussed f