The Caputo definition of fractional derivatives introduces solution to the difficulties appears in the numerical treatment of differential equations due its consistency in differentiating constant functions. In the same time the memory and hereditary behaviors of the time fractional order derivatives (TFODE) still common in all definitions of fractional derivatives. The use of properties of companion matrices appears in reformulating multilevel schemes as generalized two level schemes is employed with the Gerschgorin disc theorems to prove stability condition. Caputo fractional derivatives with finite difference representations is considered. Moreover the effect of using the inverse operator which transmit the memory and hereditary effects to other terms is examined. The theoretical results is applied to a numerical example. The calculated solution has a good agreement with the exact solution.
Background: The insertion torque (IT) values and implant stability quotient (ISQ) values are the measurements most used to assess primary implant stability. This study aimed to assess the relationship between ISQ values and IT. Materials and methods: This study included 24 patients with a mean (SD) age of 47.9 (13.64) years (range 25-75 years). The patients received 42 dental implants (DI), 33 in the mandible and 9 in the maxilla. The DI were installed using the motorized method with 35 Ncm torque, When DI could not be inserted to the requisite depth by the motorized method, a hand ratchet was used and the IT was recorded as ˃ 35 Ncm. Implant stability was measured utilizing Osstell® ISQ. The secondary stability was measured after 16
... Show MoreThis work aims to analyze a three-dimensional discrete-time biological system, a prey-predator model with a constant harvesting amount. The stage structure lies in the predator species. This analysis is done by finding all possible equilibria and investigating their stability. In order to get an optimal harvesting strategy, we suppose that harvesting is to be a non-constant rate. Finally, numerical simulations are given to confirm the outcome of mathematical analysis.
This paper presents a study for the influence of magnetohydrodynamic (MHD) on the oscillating flows of fractional Burgers’ fluid. The fractional calculus approach in the constitutive relationship model is introduced and a fractional Burgers’ model is built. The exact solution of the oscillating motions of a fractional Burgers’ fluid due to cosine and sine oscillations of an infinite flat plate are established with the help of integral transforms (Fourier sine and Laplace transforms). The expressions for the velocity field and the resulting shear stress that have been obtained, presented under integral and series form in terms of the generalized Mittag-Leffler function, satisfy all imposed initial and boundary conditions. Finall
... Show MoreBackground: Prostatic adenocarcinoma is the most widely recognized malignancy in men and the second cause of cancer-related mortality encountered in male patients after lung cancer.
Aim of the study: To assess the diagnostic value of diffusion weighted imaging (DWI) and its quantitative measurement, apparent diffusion coefficient (ADC), in the identification and localization of prostatic cancer compared with T2 weighted image sequence (T2WI).
Type of the study: a prospective analytic study
Patients and methods: forty-one male patients with suspected prostatic cancer were examined by pelvic MRI at the MRI department of the Oncology Teaching Hospital/Medical City in Baghdad
... Show MoreIn this paper, a new hybrid algorithm for linear programming model based on Aggregate production planning problems is proposed. The new hybrid algorithm of a simulated annealing (SA) and particle swarm optimization (PSO) algorithms. PSO algorithm employed for a good balance between exploration and exploitation in SA in order to be effective and efficient (speed and quality) for solving linear programming model. Finding results show that the proposed approach is achieving within a reasonable computational time comparing with PSO and SA algorithms.
Idioms are a very important part of the English language: you are told that if you want to go far (succeed) you should pull your socks up (make a serious effort to improve your behaviour, the quality of your work, etc.) and use your grey matter (brain).1 Learning and translating idioms have always been very difficult for foreign language learners. The present paper explores some of the reasons why English idiomatic expressions are difficult to learn and translate. It is not the aim of this paper to attempt a comprehensive survey of the vast amount of material that has appeared on idioms in Adams and Kuder (1984), Alexander (1984), Dixon (1983), Kirkpatrick (2001), Langlotz (2006), McCarthy and O'Dell (2002), and Wray (2002), among others
... Show MoreReading Article First of Section 25 of Penal Trials Principles Law of Internal Forces Law makes us say that there are personal and objective regulations governing presence of jurisdiction of internal forces courts. It should be a source of law embodied by the personality of police as law in essence is a law of persons and the character of the perpetrator is not sufficient to determine jurisdiction of these courts. It should be linked with the subject condition, which completes the presence of jurisdiction for these courts, focusing on the essence of the crime and the interest to be protected by the criminal text with respect with the link between the crime and being a policeman. Thes
... Show More