The aim of this article is to solve the Volterra-Fredholm integro-differential equations of fractional order numerically by using the shifted Jacobi polynomial collocation method. The Jacobi polynomial and collocation method properties are presented. This technique is used to convert the problem into the solution of linear algebraic equations. The fractional derivatives are considered in the Caputo sense. Numerical examples are given to show the accuracy and reliability of the proposed technique.

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

the student of the structure of the city and its constituent elements will clearly sense the invisible relationships that underlie the different forms of urban activity, which in turn are defined by the generality of the urban patterns in that city, which will vary clearly according to the location in the city. These relations will be embodied in their true form in the interactions between the different uses of the earth, and the change that will result from their regularity in the form of entities in independent groups, which may share with each other a component of it.
Therefore, the process of controlling the functional interactions between the uses of the urban land and the awareness of t

Background: Diabetes mellitus a major factor that has adverse effects on the vascular system and the heart. It causes an increase in cardiac muscle thickness, resulting in decreased compliance and increased peripheral arterial stiffness. This study aims to assess the left ventricular mass (LVM) and left ventricular hemodynamic changes in diabetic patients measured by Doppler echocardiography. Patients and Methods: The study included 50 diabetic patients ranging in age between 25 and 80 years, (mean age: 54.1 ± 15.10, 19 males, 31 females) and 50 healthy subjects, aged 25 to 80 years (mean age: 48.52 ± 14.45, 11 males, 39 females). Doppler echocardiography was used to assess left ventricular function. The measurements included

The issue of the public in the directions and theories of the theater director in the world theater, especially after the emergence of realism and the crystallization of the term direction and the definition of the role of the director in 1850 AD by the Duke Max Mengen took different paths to the Greek, Roman and even Elizabethan audience because it was here subjected to the theatrical equation from  its production and presentation due to the fact that the  theatrical performance is a technical artistic production, and the audience participation, watching and consumption, and here the participation of the audience was subjected to three directions:  the enlightenment in the sense of arousing sense, the incitement in the se

The present study was conducted as atrial to treat secondary hydatidosis in white mice of species Mus musculus. (Balb/c strain), experimentally infected with secondary hydatid cysts of sheep origin. The immunization process was carried by using CF/PS antigen which consist hydatid cyst fluid (CF) antigen, and protoscolices (PS) antigen mixed together and by using two concentrations 7.5, 15 mg/ml. Then derivatives of Benzimidazole, Mebendazole (M) and drugs Albendazole (A) were used 10 and 40 μm/gm body weight respectively. The mixture of drugs was used one week after challenged dose. Criteria taken into consideration to define the activity of the immunization and chemotherapy in this study were reduction in the numeral of cysts, the coeffic

Heat transfer process and fluid flow in a solar chimney used for natural ventilation are investigated numerically in the present work. Solar chimney was tested by selecting different positions of absorber namely: at the back side, front side, and at the middle of the air gap. CFD analysis based on finite volume method is used to predict the thermal performance, and air flow in two dimensional solar chimney under unsteady state condition, to identify the effect of different parameters such as solar radiation. Results show that a solar chimney with absorber at the middle of the air gap gives better ventilation performance. A comparison between the numerical and previous experimental results shows fair agreement.

Heat transfer process and fluid flow in a solar chimney used for natural ventilation are investigated numerically in the present work. Solar chimney was tested by selecting different positions of absorber namely: at the back side, front side, and at the middle of the air gap. CFD analysis based on finite volume method is used to predict the thermal performance, and air flow in two dimensional solar chimney under unsteady state condition, to identify the effect of different parameters such as solar radiation. Results show that a solar chimney with absorber at the middle of the air gap gives better ventilation performance. A comparison between the numerical and previous experimental results shows fair agreement.