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 tr
Catalytic wet air oxidation of aqueous phenol solution was studied in a pilot plant trickle bed reactor using copper
oxide catalyst supported on alumina and silica. Catalysts were prepared by impregnating method. Effect of feed solution
pH (5.9, 7.3, and 9.2), gas flow rate (20%, 50%, 80%, and 100%), WHSV (1, 2, and 3 h-1), temperature (120°C, 140°C,
and 160°C), oxygen partial pressure (6, 9, 12 bar), and initial phenol concentration (1, 2, and 4 g/l).Generally, the
performance of the catalysts was better when the pH of feed solution was increased. The catalysts deactivation is related
to the dissolution of the metal oxides from the catalyst surface due to the acidic conditions. Phenol oxidation reaction
was strongly
Background: Fiber-optic endoscopy is an important
investigation of the large intestine, whether or not the
radiologist (barium enema) has discovered a lesion in
the bowel. Colonoscopy affords a unique opportunity
to direct visualization of entire colonic mucosa. At
the same time, the physician can obtain biopsy specimens, remove polyps, and decompress volvuli.
Most experienced endoscopists and well prepared
patients can reach the cecum in over 90% of patients.
If colonoscopy is properly performed, it has a low
risk of complications, such as perforation and bleeding.
Methods: A total of 70 consecutive patients admitted
to Endoscopy department at Al-Kindy Teaching hospital from September- 2008 to July-2009.
A field experiment was conducted on the form of the Dept. of Field Crop Sci. / College of Agriculture / University of Baghdad in spring and fall seasons of 2009 and 2010 . Ten inbreds of maize were planted and crossed to each other to produce single crosses . In the second season, single crosses were planted along with thin parent to produce three – way and double crosses . In the third seasons panet and crosses were planted . Crosses were selfed to produce F2 seeds and increase seeds of inbreds . In the fourth season, all grin types were planted , and their agronomic traits were evaluated . Values of P of inbreds , F1 and F2 were calculated for agronomic traits . The new formula to predict inbreeding depression ( ID ) F2 plant without gr
... Show Moreيعد هذا النص أحد النصوص المسمارية المصادرة التي بحوزة المتحف العراقي، ويحمل الرقم المتحفي (235869)، قياساته )12،7x 6x 2،5سم). يتضمن مدخولات كميات من الشعير،أرخ النص الى عصر أور الثالثة (2012-2004 ق.م) و يعود الى السنة الثالثة من حكم الملك أبي-سين (2028-2004 ق.م)،أن الشخصية الرئيسة في هذا النص هو)با-اَ-كا مسمن الماشية( من مدينة أري-ساكرك، ومقارنته مع النصوص المسمارية المنشورة التي تعود الى أرشيفه يبلغ عددها (196) نصاً تضمنت نشاطاته م
... Show MoreIn this paper, the dynamical behavior of a three-dimensional fractional-order prey-predator model is investigated with Holling type III functional response and constant rate harvesting. It is assumed that the middle predator species consumes only the prey species, and the top predator species consumes only the middle predator species. We also prove the boundedness, the non-negativity, the uniqueness, and the existence of the solutions of the proposed model. Then, all possible equilibria are determined, and the dynamical behaviors of the proposed model around the equilibrium points are investigated. Finally, numerical simulations results are presented to confirm the theoretical results and to give a better understanding of the dynami
... Show MoreKE Sharquie, GA Ibrahim, AA Noaimi, HK Hamudy, J Saudi Soc Dermatol Dermatol Surg, 2010 - Cited by 2
Water flow into unsaturated porous media is governed by the Richards’ partial differential equation expressing the mass conservation and Darcy’s laws. The Richards’ equation may be written in three forms,where the dependent variable is pressure head or moisture content, and the constitutive relationships between water content and pressure head allow for conversion of one form into the other. In the present paper, the “moisture-based" form of Richards’ equation is linearized by applying Kirchhoff’s transformation, which
combines the soil water diffusivity and soil water content. Then the similarity method is used to obtain the analytical solution of wetting front position. This exact solution is obtained by means of Lie’s
Objective: To conduct a standardized method for cavity preparation on the palatal surface of rat maxillary molars and to introduce a standardized method for tooth correct alignment within the specimen during the wax embedding procedure to better detect cavity position within the examined slides. Materials and methods: Six male Wistar rats, aged 4-6 weeks, were used. The maxillary molars of three animals were sectioned in the frontal plane to identify the thickness of hard tissue on the palatal surface of the first molar which was (250-300µm). The end-cutting bur (with a cutting head diameter of 0.2mm) was suitable for preparing a dentinal cavity (70-80µm) depth. Cavity preparation was then performed using the same bur on the tooth
... Show MoreOur goal in the present paper is to recall the concept of general fuzzy normed space and its basic properties in order to define the adjoint operator of a general fuzzy bounded operator from a general fuzzy normed space V into another general fuzzy normed space U. After that basic properties of the adjoint operator were proved then the definition of fuzzy reflexive general fuzzy normed space was introduced in order to prove that every finite dimensional general fuzzy normed space is fuzzy reflexive.