In this study, a new technique is considered for solving linear fractional Volterra-Fredholm integro-differential equations (LFVFIDE's) with fractional derivative qualified in the Caputo sense. The method is established in three types of Lagrange polynomials (LP’s), Original Lagrange polynomial (OLP), Barycentric Lagrange polynomial (BLP), and Modified Lagrange polynomial (MLP). General Algorithm is suggested and examples are included to get the best effectiveness, and implementation of these types. Also, as special case fractional differential equation is taken to evaluate the validity of the proposed method. Finally, a comparison between the proposed method and other methods are taken to present the effectiveness of the proposal meth

This paper is concerned with the numerical solutions of the vorticity transport equation (VTE) in two-dimensional space with homogenous Dirichlet boundary conditions. Namely, for this problem, the Crank-Nicolson finite difference equation is derived.  In addition, the consistency and stability of the Crank-Nicolson method are studied. Moreover, a numerical experiment is considered to study the convergence of the Crank-Nicolson scheme and to visualize the discrete graphs for the vorticity and stream functions. The analytical result shows that the proposed scheme is consistent, whereas the numerical results show that the solutions are stable with small space-steps and at any time levels.

Results showed that the optimum conditions for production of inulunase from isolate Kluyveromyces marxianus AY2 by submerged culture could be achieved by using inulin as carbon source at a concentration of 2% with mixture of yeast extract and ammonium sulphate in a ratio of 1:1 in a concentration of 1% at initial pH 5.5 after incubation for 42 hours at 30ºC.

The Purpose of this study are  analyze financial lease advantage through analyze and discuss financial lease cost, and achieve tax advantage to reach study objective. study include two firms ,oil firm and construction firm with limited liability. The inductive method is used for the applied part in analyzing the financial data of the companies considered in 2011-2015.The result of the study shows that the financial  lease achieve present value of the costs is positive. This study found out the results that verify the hypothesis: The tax advantage of financial Leasing is characterized by decreasing cost and achieving higher tax shield. The study also found the most important recommendations of awareness of the benefits arising f

The present work describes the adsorption of Ba2+ and Mg2+ions from aqueous solutions by activated alumina in single and binary system using batch adsorption. The effect of different parameters such as amount of alumina, concentration of metal ions, pH of solution, contact time and agitation speed on the adsorption process was studied. The optimum adsorbent dosage was found to be 0.5 g and 1.5 g for removal of Ba2+ and Mg2+, respectively. The optimum pH, contact time and agitation speed, were found to be pH 6, 2h and 300 rpm, respectively, for removal of both metal ions. The equilibrium data were analyzed by Langmuir and Freundlich isotherm models and the data fitted well to both isotherm modes as indicated by higher correlation of deter

The research aims to find a contemporary model in analyzing the reasons behind the delay of the investment plan projects suffered by the North Oil Company. This model is able to understand the environment surrounding the implementation of projects in the light of the changes facing the company at the present time, which in turn requires the need to identify the most important strengths and weaknesses Internal and external opportunities and threats using the SWOT matrix and identify the appropriate strategic alternative based on clear policy, strategies and programs to address weaknesses and look to the future prospects as the company can be stronger and more flexible environmental changes surrounding the reality of implementation

Conditional logistic regression is often used to study the relationship between event outcomes and specific prognostic factors in order to application of logistic regression and utilizing its predictive capabilities into environmental studies. This research seeks to demonstrate a novel approach of implementing conditional logistic regression in environmental research through inference methods predicated on longitudinal data. Thus, statistical analysis of longitudinal data requires methods that can properly take into account the interdependence within-subjects for the response measurements. If this correlation ignored then inferences such as statistical tests and confidence intervals can be invalid largely.

When employing shorter (sub picosecond) laser pulses, in ablation kinetics the features appear which can no longer be described in the context of the conventional thermal model. Meanwhile, the ablation of materials with the aid of ultra-short (sub picosecond) laser pulses is applied for micromechanical processing. Physical mechanisms and theoretical models of laser ablation are discussed. Typical associated phenomena are qualitatively regarded and methods for studying them quantitatively are considered. Calculated results relevant to ablation kinetics for a number of substances are presented and compared with experimental data. Ultra-short laser ablation with two-temperature model was quantitatively investigated. A two-temperature model

Municipal wastewater sources are becoming increasingly important for reuse, for irrigation purposes, so they must be treated to meet environmentally friendly local or global standards. The aim of this study is to establish, calibrate, and validate a model for predicting chemical oxygen demand for the pilot plant of mobile biofilm reactors operating from municipal wastewater in Maaymyrh located in Hilla city Using the approach of dimensional analysis. The approach of Buckingham's theorem was used to derive a model of dimensional analysis design for the forecast of (COD) in the pilot plant. The effluent concentration (COD) It has been derived as a result of the influential concentration of (COD), dissolved oxygen (DO), volume of pilot plant

This research presents a statistical study of radiation generated from communication towers in the Nineveh Plain region Baghdeda. The intensity of radiation energy was measured at 10 meters away from the communication tower in different locations, using a (1PC XH-901 Dosimeter/ Personal Dose Alarm / Radiation Detector, dosage rate: 0.01 μSv/h to 150μSv/h) to measure the amount of radiation at various times. Energy densities were measured and compared with standard limits provided by other authorities, such as the International Committee for Radiation Protection. Results were analyzed using SPSS version 26 to implement the data. The results show that the means of the radiation levels measured at all the zones do not statistically differ