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.
generator the metal conductor is replaced by conducting gas plasma.
This work deals with determination of optimum conditions of direct diffusion bonding welding of austenitic stainlesssteel type AISI 304L with Oxygen Free High Conductivity (OFHC) pure copper grade (C10200) in vacuum atmosphere of (1.5 *10-5 mbr.). Mini tab (response surface) was applied for optimizing the influence of diffusion bonding parameters (temperature, time and applied load) on the bonding joints characteristics and the empirical relationship was evaluated which represents the effect of each parameter of the process. The yield strength of diffusion bonded joint was equal to 153 MPa and the efficiency of joint was equal to 66.5% as compared with hard drawn copper. The diffusion zone reveals high microhardness than coppe
... Show MoreEquilibrium and rate of mixing of free flowing solid materials are found using gas fluidized bed. The solid materials were sand (size 0.7 mm), sugar (size0.7 mm) and 15% cast iron used as a tracer. The fluidizing gas was air with velocity ranged from 0.45-0.65 m/s while the mixing time was up to 10 minutes. The mixing index for each experiment was calculated by averaging the results of 10 samples taken from different radial and axial positions in fluidized QVF column 150 mm ID and 900 mm height.
The experimental results were used in solving a mathematical model of mixing rate and mixing index at an equilibrium proposed by Rose. The results show that mixing index increases with inc
... Show MoreModeling data acquisition systems (DASs) can support the vehicle industry in the development and design of sophisticated driver assistance systems. Modeling DASs on the basis of multiple criteria is considered as a multicriteria decision-making (MCDM) problem. Although literature reviews have provided models for DASs, the issue of imprecise, unclear, and ambiguous information remains unresolved. Compared with existing MCDM methods, the robustness of the fuzzy decision by opinion score method II (FDOSM II) and fuzzy weighted with zero inconsistency II (FWZIC II) is demonstrated for modeling the DASs. However, these methods are implemented in an intuitionistic fuzzy set environment that restricts the ability of experts to provide mem
... Show MoreThe Tigris River, a vital water resource for Iraq, faces significant challenges due to urbanization, agricultural runoff, industrial discharges, and climate change, leading to deteriorating water quality. Traditional methods for assessing irrigation water quality, such as laboratory testing and statistical modeling, are often insufficient for capturing dynamic and nonlinear relationships between parameters. This study proposes a novel application of the Gravitational Search Algorithm (GSA) to estimate the Irrigation Water Quality Index (IWQI) along the Tigris River. Using data from multiple stations, the study evaluates spatial variability in water quality, focusing on key paramete
Market share is a major indication of business success. Understanding the impact of numerous economic factors on market share is critical to a company’s success. In this study, we examine the market shares of two manufacturers in a duopoly economy and present an optimal pricing approach for increasing a company’s market share. We create two numerical models based on ordinary differential equations to investigate market success. The first model takes into account quantity demand and investment in R&D, whereas the second model investigates a more realistic relationship between quantity demand and pricing.
Find interested in the harmonization of variables and determinants of supply chain planning needs of the material, leading to the results start effective supply chain management, and end up quickly modify the sizes to suit the demand and turnover in the market. As well as identifying relationships between variables, and type of relationship used by the company with the processors and their feasibility, and indicate the level of interest and willingness to redesign the supply chain Company for Electrical Industries and build an integrated model for supply chain with the MRP system can be applied in the company.
Research depend on quantitative and descriptive method, It
... Show MoreAn aircraft's landing stage involves inherent hazards and problems associated with many factors, such as weather, runway conditions, pilot experiences, etc. The pilot is responsible for selecting the proper landing procedure based on information provided by the landing console operator (LCO). Given the likelihood of human decisions due to errors and biases, creating an intelligent system becomes important to predict accurate decisions. This paper proposes the fuzzy logic method, which intends to handle the uncertainty and ambiguity inherent in the landing phase, providing intelligent decision support to the pilot while reducing the workload of the LCO. The fuzzy system, built using the Mamdani approach in MATLAB software, considers critical
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