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 method in solving these problems.
Mixture experiments are response variables based on the proportions of component for this mixture. In our research we will compare the scheffʼe model with the kronecker model for the mixture experiments, especially when the experimental area is restricted.
Because of the experience of the mixture of high correlation problem and the problem of multicollinearity between the explanatory variables, which has an effect on the calculation of the Fisher information matrix of the regression model.
to estimate the parameters of the mixture model, we used the (generalized inverse ) And the Stepwise Regression procedure
... Show MoreDensity data of alum chrom in water and in aqueous solution of poly (ethylene glycol) (1500) at different temperatures (288.15, 293.15, 298.15) k have been used to estimate the apparent molar volume (Vθ), limiting apparent molar volume (Vθ˚) experimental slope (Sv) and the second derivative of limiting partial molar volume [δ2 θ v° /δ T2] p .The viscosity data have been analyzed by means of Jones –Dole equation to obtain coefficient A, and Jones –Dole coefficient B, Free activation energy of activation per mole of solvent, Δμ10* solute, Δμ20* the activation enthalpy ΔH*,and entropy, ΔS*of activation of viscous flow. These results have been discussed in terms of solute –solvent interaction and making/breaking ability of so
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This work involves studying the effect of adding some selective organic component mixture on corrosion behavior of pure Al and its alloys in condensed synthetic automotive solution (CSAS) at room temperature. This mixture indicates the increasing of octane number in previous study and in this study show the increasing in corrosion resistance through the decreasing in corrosion rate values.
Electrochemical measurements were carried out by potentiostat at 3 mV/sec to estimate the corrosion parameters using Tafel extrapolation method, in addition to cyclic polarization test to know the pitting susceptibility of materials in tested medium.
The cathodic Tafel slope
... Show MoreThe nanostructured MnO2 /carbon fiber (CF) composite electrode was prepared using the anodic electrodeposition process. The crystal structure and morphology of MnO2 particles were determined with X-ray diffraction and field-emission scanning electron microscopy. The electrosorptive properties of the prepared electrode were investigated in the removal of cadmium ions from aqueous solution, and the effect of pH, cell voltage, and ionic strength was optimized and modeled using the response surface methodology combined with Box–Behnken design. The results confirm that the optimum conditions to remove Cd(II) ions were: pH of 6.03, a voltage of 2.77 V, and NaCl concentration of 3 g/L. The experimental results showed a good fit for the Freundli
... Show MoreThis research presents a new study in kinetics under reactive distillation by using consecutive two – step reaction : the saponification reaction of diethyl adipate with sodium hydroxide solution . The distillation process takes the role of withdrawing the intermediate product (sodium monoethyladipate SMA) which otherwise converts to the final product of low purity.The effect of three parameters were studied through a design of experiments applying 23 factorial design. These parameters were : the mole ratio of DA to NaOH solution (0.1 and 1) , NaOH solution concentration (3 N and 8 N) , and batch time (1.5 hr. and 3.5 hr.) . The conversion of DA to sodium monoethyladipate(SMA)(intermediate product) was the effect of these pa
... Show MoreThe present researchers are trying to enhance the properties of paper sheet that used widely in many fields such as printing and packaging. The enhancement of paper quality is also possible to preserve paper documents of all kinds, as they are the true record, full of the history, achievements of the human being and the intellectual and cultural of the country. It is possible to improve its physical and mechanical properties and preserve them from damage through the use of some solutions of polymeric adhesives, which act as protective barriers against water and moisture penetration. The paper also has the advantage of porosity, which has been overcome by using three types of polymeric adhesives (Nitro Cellulose, Polyvinyl alcohol acetate, a
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