Application of Rational Second Kind Chebyshev Functions for System of Integrodifferential Equations on Semi-Infinite Intervals

Rational Chebyshev bases and Galerkin method are used to obtain the approximate solution of a system of high-order integro-differential equations on the interval [0,∞). This method is based on replacement of the unknown functions by their truncated series of rational Chebyshev expansion. Test examples are considered to show the high accuracy, simplicity, and efficiency of this method

Application of Homotopy Analysis Method to SIR Epidemic Model

Abstract In this article, the problem of the spread of a non-fatal disease in a population which is assumed to have constant size over the period of the epidemic is considered. Mathematical modeling of the problem leads to a system of nonlinear ordinary differential equations. Homotopy analysis method is employed to solve this system of nonlinear ordinary differential equations

A legendre wavelet spectral collocation method for solving oscillatory initial value problems.

In this paper, we propose an iterative spectral method for solving differential equations with initial values on large intervals. In the proposed method, we first extend the Legendre wavelet suitable for large intervals, and then the Legendre-Guass collocation points of the Legendre wavelet are derived. Using this strategy, the iterative spectral method converts the differential equation to a set of algebraic equations. Solving these algebraic equations yields an approximate solution for the differential equation. The proposed method is illustrated by some numerical examples, and the result is compared with the exponentially fitted Runge-Kutta method. Our proposed method is simple and highly accurate

New construction of wavelets base on floor function.

In this paper, the properties of the floor function has been used to find a function which is one on the interval [0, 1) and is zero elsewhere. The suitable dilation and translation parameters lead us to get similar function corresponding to the interval [a,b)[a,b). These functions and their combinations enable us to represent the stepwise functions as a function of floor function. We have applied this method on Haar wavelet, Sine–Cosine wavelet, Block-Pulse functions and Hybrid Fourier Block-Pulse functions to get the new representations of these functions

The effect of different types of hepatic injury on the estrogen and androgen receptor activity of liver

Mammalian liver contains receptors for both estrogens and androgens. Hepatic regeneration after partial hepatectomy in male rats is associated with a loss of certain male-specific hepatic characteristics. In this study we investigated the effects of lesser forms of hepatic injury on the levels of estrogen and androgen receptor activity in the liver. Adult male rats were subjected to portacaval shunt, partial portal vein ligation, hepatic artery ligation, or two-thirds partial hepatectomy. Another group of animals was treated with cyclosporine. At the time of sacrifice the livers were removed and used to determine the estrogen and androgen receptor activity in the hepatic cytosol. A significant reduction (p < 0.05) in the hepatic cytosolic androgen receptor activity and a slight increase in the estrogen receptor activity occurred following total portosystemic shunting. Partial ligation of the portal vein, which produces a lesser degree of portosystemic shunting, had no effect on the levels of the estrogen and androgen receptor activity present within hepatic cytosol. Cyclosporine-treated animals had significantly greater (p < 0.01) levels of estrogen receptor activity in the hepatic cytosol compared to vehicle-treated control animals. Levels of estrogen and androgen receptor activity within the hepatic cytosol remained unchanged after ligation of the hepatic artery. The reduction in the cytosolic estrogen and androgen receptor activity in the liver after partial hepatectomy was confirmed. In summary, certain types of hepatic injury are associated with profound changes in the estrogen and androgen receptor content within the liver. © 1989 Informa UK Ltd All rights reserved: reproduction in whole or part not permitted

Fuzzy Modeling for Uncertain Nonlinear Systems Using Fuzzy Equations and Z-Numbers

In this paper, the uncertainty property is represented by Z-number as the coefficients and variables of the fuzzy equation. This modification for the fuzzy equation is suitable for nonlinear system modeling with uncertain parameters. Here, we use fuzzy equations as the models for the uncertain nonlinear systems. The modeling of the uncertain nonlinear systems is to find the coefficients of the fuzzy equation. However, it is very difficult to obtain Z-number coefficients of the fuzzy equations. Taking into consideration the modeling case at par with uncertain nonlinear systems, the implementation of neural network technique is contributed in the complex way of dealing the appropriate coefficients of the fuzzy equations. We use the neural network method to approximate Z-number coefficients of the fuzzy equations

Effect of partial portal vein ligation on hepatic regeneration

To evaluate the effect of portal hypertension and diminished portal venous blood flow to the liver on hepatic regeneration, male rats were subjected to partial portal vein ligation and subsequently to a two-thirds partial hepatectomy. The levels of ornithine decarboxylase activity at 6 h after partial hepatectomy were greater (p > 0.001) in the rats with prior partial portal vein ligation than in those without portal hypertension. The rats with prior partial portal vein ligation also had greater (p > 0.005) levels of thymidine kinase activity at 48 h after partial hepatectomy than did those without portal hypertension. Hepatic sex hormone receptor activity was not affected by prior partial portal vein ligation either before or after partial hepatectomy. The reductions in both estrogen and androgen receptor activity observed in the hepatic cytosol after partial hepatectomy were similar to those observed in control animals. These data indicate that animals with portal hypertension having a diminished hepatic portal blood flow have a normal capacity to regenerate hepatic mass following a hepatic resection © 1988 Informa UK Ltd All rights reserved: reproduction in whole or part not permitted