Narrow Results

This paper is devoted to the Euler–Poisson equations for fluids with non-zero heat conduction, arising in semiconductor science. Due to the thermal effect of the temperature equation, the local well-posedness theory by Xu and Kawashima (2014) for generally symmetric hyperbolic systems in spatially critical Besov spaces does not directly apply. To deal with this difficulty, we develop a generalized version of the Moser-type inequality by using Bony's decomposition. With a standard iteration argument, we then establish the local well-posedness of classical solutions to the Cauchy problem for intial data in spatially Besov spaces.

Infection of human immunodeficiency virus (HIV) is determined through the decay of healthy CD4+ T-cells in a well-mixed compartment, such as a bloodstream. A mathematical model is considered to illustrate the effects of combined drug therapy, i.e. reverse transcription plus protease inhibitor, on viral growth and T-cell population dynamics. This model is used to explain the existence and stability of infected and uninfected steady states in HIV growth. An analytical technique, called variational iteration method (VIM), is used to solve the mathematical model. This method is modified to obtain the rapidly convergent successive approximations of the exact solution. These approximations are obtained without any restrictions or the transformations that may change the physical behavior of the problem. Numerical simulations are computed and exhibited to illustrate the effects of proposed drug therapy on the growth or decay of infection.

In this paper, a modified iteration method (MIM) has been proposed to solve nonlinear second-order ODEs. Convergence analysis and error estimate of the proposed method are also discussed. Computational efficiency of this method is illustrated through numerical examples.

This paper presents a theoretical foundation for the newly developed methodology that enables the prediction of blood pressures based on the heart sounds measured directly on the chest of a patient. The key to this methodology is the separation of heart sounds into first heart sound and second heart sound, from which components attributable to four heart valves, i.e.: mitral; tricuspid; aortic; and pulmonary valve-closure sounds are separated. Since human physiology and anatomy can vary among people and are unknown a priori, such separation is called blind source separation. Moreover, the sources locations, their surroundings and boundary conditions are unspecified. Consequently, it is not possible to obtain an exact separation of signals. To circumvent this difficulty, we extend the point source separation method in this paper to an inhomogeneous fluid medium, and further combine it with iteration schemes to search for approximate source locations and signal propagation speed. Once these are accomplished, the signals emitted from individual sources are separated by deconvoluting mixed signals with respect to the identified sources. Both numerical simulation example and experiment have demonstrated that this approach can provide satisfactory source separation results.