Analysis of previously published target-cell limited viral dynamic models for pathogens such as HIV, hepatitis, and influenza generally rely on standard techniques from dynamical systems theory or numerical simulation. We use a quasi-steady-state approximation to derive an analytic solution for the model with a non-cytopathic effect, that is, when the death rates of uninfected and infected cell...

We present an analytic solution for the scattering of diffuse photon density waves by spherical inhomogeneities within turbid media. The analytic result is compared to experimental measurements. Close agreement between theory and experiment permits the use of the theory to determine the properties of unknown sphere-like objects embedded in turbid media. The analytic solution is extended to enco...

In this paper, two inverse problems of Stephen kind with local (Dirichlet) boundary conditions are investigated. In the first problem only a part of boundary is unknown and in the second problem, the whole of boundary is unknown. For the both of problems, at first, analytic expressions for unknown boundary are presented, then by using these analytic expressions for unknown boundaries and bounda...

the complex-step derivative approximation is applied to compute numerical derivatives. in this study, we propose a new formula of fractional complex-step method utilizing jumarie definition. based on this method, we illustrated an approximate analytic solution for the fractional cauchy-euler equations. application in image denoising is imposed by introducing a new fractional mask depending on s...

We investigate the exact analytic solutions for the growths of the dark matter and the baryon in sub-horizon scale. The growth of the dark matter δDM is related to that of the halos. Thus, the exact solution for the growth of the dark matter is important to obtain the proper properties of dark matter halos. However, the dark energy model dependence of δDM is confused with the δDM dependence on ...

We study a recurrence relation, where the generating function, as a formal power series, satisfies a differential equation that can be solved in a suitable domain; this yields an analytic function in a domain, but the solution is singular at the origin and the generating function has radius of convergence 0. Nevertheless, the solution to the recurrence can be obtained from the analytic solution...

We develop a full numerical as well as an approximate analytic solution for two-step holographic recording with high intensity pulses in LiNbO3 :Fe crystals. We find the unknown material parameters by fitting the numerical solution to the experimental results. The two important parameters that were unknown so far and found in this work are the bulk photovoltaic coefficient and absorption cross ...