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In this paper we present a simple mathematical model that adequately accounts for at least the initial vasculature that is established in a melanoma transplant. It is assumed that the tumor produces a substance (tumor angiogenesis factor--TAF) that elicits capillary sprouts from the vascular bed of the host. These sprouts then invade the tumor along the… (More)
A model for the growth of a tumor by diffusion is considered for spheroids which are grown in a normal medium in suspension culture. The experimental evidence indicates that, upon the onset of necrosis in the centre of the spheroid, the viable rim thickness decreases relatively slowly. This evidence contradicts the results of the usual model in which the… (More)
We consider a convertible security where the underlying stock price obeys a lognormal random walk and the risk-free rate is given by the Vasicek model. Using a Laplace transform in time and a Mellin transform in the stock price, we derive a Green's function solution for the value of the convertible bond.