The kinetics of a diffusing particle near a reversible trap may be described by an extension of the Feynman-Kac equation to the case of reversible binding, which can occur within a finite reaction sphere. We obtain the Green's function solution for the Laplace transform of this equation when the particle is initially either bound or unbound. We study the solution in the time-domain by either in...

An axial dispersion reactor model for gas–liquid reaction systems is proposed in this paper based on the penetration theory. The mass transfer mechanism accompanied by a chemical irreversible first-order reaction is mathematically treated in a new way in order to use its results to develop the model conveniently. Analytical solutions can be obtained for the equation system involving linear diff...

The enzymic formation of enzyme-bound amino acyl adenylates from adenosine triphosphate and amino acid (Equation 1) has been recognized for several years (l-8) and enzymes specific for certain of the amino acids have been isolated in a number of laboratories (2, 9, 10). These same enzymes are now known (11-15) to catalyze a second reaction involving the transfer of the amino acyl moiety from th...

We consider radial decreasing solutions of the semilinear heat equation with exponential nonlinearity. provide a relatively simple proof sharp upper estimates for final blowup profile and refined space-time behavior. actually establish global, estimate, which contains those profiles as special cases.