Exact solutions for mass-dependent irreversible aggregations

Exact solutions for mass-dependent irreversible aggregations.

We consider the mass-dependent aggregation process (k+1)X→X, given a fixed number of unit mass particles in the initial state. One cluster is chosen proportional to its mass and is merged into one, either with k neighbors in one dimension, or--in the well-mixed case--with k other clusters picked randomly. We find the same combinatorial exact solutions for the probability to find any given confi...

Exact solutions of effective mass Schrödinger equations

We outline a general method of obtaining exact solutions of Schrödinger equations with a position dependent effective mass. Exact solutions of several potentials including the shape invariant potentials have also been obtained.

Exact and asymptotic scaling solutions for fragmentation with mass loss.

Exact Solutions to Time-Dependent MDPs

We describe an extension of the Markov decision process model in which a continuous time dimension is incllMcd in the stat(', space. This allows tbr the representation and exact solution of a wide range of prohleins in which transitions or rewards vary over time. We examine problems based on route planning with public transportation and telescope observation scheduling.

Explicit exact solutions for variable coefficient Broer-Kaup equations

Based on symbolic manipulation program Maple and using Riccati equation mapping method several explicit exact solutions including kink, soliton-like, periodic and rational solutions are obtained for (2+1)-dimensional variable coefficient Broer-Kaup system in quite a straightforward manner. The known solutions of Riccati equation are used to construct new solutions for variable coefficient Broer...