| Stochastic (Monte Carlo) solutions of the general balance ordinary diierential equations for measures are considered. For this purpose a wide class of n-particle processes is studied from the viewpoint of the main terms of asymptotical (n ! 1) bias and variance for the corresponding estimates. Boltzmann-like and linear equations are considered as the particular cases of balance equations, sev...

in this paper, the modified simplest equation method is successfully implemented to find travelling wave solutions of the generalized forms $b(n,1)$ and $b(-n,1)$ of burgers equation.this method is direct, effective and easy to calculate, and it is a powerful mathematical tool for obtaining exact travelling wave solutions of the generalized forms $b(n,1)$ and $b(-n,1)$ of burgers equation and c...

Carothers and Flory established the fundamental principles of homogeneous two-component polycondensation reactions by which a variety of commonly used polymers such as polyesters and polyamides (nylons) are synthesized even now. One of the most critical factors to achieve a high degree of polymerization is a strict adherence of stoichiometric balance of the two components. An imbalanced ratio o...

In this paper, we establish exact solutions for nonlinear evolution equations. The homogeneous balance method is used to construct exact travelling wave solutions of the CalogeroDegasperis (CD) and Potential Kadomstev-Petviashvili (PKP) equations, in which the homogeneous balance method is applied to solve the Riccati equation and the reduced nonlinear ordinary differential equation. Many new f...

A Bäcklund transformation(BT) and a recurrence formula are derived by the homogeneous balance(HB) method. A initial problem of Burgers equations is reduced to a initial problem of heat equation by the BT, the initial problem of heat equation is resolved by the Fourier transformation method, substituting various solutions of the initial problem of the heat equation will yield solutions of the in...

We report on measurements of the rate of homogeneous ice nucleation in supercooled water microdroplets levitated in an electrodynamic balance. By comparison of the freezing probability for droplets of radius 49 µm and 19 µm, we are able to conclude that homogeneous freezing is a volume-proportional process and that surface nucleation might only be important, if at all, for much smaller droplets.