The explicit entire solution of the Baouendi-Grushin equation with critical exponent and the Sobolev embedding constant;

The explicit solution expressed by elementary function of equations of heat and mass transfer in spray air washer is solved.

Based on the discrete-time difference equation of the plant,an explicit solution of Diophantine matrix polynomial equations in multivariable generalized predictive control is derived without appealing to Diophantine matrix polynomial equations recursions or iterations,which makes the applications of generalized predictive control much more convenient.

Based on the relationship between the discrete-time difference equation and its observable state-space canonical form, the explicit solution to Diophantine equation in generalized predictive control is derived.

New explicit solutions for a class of generalized nonlinear sine-Gordon equation;

By selecting appropriate transformations, we find some new explicit solutions to 2 + 1 dimensional nonlinear SchrOdinger equations, such as elliptic function solutions, trigonometric function solutions and so on.

In this paper,we assuming the volatility follows a log-normal stochastic process,this paper derived the explicit solutions to the local R-minimized pricing and hedging of European option by means of the gradient operator method.

In this paper,the approximate explicit solution of optical output power for P-doped cascaded Raman fiber lasers was acquired by linear model.