TIME ANALYTICITY FOR THE HEAT EQUATION ON GRADIENT SHRINKING RICCI SOLITONS

On a complete non-compact gradient shrinking Ricci soliton,we prove the analyticity in time for smooth solutions of the heat equation with quadratic exponential growth in the space variable.This growth condition is sharp.As an application,we give a necessary and sufficient condition on the solvability of the backward heat equation in a class of functions with quadratic exponential growth on shrinkers.

Relativistic algorithm for time transfer in Mars missions under IAU Resolutions: an analytic approach

With tremendous advances in modem techniques, Einstein＇s general rela- tivity has become an inevitable part of deep space missions. We investigate the rela- tivistic algorithm for time transfer between the proper time - of the onboard clock and the Geocentric Coordinate Time, which extends some previous works by including the effects of propagation of electromagnetic signals. In order to evaluate the implicit algebraic equations and integrals in the model, we take an analytic approach to work out their approximate values. This analytic model might be used in an onboard com- puter because of its limited capability to perform calculations. Taking an orbiter like Yinghuo-1 as an example, we find that the contributions of the Sun, the ground station and the spacecraft dominate the outcomes of the relativistic corrections to the model.

Study on Effect of Time Factor on Tree Growth

According to the data of analytic trees,an empirical equation of tree growth was constructed,with annual growth as variable and time and annual precipitation as independent variables. Through arithmetical operation including derivation of function and so on,the effect of precipitation on tree growth was studied through the rejection of effect of time factor.

The transformation between τ and TCB for deep space missions under IAU resolutions

For tracking spacecraft and performing radio science, the transformation between the proper time （τ） given by a clock carried onboard a spacecraft and the barycentric coordinate time （TCB） is investigated under IAU resolutions. In order to more clearly demonstrate manifestations of a physical model and improve computa- tional efficiency, an analytic approach is adopted. After numerical verification, it is confirmed that this method is adequate to describe a Mars orbiter during one year, and is particularly good at describing the influence from perturbing bodies. Further analyses demonstrate that there are two main effects in the transformation： the gravi- tational field of the Sun and the velocity of the spacecraft in the barycentric coordinate reference system. The combined contribution of these effects is at the level of a few sub-seconds.

Numerical modelling of storm surges in the Beibu Gulf with SCM

On the basis of 3-dimensional nonlinear hydrodynamical equations and by using the improved SCM the tides and storm surges induced by Typhoons 7109 and 8007 in the Beibu Gulf are simulated. In addition, the nonlinear interaction between the tide and storm surge in the gulf is discussed and some significant results are obtained.

The Polynomially Exponential Time Restrained Analytical Hierarchy

A polynomially exponential time restrained analytical hierarchy is introduced with the basic proper ties of the hierarchy followed.And it will be shown that there is a recursive set A such that A does not belong to any level of the p-arithmetical hierarchies.Then we shall prove that there are recursive sets A and B such that the different levels of the analytical hierarchy relative to A are different and for some n every level higher than n of the analytical hierarchy relative to B is the same as the n-th level. And whether the higher levels are collapsed into some lower level is neither provable nor disprovable in set theory and several other results.