Monthly gravity field recovery from GRACE orbits and K-band measurements using variational equations approach

The Gravity Recovery and Climate Experiment（GRACE） mission can significantly improve our knowledge of the temporal variability of the Earth＇s gravity field.We obtained monthly gravity field solutions based on variational equations approach from GPS-derived positions of GRACE satellites and K-band range-rate measurements.The impact of different fixed data weighting ratios in temporal gravity field recovery while combining the two types of data was investigated for the purpose of deriving the best combined solution.The monthly gravity field solution obtained through above procedures was named as the Institute of Geodesy and Geophysics（IGG） temporal gravity field models.IGG temporal gravity field models were compared with GRACE Release05（RL05） products in following aspects：（i） the trend of the mass anomaly in China and its nearby regions within 2005-2010; （ii） the root mean squares of the global mass anomaly during 2005-2010; （iii） time-series changes in the mean water storage in the region of the Amazon Basin and the Sahara Desert between 2005 and 2010.The results showed that IGG solutions were almost consistent with GRACE RL05 products in above aspects（i）-（iii）.Changes in the annual amplitude of mean water storage in the Amazon Basin were 14.7 ± 1.2 cm for IGG,17.1 ± 1.3 cm for the Centre for Space Research（CSR）,16.4 ± 0.9 cm for the GeoForschungsZentrum（GFZ） and 16.9 ± 1.2 cm for the Jet Propulsion Laboratory（JPL） in terms of equivalent water height（EWH）,respectively.The root mean squares of the mean mass anomaly in Sahara were 1.2 cm,0.9 cm,0.9 cm and 1.2 cm for temporal gravity field models of IGG,CSR,GFZ and JPL,respectively.Comparison suggested that IGG temporal gravity field solutions were at the same accuracy level with the latest temporal gravity field solutions published by CSR,GFZ and JPL.

Stability of Dirac Equation in Four-Dimensional Gravity

We introduce the Dirac equation in four-dimensional gravity which is a generally covariant form. We choose the suitable variable and solve the corresponding equation. To solve such equation and to obtain the corresponding bispinor, we employ the factorization method which introduces the associated Laguerre polynomial. The asso- ciated Laguerre polynomials help us to write the Dirac equation of four-dimensional gravity in the form of the shape invariance equation. Thus we write the shape invariance condition with respect to the secondary quantum number. Finally, we obtain the spinor wave function and achieve the corresponding stability of condition for the four-dimensional gravity system.

Effects of non-Newtonian gravity on the properties of strange stars

The properties of strange star matter are studied in the equivparticle model with inclusion of non-Newtonian gravity. It is found that the inclusion of non-Newtonian gravity makes the equation of state stiffer if Witten＇s conjecture is true. Correspondingly, the maximum mass of strange stars becomes as large as two times the solar mass, and the maximum radius also becomes bigger. The coupling to boson mass ratio has been constrained within the stability range of strange quark matter.

Trade Politics： A Brief Survey of International Political Economy

International political economy has already been shown to be powerful to explain the global trade growth. In this paper we offer a brief survey of international political economy of trade policy. In addition to this, we also try to address three questions： （1） How does electoral competition affect trade policy？ Suppose two parties compete for the power over trade policy, would the two parties choose the same tariff？. （2） We observe that the US tariffs decline over time, so do the declining U.S. tariffs lead to the fall of the Democratic vote share in the election？ （3） What is the relationship between trade globalization and political liberalization？ Put it another way, how does trade affect democracy？ And conversely, how does democracy affect trade？