Expanding Einstein-Yang-Mills by Yang-Mills in CHY frame

Using the Cachazo-He-Yuan (CHY) formalism, we prove a recursive expansion of tree level single trace Einstein-Yang-Mills (EYM) amplitudes with arbitrary number of gluons and gravitons, which is valid for general spacetime dimensions and any helicity configurations. The recursion is written in terms of fewer-graviton EYM amplitudes and pure Yang-Mills (YM) amplitudes, which can be further carried out until we reach an expansion in terms of pure YM amplitudes in Kleiss-Kuijf (KK) basis. Our expansion then generates naturally a spanning tree structure rooted on gluons whose vertices are gravitons. We further propose a set of graph theoretical rules based on spanning trees that evaluate directly the pure YM expansion coefficients.Comment: 36 pages, 3 captioned figures; v2: more details added, revised and published versio

Invariant Solutions to the Strominger System on Complex Lie Groups and Their Quotients

Using canonical 1-parameter family of Hermitian connections on the tangent bundle, we provide invariant solutions to the Strominger system on complex Lie groups. Both flat and non-flat cases are discussed in detail.Comment: 11 pages, comments are welcome. Updates in v2: minor typos are corrected. Updates in v3: small revisions, to be consistent with published versio

Gevrey Smoothing Effect for Solutions of the Non-Cutoff Boltzmann Equation in Maxwellian Molecules Case

In this paper we study the Gevrey regularity for the weak solutions to the Cauchy problem of the non-cutoff spatially homogeneous Botlzmann equation for the Maxwellian molecules model with the singularity exponent $s\in (0,1)$. We establish that any weak solution belongs to the Gevrey spaces for any positive time.Comment: 35 page

Climate Change: National and Local Policy Opportunities in China

Climate Change poses a wide range of potentially very severe threats in China. This aggravates the existing vulnerability of China and is one of the big challenges faced by the Chinese government. Adaptation programmes and projects are being developed and implemented at national and local level. As China is engaged in heavy investment in infrastructure development as a consequence of the rapid process of development and urbanization, mainstreaming adaptation into such development process is a priority for China. China has also made positive contributions to reducing greenhouse gas emissions through participations in the CDM under the Kyoto Protocol framework. Although mitigation is not a priority at national or local level, it has been integrated into national and local development plans explicitly. This paper addresses the following questions: What is the policy space for climate change mitigation and adaptation policy at national and local level and what is already being done? The three case studies at local level - Beijing, Guangdong and Shanghai – presented here, highlight the local benefits in terms of local pollution of integrating mitigation policies into local development. However, financial constraints usually prevent such a positive policy integration. National policies and international cooperation aiming at bridging the financial gap and promoting technology transfer would help in integrating local pollution control and mitigation efforts in China today.Climate Change, Local Policy, National Policy, Mitigation, Local Pollution