Two problems related to prescribed curvature measures

Existence of convex body with prescribed generalized curvature measures is discussed, this result is obtained by making use of Guan-Li-Li's innovative techniques. In surprise, that methods has also brought us to promote Ivochkina's $C^2$ estimates for prescribed curvature equation in \cite{I1, I}.Comment: 12 pages, Corrected typo

Assessment of China's virtual air pollution transport embodied in trade by using a consumption-based emission inventory

Substantial anthropogenic emissions from China have resulted in serious air pollution, and this has generated considerable academic and public concern. The physical transport of air pollutants in the atmosphere has been extensively investigated; however, understanding the mechanisms how the pollutant was transferred through economic and trade activities remains a challenge. For the first time, we quantified and tracked China's air pollutant emission flows embodied in interprovincial trade, using a multiregional input - output model framework. Trade relative emissions for four key air pollutants (primary fine particle matter, sulfur dioxide, nitrogen oxides and non-methane volatile organic compounds) were assessed for 2007 in each Chinese province. We found that emissions were significantly redistributed among provinces owing to interprovincial trade. Large amounts of emissions were embodied in the imports of eastern regions from northern and central regions, and these were determined by differences in regional economic status and environmental policy. It is suggested that measures should be introduced to reduce air pollution by integrating cross-regional consumers and producers within national agreements to encourage efficiency improvement in the supply chain and optimize consumption structure internationally. The consumption-based air pollutant emission inventory developed in this work can be further used to attribute pollution to various economic activities and final demand types with the aid of air quality models

Weakly Coupled Motion of Individual Layers in Ferromagnetic Resonance

We demonstrate a layer- and time-resolved measurement of ferromagnetic resonance (FMR) in a Ni81Fe19 / Cu / Co93Zr7 trilayer structure. Time-resolved x-ray magnetic circular dichroism has been developed in transmission, with resonant field excitation at a FMR frequency of 2.3 GHz. Small-angle (to 0.2 degree), time-domain magnetization precession could be observed directly, and resolved to individual layers through elemental contrast at Ni, Fe, and Co edges. The phase sensitivity allowed direct measurement of relative phase lags in the precession oscillations of individual elements and layers. A weak ferromagnetic coupling, difficult to ascertain in conventional FMR measurements, is revealed in the phase and amplitude response of individual layers across resonance.Comment: 22 pages, 6 figures submitted to Physical Review

Corrigendum to "Assessment of China's virtual air pollution transport embodied in trade by using a consumption-based emission inventory" published in Atmos. Chem. Phys., 15, 5443-5456, 2015

No abstract available

The openness conjecture and complex Brunn-Minkowski inequalities

We discuss recent versions of the Brunn-Minkowski inequality in the complex setting, and use it to prove the openness conjecture of Demailly and Koll\'ar.Comment: This is an account of the results in arXiv:1305.5781 together with some background material. It is based on a lecture given at the Abel symposium in Trondheim, June 2013. 13 page

Standard random walks and trapping on the Koch network with scale-free behavior and small-world effect

A vast variety of real-life networks display the ubiquitous presence of scale-free phenomenon and small-world effect, both of which play a significant role in the dynamical processes running on networks. Although various dynamical processes have been investigated in scale-free small-world networks, analytical research about random walks on such networks is much less. In this paper, we will study analytically the scaling of the mean first-passage time (MFPT) for random walks on scale-free small-world networks. To this end, we first map the classical Koch fractal to a network, called Koch network. According to this proposed mapping, we present an iterative algorithm for generating the Koch network, based on which we derive closed-form expressions for the relevant topological features, such as degree distribution, clustering coefficient, average path length, and degree correlations. The obtained solutions show that the Koch network exhibits scale-free behavior and small-world effect. Then, we investigate the standard random walks and trapping issue on the Koch network. Through the recurrence relations derived from the structure of the Koch network, we obtain the exact scaling for the MFPT. We show that in the infinite network order limit, the MFPT grows linearly with the number of all nodes in the network. The obtained analytical results are corroborated by direct extensive numerical calculations. In addition, we also determine the scaling efficiency exponents characterizing random walks on the Koch network.Comment: 12 pages, 8 figures. Definitive version published in Physical Review

Maximal planar scale-free Sierpinski networks with small-world effect and power-law strength-degree correlation

Many real networks share three generic properties: they are scale-free, display a small-world effect, and show a power-law strength-degree correlation. In this paper, we propose a type of deterministically growing networks called Sierpinski networks, which are induced by the famous Sierpinski fractals and constructed in a simple iterative way. We derive analytical expressions for degree distribution, strength distribution, clustering coefficient, and strength-degree correlation, which agree well with the characterizations of various real-life networks. Moreover, we show that the introduced Sierpinski networks are maximal planar graphs.Comment: 6 pages, 5 figures, accepted by EP

Evidence for a direct band gap in the topological insulator Bi2Se3 from theory and experiment

Using angle-resolved photoelectron spectroscopy and ab-initio GW calculations, we unambiguously show that the widely investigated three-dimensional topological insulator Bi2Se3 has a direct band gap at the Gamma point. Experimentally, this is shown by a three-dimensional band mapping in large fractions of the Brillouin zone. Theoretically, we demonstrate that the valence band maximum is located at the Brillouin center only if many-body effects are included in the calculation. Otherwise, it is found in a high-symmetry mirror plane away from the zone center.Comment: 8 pages, 4 figure

SU(3) Richardson-Gaudin models: three level systems

We present the exact solution of the Richardson-Gaudin models associated with the SU(3) Lie algebra. The derivation is based on a Gaudin algebra valid for any simple Lie algebra in the rational, trigonometric and hyperbolic cases. For the rational case additional cubic integrals of motion are obtained, whose number is added to that of the quadratic ones to match, as required from the integrability condition, the number of quantum degrees of freedom of the model. We discuss different SU(3) physical representations and elucidate the meaning of the parameters entering in the formalism. By considering a bosonic mapping limit of one of the SU(3) copies, we derive new integrable models for three level systems interacting with two bosons. These models include a generalized Tavis-Cummings model for three level atoms interacting with two modes of the quantized electric field.Comment: Revised version. To appear in Jour. Phys. A: Math. and Theo