Abstract:
We develop the generalized Cartan Calculus for the groups $G=$SL$(2,\mathbb{R})\times\mathbb{R}^+$, SL$(5,\mathbb{R})$ and SO(5,5). They are the underlying algebraic structures of $d=9,7,6$ exceptional field theory, respectively. These algebraic identities are needed for the "tensor hierarchy" structure in exceptional field theory. The validity of Poincar\'e lemmas in this new differential geometry is also discussed. Finally we explore some possible extension of the generalized Cartan calculus beyond the exceptional series.

Abstract:
This article introduced a novel computer system,named NHD(Network Hard Disk),which was based on the theory model of the separation between computation and storage resources.In order to meet different applications' requirements,the NHD system utilized a specialized hardware equipment installed on the side of client to combine those two resources on demand.This newly reconstructed computing environment has advantages of dynamics,individuation and easy management.

Abstract:
On the basis of observations by Spitzer and Herschel, we present and analyse the correlations between various monochromatic infrared (IR) luminosities for star-forming galaxies, selected from two northern Spitzer Wide-area InfraRed Extragalactic Survey (SWIRE) fields. The 24- and 70 micron luminosities (L[24] and L[70]), which are dominated by the continuum of very small grains (VSGs) and warm dust in thermal equilibrium, respectively, correlate tightly with ongoing star formation. The contribution from cool dust excited by evolved stars also increases as the wavelength increases in the far-infrared (FIR) wavelength range. The spectral features of ionized polycyclic aromatic hydrocarbons (PAHs) around rest-frame 8 micron are excited by the moderated radiation field related to evolved stars as well, rather than by the intensive radiation field related to young stars. Even though the carriers of PAHs could be treated as types of VSG with a smaller scale, the radiation condition between PAHs and classic VSGs seems to be significantly different. The formulae to calculate the total infrared luminosity L[TIR] using L[8(dust)] and L[24] are re-scaled and we find that the L[8(dust)] (L[24]) formula likely underestimates (overestimates) L[TIR] for galaxies with unusual current star formation activity.

Abstract:
As a quenching mechanism, AGN feedback could suppress on-going star formation in their host galaxies. On the basis of a sample of galaxies selected from ALFALFA HI survey, the dependence of their HI mass M[HI], stellar mass M[*] & HI-to-stellar mass ratio M[HI]/M[*] on various tracers of AGN activity are presented and analyzed in this paper. Almost all the AGN-hostings in this sample are gas-rich galaxies, and there is no any evidence to be shown to indicate that the AGN activity could increase/decrease either M[HI] or M[HI]/M[*]. The cold neutral gas can not be fixed positions accurately just based on available HI data due to the large beam size of ALFALFA survey. In addition, even though AGN-hostings are more easily detected by HI survey compared with absorption line galaxies, these two types of galaxies show similar star formation history. If an AGN-hosting would ultimately evolve into an old red galaxy with few cold gas, then when and how the gas has been exhausted have to be solved by future hypotheses and observations.

Abstract:
We construct exceptional field theory for the duality group SL(3)$\times$SL(2). The theory is defined on a space with 8 `external' coordinates and 6 `internal' coordinates in the $(3,2)$ fundamental representation, leading to a 14-dimensional generalized spacetime. The bosonic theory is uniquely determined by gauge invariance under generalized external and internal diffeomorphisms. The latter invariance can be made manifest by introducing higher form gauge fields and a so-called tensor hierarchy, which we systematically develop to much higher degree than in previous studies. To this end we introduce a novel Cartan-like tensor calculus based on a covariant nil-potent differential, generalizing the exterior derivative of conventional differential geometry. The theory encodes the full $D=11$ or type IIB supergravity, respectively.

Abstract:
Gamma-ray bursts (GRBs) usually occurs in a dense star-forming region with massive circum-burst medium. The small-angle scattering of intense prompt X-ray emission off the surrounding dust grains will have observable consequences, and sometimes can dominate the X-ray afterglow. In most of the previous studies, only Rayleigh-Gans (RG) approximation is employed for describing the scattering process, which works accurately for the typical size of grains (with radius $a\leq 0.1\,{\rm \mu m}$) in the diffuse interstellar medium. When the size of the grains may significantly increase as in a more dense region where GRBs would occur, the RG approximation may not be valid enough for modeling detailed observational data. In order to study the temporal and spectral properties of the scattered X-ray emission more accurately with potentially larger dust grains, we provide a practical approach using the series expansions of anomalous diffraction (AD) approximation based on the complicated Mie theory. We apply our calculations to understanding the puzzling X-ray afterglow of recently observed GRB~130925A which showed a significant spectral softening. We find that the X-ray scattering scenarios with either AD or RG approximation adopted could both well reproduce the temporal and spectral profile simultaneously. Given the plateau present in early X-ray light curve, a typical distribution of smaller grains as in the interstellar medium would be suggested for GRB 130925A.

Abstract:
We develop a combinatorial approach to the construction of general smooth compact base surfaces that support elliptic Calabi-Yau threefolds. This extends previous analyses that have relied on toric or semi-toric structure. The resulting algorithm is used to construct all classes of such base surfaces $S$ with $h^{1, 1} (S) < 8$ and all base surfaces over which there is an elliptically fibered Calabi-Yau threefold $X$ with Hodge number $h^{2, 1} (X) \geq 150$. These two sets can be used todescribe all 6D F-theory models that have fewer than seven tensor multiplets or more than 150 neutral scalar fields respectively in their maximally Higgsed phase. Technical challenges to constructing the complete list of base surfaces for all Hodge numbers are discussed.

Abstract:
In complex environment with hybrid terrain, different regions may have different terrain. Path planning for robots in such environment is an open NP-complete problem, which lacks effective methods. The paper develops a novel global path planning method based on common sense and evolution knowledge by adopting dual evolution structure in culture algorithms. Common sense describes terrain information and feasibility of environment, which is used to evaluate and select the paths. Evolution knowledge describes the angle relationship between the path and the obstacles, or the common segments of paths, which is used to judge and repair infeasible individuals. Taken two types of environments with different obstacles and terrain as examples, simulation results indicate that the algorithm can effectively solve path planning problem in complex environment and decrease the computation complexity for judgment and repair of infeasible individuals. It also can improve the convergence speed and have better computation stability.

Abstract:
Nine diffusion couples and 32 key samples were prepared to map the phase diagram of the Ca–Mg–Zn system. Phase relations and solubility limits were determined for binary and ternary compounds using scanning electron microscopy, electron probe microanalysis and x-ray diffraction (XRD). The crystal structure of the ternary compounds was studied by XRD and electron backscatter diffraction. Four ternary intermetallic (IM) compounds were identified in this system: Ca3MgxZn15 x (4.6≤x≤12 at 335 °C, IM1), Ca14.5Mg15.8Zn69.7 (IM2), Ca2Mg5Zn13 (IM3) and Ca1.5Mg55.3Zn43.2 (IM4). Three binary compounds were found to have extended solid solubility into ternary systems: CaZn11, CaZn13 and Mg2Ca form substitutional solid solutions where Mg substitutes for Zn atoms in the first two compounds, and Zn substitutes for both Ca and Mg atoms in Mg2Ca. The isothermal section of the Ca–Mg–Zn phase diagram at 335 °C was constructed on the basis of the obtained experimental results. The morphologies of the diffusion couples in the Ca–Mg–Zn phase diagram at 335 °C were studied. Depending on the terminal compositions of the diffusion couples, the two-phase regions in the diffusion zone have either a tooth-like morphology or contain a matrix phase with isolated and/or dendritic precipitates.