Killing spinors on Lorentzian manifolds

The aim of this paper is to describe some results concerning the geometry of Lorentzian manifolds admitting Killing spinors. We prove that there are imaginary Killing spinors on simply connected Lorentzian Einstein–Sasaki manifolds. In the Riemannian case, an odd-dimensional complete simply connected manifold (of dimension n≠7) is Einstein–Sasaki if and only if it admits a non-trivial Killing spinor to . The analogous result does not hold in the Lorentzian case. We give an example of a non-Einstein Lorentzian manifold admitting an imaginary Killing spinor. A Lorentzian manifold admitting a real Killing spinor is at least locally a codimension one warped product with a special warping function. The fiber of the warped product is either a Riemannian manifold with a real or imaginary Killing spinor or with a parallel spinor, or it again is a Lorentzian manifold with a real Killing spinor. Conversely, all warped products of that form admit real Killing spinors.     

On the Curvature of the Central Path of Linear Programming Theory

We prove a linear bound on the average total curvature of the central path of linear programming theory in terms of the number of independent variables of the primal problem, and independent of the number of constraints.     

燃煤烟气中As、Se、Pb的形态分布及S、Cl元素对其形态分布的影响

基于化学热力学平衡分析方法，计算分析了燃煤烟气中重金属As、Se、Pb的形态分布规律，研究了S、Cl等元素对As、Se、Pb的形态分布规律的影响。结果表明，氧化性气氛下，As以As₂O₅、As₄O₆、AsO等氧化物的形式存在；Se主要以SeO₂形式存在；Pb在1000 K以下主要是固态PbSO₄，1200 K以上为气态PbO。还原性气氛下，As在较低温度时为固态As₂S₂，900-1400 K以As₂、AsS、AsN气体共存，2000 K以上全部转化为气态AsO。Se在1100 K以下主要以气态H₂Se存在，1100 K开始生成SeS和Se₂气体，1800 K时主要是气态Se和少量气态SeO；Pb在中低温时主要是PbS，1800 K以上气态Pb为主要存在形态。S在还原性气氛下增大了AsS（g）、PbS（g）、SeS（g）的比例，氧化性气氛下对As、Se、Pb形态分布基本无影响；Cl无论在氧化还是还原气氛下对As、Se影响均较小，但对Pb的形态分布影响较大。     

Packing two disks into a polygonal environment

We consider the following problem. Given a polygon P, possibly with holes, and having n vertices, compute a pair of equal radius disks that do not intersect each other, are contained in P, and whose radius is maximized. Our main result is a simple randomized algorithm whose expected running time, on any input, is O(nlogn). This is optimal in the algebraic decision tree model of computation.     

Some Further Properties of the Accelerated Kerr-Schild Metrics

We extend the previously found accelerated Kerr-Schild metrics for Einstein-Maxwell-null dust and Einstein-Born-Infeld-null dust equations to the cases including the cosmological constant. This way we obtain the generalization of the charged de Sitter metrics in static space-times. We also give a generalization of the zero acceleration limit of our previous Einstein-Maxwell and Einstein-Born-Infeld solutions.     

The Statistical Mechanics of Semiflexible Equilibrium Polymers

We give an overview of studies of models for semiflexible, equilibrium polymers with special emphasis on our work on both lattice and continuum models for such systems. We show, principally by Monte Carlo simulations, that, once monomers self assemble to form polymers, their semiflexibility leads to nematic phases at low temperatures. Attractive wall potentials encourage the adsorption of these equilibrium polymers on surfaces. Rapid cooling leads to the formation of glasses with entangled polymers. Shear promotes nematic ordering, but, at high shear rates, this tendency decreases since the equilibrium polymers are torn apart. A version of our model in which the polymers are directed shows the polymer analog of bosonic Mott-insulating, mass-density-wave, and supersolid phases. We give a brief comparison of our work with other studies and also explore the experimental implications of our study.     

S3上阿诺德弦猜想中的变分方法

本文使用变分方法证明了三维标准切触球的标准勒让德扭结，至少存在一个弦连结适应于标准切触结构的任何选定切触形式，这部分证明了著名的阿诺德弦猜想。     

Silane photoabsorption spectra mear the Si 2p thresholds：the geometry of Si 2p excited SiH4

Based on the multiple-scattering self-consistent-field method, we have studied the photoabsorption spectra near the Si 2p thresholds of silane. According to our calculations, the clear assignments of the inner-shell photoabsorption spectra are provided. In comparison with the high-resolution experimental spectra, the geometric structure of the Si 2p-excited SiH_{4}^{**} is recommended to be of a C_{2v} symmetry. More specifically, the Si 2p-excited SiH_{4}^{**} have two bond lengths of 2.50 a.u. and another two bond lengths of 2.77 a.u., and the corresponding two bond angles are 104.0° and 112.5° respectively.     

Diameter graphs of polygons and the proof of a conjecture of Graham

We show that for an n-gon with unit diameter to have maximum area, its diameter graph must contain a cycle, and we derive an isodiametric theorem for such n-gons in terms of the length of the cycle. We then apply this theorem to prove Graham's 1975 conjecture that the diameter graph of a maximal 2m-gon (m?3) must be a cycle of length 2m−1 with one additional edge attached to it.     

HT—6M闭环反馈平衡控制系统

本文描述HT-6M托卡马克装置闭环反馈平衡控制系统的结构组成,通过对各个环节的简化,得到了有效实用的数学模型,进而分析了系统稳态和动态性能。实验结果表明,该系统运行可靠;并且,将等离子体环水平位移控制在2mm以内。