Coxeter complexes and graph-associahedra

Given a graph Γ, we construct a simple, convex polytope, dubbed graph-associahedra, whose face poset is based on the connected subgraphs of Γ. This provides a natural generalization of the Stasheff associahedron and the Bott-Taubes cyclohedron. Moreover, we show that for any simplicial Coxeter system, the minimal blow-ups of its associated Coxeter complex has a tiling by graph-associahedra. The geometric and combinatorial properties of the complex as well as of the polyhedra are given. These spaces are natural generalizations of the Deligne-Knudsen-Mumford compactification of the real moduli space of curves.     

氪灯和氙灯光谱强度分布和光谱效率测量

氪灯、氙灯光谱强度分布和光谱效率测量是反映氪灯、氙灯性能的关键指标。介绍了一套新型的氪灯、氙灯光谱强度分布和光谱效率检测系统。该系统是一套测量连续发光灯和脉冲闪光灯发光性能及效果的综合检测设备。该检测单元采用计算机进行操控,人机界面良好,便于检验人员进行氪灯和氙灯光谱强度分布和光谱效率的批量检测。检验人员利用该系统可进行装机模拟试验和可靠性试验,可对氪灯和氙灯的性能进行必要的分析研究,不断地积累了氪灯和氙灯的检验数据和经验。     

A comparative study of the structure and crystallization of bulk metallic amorphous rod Pr60Ni30Al10 and melt-spun metallic amorphous ribbon Al87Ni10Pr3

Pr-based bulk metallic amorphous （BMA） rods （Pr60Ni30Al10） and Al-based amorphous ribbons （Al87Ni10Pr3） have been prepared by using copper mould casting and single roller melt-spun techniques, respectively. Thermal parameters deduced from differential scanning calorimeter （DSC） indicate that the glass-forming ability （GFA） of Pr60Ni30Al10 BMA rod is far higher than that of Al87Ni10Pr3 ribbon. A comparative study about the differences in structure between the two kinds of glass-forming alloys, superheated viscosity and crystallization are also made. Compared with the amorphous alloy Al87Ni10Pr3, the BMA alloy Pr60Ni30Al10 shows high thermal stability and large viscosity, small diffusivity at the same superheated temperatures. The results of x-Ray diffraction （XRD） and transmission electron microscope （TEM） show the pronounced difference in structure between the two amorphous alloys. Together with crystallization results, the main structure compositions of the amorphous samples are confirmed. It seems that the higher the GFA, the more topological type clusters in the Pr-Ni-Al amorphous alloys, the GFAs of the present glass-forming alloys are closely related to their structures.     

静态球对称黑洞Dirac场的统计熵

利用改进的brickwall模型,给出了一类静态球对称黑洞Dirac场的熵,结果表明,在取相同的截断因子时,Dirac场的熵均为标量场的熵的72倍 关键词： 黑洞 统计熵 brickwall模型 Dirac场     

Tagging of the Magnetization with the Transition Zones of 360° Rotations Generated by a Tandem of Two Adiabatic DANTE Inversion Sequences

A new technique is presented for generating myocardial tagging using the signal intensity minima of the transition zones between the bands of 0° and 360° rotations, induced by a tandem of two adiabatic delays alternating with nutations for tailored excitation (DANTE) inversion sequences. With this approach, the underlying matrix corresponds to magnetization that has experienced 0° or 360° rotations. The DANTE sequences were implemented from adiabatic parent pulses for insensitivity of the underlying matrix to B₁ inhomogeneity. The performance of the proposed tagging technique is demonstrated theoretically with computer simulations and experimentally on phantom and on the canine heart, using a surface coil for both RF transmission and signal reception. The simulations and the experimental data demonstrated uniform grid contrast and sharp tagging profiles over a twofold variation of the B₁ field magnitude.     

Every diassociative A-loop is Moufang

An A-loop is a loop in which every inner mapping is an automorphism. A problem which had been open since 1956 is settled by showing that every diassociative A-loop is Moufang.

     

The Linear Fokker-Planck Equation for the Ornstein-Uhlenbeck Process as an (Almost) Nonlinear Kinetic Equation for an Isolated N-Particle System

It is long known that the Fokker-Planck equation with prescribed constant coefficients of diffusion and linear friction describes the ensemble average of the stochastic evolutions in velocity space of a Brownian test particle immersed in a heat bath of fixed temperature. Apparently, it is not so well known that the same partial differential equation, but now with constant coefficients which are functionals of the solution itself rather than being prescribed, describes the kinetic evolution (in the N→∞ limit) of an isolated N-particle system with certain stochastic interactions. Here we discuss in detail this recently discovered interpretation. An erratum to this article can be found at     

Constructing Invariant Fairness Measures for Surfaces

The paper proposes a rational method to derive fairness measures for surfaces. It works in cases where isophotes, reflection lines, planar intersection curves, or other curves are used to judge the fairness of the surface. The surface fairness measure is derived by demanding that all the given curves should be fair with respect to an appropriate curve fairness measure. The method is applied to the field of ship hull design where the curves are plane intersections. The method is extended to the case where one considers, not the fairness of one curve, but the fairness of a one parameter family of curves. Six basic third order invariants by which the fairing measures can be expressed are defined. Furthermore, the geometry of a plane intersection curve is studied, and the variation of the total, the normal, and the geodesic curvature and the geodesic torsion is determined.     

Bis(μ6‐cis‐2,4,6,8,10,12,14,16‐octa­methyl­cyclo­octa­siloxane‐2,4,6,8,10,12,14,16‐octolato)octa­kis[(dimethyl­formamide)copper(II)] dimethyl­formamide solvate enclosing a pyrazine mol­ecule

The title compound, [Cu₈(C₈H₂₄O₂Si)₂(C₃H₇NO)₈]·C₄H₄N₂·C₃H₇NO, features a sandwich‐like cage enclosing a pyrazine mol­ecule, both situated on a centre of inversion. In addition, the crystal structure contains one dimethyl­formamide mol­ecule which is disordered over a centre of inversion. The copper layer, containing eight atoms, is located between two siloxanolate fragments. The whole structure of Cu atoms and siloxanolate rings is distorted by the pyrazine mol­ecule, leading to an oval form. As a result, the angles between the Cu atoms differ at the copper layer. The difference in the angles could lead to some deviations in the Cu–Cu exchange inter­actions within the copper ring, which is of inter­est for mol­ecular magnetism.