LiCl急冷玻璃形成过程中局部结构的分子动力学模拟——基于周期性边界条件的Voronoi多面体计算

我们建立的在周期性边界条件下由定义直接构算模拟立方元胞中各粒子Voronoi多面体的逐次切割法,以及对熔融LiCl在急冷过程的四个温度下共二万余个Voronoi多面体的面数、体积、侧面多边形、侧面面积等信息的统计分析结果。讨了退化和非退化的Voronoi多面体与计算精度的关系。计算清楚地表明,不同的相具有不同的局部结构特征。特别值得注意的是在298K,系统的Voronoi多面体分布极为集中。文中还根据Voronoi多面体的信息计算了各温下Li~+离子和Cl~-离子的配位数和配位数的组成。     

Synthesis and Uncommon Structural Characterization of Novel Zinc and Cadmium Complexes with Imino Nitroxide Radical

Two novel complexes {[Zn(IM4py)2(tp)(H2O)]·2H2O}n 1 and {[Cd(IM4py)2(tp)- (H2O)]·1.25H2O}n 2 (IM4py = 2-(4'-pyridinyl)-4,4,5,5-tetramethylimidazoline-1-oxyl and tp = terephthalate dianion) have been synthesized and characterized by elemental analyses, IR spectrum and single-crystal X-ray diffraction. Crystal data for complex 1: monoclinic, space group C2/c, a = 20.648(7), b = 12.130(4), c = 14.036(4) , β = 106.351(5)o, C32H42N6O9Zn, Mr = 720.09, V = 3373.3(2) 3, Z = 4, Dc = 1.418 g/cm3, μ(MoKα) = 0.790 mm-1, F(000) = 1512, the final R = 0.0407 and wR = 0.0894 for 3480 independent reflections with Rint = 0.0432. Crystal data for complex 2: monoclinic, space group C2/c, a = 21.332(6), b = 12.063(3), c = 14.246(4) , β = 106.704(4)o, C32H40.50N6O8.25Cd, Mr = 753.60, V = 3511.2(2) 3, Z = 4, Dc = 1.426 g/cm3, μ(MoKα) = 0.679 mm-1, F(000) = 1554, the final R = 0.0419 and wR = 0.0961 for 3627 independent reflections with Rint = 0.0440. The framework structures of complexes 1 and 2 are 3-D networks via the hydrogen bonds among 1-D chains. The notable characteristics of the two complexes are that the coordination polyhedron of Zn(II) adopts a rare distorted five-coordinate square pyramidal geometry in 1, and the Cd(II) complex exhibits an unusual distorted seven-coordinate pentagonal bipyramid in 2.     

How tight is the corner relaxation?

Given a mixed-integer linear programming (MILP) model and an optimal basis of the associated linear programming relaxation, the Gomory’s corner relaxation is obtained by dropping nonnegativity constraints on the basic variables. Although this relaxation received a considerable attention in the literature in the last 40 years, the crucial issue of evaluating the practical quality of the corner-relaxation bound was not addressed so far. In the present paper we report, for the first time, the optimal value of the corner relaxation (in two possible variants) for a very large set of MILP instances from the literature, thus providing a missing yet very important piece of information about the practical relevance of this relaxation. The outcome of our experiments is that the corner relaxation often gives a tight approximation of the integer hull, the main so for MILPs with general-integer variables—the approximation tends to be less satisfactory when a consistent number of binary variables exists.     

Compact almost automorphic solutions to semilinear Cauchy problems with non-dense domain

In this work we study the existence and uniqueness of compact almost automorphic solutions to a first-order differential equation with a linear part dominated by a Hille-Yosida type operator with non dense domain.     

Asymptotic expansion of the one-loop approximation of the Chern–Simons integral in an abstract Wiener space setting

In an abstract Wiener space setting, we construct a rigorous mathematical model of the one-loop approximation of the perturbative Chern–Simons integral, and derive its explicit asymptotic expansion for stochastic Wilson lines.     

Cuts, matrix completions and graph rigidity

This paper brings together several topics arising in distinct areas: polyhedral combinatorics, in particular, cut and metric polyhedra; matrix theory and semidefinite programming, in particular, completion problems for positive semidefinite matrices and Euclidean distance matrices; distance geometry and structural topology, in particular, graph realization and rigidity problems. Cuts and metrics provide the unifying theme. Indeed, cuts can be encoded as positive semidefinite matrices (this fact underlies the approximative algorithm for max-cut of Goemans and Williamson) and both positive semidefinite and Euclidean distance matrices yield points of the cut polytope or cone, after applying the functions 1/π arccos(.) or √. When fixing the dimension in the Euclidean distance matrix completion problem, we find the graph realization problem and the related question of unicity of realization, which leads to the question of graph rigidity. Our main objective here is to present in a unified setting a number of results and questions concerning matrix completion, graph realization and rigidity problems. These problems contain indeed very interesting questions relevant to mathematical programming and we believe that research in this area could yield to cross-fertilization between the various fields involved.     

多面体共替代对Sr_2(Al_(1–x) Mg_x)(Al_(1–x) Si_(1+x))O_7:Eu~(2+)晶体结构和发光颜色的影响

采用高温固相法合成Sr_(1.98)(Al_(1–x) Mg_x)(Al_(1–x) Si_(1+x))O_7: 2%Eu~(2+)荧光粉完全固溶体,利用X射线衍射、光致发光光谱和光学显微镜进行晶体结构和发光性能的研究. Sr_2Al_2SiO_7和Sr_2MgSi_2O_7同构化合物中包含[MgO_4]、[SiO_4]和[AlO_4]四面体,较大体积的[MgO_4]和较小体积的[SiO_4],共同替代体积相似的[AlO_4],导致[(Si/Al)O_4]收缩和[(Mg/Al)O_4]膨胀,晶胞参数c减少, a和V增大,使Eu~(2+)周围的环境发生改变,晶体场劈裂程度减小,发射峰位从503 nm蓝移至467 nm,实现发光光谱从绿色(0.2384, 0.3919)到蓝色(0.1342,0.1673)的转变.当x为0时,发射峰的半高宽为120 nm, x从0.25增加到1时,半高宽由89 nm逐渐减小至50 nm,多面体的替代会改变荧光粉的发光性能.     

Lp Sobolev regularity of averaging operators over hypersurfaces and the Newton polyhedron

$L^p$ to $L_{\beta }^p$ boundedness results are proven for translation invariant averaging operators over hypersurfaces in Euclidean space. The operators can either be Radon transforms or averaging operators with multiparameter fractional integral kernel. In many cases, the amount $\beta >0$ of smoothing proven is optimal up to endpoints, and in such situations this amount of smoothing can be computed explicitly through the use of appropriate Newton polyhedra.     

Prospective teachers’ unified understandings of the structure of identities

United States curriculum standards advise mathematics teachers to teach students to attend to structure and understand how mathematical concepts are related. This requires teachers to have a structural perspective and a coherent, unified understanding of mathematical structures that span curricula. This study explores Prospective Secondary Mathematics Teachers’ (PSMTs) unified understandings of identities and characterizes the structural features of identities that PSMTs attend to. I contribute a theoretical framework of three ways in which PSMTs reason about identities: a do-nothing element, a result of undoing something, and a coordination with inverse, binary operation, and set. I classify the level of coherence of their identity schemas demonstrated as they reasoned about the structural connections among additive, multiplicative, and compositional identities. I illustrate how having unified, coherent understandings of identities can lead PSMTs to reason productively about inverse and identity functions, while having incoherent understandings of identities can lead to inaccurate reasoning about inverse and identity functions. I conclude with teaching implications for fostering PSMTs’ unified understandings of algebraic concepts.