Simulation of Wave Focusing in Cavities

Simulation results are presented for the focusing of shock waves in conical and wedge-shaped cavities. Results are reported for plane waves and explosion waves. The distribution of parameters in the focusing zone is found to depend on the specific conditions.     

Bundles, Handcuffs, and Local Freedom

We answer a question of J. Anderson's by producing infinitely many commensurability classes of fibered hyperbolic 3-manifolds whose fundamental groups contain subgroups that are locally free and not free. These manifolds are obtained by performing 0–surgery on a collection of knots with the same properties.     

Crystal Structure of Ternary Molybdate Rb5FeHf(MoO4)6 — a New Phase in the Rb2MoO4-Fe2(MoO4)3-Hf(MoO4)2 System

Physicochemical analysis (XRPA, DTA) was used to study phase equilibria in a ternary salt system Rb₂MoO₄-Fe₂(MoO₄)₃-Hf(MoO₄)₂ in the subsolidus region. Ternary molybdates with compositions 5:1:3, 5:1:2, and 1:1:1 have been found and synthesized. Crystal and thermal characteristics have been determined. Single crystals of the ternary molybdate Rb₅FeHf(MoO₄)₆ with a composition of 5:1:2 were grown. The crystal structure of the compound was solved using X-ray diffractometry (CAD-4 automatic diffractometer, MoK _α radiation, 1766 F(hkl), R = 0.0298). Hexagonal crystals with unit cell dimensions: a = b = 10.124(1) Å, c =15.135(3) Å, V = 1343.4(4) ų, Z = 2, ρ_calc = 4.008 g/cm³, space group P6₃. The mixed three-dimensional framework of the structure is formed from two sorts of MoO₄ tetrahedra and Fe and Hf octahedra linked through their common O-vertices. Rubidium atoms of three varieties occupy the large voids of the framework.Original Russian Text Copyright © 2004 by B. G. Bazarov, R. F. Klevtsova, A. D. Tsyrendorzhieva, L. A. Glinaskaya, and Zh. G. Bazarova__________Translated from Zhurnal Strukturnoi Khimii, Vol. 45, No. 6, pp. 1038–1043, November–December, 2004.     

三氟化硼引发四氢呋喃聚合的研究——Ⅳ.1,4-丁二醇的影响

前报中已证明用三氟化硼-环氧氯丙烷(ECH)引发四氢呋喃(THF)聚合具有较高的引发效率,并对在Ac_2O、水和无水存在下的聚合反应进行了研究。本文报道1,4-丁二醇(BG)对BF_3引发THF聚合反应的影响。通常认为在BG存在下,BF_3是不能引发THF聚合的,但本工作证明BG是有效的分子量调节剂,制备分子量在     

以硫醚为主链的螯合树脂研究Ⅳ．含硫代硫酸根、叠氮基树脂的合成及吸附性能

聚环硫氯丙烷或环硫氯丙烷与环氧氯丙烷共聚物，在少量二乙烯三胺存在下制得交联预聚物，将交联预聚物分别与硫代硫酸钠，叠氮化钠反应，制得四种侧链带有硫代硫酸根或叠氮基的新型螯合树脂。它们对贵金属离子具有较高的吸附容量和较好的吸附选择性。     

Synthesis and crystal structure of ternary molybdate compound K<Subscript>5</Subscript>Pb<Subscript>0.5</Subscript>Hf<Subscript>1.5</Subscript>(MoO<Subscript>4</Subscript>)<Subscript>6</Subscript>

Single crystals of triple molybdate of composition 5:1:3 K₅Pb_0.5Hf_1.5(MoO₄)₆ have been grown and their crystal structure has been solved from X-ray diffraction data (an automated diffractometer X8 APEX, MoK _α -radiation, 2173 F(hkl), R = 0.0321). Trigonal unit cell parameters are: a = b = 10.739(2) Å, c = 37.933(9) Å; V = 3789(1) ų, Z = 6, ρ_calc = 4.014 g/cm³, space group \(R\bar 3\). Three-dimensional mixed framework of the structure is formed by two types of MoO₄ tetrahedra and Pb and Hf octahedra linking via common O-vertices. Potassium atoms of three types occupy large vacancies in the framework.     

Systems Tl2MoO4-E(MoO4)2, where E = Zr or Hf, and the crystal structure of Tl8Hf(MoO4)6

Systems Tl₂MoO₄-E(MoO₄)₂ (E = Zr, Hf) are studied using X-ray powder diffraction, DTA, and IR spectroscopy. Compounds Tl₈E(MoO₄)₆ and Tl₂E(MoO₄)₂ are found in these systems. T-x diagrams for the Tl₂MoO₄-Zr(MoO₄)₂ system are designed. Single crystals are grown and structure is solved for Tl₈Hf(MoO₄)₆. The compound crystallizes in a monoclinic structure with the unit cell parameters a = 9.9688(6) Å, b = 18.830(1) Å, c = 7.8488(5) Å, β = 108.538(1)°, Z = 2, space group C2/m. The main structural fragment is a [HfMo₆O₂₄]^8? isle group. Three crystallographically independent types of Tl polyhedra uniformly fill spaces between [HfMo₆O₂₄]^8? fragments to form a three-dimensional framework.     

Automatic generation of linear programming problems for computer aided instruction

The paper presents a method for generating random linear programming problems with a previously selected type of solution. The user can choose a problem whose solution is unbounded, bounded for minima, maxima or both, unique or multiple, with given structure, at wish. Initially, the feasible solution of the LPP is generated as the sum of a linear space, a cone, and a polytope, depending on the desired properties of the solution. With the aim of obtaining a simple set of constraints, the generators of these three structures are selected as random vectors with integer simple components, the range of which can be given. Next, an objective function that satisfies the required conditions, i.e. leads to a solution of the desired type, is obtained. The generating algorithms have been implemented in Mathematica and some illustrative examples are given to clarify the generation process. With this tool, a LPP can be generated, according to the instructor requirements, where this is a human or an expert system. They can control student progress and generate a sequence of problems covering all possible cases, in steps of increasing difficulty. Combining this tool with another (also produced by the same authors) that solves the problems and explains the whole process, step by step, a computer aided module for learning LPP, which is completely autonomous, can be easily obtained.     

IN AQUA SYNTHESIS OF A HIGH MOLECULAR WEIGHT ARYLETHYNYLENE POLYMER EXHIBITING REVERSIBLE HYDROGEL PROPERTIES

ABSTRACT

A high molecular weight poly(aryleneethynylene) (M_w ～ 60,000) is prepared by the palladium catalyzed copolymerization of 3,5-diiodobenzoic acid and acetylene gas in a basic aqueous medium. The polymer has a “zig-zag”, fully conjugated backbone. The polymer has been characterized by a variety of methods and exhibits high thermal stability. Furthermore, the polymer is readily soluble in aqueous base and is reversibly switchable from the solution state to a hydrogel state, in water, by changing the pH of the solvent.