Toeplitz Operators Associated to Unimodular Algebras

We introduce a class of function algebras, that we call unimodular, and study Toeplitz operators on the Hardy spaces associated to representing measures on these algebras.We show that our class of function algebras is very extensive and that a number of important results for Toeplitz operators and their associated C*-algebras extend to the very general setting we consider. Submitted: July 1. 2001.     

5′-DEOXYADENOSINE COMPLEXES WITH DIVALENT 3d METAL PERCHLORATES

Abstract

5′-deoxyadenosine (LH) complexes with divalent 3d metal perchlorates were prepared by refluxing mixtures of LH and salt in triethylorthoformate-ethylacetate. With one exception (M = Co), adducts of the types M(LH)₂(ClO₄)₂.3EtOH (M = Mn, Fe, Ni, Zn) and Cu(LH)₃(ClO₄)₂.EtOH were obtained. Ethanol is introduced to the system by hydrolysis of triethylorthoformate during the dehydration of the metal salts. Co(II) perchlorate yielded a complex involving both neutral LH and monoanionic L^? ligands, i. e., Co₂(LH)L₂(ClO₄)₂.4EtOH. An analogous Cu(II) complex, Cu₂(LH)L₂(ClO₄)₂.EtOH.3H₂O, was also obtained by refluxing substantially more dilute suspensions of LH and Cu salt, relative to the standard preparative method employed. The new complexes were characrerized as dimers or linear polymers, involving bridging bidentate N1,N7-bound LH ligands between adjacent metal ions and coordination number six. The new adducts also involve terminal N7-bound LH and EtOH ligands and ionic perchlorate, and the Co and Cu complexes a chelating N6,N7-bound L^? (monodeprotonation of the exocyclic NH₂ group) per metal ion and terminal -OClO₃ and ROH (R = Et or H) ligands.     

Gaussian basis sets for calculation of spin densities in first-row atoms

Summary The suitability of Gaussian basis sets for ab initio calculation of Fermi contact spin densities is established by application to the prototype first-row atoms B-F having open shell p electrons. Small multiconfiguration self-consistent-field wave functions are used to describe relevant spin and orbital polarization effects. Basis sets are evaluated by comparing the results to highly precise numerical grid calculations previously carried out with the same wave function models. It is found that modest contracted Gaussian basis sets developed primarily for Hartree-Fock calculations can give semiquantitative results if augmented by diffuse functions and if further uncontracted in the outer core-inner valence region.     

ADDUCTS OF THEOBROMINE WITH 3d METAL PERCHLORATES

Abstract

Adducts of theobromine (tbH) with 3d metal perchlorates (Mⁿ⁺ = Cr^3-. Mn²⁺, Fe²⁺, Fe³⁺, Co²⁺, Ni²⁺, Cu²⁺, Zn^2- I here prepared by refluxing mixtures of the Iigand and a metal salt in ethyl acetate-triethyl orthoformate. The new complexes invariably involve 2: 1 molar ratios of tbH to metal ion and are apparently monomeric with terminal tbH ligands binding riaa ring nitrogen (N9 or Nl). The Mn²⁺, Cu²⁺ and Zn^2- complexes are distorted tetrahedral, involving tuo tbH and two unidentate perchlorato ligands in the first coordination sphere of the metal ion. The remaining metal(II) complexes (Fe, Co, Ni) were obtained as monohydrates. These compounds are pentacoordinated of the [M(tbH)₂(OClO₃)₂(OH₂)] type, containing one aqua ligand in addition to the tbH and perchlorato ligands. The Cr³⁺ and Fe³⁺ complexes are low-symmetry hexacoordinated, with two tbH ligands. two unidentate and one bidentate chelating perchlorate Iigands.     

Second row transition metal mixed hydride-halide triatomic molecules

Summary The ground state structures and bond energies have been obtained for the triatomic MHX systems where M is the entire sequence of second row transition metal atoms and X is a halide. The most interesting results of this study appear when these systems are compared to the triatomic MH₂ and MX₂ systems. It turns out that the structure of the MHX systems are quite similar to the corresponding MH₂ systems in general. Most of the MHX systems to the right thus have bent low-spin ground states, indicating large covalent contributions to the bonding. RuHX is a special case and has a high-spin linear ground state. For the systems to the left ionicity dominates the bonding. An important result, with implications for halide ligand effects on carbonyl and olefin insertion into M-H and M-R bonds, is that the M-H bonds for the systems to the right have a different character and are significantly weaker for the MHX than for the MH₂ systems. A similar effect is noted when the M-Cl bond strengths of MCl₂ are compared to the ones in MHCl. Both these effects can be explained by a more cationic metal with mores ⁰-state character when halide ligands are present.     

The activation of the C-H bond in acetylene by second row transition metal atoms

Summary The C-H activation reaction of acetylene by second row transition metal atoms has been studied including electron correlation of all valence electrons. Binding energies have been computed for both -coordinated complexes and C-H insertion products. It is found that for most atoms the -coordinated complexes are thermodynamically favoured, just as in the case for the corresponding ethylene reaction. The barrier height for the C-H insertion increases from acetylene to ethylene and to methane. This is in line with the experimental finding that there should be an inverse relation between C-H bond strengths and the difficulty to activate these bonds. To explain the detailed differences between the C-H activation of acetylene and ethylene, the interaction with two, rather than one, - and *-orbitals for acetylene is of key importance. The barrier height for the acetylene reaction increases significantly between niobium and molybdenum going to the right in the periodic table, just as for all oxidative addition reactions previously studied. The origin of this increase is that noibium has one empty 4d-orbital but for molybdenum all 4d-orbitals are occupied. Rhodium has the lowest barrier for C-H activation for all systems studied.     

使用槽道平均模型的多叶片排N-S方程并行计算

1前言多叶片排三元粘性计算，正在成为压气机、涡轮设计的重要工具。与混合平面模型山相比，槽道平均模型p］能够更加精确地模拟动静叶片间相互作用。它减少了内边界信息传递积累误差，增强了计算程序的鲁棒性。国内很多单位开展了有关的研究工作［‘－’］。本文发展了使用槽道平均模型多叶片N－S方程并行计算程序，并对一多级压气机设计中间方案的前3级进行了试算。2关于槽道周向平均模型这一模型是由Ad。mCZyk［’l提出，它不但被应用于三维直接计算数值模拟，其中的一些基本概念还曾被应用于两类流面迭代平均SZ流面计算。其主要思路…     

大北窑地铁隧道顶板稳定性控制研究

分析大北窑地铁隧道饱水粉细砂层顶板的地质环境及其工程特性,用超细水泥注浆加固新工艺稳定流砂段及其扰动段的顶板。运用地质工程观点,充分利用顶板底部的粉砂薄层,用钢管加固未扰动段顶板。地面监测资料说明,本文的措施对其顶板稳定性控制非常有效。     

Z[6~(1/2)]上的正定么模格的分类

本文利用推广的邻格方法，完成了Ｚ[ ］上秩 ４判别式 １的所有正定么模格的分类．     

Characteristic Elements of Unimodular -lattices

Characteristic elements have been useful in the classification of unimodular lattices over the integers. This article gives an explicit formula for characteristic elements of a lattice in terms of a basis for the lattice and the dual of that basis.