Synthesis and Structure of a Molecular Zinc Phosphate [(C12H8N2Zn)2(HPO4)(H2PO4)2]

A hydrothermal reaction of a mixture of ZnCO₃, phosphoric acid, 1, 10‐phenanthroline in H₂O gave rise to large plates of a new zinc phosphate, [(C₁₂H₈N₂Zn)₂(HPO₄)(H₂PO₄)₂], I . The structure consists of ZnO₃N₂ distorted trigonal‐bipyramidal and PO₄ tetrahedral units linked through their vertices to give rise to a zero‐dimensional molecular solid (monomer). The structure of the monomer appears to be similar to the secondary building unit (SBU) 4 = 1, commonly found in many fibrous zeolites. To our knowledge, this is the first time this building unit has been isolated. The structure, with a unique composition, is stabilized by hydrogen bond interactions between the terminal —OH groups forms a one‐dimensional molecular wire and also by strong π…π interactions between the 1, 10‐phenanthroline units. Photoluminescence studies show that there is a ligand‐to‐metal charge transfer (LMCT). Crystal data: orthorhombic, space group = Fdd2 (no. 43), a = 40.4669(1), b = 7.4733(2), c = 17.4425(5)Å, V = 5274.9(2)ų, Z = 8.     

On a class of least-element complementarity problems

The present paper studies the linear complementarity problem of finding vectorsx andy inR ₊ ⁿ such thatc + Dx + y 0,b – x 0 andx ^T (c + Dx + y) = y ^T (b – x) = 0 whereD is aZ-matrix andb > 0. Complementarity problems of this nature arise, for example, from the minimization of certain quadratic functions subject to upper and lower bounds on the variables. Two least-element characterizations of solutions to the above linear complementarity problem are established first. Next, a new and direct method to solve this class of problems, which depends on the idea of least-element solution is presented. Finally, applications and computational experience with its implementation are discussed.Research partially supported by the National Science Foundation Grant MCS 71-03341 A04 and the Air Force Office of Scientific Research Contract F 44620 14 C 0079.     

Variational approximations for renormalization group transformations

Approximate recursion relations which give upper and lower bounds on the free energy are described. Optimal calculations of the free energy can then be obtained by treating parameters within the renormalization equations variationally. As an example, a particularly simple lower bound approximation which preserves the symmetry of the Hamiltonian (the one-hypercube approximation) is described. The approximation is applied to both the Ising model and the Wilson-Fisher model. At the fixed point a parameter is set variationally and critical indices are calculated. For the Ising model the agreement with the exact results atd = 2 is surprisingly good, 0.1%, and is good atd=3 and evend=4. For the Wilson-Fisher model the recursion relation is reduced to a one-dimensional integral equation which can be solved numerically givingv=0.652 atd=3, or by expansion in agreement with the results of Wilson and Fisher to leading order in . The method is also used to calculate thermodynamic functions for thed = 2 Ising model; excellent agreement with the Onsager solution is found.Supported in part by the National Science Foundation under Grants Nos. MPS73-04886A01 and GH-41512 and by the Brown University Materials Research Laboratory supported by the National Science Foundation. M.C.Y. was supported by a grant from the Scientific and Technical Research Council of Turkey.     

A New Entropy Function to Analyze Isentropic Processes of Ideal Gases with Variable Specific Heats

A new entropy function s⁺ is defined in terms of the existing entropy function s° and temperature as s⁺ = s° − R lnT to facilitate the analysis of isentropic processes of ideal gases with variable specific heats. The function s⁺ also makes it possible to calculate the entropy changes of ideal gases during processes when volume information is available instead of pressure information and the variation of specific heats with temperature is to be accounted for. The introduction of the function s⁺ eliminates the need to use the dimensionless isentropic functions relative pressure P_r and relative specific volume v_r of ideal gases and to tabulate their values. The P_r and v_r data are often confused with pressure and specific volume, with an adverse effect on the study of the second law of thermodynamics. The new s⁺ function nicely complements the existing s° function in entropy change calculations: the former is conveniently used when volume information is given while the latter is used when pressure information is available. Therefore, the introduction of the new entropy function s⁺ is expected to make a significant contribution to the thermodynamics education and research by streamlining entropy analysis of ideal gases.     

Regge Models of Proton Diffractive Dissociation Based on Factorisation and Structure Functions

Recent results by the authors on proton diffractive dissociation (single, double and central) in the low-mass resonance region with emphasis on the LHC kinematics are reviewed and updated. Based on the previous ideas that the contribution of the inelastic proton–Pomeron vertex can be described by the proton structure function, the contribution of the inelastic Pomeron–Pomeron vertex appearing in central diffraction is now described by a Pomeron structure function.     

全球治理困境与国家“再现”的最终逻辑

在全球治理危机频现和大国战略竞争加剧的背景下,“国家中心主义”回归引发了人们对经济全球化走势的担忧。本轮国家中心主义回归的逻辑是：此前自由主义全球化的过度发展导致国家功能隐退;而当全球治理状况恶化时,国家的重要性再度凸现,成为各国社会谋求自我体系安全的唯一“阀门”,民族主义、保护主义思潮亦大行其道。从中期看,未来的全球体系重建过程将充满国家中心主义与自由主义两种理性的持续角力,国家与市场的作用都将在“拉锯战”相互影响与重塑。从远期看,新型全球化将是国家与市场关系再平衡的产物,国家仍是兼具服务本民族发展及其外部性的主要工具。国家处理内外发展与治理多重挑战的“灵活度”即为评判其核心竞争力的最终标准。     

Direct Synthesis of a Dimeric Mixed-Anions Bismuth(III) Complex: Synthesis and Structural Characterization of [Bi2(Phen)4(No3)4.4I0.6]I3 (A New Dimeric Compound)

A direct synthetic method of mixing Bi(NO₃)₃ and NaI with 1,10-phenanthroline yielded red crystals of [Bi₂(phen)₄(NO₃)_4.4I_0.6]I₃. In this complex the cationic part is in fact binuclear and contains two [Bi(phen)(NO₃)_1.7I_0.3] groups linked via a bridging NO^? ₃ anion. The I^? ₃ anion was not coordinated to bismuth(III) and the lone pair of valence electrons of the bismuth(III) ions appears to be stereochemically inactive. There are two independent NO^? ₃ anions, one coordinated to bismuth but another shares a position with I^? anion. The final results of crystallography show that 40% of these positions are occupied by NO^? ₃ anions and 60% by I^? anions that are coordinated to bismuth atom in bidentate fashion (NO^? ₃) and in unidentate fashion (I^?). An interesting point is that the I^? ₃ anion was produced by direct synthetic method (Branched tube method). There is a π-π stacking interaction between the parallel aromatic rings around the Bi(III) ion.     

原子模型势理论中径向微分算符矩阵元的计算

本文推广［７，８］的工作，导出了多电子原子模型势理论中含径向微分算符的矩阵元通式，可直接用于以“速度”及“加速度”形式跃迁振子强度计算。     

关于虚拟激励法的一个注记

从具有随机频率与随机相位的随机谐和函数出发,证明了当随机频率与相位均为均匀分布而随机幅值与功率谱密度平方根成正比时,该随机过程的功率谱即精确地等于目标功率谱.进而表明:只需遍历频率区间,即可由单一谐和函数激励下的响应幅值给出响应的功率谱密度,从而揭示了虚拟激励法的物理意义.研究还表明:为了给出结构响应的功率谱密度,实际...