RECURSIVE BAIRE CLASSIFICATION AND SPEEDABLE FUNCTIONS

Using recursive variants of Baire notions of nowhere dense and meagre sets we study the topological size of speedable and infinitely often speedable functions in a machine-independent framework. We show that the set of speedable functions is not “small” whereas the set of infinitely often speedable functions is “large”. In this way we offer partial answers to a question in [4].     

Geometry and electronic structure of a heterometallic cluster Mo<Subscript>2</Subscript>Mg<Subscript>2</Subscript> in different oxidation states of Mo: a DFT study

Reduction of tetranuclear heterometallic complex Mo₂Mg₂ was simulated using the B3LYP and PBE density functional methods. The results of geometry calculations of the initial complex [Mo^VIO₂Mg(MeOH)₂(OMe)₄]₂ and a partially reduced Mo^V complex are in good agreement with experimental data. The reduced Mo^III complex is characterized by a decrease in the binding energy of aqua ligands. Structural rearrangement of the complex with release of a coordination position at the Mo atoms requires small energy expenditure. One can assume that the reduction of the polynuclear complex causes overcrowding of its coordination sphere, which favors formation of dinitrogen complexes. Published in Russian in Izvestiya Akademii Nauk. Seriya Khimicheskaya, No. 3, pp. 441–457, March, 2008.     

等厚双层涂层材料受集中力作用的平面问题理论解

界面应力的正确评价是分析薄膜涂层材料力学特性的难题之一。利用镜像点法和Dirichlet等值性原理，本文推导了等厚双层薄膜涂层材料受表面集中力作用的平面问题理论解。该显式理论解是以固定在各镜像点上的局部坐标系下的Goursat应力函数的形式给出的。对应于高阶镜像点的应力函数，可通过递推的方法，从对应于低阶镜像点的应力函数求得，而且也易于计算机编程。随着镜像点阶数的增大，它与界面的距离也越来越大，因而相对应的应力函数对界面应力的影响越来越小。最后的算例表明，只需考虑前面有限个镜像点，便可获得足够精度的解。该理论解可作为格林函数，以求解复杂问题的理论解，也可用作边界元法的基本解，提高数值计算的精度和效率。     

A fourth‐order compact finite difference scheme for the steady stream function–vorticity formulation of the Navier–Stokes/Boussinesq equations

A fourth‐order compact finite difference scheme on the nine‐point 2D stencil is formulated for solving the steady‐state Navier–Stokes/Boussinesq equations for two‐dimensional, incompressible fluid flow and heat transfer using the stream function–vorticity formulation. The main feature of the new fourth‐order compact scheme is that it allows point‐successive overrelaxation (SOR) or point‐successive underrelaxation iteration for all Rayleigh numbers Ra of physical interest and all Prandtl numbers Pr attempted. Numerical solutions are obtained for the model problem of natural convection in a square cavity with benchmark solutions and compared with some of the accurate results available in the literature. Copyright © 2003 John Wiley & Sons, Ltd.     

Failure of the Quasiparticle Picture of X-ray Absorption?

The Golden rule expression for x-ray absorption spectra (XAS) is typically calculated within a one-particle (quasiparticle) approximation and generally leads to good agreement between theory and experiment. The fact that a quasiparticle approximation works fairly well is surprising, since it neglects satellite excitations and intrinsic losses due to a suddenly created core-hole. The resolution of this paradox requires physics beyond the independent particle approximation. This is discussed here using an effective Green's function formulation based on a quasi-boson model that takes interference between inelastic losses into account. This approach shows that inelastic excitations such as multi-electron excitations tend to be suppressed, and that the XAS is given by a broadened quasiparticle particle approximation, together with weak satellite structure and edge singularity effects.     

NMR studies on a palladium(II) complex containing an incompletely coordinated facultative pentadentate Schiff base ligand

Palladium(II) dichloride reacts with 1,10‐bis(2‐pyrrolyl)‐2,5,9‐triaza‐1,9‐decadiene to give a [Pd(C₁₅H₂₀N₅)]Cl complex in which the ligand is four‐coordinated, leaving one pyrrole group dangling. By using COSY, gHSQC, gHMBC connectivities and NOE experiments it has been concluded that one linkage isomer exists in DMSO solution, in spite of the fact that different sets of N atoms of potentially pentadentate ligand might be involved in coordination, and that the three chelate rings in the complex cation are arranged in a sequence: five‐membered, six‐membered, five‐membered which is different from that (5–5–6) found by x‐ray studies on the related [Ni(C₁₅H₂₀N₅)]Cl compound. NMR studies allowed an unambiguous assignment of all ¹H and ¹³C NMR resonances for the complex. Results of x‐ray structural analysis of [Pd(C₁₅H₂₀N₅)](CH₃COO)H₂O supported the five‐membered, six‐membered, five‐membered ring sequence in the [Pd(C₁₅H₂₀N₅)]⁺ complex cation and show an E (trans) orientation of the dangling pyrrole group with respect to the metal center. Copyright © 2002 John Wiley & Sons, Ltd.     

AGS能量下π~－π~－的Bose—Einstein关联

全同粒子间的玻色－爱因斯坦关联可以用来研究相对论性核碰撞中次级粒子源分布及有关的物理问题．本文用强子级联模型（ＨＣＭ）模拟２８Ｓｉ（１４．６ＡＧＣＶ／ｃ）＋Ａｕ反应，得到π－粒子的ｆｒｅｅｚｅ－ｏｕｔ状态，进而计算了π－π－关联函数，取得与实验一致的结果．还计算了ｆｒｅｅｚｅ—ｏｕｔπ－源的均方根线度，并讨论了它与拟合方法抽取的源参数间的关系．     

Statistical approach to light scattering from deformed textured heterogeneous polymer materials

A statistical theory of light scattering from deformed isotropic and textured heterogeneous polymer materials is formulated. Two types of textured structures are analyzed: assemblies of optically isotropic and anisotropic rods and a spatially anisotropic distribution of isotropic spherical inclusion centers. The small-angle H_v light-scattering patterns are calculated. The appearance of scattering from isotropic rods and spheres in deformed materials has been demonstrated. The changes of the H_v scattering patterns as a function of elongation and strucuture parameters are discussed. © 1993 John Wiley & Sons, Inc.     

Spectral shift function and trace formula

The complete proofs of Krein’s theorem on the spectral shift function and the trace formula are given for a pair of self-adjoint operators such that either (i) their difference is trace-class or (ii) the difference of their resolvents is trace-class. The proofs, essentially due to Krein, is based on Herglotz’s theorem on the boundary value of the analytic functions whose imaginary part is non-negative on the upper half plane, and an almost optimal class of functions are obtained for which the trace formula is valid. Also an alternative method based on Weyl-von Neumann’s theorem for self-adjoint operators, avoiding the complex function theory and inspired by Voiculescu’s work, is given for the first case. Furthermore, some applications of the spectral shift function have been discussed.     

Syntheses,crystal structures and blue emission of three zinc(II) coordination polymers with a 4,4′‐dicarboxybiphenyl sulfone ligand

Three novel zinc complexes [Zn(dbsf)(H₂O)₂] ( 1 ), [Zn(dbsf)(2,2′‐bpy)(H₂O)]·(i‐C₃H₇OH) ( 2 ) and [Zn(dbsf)(DMF)] ( 3 ) (H₂dbsf = 4,4′‐dicarboxybiphenyl sulfone, 2,2′‐bpy = 2,2′‐bipyridine, i‐C₃H₇OH = iso‐propanol, DMF = N,N‐dimethylformamide) were first obtained and characterized by single crystal X‐ray crystallography. Although the results show that all the complexes 1–3 have one‐dimensional chains formed via coordination bonds, unique three‐dimensional supramolecular structures are formed due to different coordination modes and configuration of the dbsf^2? ligand, hydrogen bonds and π–π interactions. Iso‐propanol molecules are in open channels of 2 while larger empty channels are formed in 3 . As compared with emission band of the free H₂dbsf ligand, emission peaks of the complexes 1–3 are red‐shifted, and they show blue emission, which originates from enlarging conjugation upon coordination. Copyright © 2006 John Wiley & Sons, Ltd.