Proof of the Fukui conjecture via resolution of singularities and related methods. II $$^{\star}$$

The present article is a direct continuation of the first part of this series. We reduce a proof of the Fukui conjecture (concerning the additivity problem of the zero-point vibrational energies of hydrocarbons) to that of a proposition related to the theory of algebraic curves, so that we can focus on the key mechanism of the additivity phenomena. Namely, by establishing what is called the Basic Piecewise Monotone Theorem (BPMT), we reduce a proof of the Fukui conjecture to that of a proposition, called the Local Analyticity Proposition, Version 1 (LAP1), which admits a proof via resolution of singularities. By LAP1, the essential part of the mechanism of the asymptotic linearity phenomena is extracted and is elucidated by using tools from the mathematical theory of algebraic curves, whose language is of vital importance in analyzing the crux of the additivity mechanism. Dedicated to the memory of Prof. Kenichi Fukui (1918–1998).     

酶的分子仿生研究进展

回顾了近几十年来印迹高分子和有机团簇对酶的仿生发展历程，总结了目前的 研究现状，探讨了电子效应和空间效应（柔性空间效应）对仿对酶在催化过程中实 现类似酶的识别和诱导契合的影响，并展望了酶的仿生发展趋势。     

γ-sets and other singular sets of real numbers

A family of $\text{J}$ of open subsets of the real line is called an ω-cover of a set X iff every finite subset of X is contained in an element of $\text{J}$. A set of reals X is a γ-set iff for every ω-cover $\text{J}$ of X there exists $\text{〈D}{}_{\mathrm{n}}\text{: n < ω〉?}\text{J}{}^{\mathrm{\omega }}$ such that

In this paper we show that assuming Martin's axiom there is a γ-set X of cardinality the continuum.     

The convergence of the Rayleigh-Ritz Method in quantum chemistry

Two sufficient criteria for the convergence of the Rayleigh-Ritz Method (RRM) with respect to the eigenvalues (E-convergence) of non-relativistic electronic Hamiltonians of molecules are discussed and compared. Moreover, a necessary and sufficient criterion is given. By example (Sect. 9) it is shown that the L ²-completeness of the basis is not sufficient to guarantee E-convergence. The convergence of the wave functions in different norms (-convergence) is also investigated. In particular, sufficient conditions for the one-particle basis functions (orbitals) are given, such that a CI calculation in this basis is both E- and -convergent.     

Synthesis and Crystal Structur of (4,4''-H2bipy)[CdBr4]·H2O

The title compound (4,4'-H2bipy)[CdBr4]·H2O 1 has been synthesized via hydrothermal reaction and characterized by X-ray diffraction. The crystal belongs to monoelinic,space group P21/c with a=8.260(3), b=23.926(7), c=9.774(2) (A), β=106.777(9)°,C10H12Br4CdN2O, Mr=608.26, V=1849.4(9)(A)3, Z=4, Dc=2.185 g/cm3, S=1.005, μ(MoKα)=9.814 mm-1, F(000)=1128, R=0.0646 and wR=0.0989. The crystal structure analysis of 1reveals that the title compound features an isolated structure, based on discrete 4,4'-H2bipy moieties and lattice water molecules which are linked by hydrogen bonds together with tetrahedral cadmium atoms terminally coordinated by four bromine atoms.     

Two-electron atomic wave functions which satisfy proportionality relations between one-and two-electron moments

Based on momentum- and position-space analyses of the moment operators for two-electron atoms, it is shown that there exists a family of two-electron wave functions which satisfy a proportionality relation, r/ ₁ ^v /r ₁₂ ^v =p/ ₁ ^v /p ₁₂ ^v =2^–v/2, between the one and two-electron moments in position and momentum spaces, where v is an arbitrary number for which the moments are well-defined.     

Length of the flooded zone in the column inlet and evaluation of different retention gaps for capillary gas chromatography

In on-column or in splitless injection with recondensation of the solvent, the length of the flooded zone in the column inlet depends primarily on the wettability of the internal wall of the inlet. For columns with a coated inlet this explains why peak distortion due to band broadening in space by a certain sample volume is pronounced in one case and hardly observable in another. Glass or fused silica capillaries silylated with diphenyltetramethyldisilazane were found to give optimal retention gaps. They combine thorough and thermostable deactivation with good wettability and low retention power. On the other hand it is very easy to deactivate fused silica capillaries with Carbowax. The resulting retention gaps are suitable for a wide range of applications and are particularly attractive for the analysis of dirty samples which require frequent replacement of the inlet.     

Understanding the conformational dependence of spin-spin coupling constants: through-bond and through-space J(31P,31P) coupling in tetraphosphane-1,4-diides [M(L)x]2[P4R4

The characteristic dependence of J(31P,31P) spin-spin coupling constants of alkali metal tetraphosphane-1,4-diides on structure and composition has been analyzed by density functional methods. The computations confirm that the structure of the contact ion pairs is conserved in solution. Calculations on model systems M2P4H4, on naked P4H4(2-) anions, and on models including point charges, show that the role of the cations is mainly structural and to a smaller extent electrostatic. Three of the four J(P,P) coupling constants depend characteristically on the conformation of the anion, which in turn is determined by the substituents R and by cation-anion interactions. Several couplings exhibit a large through-space component and are thus strongly dependent on the relative orientation of nonbonding electron pairs on the phosphorus atoms involved. This is shown by visualization of coupling pathways using the recently introduced coupling energy density (CED), in combination with the electron localization function (ELF).     

有限线性扩散区域内EC＇反应催化电流

有限线性扩散区域内ＥＣ＇反应催化电流吴志斌，董绍俊，吴浩青（同济大学化学系，上海，２０００９２）（中国科学院长春应用化学研究所）（复旦大学化学系）关键词有限线性扩散空间，ＥＣ＇反应，催化电流化学修饰电极等有关膜电极及薄层池的电极过程动力学问题均涉及到...