Generalized solutions of a stochastic partial differential equation

We discuss the Cauchy problem of a certain stochastic parabolic partial differential equation arising in the nonlinear filtering theory, where the initial data and the nonhomogeneous noise term of the equation are given by Schwartz distributions. The generalized (distributional) solution is represented by a partial (conditional) generalized expectation ofT(t)° _0,t ^–1 , whereT(t) is a stochastic process with values in distributions and _s,t is a stochastic flow generated by a certain stochastic differential equation. The representation is used for getting estimates of the solution with respect to Sobolev norms.Further, by applying the partial Malliavin calculus of Kusuoka-Stroock, we show that any generalized solution is aC -function under a condition similar to Hörmander's hypoellipticity condition.     

An Electrostatic Bond Energy Model for Enthalpies of Formation of Chloroalkanes in Gaseous States

An electrostatic bond energy model is formulated to fit the enthalpies of formation and dipole moments of the alkanes and chloroalkanes. In this model, the charge distributions are calculated by an electrostatic approach similar to the "MSE" method, and the enthalpy of formation of a molecule is the sum of the bond energy terms plus the electrostatic energy of the interactions between the charges on all atoms. All parameters of this model are obtained by parameterization. The calculated dipole moments for 13 chloroalkanes and enthalpies of formation for 19 alkanes and non-geminal chloroalkanes agree with the determined values very well. To calculate the enthalpies of formation of geminal chloroalkanes, a correction mainly attributed to the van der Waals interactions in the geminal substituted group, about 24 kJ/mol per pair of geminal chlorine atoms, is introduced.     

银微电极微分电位溶出分析法研究

本文首次报道了银微电极微分电位溶出分析法。用化学刻蚀法方便地制作了银微电极，用于ＤＰＳＡ具有背景值低，分辨率好、精密度及灵敏度高，在不搅拌，仅需一定酸度而酸度而无其它介质的条件下就能测试等优点，对人工试样及自来水样分析，结果令人满意。     

The initial oxidation of magnesium: an in situ study with XPS,HERDA and ellipsometry

The initial oxidation of magnesium at oxygen partial pressures between 1.3 × 10^?8 and 1.3 × 10^?5 Pa and at temperatures ranging from 273 to 550 K has been investigated in situ with X‐ray photoelectron spectroscopy (XPS), ellipsometry and high resolution elastic recoil detection analysis (HERDA). Quantitative analysis of the XPS spectra showed a clear oxygen deficiency with respect to MgO for the initial oxide. HERDA measurements confirmed this relatively low oxygen content in the thin oxide layers formed. Ellipsometry measurements showed that the electronic structure of the initially formed oxide differs significantly from that of bulk MgO. The band gap values at room temperature for the oxide layers investigated are clearly smaller than the value for bulk MgO. Copyright © 2006 John Wiley & Sons, Ltd.     

停留—催化反应速差动力学法同时测定Fe,Mo

根据Ｆｅ（Ⅲ）、Ｍｏ（Ⅵ）对Ｈ２Ｏ２氧化邻氨基酚的催化反应速率不同，结合流动注射停留技术，建立了同时测定Ｆｅ（Ⅲ）、Ｍｏ（Ⅵ）的速差动力学分光光度法．测定铁和钼的线性范围分别为０．１～２．５μｇ／ｍＬ和０．５～１５μｇ／ｍＬ．除Ｗ（Ⅵ）的允许量较小外，其它离子不干扰测定．用本法测定了合成样液中铁和钼含量，结果满意．     

Calculation of the proton affinities of polyfluorobenzenes and the activation energies for 1,2-hydrogen shifts in their carbocations

Isolated polyfluorobenzene (PFB) molecules and their protonated forms are investigated by the AM1 method with full geometry optimization. The proton affinities of PFB are estimated for different protonated positions. The proton affinity of PFB averaged over all isomers is shown to decrease monotonically as the number of fluorine atoms in the molecule increases. The relative populations of different isomers of arenonium ions (AI) formed by PFB protonation are determined. From the calculated data, the value of ⁺ for the F atom in theipso-position is estimated as 1.00. The activation energies of the 1,2-hydrogen shifts in AI are calculated. The dependences of the proton affinity and the activation energies of 1,2-hydrogen shifts on the number of halogen atoms are found to have distinct characters for PFB and polychlorobenzenes. The physical reasons for these difference are discussed.Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya, No. 11, pp. 1878–1882, November, 1993.     

Structure‐Dependent Photoinduced Electron Transfer in Fullerodendrimers with Light‐Harvesting Oligophenylenevinylene Terminals

Oligophenylenevinylene (OPV)‐terminated phenylenevinylene dendrons G1 – G4 with one, two, four, and eight “side‐arms”, respectively, were prepared and attached to C₆₀ by a 1,3‐dipolar cycloaddition of azomethine ylides generated in situ from dendritic aldehydes and N‐methylglycine. The relative electronic absorption of the OPV moiety increases progressively along the fullerodendrimer family C₆₀G1 – C₆₀G4 , reaching a 99:1 ratio for C₆₀G4 (antenna effect). UV/Vis and near‐IR luminescence and transient absorption spectroscopy was used to elucidate photoinduced energy and electron transfer in C₆₀G1 – C₆₀G4 as a function of OPV moiety size and solvent polarity (toluene, dichloromethane, benzonitrile), taking into account the fact that the free‐energy change for electron transfer is the same along the series owing to the invariability of the donor–acceptor couple. Regardless of solvent, all the fullerodendrimers exhibit ultrafast OPV→C₆₀ singlet energy transfer. In CH₂Cl₂, the OPV→C₆₀ electron transfer from the lowest fullerene singlet level (¹C₆₀*) is slightly exergonic (ΔG_CS≈0.07 eV), but is observed, to an increasing extent, only in the largest systems C₆₀G2 – C₆₀G4 with lower activation barriers for electron transfer. This effect has been related to a decrease of the reorganization energy upon enlargement of the molecular architecture. Structural factors are also at the origin of an unprecedented OPV→C₆₀ electron transfer observed for C₆₀G3 and C₆₀G4 in apolar toluene, whereas in benzonitrile, electron transfer occurs in all cases. Monitoring of the lowest fullerene triplet state by sensitized singlet oxygen luminescence and transient absorption spectroscopy shows that this level is populated through intersystem crossing and is not involved in photoinduced electron transfer.     

Mixed strategy solutions forN-person quadratic games

Mixed strategy -equilibrium points are given forN-person games with cost functions consisting of quadratic, bilinear, and linear terms and strategy spaces consisting of closed balls in Hilbert spaces. The results are applied to linear-quadratic differential games with no information and quadratic integral constraints on the control functions.This work was supported by a Commonwealth of Australia, Postgraduate Research Award.     

A central limit theorem for age- and density-dependent population processes

Consider a population consisting of one type of individual living in a fixed region with area A. In [8], we constructed a stochastic population model in which the death rate is affected by the age of the individual and the birth rate is affected by the population density P_A(t), i.e., the population size divided by the area A of the given region. In [8], we proposed a continuous deterministic model which in general is a nonlinear Volterra type integral equation and proved that under appropriate conditions the sequence P_A(t) would converge to the solution P(t) of our integral equation in the sense that

$\text{lim}\text{→∞}\text{P}\text{sup}\text{0?s?t}\text{|P}{}_{\mathrm{A}}\text{(s) ? P(s)|>ε}\text{=0}\text{for every}\text{ε > 0}$

.In this paper, we obtain a “central limit theorem” for the random element √A(P_A(t)?P(t)). We prove that under appropriate conditions √A(P_A(t)?P(t)) will converge to a Gaussian process. (See Theorem 3.4 for the explicit formula of this Gaussian process.)