线性泛函方程解的振动性的新结果

本文研究高阶泛函方程x(g(t))=P(t)x(t)+Q1(t)x(g2(t))+…+Qk(t)x(gk+1(t))解的振动性,得到了一些新的振动条件.改进和推广了已有结果.     

Spin polarization effect for Tc2 molecule

Density functional method (DFT) (B3p86) of Gaussian98 has been used to optimize the structure of the Tc_2 molecule. The result shows that the ground state for Tc_2 molecule is an 11-multiple state and its electronic configuration is {}^{11}Σ_g^-, which shows the spin polarization effect of Tc_2 molecule of a transition metal element for the first time. Meanwhile, we have not found any spin pollution because the wavefunction of the ground state does not mingle with wavefunctions of higher energy states. So, that the ground state for Tc_2 molecule is an 11-multiple state is indicative of the spin polarization effect of Tc_2 molecule of a transition metal element: that is, there exist 10 parallel spin electrons. The non-conjugated electron is greatest in number. These electrons occupy different spacious tracks, so that the energy of Tc_2 molecule is minimized. It can be concluded that the effect of parallel spin of the Tc_2 molecule is larger than the effect of the conjugated molecule, which is obviously related to the effect of electron d delocalization. In addition, the Murrell--Sorbie potential functions with the parameters for the ground state {}^{11}Σ_g^- and other states of Tc_2 molecule are derived. Dissociation energy D_e for the ground state of T_{c2} molecule is 2.266eV, equilibrium bond length R_e is 0.2841nm, vibration frequency ω_e is 178.52cm^{-1}. Its force constants f_2, f_3, and f_4 are 0.9200aJ·nm^{-2}, --3.5700aJ·nm^{-3}, 11.2748aJ·nm^{-4} respectively. The other spectroscopic data for the ground state of Tc_2 molecule ω_eχ_e, B_e, α_e are 0.5523cm^{-1}, 0.0426cm^{-1}, 1.6331×10^{-4}cm^{-1} respectively.     

Novel,biodegradable, functional poly(ester‐carbonate)s by copolymerization of trans‐4‐hydroxy‐L‐proline with cyclic carbonate bearing a pendent carboxylic group

Water‐soluble poly(ester‐carbonate) having pendent amino and carboxylic groups on the main‐chain carbon is reported for the first time. This article describes the melt ring‐opening/condensation reaction of trans‐4‐hydroxy‐N‐benzyloxycarbonyl‐L ‐proline (N‐CBz‐Hpr) with 5‐methyl‐5‐benzyloxycarbonyl‐1,3‐dioxan‐2‐one (MBC) at a wide range of molar fractions. The influence of reaction conditions such as catalyst concentration, polymerization time, and temperature on the number average molecular weight (M_n) and molecular weight distribution (M_w/M_n) of the copolymers was investigated. The polymerizations were carried out in bulk at 110 °C with 3 wt % stannous octoate as a catalyst for 16 h. The poly(ester‐carbonate)s obtained were characterized by Fourier transform infrared spectroscopy, ¹H NMR, differential scanning calorimetry, and gel permeation chromatography. The copolymers synthesized exhibited moderate molecular weights (M_n = 6000–14,700 g mol^?1) with reasonable molecular weight distributions (M_w/M_n = 1.11–2.23). The values of the glass‐transition temperature (T_g) of the copolymers depended on the molar fractions of cyclic carbonate. When the MBC content decreased from 76 to 12 mol %, the T_g increased from 16 to 48 °C. The relationship between the poly(N‐CBz‐Hpr‐co‐MBC) T_g and the compositions was in approximation with the Fox equation. In vitro degradation of these poly(N‐CBz‐Hpr‐co‐MBC)s was evaluated from weight‐loss measurements and the change of M_n and M_w/M_n. Debenzylation of 3 by catalytic hydrogenation led to the corresponding linear poly(ester‐carbonate), 4 , with pendent amino and carboxylic groups. © 2004 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 42: 2303–2312, 2004     

氟代吡啶阳离子的理论研究

利用量子化学密度泛函理论B3LYP方法及 6 31G(d ,p)、6 311G(d ,p)、6 31+G(d ,p)和 6 311+G(d ,p)基组对五氟代吡啶、2 ,6 二氟代吡啶和 2 氟代吡啶分子的阳离子进行了计算研究 .B3LYP构型优化和频率分析计算结果表明这三种氟代吡啶阳离子的结构分别具有C2v、C2v和Cs 对称性 ,电子基态分别为2 A2 、2 A2 和2 A″ .对离子和分子的计算构型做了比较 .利用B3LYP方法和不同的基组对这三种阳离子及其分子进行了自然布居分析计算 .用B3LYP方法对这三种阳离子 (自由基 )中的超精细结构进行了计算 ,对五氟代吡啶、2 ,6 二氟代吡啶和2 氟代吡啶分子的垂直电离势和绝热电离势进行了计算 ,与实验值符合得很好     

Moments of an exponential functional of random walks and permutations with given descent sets

The exponential functional of simple, symmetric random walks with negative drift is an infinite polynomial Y = 1 + ξ₁ + ξ₁ξ₂ + ξ₁ξ₂ξ₃ + ⋯ of independent and identically distributed non-negative random variables. It has moments that are rational functions of the variables μ _k = E(ξ ^k ) < 1 with universal coefficients. It turns out that such a coefficient is equal to the number of permutations with descent set defined by the multiindex of the coefficient. A recursion enumerates all numbers of permutations with given descent sets in the form of a Pascal-type triangle. This revised version was published online in August 2006 with corrections to the Cover Date.     

Local adsorption sites and bondlength changes in Ni(1 0 0)/H/CO and Ni(1 0 0)/CO

The local adsorption geometry of CO adsorbed in different states on Ni(1 0 0) and on Ni(1 0 0) precovered with atomic hydrogen has been determined by C 1s (and O 1s) scanned-energy mode photoelectron diffraction, using the photoelectron binding energy changes to characterise the different states. The results confirm previous spectroscopic assignments of local atop and bridge sites both with and without coadsorbed hydrogen. The measured Ni–C bondlengths for the Ni(1 0 0)/CO states show an increase of 0.16 ± 0.04 Å in going from atop to bridge sites, while comparison with similar results for Ni(1 1 1)/CO for threefold coordinated adsorption sites show a further lengthening of the bond by 0.05 ± 0.04 Å. These changes in the Ni–CO chemisorption bondlength with bond order (for approximately constant adsorption energy) are consistent with the standard Pauling rules. However, comparison of CO adsorbed in the atop geometry with and without coadsorbed hydrogen shows that the coadsorption increases the Ni–C bondlength by only 0.06 ± 0.04 Å, despite the decrease in adsorption energy of a factor of 2 or more. This result is also reproduced by density functional theory slab calculations. The results of both the experiments and the density functional theory calculations show that CO adsorption onto the Ni(1 0 0)/H surface is accompanied by significant structural modification; the low desorption energy may then be attributed to the energy cost of this restructuring rather than weak local bonding.     

On a Class of Functionals Whose Local Minima are Global

In this note we introduce a suitable class of functionals, including the class of integral functionals, and prove that any (strict) local minimum of a functional of this class, defined on a decomposable space, is a (strict) global minimum. So, the recent result obtained by Giner in [1] is specified and extended.     

一阶非线性时滞微分方程解的振动性

本文通过使用化多时滞为单时滞的技巧，研究了一类广泛的非线性泛函微分方程解的振动性，所得结果包含和改进了Hunt，Yorke等多人的结果．     

Quadratic Functionals with General Boundary Conditions

The purpose of this paper is to give the Reid ``Roundabout Theorem' for quadratic functionals with general boundary conditions. In particular, we describe the so-called coupled point and regularity condition introduced in [16] in terms of Riccati equation solutions. Accepted 27 February 1996     

具连续分布滞量的非线性中立型抛物偏泛函微分方程的振动性

考虑一类具连续分布滞量的非线性中立型抛物偏泛函微分方程解的振动性,借助Green定理和时滞微分不等式获得了这类方程在Robin,Dirichlet边值条件下所有解振动的若干充分条件.