Quantum Dynamics of Systems Connected by a Canonical Transformation

Quantum Hamiltonian systems corresponding to classical systems related by a general canonical transformation are considered. The differential equation to find the unitary operator, which corresponds to the canonical transformation and connects quantum states of the original and transformed systems, is obtained. The propagator associated with their wave functions is found by the unitary operator. Quantum systems related by a linear canonical point transformation are analyzed. The results are tested by finding the wave functions of the under-, critical-, and over-damped harmonic oscillator from the wave functions of the harmonic oscillator, free-particle system, and negative harmonic potential system, using the unitary operator to connect them, respectively.     

Unique continuation along curves and hypersurfaces for second order anisotropic hyperbolic systems with real analytic coefficients

In this paper we prove the following kind of unique continuation property. That is, the zero on each geodesic of the solution in a real analytic hypersurface for second order anisotropic hyperbolic systems with real analytic coefficients can be continued along this curve.

     

Second order parabolic equations in Banach spaces with dynamic boundary conditions

In this paper, we exhibit a unified treatment of the mixed initial boundary value problem for second order (in time) parabolic linear differential equations in Banach spaces, whose boundary conditions are of a dynamical nature. Results regarding existence, uniqueness, continuous dependence (on initial data) and regularity of classical and strict solutions are established. Moreover, several examples are given as samples for possible applications.

     

质子化丙酮分子团簇的结构和振动光谱

用密度泛函B3LYP/ 6 3 1G(d)方法 ,对质子化丙酮分子团簇 (CH3COCH3) nH+ (n =1～ 7)弱相互作用体系进行了全自由度能量梯度优化 ,得到了该系列团簇的稳定结构及其对应的体系能量 .通过对构型的分析得出了质子化丙酮分子团簇 (CH3COCH3) nH+ (n =1～ 7)的生长规律 .计算了中性丙酮分子团簇体系的质子亲合能并总结出其变化趋势 .分析讨论了质子化团簇的红外振动光谱 ,发现质子化团簇的振动光谱普遍较中性环型团簇的振动光谱复杂 ,最强的振动峰来源于质子在溶剂壳中两个氧原子之间的振动 ,而且随着团簇尺寸的增加羰基的伸缩振动峰的数目也随之增多     

Investigation of the Li1+xV3O8 electrode–organic electrolyte interface by scanning photoelectron microscopy

To investigate the formation of a solid electrolyte interface (SEI) on the Li_1+xV₃O₈ electrode surface in the thermodynamic stability range of the organic electrolyte, we applied scanning photoelectron microscopy (SPEM) to a pristine electrode and to an electrode after ten cycles. The F K-edge absorption spectrum of the cycled electrode showed that LiF forms on the electrode surface during the lithium insertion–extraction process in the Li_1+xV₃O₈/Li cell. The photoelectron spectrum for the cycled electrode showed intense spectral features corresponding to Li 1s, F 2s, F 2p, and P 2p electron signals, whereas these spectral features were of negligible intensity for the pristine electrode. The above results give strong support for the formation of an SEI that consists of LiF and compounds containing phosphorus during operation of the battery. The SPEM images also revealed that the fluorine distribution on the surface of the cycled electrode was inhomogeneous.     

Synthesis and adsorption properties of gold nanoparticles within pores of surface‐functional porous polymer microspheres

Mesoporous polymer microspheres with gold (Au) nanoparticles inside their pores were prepared considering their surface functionality and porosity. The Au/polymer composite microspheres prepared were characterized by transmission electron microscope (TEM), X‐ray diffraction (XRD), and Brunauer–Emmett–Teller (BET) techniques. The results showed that the adsorption of Au nanoparticles could be increased by imparting the pore structure and surface‐functional groups into the supporting polymer microspheres (in this study, poly (ethylene glycol dimethacrylate‐co‐acrylonitrile) and poly (EGDMA‐co‐AN) system). Above all, from this study, it was established that the porosity of the polymer microspheres is the most important factor that determines the distribution and adsorption amount of face‐centered cubic (fcc) Au nanoparticles in the final products. Our study showed that the continuous adsorption of Au nanoparticles with the aid of the large surface area and surface interaction sites formed more favorably the Au/polymer composite microspheres. The BET measurements of Au/poly(EGDMA‐co‐AN) composite microspheres reveals that the adsorption of Au nanoparticles into the pores kept the pore structure intact and made it more porous. © 2004 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 42: 5627–5635, 2004     

高阶线性微分方程的解及其解的导数的不动点

研究了复域齐次和非齐次线性微分方程的解及其解的导数的不动点与超级问题,得到了整函数系数的齐次和非齐次线性微分方程的解及其解的导数的不动点的两个结果,所得结果推广了一些相关结果.     

Analysis on plasma chemistry and particle growth in corona discharge process for NO/sub x/ removal using discrete-sectional method

The particle formation and growth combined with plasma chemistry in the pulsed corona discharge process (PCDP) to remove NO/sub x/ were analyzed by the discrete-sectional model. In the PCDP, most of the NO is converted into NO/sub 2/ and, later, into HNO/sub 3/ which reacts with NH/sub 3/ to form the NH/sub 4/NO/sub 3/ particle. In the beginning of the reactor, we have the high concentration of small size particles and, later, the particle size distribution in the reactor becomes bimodal with the large size and small size particles and, finally, becomes monodisperse with the large size particles. As the average electron concentration increases, it takes a shorter reactor length to remove the NO/sub x/. As the initial NO and H/sub 2/O concentrations decrease, the NH/sub 3/ is consumed more slowly to form the ammonium nitrates particles. As the averaged electron concentration and initial H/sub 2/O concentration increase, the large size particles grow more quickly and the particle size distribution becomes bimodal earlier. As the initial NO and NH/sub 3/ concentrations increase, the diameter of large size particles becomes larger by the faster coagulation between particles. The predicted NO/sub x/ conversion and particle size distribution were in close agreements with the published experimental results at the averaged electron concentration of 2/spl times/10/sup 5/ cm/sup -3/ in this study.     

The effect of olefinic terminal chains on the mesomorphic properties of 4,4'-disubstituted diphenyldiacetylenes

New diphenyldiacetylenes of the type with A, B = H and/or F; m = 0, 1; n = 1-4; and X = C n H 2n + 1 , F, CF 3 or CN were synthesized and their mesomorphic properties determined by hot stage polarizing microscopy and DSC. When m = 0, all of these compounds showed only a nematic phase except when X = CF 3 when both nematic and smectic A phases were seen. Both clearing and melting temperatures were higher than those reported for substitution with the corresponding alkyl chains but the much larger increase in clearing temperatures produced considerably wider nematic phases. Eutectic mixtures of a few of these olefins yielded nematic materials also having much wider temperature ranges and higher clearing temperatures than the eutectic mixtures of the alkyl compounds, while retaining their high birefringence and low viscosities. Such materials are of interest for beam-steering devices.

Four of the diacetylenes with m = 1 ( A, B = H) were also prepared ( X = C 6 H 13 , F, n = 2, 3). When X was C 6 H 13 ( n = 2), the nematic range was smaller in the 2- than in the 1-olefin but wider than in the alkyl series. When X = F, either no nematic phase or a monotropic one was observed, whereas the 1-olefins gave a much wider nematic phase. Both transition temperatures were lower than those for the corresponding 1-olefin and alkyl analogues. The compound with X = C 6 H 13 and n = 2 had a melting temperature below room temperature.