基于不确定控制理论的最优策略研究

本文在不确定理论的框架下,研究一类带背景状态变量的最优控制模型.在乐观值准则下,利用不确定动态规划的方法,证明了不确定最优性原则,得到最优性方程.作为应用,求解一个固定缴费(DC)型养老金的最优投资策略问题,在乐观值准则下,以工资变量为背景状态变量,建立养老金模型.通过求解不确定最优性方程得到最优投资策略和最优支付率.     

零维到三维结构中三核铜自旋阻挫簇单元的磁构关系和反对称交换

量子自旋液体是最近几年刚被人们证实除铁磁体、反铁磁体之外的第三种磁性类型,因其有望解释高温超导的运行机制、改变计算机硬盘信息存储方式而在物理、材料等领域备受关注。自旋阻挫作为量子自旋液体的最小单元可能是解开量子自旋液体诸多问题的钥匙,所以在磁学、电学研究领域再一次成为人们研究的热点。基于文献报道的三核铜配合物[Cu3(μ3-OH)(μ-OPz)3(NO3)2(H2O)2]·CH3OH(1),我们合成了三维金属有机框架配合物{[Ag(HOPz)Cu3(μ3-OH)(NO3)3(OPz)2Ag(NO3)]·6H2O}n(2)(HOPz=甲基(2-吡嗪基)酮肟),并从自旋阻挫的角度对二者磁性质进行对比和详细分析。磁化率数据表明自旋间有很强的反铁磁相互作用和反对称交换。通过包含各向同性和反对称交换的哈密顿算符对两者磁学数据进行拟合并研究其磁构关系,所获最佳拟合参数为:配合物1:Jav=-426 cm^-1,g⊥=1.83,g∥=2.00;配合物2:Jav=-401 cm^-1,g⊥=1.85,g∥=2.00。     

Surface of room temperature ionic liquid [bmim][PF6] studied by polarization- and experimental configuration-dependent sum frequency generation vibrational spectroscopy

Understanding and control of the surface properties such as molecular orientations are of great importance in numerous applications of ionic liquids. However, there remain discrepancies among the previous experimental and theoretical studies on the surface orientation and structures of room temperature ionic liquids(RTIL) systems. In this article, the orientation of 1-butyl-3-methylimidazolium([bmin]) cation at the air/liquid interface of a characteristic RTIL, 1-butyl-3-methylimidazolium hexafluorophosphate([bmim][PF6]), was investigated by the sum frequency generation vibrational spectroscopy(SFG-VS). Detailed polarization and experimental configuration analyses of the SFG-VS spectra showed the possibility of a small spectral splitting in the CH3 symmetric stretching region, which can be further attributed to the probable existence of multiple orientations for the interfacial [bmim] cations. In addition, the(N)–CH3 vibrations were absent, ruling out the prediction by several recent molecular dynamics simulations which state that portions of the [bmim] cations orient with a standing-up(N)–CH3 group at the ionic liquid surface. Hence, new realistic theoretical models have to be developed to reflect the complex nature of the ionic liquid surface.     

Nb(iPrNPMe2)3Fe–PMe3: A potential high reactivity heterobimetallic catalyst for acetylene cycloadditions

Alkynes cycloaddition reactions are powerful tools for constructing cyclic molecules with optimal atom efficiency, but these reactions cannot proceed at ambient temperature without transition-metal catalysts. In this work, a heterobimetallic complex featuring an Nb–Fe triple bond, Nb(ⁱPrNPMe₂)₃Fe–PMe₃, has been evaluated as the potential catalyst for acetylene cycloaddition, using density functional theory. The calculated results show that the singlet-state (i.e. ground-state) Nb(ⁱPrNPMe₂)₃Fe–PMe₃ can be applied to benzene synthesis, but is not suitable for cyclobutadiene. Benzene can be obtained easily at room temperature and is the unique product on the singlet potential surface. The irradiation of infrared-red light can drive the excitation of singlet Nb(ⁱPrNPMe₂)₃Fe–PMe₃ to its triplet state. Both benzene and cyclobutadiene can be formed on the triplet reaction potential surface due to their low energy barriers. Therefore, Nb(ⁱPrNPMe₂)₃Fe–PMe₃ is a potential high reactivity heterobimetallic catalyst for the cyclotrimerization of alkynes. In the reaction process, the catalytic active site of Nb(ⁱPrNPMe₂)₃Fe–PMe₃ moves from niobium to iron.     

Temperature effects on surface activity and application in oxidation of toluene derivatives of CTAB-SDS with KMnO4

The γ_cmc values of CTAB-SDS decrease from 63.67 mN/m at 10‡C to 36.38 mN/m at 90‡C, slightly lower than those of either CTAB or SDS. Correspondingly, the CMC of CTAB-SDS decreases almost by half. The increase of surface activity of CTAB-SDS can be attributed to the relatively weak electrostatic interaction at high temperature, which is supported by the increase of solubility of CTAB-SDS with rise in temperature. Catalytic effect on oxidation of toluene derivatives with potassium permanganate follows the order CTAB-SDS > SDS > CTAB. This is not caused by the dissociative effect of CTAB-SDS with low surface activity at low temperature, as seen from the fact that almost all oxidative products can be retrieved for different toluene derivatives and surfactants by mimicking the conditions of reaction. In the emulsifications of toluene derivatives at 90‡C, the time that turbid water layers of surfactant solutions take to become clear is the same as that of the catalytic effect on oxidation of toluene derivatives. Thus, it can be inferred that surfactants can improve the oxidation yields of toluene derivatives by increasing the contact between two reacting phases.     

An Efficient Selective Oxidation of Alcohols with Potassium Permanganate Adsorbed on Aluminum Silicate under Solvent-free Conditions and Shaking

A new procedure for the selective oxidation of alcohols to the corresponding aldehydes and ketones with potassium permanganate supported on aluminum silicate at room temperature under solvent-free conditions and shaking is reported.     

Existence of the uniformly minimum risk equivariant estimators of parameters in a class of normal linear models

In this paper, we study the existence of the uniformly minimum risk equivariant (UMRE) estimators of parameters in a class of normal linear models, which include the normal variance components model, the growth curve model, the extended growth curve model, and the seemingly unrelated regression equations model, and so on. The necessary and sufficient conditions are given for the existence of UMRE estimators of the estimable linear functions of regression coefficients, the covariance matrixV and (trV)^α, where α > 0 is known, in the models under an affine group of transformations for quadratic losses and matrix losses, respectively. Under the (extended) growth curve model and the seemingly unrelated regression equations model, the conclusions given in literature for estimating regression coefficients can be derived by applying the general results in this paper, and the sufficient conditions for non-existence of UMRE estimators ofV and tr(V) are expanded to be necessary and sufficient conditions. In addition, the necessary and sufficient conditions that there exist UMRE estimators of parameters in the variance components model are obtained for the first time.     

双掺(Tm3+,Tb3+)LiYF4激光器1.5 μm波长激光阈值分析

由速率方程推出了双掺（Tm^3 ,Tb^3 ）离子准四能级系统的激光阈值解析式，讨论了Tm^3 和Tb^3 离子之间的相互作用。分析了1.5μm波长附近的激光阈值和Tm^3 、Tb^3 离子的掺杂原子数分数及晶体长度的关系。结果表明，对于对应Tm^3 离子^3H4→^3F4跃迁的约1.5μm波长的激光，激活离子Tm^3 的掺杂原子数分数过大时，交叉弛豫作用将使系统阈值迅速增加。Tb^3 离子的加入，一方面能抽空激光下能级，起到降低阈值的作用；另一方面亦减少了激光上能级的寿命，使阈值升高。故Tb^3 离子有最佳掺杂原子数分数。对于Tm原子数分数为y=0.01的Tm:LiYF4晶体，Tb^3 离子的最佳掺杂原子数分数为0.002左右，同时表明，激光阈值与晶体长度有关。最佳晶体长度与Tm^3 、Tb^3 离子的掺杂原子数分数以及晶体的衍射损耗和吸收损耗有关。     

Comparison of stimulated-emission-pumping fluorescence dip spectrometry and conventional fluorescence spectrometry in application to supersonic jet spectrometry

Summary A supersonic jet spectrum of 9,10-dichloroanthracene is measured by stimulated-emission-pumping fluorescence dip spectrometry and conventional fluorescence spectrometry. The performance obtained is compared for these spectrometric methods, providing same information concerned with the energy level of the ground state. The former is more preferential for measurement of a high-resolution spectrum, since the spectral resolution is determined by the linewidth of the dumping laser. On the other hand, the latter is more preferential for measurement with better sensitivity at the expense of the spectral resolution, since the fluorescence throughput can be improved by increasing the slit width of the monochromator.Dedicated to Professor Dr. Wilhelm Fresenius on the occasion of his 80th birthday