线性分式规划最优解集的求法

本文使用多面集的表示定理，导出了线性分式规划最优解集的结构，并给出确定全部最优解的计算步骤。     

Luttinger liquid with asymmetric dispersion

We present an extension of the Tomonaga-Luttinger model in which left and right-moving particles have different Fermi velocities. We derive expressions for one-particle Green's functions, momentum-distributions, density of states, charge compressibility and conductivity as functions of both the velocity difference ε and the strength of the interaction β. This allows us to identify a novel restricted region in the parameter space in which the system keeps the main features of a Luttinger liquid but with an unusual behavior of the density of states and the static charge compressibility κ. In particular κ diverges on the boundary of the restricted region, indicating the occurrence of a phase transition. Received 20 May 2002 / Received in final form 23 August 2002 Published online 19 November 2002     

Winning controllers and regions in competitive nonlinear dynamic games with two qualitative objectives and uncertain information

The Liapunov technique has been introduced in differential games in a sequence of works over the last decade. We discuss application of this technique to the interface between two competitive semi-games, each with different qualitative objective. The feedback information for controllers is provided from designed, analytically integrable state predictors with reduced dynamics, which considerably shortens the computing time. The case is illustrated on the scenario of target reaching before being intercepted, and intercepting before target is reached.Deceased.     

An analysis of reduced Hessian methods for constrained optimization

We study the convergence properties of reduced Hessian successive quadratic programming for equality constrained optimization. The method uses a backtracking line search, and updates an approximation to the reduced Hessian of the Lagrangian by means of the BFGS formula. Two merit functions are considered for the line search: the ₁ function and the Fletcher exact penalty function. We give conditions under which local and superlinear convergence is obtained, and also prove a global convergence result. The analysis allows the initial reduced Hessian approximation to be any positive definite matrix, and does not assume that the iterates converge, or that the matrices are bounded. The effects of a second order correction step, a watchdog procedure and of the choice of null space basis are considered. This work can be seen as an extension to reduced Hessian methods of the well known results of Powell (1976) for unconstrained optimization.This author was supported, in part, by National Science Foundation grant CCR-8702403, Air Force Office of Scientific Research grant AFOSR-85-0251, and Army Research Office contract DAAL03-88-K-0086.This author was supported by the Applied Mathematical Sciences subprogram of the Office of Energy Research, U.S. Department of Energy, under contracts W-31-109-Eng-38 and DE FG02-87ER25047, and by National Science Foundation Grant No. DCR-86-02071.     

Likelihood estimation of soft-core interaction potentials for Gibbsian point patterns

The likelihood method is developed for the analysis of socalled regular point patterns. Approximating the normalizing factor of Gibbs canonical distribution, we simultaneously estimate two parameters, one for the scale and the other which measures the softness (or hardness), of repulsive interactions between points. The approximations are useful up to a considerably high density. Some real data are analyzed to illustrate the utility of the parameters for characterizing the regular point pattern.     

Crystal Structure, Infrared Spectrum and Isotope Effect of Uranium-Crown Ether Complexes

According to the experiment results of X-ray diffraction and IR, the reduced partition function ratio (RPFR) and the contribution of various related vibration modes of uranium-crown ether complex (DCH18C6·H_3O)_2UO_2Cl_4 were theoreticallv calculated in detail. The equilibrium constant K_(eq) (that is, the single stage isotopic separation factor α) of exchange reaction for uranium isotopic chemical exchange system UO_2~(2+)(H_2O)_5—(DCH18C6.H_3O)_2UO_2Cl_4 is estimated to be 1.000746 at 12℃ and 1.000672 at 29℃, respectively, which are quite close to the experimental values 1.0010±0.0002 arid 1.0012±0.0004. Theoretical analysis shows that in the course of forming the complex of uranium with crown ether, the coordinated water of uranium is stripped, which performs a key action on the remarkable isotope effect for this system.     

硼掺杂还原态氧化石墨烯催化剂的制备及其蒽催化加氢性能的研究

制备了一系列硼掺杂的还原氧化态石墨烯催化剂并应用于蒽加氢反应。结果表明，随着催化剂处理温度的升高，催化剂中有序碳结构会发生变化，硼会取代材料骨架中的碳，进而影响蒽和氢气的吸附活化。经硼改性后，催化剂对蒽加氢反应表现出了很高的加氢活性，蒽的最高转化率可达97%，深度加氢产物八氢蒽的最高选择性可达19%。     

Reduced parabolic model for radical addition reactions

The transition state of addition of free radicals and atoms to multiple bonds is considered as a result of intersecting of two parabolic potential curves. One of them characterizes the stretching vibration of the attacked multiple bond, and another curve characterizes the stretching vibration of the bond formed in the transition state. The force constant of the latter is calculated by an empirical equation that correlates the force constant with the bond dissociation energy. In the framework of this model, the thermally neutral activation energy (E _e0) and the elongation of the attacked and formed bonds (r _e) in the transition state were calculated from the experimental data (activation energy (E _e) and enthalpy of reaction (H _e)) for the addition of an H atom and methyl, alkoxyl, aminyl, triethylsilyl, and peroxyl radicals to the C=C bond and the addition of H and CH₃ to the C=O and CC bonds. Analysis of the data obtained showed that E _e0 depends linearly on the |H _e| + E_e sum, i.e., E_e0/kJ mol^–1 = 14.2 + 0.61 · (E_e – H _e), and the bond elongation in the transition state for addition of the most part of radicals to ethylene and acetylene vary within (0.65–0.87)·10_–10 m. The factors affecting the activation energy of the radical addition reactions are discussed.Published in Russian in Izvestiya Akademii Nauk. Seriya Khimicheskaya, No. 8, pp. 1542–August, 2004.     

溶胶-凝胶法制备还原态K-Co-Mo催化剂的合成醇性能

应用溶胶-凝胶法制备了还原态K-Co-Mo催化剂, 比较了不同的组分和不同的反应条件对合成醇性能的影响。实验结果表明，适量钾和钴助剂的添加能显著提高催化剂合成醇的性能，尤其是提高了C2+醇的选择性。此外，反应温度、压力以及空速对合成醇影响明显，升高温度可以提高催化反应中低碳醇的收率，但选择性下降；增加压力和空速可以提高低碳醇的收率和选择性，对合成低碳醇有利。在230 ℃，6.0 MPa，14 400 h－1条件下，催化剂合成低碳醇的收率为375.4 g/kg·h，选择性为70.2%，C1OH/C2+OH为0.48。