Duality and existence theory for nondifferentiable programming

Necessary and sufficient conditions of optimality are given for a nonlinear nondifferentiable program, where the constraints are defined via closed convex cones and their polars. These results are then used to obtain an existence theorem for the corresponding stationary point problem, under some convexity and regularity conditions on the functions involved, which also guarantee an optimal solution to the programming problem. Furthermore, a dual problem is defined, and a strong duality theorem is obtained under the assumption that the constraint sets of the primal and dual problems are nonempty.     

Enhancement of spectral intensities of mercury triplet lines in longitudinal magnetic field

The variation of intensity of the spectral lines of the triplet series of mercury namely (7³ S ₁ → 6³ P ₀₁₂) (λ5461 Å,λ 4358 Å,λ 4047 Å) in the presence of a longitudinal magnetic field between zero and 2000 gauss has been investigated. The effect of magnetic field is found to be different as regards the variation of intensity and the occurrence of maxima in the three lines. These variations can be explained by considering the reabsorption of the spectral lines. A mathematical theory has been presented and an expression for (I _ul ) _B /I _ul has been deduced where (I _ul ) _B and (I _ul ) are the intensities of the lines with and without the magnetic field. The experimental results agree fairly well with the theoretical model.     

Synthesis and characterization of PNIPAM‐b‐(PEA‐g‐PDEA) double hydrophilic graft copolymer

A series of well‐defined double hydrophilic graft copolymers, consisting of poly(N‐isopropylacrylamide)‐b‐poly(ethyl acrylate) (PNIPAM‐b‐PEA) backbone and poly(2‐(diethylamino)ethyl methacrylate) (PDEA) side chains, were synthesized by successive atom transfer radical polymerization (ATRP). The backbone was firstly prepared by sequential ATRP of N‐isopropylacrylamide and 2‐hydroxyethyl acrylate at 25 °C using CuCl/tris(2‐(dimethylamino)ethyl)amine as catalytic system. The obtained diblock copolymer was transformed into macroinitiator by reacting with 2‐chloropropionyl chloride. Next, grafting‐from strategy was employed for the synthesis of poly(N‐isopropylacrylamide)‐b‐[poly(ethyl acrylate)‐g‐poly(2‐(diethylamino)ethyl methacrylate)] (PNIPAM‐b‐(PEA‐g‐PDEA)) double hydrophilic graft copolymer. ATRP of 2‐(diethylamino)ethyl methacrylate was initiated by the macroinitiator at 40 °C using CuCl/hexamethyldiethylenetriamine as catalytic system. The molecular weight distributions of double hydrophilic graft copolymers kept narrow. Thermo‐ and pH‐responsive micellization behaviors were investigated by fluorescence spectroscopy, ¹H NMR, dynamic light scattering, and transmission electron microscopy. Unimolecular micelles with PNIPAM‐core formed in acidic environment (pH = 2) with elevated temperature (≥32 °C); whereas, the aggregates turned into vesicles in basic surroundings (pH ≥ 7.2) at room temperature. © 2008 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 46: 5638–5651, 2008     

Study of the RPC-Gd as thermal neutron detector

The BESⅢ RPC with Gd coating as thermal neutron detector was designed and constructed. Three prototypes were built with different techniques of producing the gadolinium converter. The performance of the cosmic ray test, the signal and the radiation spectrum were discussed in this paper. Lastly, the efficiency of one prototype with the best performance for detecting the thermal neutron was tested as 8.7%.     

On kicked quantum systems

The time evolution of a multi-dimensional quantum system which is kicked at random or periodically with a potential is obtained. An interesting aspect of the evolution is that if the operator corresponding to the potential has invariant subspaces (this is characteristic of multi-dimensional problems), the system evolves in these invariant subspaces, i.e., each evolution in the subspaces is independent and there cannot be any mixing between the states of these subspaces.     

CO2与HCN,NH3,H2O分子络合物的从头计算研究

用ab initio能量梯度法(3-21G基组)分别优化CO_2与HCN、NH_3、H_2O_3个分子络合物的平衡几何构型。结果表明HCN、NH_3和H_2O中的N或O原子与CO_2中的C原子之间形成较弱的范德华键,三者的范德华键键长分别为0.2865、0.2775、0.2543nm,稳定化能分别为14.8、27.0、31.2kJ·mol~(-1),3个分子络合物的构型都呈T型,对3个分子络合物的稳定化能的能量分解研究表明它们的形成主要靠静电作用能。     

信用组合风险度量研究

我国商业银行在信用组合风险管理方面还比较薄弱，虽然国外已有一些较为成熟的信用组合风险管理模型，但是很难在中国直接应用。另一方面，早期的信用组合风险往往只是单独考虑个别资产的风险，没有考虑资产之间的违约相关性，造成风险度量的偏差。本文在考虑了违约相关性的基础上，基于Logit回归分析，利用微模拟的方法，提出了一个符合中国商业银行资产特点的信用组合风险度量模型。