Optimality Conditions and Geometric Properties of a Linear Multilevel Programming Problem with Dominated Objective Functions

In this paper, a model of a linear multilevel programming problem with dominated objective functions (LMPPD(l)) is proposed, where multiple reactions of the lower levels do not lead to any uncertainty in the upper-level decision making. Under the assumption that the constrained set is nonempty and bounded, a necessary optimality condition is obtained. Two types of geometric properties of the solution sets are studied. It is demonstrated that the feasible set of LMPPD(l) is neither necessarily composed of faces of the constrained set nor necessarily connected. These properties are different from the existing theoretical results for linear multilevel programming problems.     

A New Cohomology Theory of Orbifold

Based on the orbifold string theory model in physics, we construct a new cohomology ring for any almost complex orbifold. The key theorem is the associativity of this new ring. Some examples are computed.Both authors partially supported by the National Science Foundation     

DIFFUSION-DRIVEN INSTABILITY IN THE GIERER-MEINHARDT MODEL OF MORPHOGENESIS

In this paper, we consider the Gierer-Meinhardt model of morphogenesis. It is shown that the homogeneous equilibrium solution and the homogeneous periodic solution become diffusively unstable if the diffusion coefficients of the two substances are chosen suitably.     

水雾化制备Fe74Al4Sn2P10C2B4Si4非晶合金粉末及其磁粉芯性能研究

采用水雾化方法制备Fe7Al4Sn2P10C2B4Si4合金粉末,研究发现该合金具有强的非晶形成能力和高热稳定性,在粉末粒度小于400目时可以形成非晶态合金.采用该非晶粉末制备的磁粉芯在高频下品质因数显著高于MPP粉芯,说明该磁粉芯高频损耗较低.分析表明,非晶合金磁粉芯高频下损耗低的主要原因是电阻率较高.     

Description of proton-calcium scattering using the α-particle model

The theoretical proton-⁴⁰Ca optical potential is constructed based on theα-particle model of the nucleus. With this potential, the differential cross section, analysing power and the spin rotation function for 200 MeV proton-⁴⁰Ca elastic scattering are calculated. The results are in good agreement with the experimental data.     

Noncollinear optical parametric amplification in lithium triborate seeded by a cw Ti:sapphire laser

Experimental investigations of a type-I noncollinear phase-matched optical parametric amplification based on lithium triborate, which was pumped by a 5-ns second-harmonic pulses from a Q-switched Nd:YAG, seeded by a cw Ti:sapphire laser at 800 nm, was presented. The experiments generated 2-ns signal output pulses at 800 nm, the maximum signal output pulse energy reached 19 μJ, the corresponding parametric gain was 44 dB. Furthermore, the experiments demonstrate that the 65 nm-FWHM parametric fluorescence gain spectrum could also be observed. A quantitative account of the ultrabroadband parametric fluorescence gain spectrum was given with our theory. The experimental measurements are in agreement with theoretical calculations.     

Hamiltonian formulation of generalized quantum dynamics

The Hamiltonian formulation of the usual complex quantum mechanics in the theory of generalized quantum dynamics is discussed. After the total trace Lagrangian, total trace Hamiltonian and two kinds of Poisson brackets are introduced, both the equations of motion of some total trace functionals which are expressed by total trace Poisson brackets and the equations of motion of some operators which are expressed by the without-total-trace Poisson brackets are obtained. Then a set of basic equations of motion of the usual complex quantum mechanics are obtained, which are also expressed by the Poisson brackets and total trace Hamiltonian in the generalized quantum dynamics. The set of equations of motion are consistent with the corresponding Heisenberg equations. Project supported by Prof. T.D. Lee’s NNSC Grant, the National Natural Science Foundation of China, the Foundation of Ph. D. Directing Programme of Chinese University, and the Chinese Academy of Sciences.     

Stereo- and enantioselective determination of pesticides in soil by using achiral and chiral liquid chromatography in combination with matrix solid-phase dispersion

The separation of enantiomers and diastereomers of 8 commonly used pesticides was investigated by liquid chromatography (LC) using a Chiralcel OD column (cellulose tris-3,5-dimethylphenylcarbamate as the chiral stationary phase) and a Pirkle-type Chirex 3020 column (urea derivative from the reaction of (R)-1-(alpha-naphthyl)ethylamine with (S)-tert-leucine, chemically bonded to 3-aminopropylsilanized silica as the chiral stationary phase). The pesticides studied included one organophosphorus insecticide (phenthoate), 3 triazole fungicides (uniconazole, diniconazole, and propiconazole), and 4 pyrethroids (fenpropathrin, beta-cypermethrin, beta-cyfluthrin, and alpha-fenvalerate). The enantiomers were separated within 20 min with a resolution of > or = 1.5 using a mixture of n-hexane and 2-propanol as the mobile phase for all the pesticides studied except propiconazole, for which only the 2 diastereomers were baseline separated. This method allows determination of the enantiomers or stereoisomers of the above pesticides in soil. The strategy was as follows: (1) First, the total concentration(s) of the enantiomer pair(s) of a chiral pesticide in soil was (were) determined by a newly developed matrix solid-phase dispersion (MSPD) procedure, followed by silica-based LC quantification. The recoveries ranged from 76.5 to 93.6% with relative standard deviations of 6.0%. (2) Second, the enantiomeric ratio(s) (ER(s)) of the chiral pesticide was (were) determined by LC with a chiral stationary phase after fractionation of the MSPD extract by silica-based LC. The determined ERs or stereoisomeric ratio(s) (SR(s); for propiconazole, only the SR of the 2 diastereomers was determined) in soil samples spiked with the above 8 racemic pesticides agreed with those of the corresponding standard solutions. (3) Third, based on the total concentrations and the corresponding ERs, the concentration of each enantiomer in soil was calculated. The proposed method is rapid, precise, and sensitive, and is appropriate for the investigation of the stereo- and enantioselective degradation of pesticides in environmental media.