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.     

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.     

Extraction of Americium(III) and Europium(III) with Two Open-Chain Crown Ethers of Amide Type

The extraction of Am³⁺ and Eu³⁺ from aqueous picric acid solution by N, N-dinaphthyl-N, N-diphenyl-3,6-dioxaoctanediamide (L^I) and 1, 1-(3, 6, 9-trioxaundecanedionyl)diphenothiazine (L^II) was investigated by a radioactive tracer technique. Extraction distribution ratios of Am³⁺ and Eu³⁺ have been measured as a function of pH, picric acid concentration, extractant concentration, diluent and temperature. The extraction of Am³⁺ is preferred to that of Eu³⁺ for both L^I and L^II, and the latter gives larger separation factor than the former. The equilibrium constants and thermodynamic parameters of extraction reactions were also calculated.     

Zig‐Zag Diphosphene Oligomers Linked by Silver(I) Cation

The coordination of silver cation to diphosphene Mes*P=PMes* ( 1 , Mes* = ^tBu₃C₆H₂) was investigated in detail. The reaction of 1 with Ag[Al(OR_F)₄] (OR_F = OC(CF₃)₃) in the ratios of 2 : 1, 3 : 2 and 1 : 2 led to the formation of the first cationic silver linked diphosphene complexes 2 — 4 . Complexes 2 and 3 contain two and three diphosphene molecules linked by the linear Ag(I) cation, respectively, and they feature unusual zig‐zag topologies. Complex 4 is a dinuclear silver complex, and each Ag(I) center features a tetrahedral geometry, coordinated by one phosphorus atom of diphosphene 1 and three chloro atoms of two CH₂Cl₂ molecules.     

Composite alignment media for the measurement of independent sets of NMR residual dipolar couplings

The measurement of independent sets of NMR residual dipolar couplings (RDCs) in multiple alignment media can provide a detailed view of biomolecular structure and dynamics, yet remains experimentally challenging. It is demonstrated here that independent sets of RDCs can be measured for ubiquitin using just a single alignment medium composed of aligned bacteriophage Pf1 particles embedded in a strained polyacrylamide gel matrix. Using this composite medium, molecular alignment can be modulated by varying the angle between the directors of ordering for the Pf1 and strained gel matrix, or by varying the ionic strength or concentration of the Pf1 particles. This approach offers significant advantages in that greater experimental control can be exercised over the acquisition of multi-alignment RDC data while a homogeneous chemical environment is maintained across all of the measured RDC data.     

MoO3、NiO、ZnO在小表面金红石上的分散行为

Dispersion of MoO3, NiO, ZnO on rutile TiO2 with low specific surface area was studied with Mercury Porosimeter, SEM, XPS and Ammonia Extraction method. The dispersion thresholds of MoO3, NiO, ZnO on three rutile TiO2 carriers were obtained with XPS, and com-pared with those on anatase TiO2 with high specific surf are area. Ammonia Extraction method was used to identify the surface oxide species interarting with support surface in different strength and it was found that the proportions of oxides that can not be extracted by ammonia extraction are different for MoO3, NiO and ZnO which are supported on rutile TiO2.