Weak singularities may help periodic solutions to exist

In a periodically forced semilinear differential equation with a singular nonlinearity, a weak force condition enables the achievement of new existence criteria through a basic application of Schauder's fixed point theorem. The originality of the arguments relies in that, contrary to the customary situation in the available references, a weak singularity facilitates the arguments of the proofs.     

One-dimensional stochastic Burgers equation driven by Lévy processes

In this paper, we proved the global existence and uniqueness of the strong, weak and mild solutions for one-dimensional Burgers equation perturbed by a Poisson form process, a Poisson form and Q-Wiener process with the Dirichlet bounded condition. We also proved the existence of the invariant measure of these models.     

Norms and perfect graphs

The weak Berge hypothesis states that a graph is perfect if and only if its complement is perfect. Previous proofs of this hypothesis have used combinatorial or polyhedral methods.In this paper, the concept of norms related to graphs is used to provide an alternative proof for the weak Berge hypothesis.This is a written account of an invited lecture delivered by the second author on occasion of the 12. Symposium on Operations Research, Passau, 9.–11. 9. 1987.     

Synthesis of monodisperse poly(chloromethylstyrene-co-divinylbenzene) beads and their application in separation of biopolymers

The monodisperse, porous poly(chloromethylstyrene-co-divinylbenzene) beads of 7.9 microm were prepared by a single-step swelling and polymerization method. The seed particles prepared by dispersion polymerization exhibited good absorption of the monomer phase. Based on this media, a weak cation-exchange (WCX) stationary phase for HPLC was synthesized by a new chemically modified method. The prepared resin has advantages of biopolymer separation, high column efficiency, low column backpressure, high protein mass recovery, and good resolution for proteins. The dynamic protein-loading capacity of the synthesized WCX packings was 18.2 mg/g. Five proteins were separated in 3.0 min using the synthesized WCX stationary phase. The experimental results show that the obtained WCX resin has very weak hydrophobicity. The WCX resin was also used for the rapid separation and purification of lysozyme from egg white in 5.0 min with only one step. The purity and specific bioactivity of the purified lysozyme were found to be more than 93% and 70 245 U/mg, respectively.     

COCl2…NH3和COCl2…H2S体系的理论研究

在MP2水平上,用aug-cc-pVTZ基组对COC l2…NH3和COC l2…H2S体系进行几何优化和频率计算,同时使用Counterpoise技术进行BSSE校正,分别得到4个COC l2…NH3和2个COC l2…H2S无虚频的稳定结构:N(S)…C连接的构型(Ⅰ,Ⅱ,Ⅴ)和N(S)…C—lC直线型连接的构型(Ⅲ,Ⅳ,Ⅵ).第一类构型比第二类构型相互作用能更大、更稳定.在得到的6个稳定络合物中,络合物Ⅰ是最稳定的.     

弱碱性阴离子交换树脂分离1,6—二磷酸果糖的研究

采用弱碱性阴离子交换树脂HJ-30对发酵液中1，6-二磷酸果糖的分离进行了研究。详细地研究了树脂的吸附和脱附性能。实验结果表明，HJ-30树脂对FDP的吸附量达0．28gFDP／g湿树脂，以0．05mol／LNaCl洗脱光机磷和1mol／LNaCl洗脱1，6-二磷酸果糖，产品的收率和纯度分别为92％和99．4％。     

The Weak Interaction on CO2 …CO van der Waals Complex : A Theoretical Study

The geometries of van der Waals complex CO2…CO were optimized at DFT and second-order Moller-Plesset perturbation(MP2) levels with the large basis set,three stable structures were found.The most stable structure has a T-shape geometry in which the CO lies along the C2 axis of CO2,with the two C atoms direct contact and R(C…C)=0.3227nm.The corresponding energies of the most stable structure were calculated by means of MP2,MP4D,MP4DQ,MP4SDTQ,MP4SDQ,CCSD and CCSD(T) methods,The BSSE (basis set superposition error) wads eliminated by the Boys-Bernardi counterpoise correction(CP) method.According to thermodynamics data.van der Waals complex CO2…CO can found at a low temperature and or a high pressure,There is a little charge transferred between the two interacted subunits.In the most stable structure,CO2 is the acceptor and CO is the donor.     

Molecular structure of di-aryl-aldimines by multinuclear magnetic resonance and X-ray diffraction

The complete ¹H, ¹³C and ¹⁵N NMR analyses for a series of 25 diaryl-aldimines containing phenyl, pyridyl, pyrazolone and furanyl moieties are described herein. Detailed evaluation of substituent chemical shift and coupling constant effects showed that interaction between the lone pair of the pyrazolone carbonyl group or the nitrogen of 2-substitued pyridines with the aldimine hydrogen increases the value and shifts the resonance signal for this hydrogen to high frequency, in the ¹H NMR spectra. The X-ray crystal structure analysis of pyrazolone substituted aldimines evidenced the planarity of the aryl groups which are conjugated with the CN double bond. In the case of the N-(2-pyridinemethylene)-1,5-dimethyl-2-phenyl-1,2-dihydro-pyrazol-3-one, two rotamers were observed in the same unit cell.     

NMR and MO Studies on the Molecular Structure of a Fluoranthene-Benzene Complex

Summary. Fluoranthene (FA) forms a 1:1 van der Waals complex with benzene in cyclohexane. The ¹H NMR spectrum of this complex shows that the FA moiety in the complex state has five kinds of hydrogen atoms and that the ¹H NMR peaks assigned to the protons attached to the naphthalene skeleton are largely shifted to higher magnetic field on complex formation with benzene. These observations indicate that the complex takes the structure of C_S symmetry, in which the benzene molecule mainly interacts with the electronic system localized on the naphthalene moiety of FA. The present ab initio calculations reproduce well the ¹H NMR spectral shifts mentioned above and the experimentally predicted C_S structure of the complex. According to the PPP calculations for the electronic absorption spectral changes on the complex formation, the FA-benzene complex is considered to take a sandwich type structure.     

带有随机初值的复值Ginzburg-Landau方程的弱平均动力学*

本文研究了无界域上的带有随机初值的复值Ginzburg-Landau方程.首先, 基于解过程的全局适定性, 建立了带有随机初值的Ginzburg-Landau方程的平均随机动力系统.然后, 证明了弱拉回平均随机吸引子的存在唯一性以及随机吸引子的周期性,并将其进一步推广到加权空间L²(?, L²_σ(R)).