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.     

Algorithms for finding proper essential surfaces in 3-manifolds

In this paper, we present an algorithm which, for a given compact orientable irreducible boundary irreducible 3-manifold M, verifies whether M contains an essential orientable surface (possibly, with boundary), whose genus is at most N. The algorithm is based on Haken’s theory of normal surfaces, and on a trick suggested by Jaco and consisting in estimating the mean length of boundary curves in an unknown essential surface of a given genus in the given manifold.     

Convergence of Riemannian Manifolds and Laplace Operators, II

We study spectral convergence of compact Riemannian manifolds or more generally certain Dirichlet spaces, obtaining some compactness results on harmonic functions and harmonic maps. Mathematics Subject Classifications (2000) 53C21, 58D17, 58J50. Atsushi Kasue: Partly supported by the Grant-in-Aid for Scientific Research (B) No. 15340053 of the Japan Society for the Promotion of Science.     

Trace Equivalence in SU(2, 1)

In this paper it is shown that one can choose an arbitrarily large number of inconjugate elements of the group Z/2Z*Z/2Z*Z/2Z which have the property that, under all representations of the group in SU(2,1) as a discrete complex hyperbolic ideal triangle group, the elements are hyperbolic and correspond to closed geodesics of equal length on the associated complex hyperbolic surface. This is an analogue of the geometric fact that the multiplicity of the length spectrum of a Riemann surface is never bounded or the equivalent algebraic phenomenon that an arbitrarily large number of conjugacy classes in a free group can have the same trace under all representations in SL(2,R ).     

Boundary control of a hyperbolic system with time lags

This paper considers an optimal boundary control problem fora hyperbolic system in which constant time lags appear in thestate equation and in the boundary condition simultaneously.Making use of Lion's scheme, necessary and sufficient conditionsof optimality for the Neumann problem are derived.     

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.     

Calculus I: The first derivative of pseudoisotopy theory

Let P be the (stable, smooth) pseudoisotopy space of the space X. For any map Y: YX of spaces, we identify the homotopy type of the fiber of P(f): P(f) P(f) in a stable range, roughly twice the connectivity of the map YX. We establish some language for discussing and manipulating such stable-range relative calculations for any homotopy functor. The theorem about P has a corollary about Waldhausen's A. Dedicated to Alexander GrothendieckResearch supported in part by NSF grant DMS-8806444 and by a Sloan Fellowship. Research at MSRI supported in part by NSF grant DMS-8505550.     

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.     

Stabilization ofEscherichia coli penicillin G acylase by polyethylene glycols against thermal inactivation

The effects of five polyethylene glycol (PEG) compounds of different molecular weight on the thermal stability of penicillin G acylase (PGA) obtained from a mutant ofEscherichia coli ATCC 11105 have been investigated. The molecular weights of PEG compounds were 400, 4000, 6000, 10,000, and 15,000. The thermal inactivation mechanisms of both native and PEG-containing PGA were considered to obey first order inactivation kinetics during prolonged heat treatments. Optimal concentrations of PEGs at molecular weights of 400,4000, 6000,10,000, and 15,000 were found to be 250,150,150,100, and 50 mM, respectively. The greatest enhancement of thermostability was observed with PEG 4000 and PEG 6000, as a nearly 20-fold increase above 50°C. PGA showed almost the same temperature activity profile and optimal temperature values both in the presence and absence of PEG. The addition of PEGs did not cause any change in the optimal temperature value of PGA, but the parametersV _m ,K _m , the activation energy, and thek _cat values of enzyme were markedly decreased because of the mixed inhibition by PEG compounds. The type of inhibition was found to be hyperbolic uncompetitive.     

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.