Novel,biodegradable, functional poly(ester‐carbonate)s by copolymerization of trans‐4‐hydroxy‐L‐proline with cyclic carbonate bearing a pendent carboxylic group

Water‐soluble poly(ester‐carbonate) having pendent amino and carboxylic groups on the main‐chain carbon is reported for the first time. This article describes the melt ring‐opening/condensation reaction of trans‐4‐hydroxy‐N‐benzyloxycarbonyl‐L ‐proline (N‐CBz‐Hpr) with 5‐methyl‐5‐benzyloxycarbonyl‐1,3‐dioxan‐2‐one (MBC) at a wide range of molar fractions. The influence of reaction conditions such as catalyst concentration, polymerization time, and temperature on the number average molecular weight (M_n) and molecular weight distribution (M_w/M_n) of the copolymers was investigated. The polymerizations were carried out in bulk at 110 °C with 3 wt % stannous octoate as a catalyst for 16 h. The poly(ester‐carbonate)s obtained were characterized by Fourier transform infrared spectroscopy, ¹H NMR, differential scanning calorimetry, and gel permeation chromatography. The copolymers synthesized exhibited moderate molecular weights (M_n = 6000–14,700 g mol^?1) with reasonable molecular weight distributions (M_w/M_n = 1.11–2.23). The values of the glass‐transition temperature (T_g) of the copolymers depended on the molar fractions of cyclic carbonate. When the MBC content decreased from 76 to 12 mol %, the T_g increased from 16 to 48 °C. The relationship between the poly(N‐CBz‐Hpr‐co‐MBC) T_g and the compositions was in approximation with the Fox equation. In vitro degradation of these poly(N‐CBz‐Hpr‐co‐MBC)s was evaluated from weight‐loss measurements and the change of M_n and M_w/M_n. Debenzylation of 3 by catalytic hydrogenation led to the corresponding linear poly(ester‐carbonate), 4 , with pendent amino and carboxylic groups. © 2004 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 42: 2303–2312, 2004     

Bounded Positive Solutions of Schrödinger Equations in Two-Dimensional Exterior Domains

We prove under quite general assumptions the existence of a bounded positive solution to the semilinear Schrödinger equation in a two-dimensional exterior domain.     

Nonlinear Free Boundary Problems with Singular Source Terms

We prove the existence of solutions to nonlinear free boundary problem with singularities at given points.     

On the Long-Time Behavior of the Quantum Fokker-Planck Equation

We analyze the long-time behavior of transport equations for a class of dissipative quantum systems with Fokker-planck type diffusion operator, subject to confining potentials of harmonic oscillator type. We establish the existence and uniqueness of a non-equilibrium steady state for the corresponding dynamics. Further, using a (classical) convex Sobolev inequality, we prove an optimal exponential rate of decay towards this state and additionally give precise dispersion estimates in those cases, where no stationary state exists.     

Invariant ideals of twisted crossed products

We will prove a result concerning the inclusion of non-trivial invariant ideals inside non-trivial ideals of a twisted crossed product. We will also give results concerning the primeness and simplicity of crossed products of twisted actions of locally compact groups on -algebras. Received: 25 January 2002; in final form: 22 May 2002/Published online: 2 December 2002 This work is partially supported by Hong Kong RGC Direct Grant.     

Construction of the fundamental solution of disturbed parabolic equation

In present paper the parabolic equation solution is built. The construction is reduced to iterative procedure. And convergence of the latter is proven.     

Meeting infinitely many cells of a partition once

We investigate several versions of a cardinal characteristic defined by Frankiewicz. Vojtáš showed , and Blass showed . We show that all the versions coincide and that is greater than or equal to the splitting number. We prove the consistency of and of . Received: 2 October 1996 / Revised version: 22 May 1997     

A real algorithm for the Hermitian eigenvalue decomposition

Modifying complex plane rotations, we derive a new Jacobi-type algorithm for the Hermitian eigendecomposition, which uses only real arithmetic. When the fast-scaled rotations are incorporated, the new algorithm brings a substantial reduction in computational costs. The new method has the same convergence properties and parallelism as the symmetric Jacobi algorithm. Computational test results show that it produces accurate eigenvalues and eigenvectors and achieves great reduction in computational time.The work of this author was supported in part by the National Science Foundation grant CCR-8813493 and by the University of Minnesota Army High Performance Computing Research Center contract DAAL 03-89-C-0038.The work of this author was supported in part by the University of Minnesota Army High Performance Computing Research Center contract DAAL 03-89-C-0038.     

白三叶草花蜜腺的发育解剖学研究

白三叶草花蜜腺突起环状，位于花丝基部并延续至花托上，属于环状花托／雄蕊蜜腺，蜜腺由分泌表皮和产蜜组织组成．在花的发育过程中，蜜腺由本身的原始细胞分裂，分化而来．分泌表皮具角质层，其上分布有变态气孔器，蜜汁经产蜜组织合成后，经变态气孔器泌出．     

Diffusing particles with electrostatic repulsion

Summary. We study a diffusion model of an interacting particles system with general drift and diffusion coefficients, and electrostatic inter-particles repulsion. More precisely, the finite particle system is shown to be well defined thanks to recent results on multivalued stochastic differential equations (see [2]), and then we consider the behaviour of this system when the number of particles goes to infinity (through the empirical measure process). In the particular case of affine drift and constant diffusion coefficient, we prove that a limiting measure-valued process exists and is the unique solution of a deterministic PDE. Our treatment of the convergence problem (as ) is partly similar to that of T. Chan [3] and L.C.G. Rogers - Z. Shi [5], except we consider here a more general case allowing collisions between particles, which leads to a second-order limiting PDE. Received: 5 August 1996 / In revised form: 17 October 1996