Behavior of cellulose in NaOH/Urea aqueous solution characterized by light scattering and viscometry

Cellulose was dissolved in 6 wt % NaOH/4 wt % urea aqueous solution, which was proven by a ¹³C NMR spectrum to be a direct solvent of cellulose rather than a derivative aqueous solution system. Dilute solution behavior of cellulose in a NaOH/urea aqueous solution system was examined by laser light scattering and viscometry. The Mark–Houwink equation for cellulose in 6 wt % NaOH/4 wt % urea aqueous solution at 25 °C was [η] = 2.45 × 10^?2 weight‐average molecular weight (M_w)^0.815 (mL g^?1) in the M_w region from 3.2 × 10⁴ to 12.9 × 10⁴. The persistence length (q), molar mass per unit contour length (M_L), and characteristic ratio (C_∞) of cellulose in the dilute solution were 6.0 nm, 350 nm^?1, and 20.9, respectively, which agreed with the Yamakawa–Fujii theory of the wormlike chain. The results indicated that the cellulose molecules exist as semiflexible chains in the aqueous solution and were more extended than in cadoxen. This work provided a novel, simple, and nonpollution solvent system that can be used to investigate the dilute solution properties and molecular weight of cellulose. © 2003 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 42: 347–353, 2004     

Kirchhoff方程的相对常值特解及其Lyapunov稳定性

对于超细长弹性杆静力学的Kirchhoff方程，用动力学的概念和方法研究其常值特解 和稳定性问题.计算了Kirchhoff方程相对固定坐标系、截面主轴坐标系以及中心线Frenet 坐标系的常值特解，进行了Kirchhoff动力学比拟，用一次近似理论分别讨论了它们的Lyapu nov稳定性，导出了若干稳定性判据，并在参数平面上绘出了稳定域. 关键词： 超细长弹性杆 Kirchhoff方程 常值特解 Lyapunov稳定性     

On the Existence of Solutions to Vector Quasivariational Inequalities and Quasicomplementarity Problems with Applications Break to Traffic Network Equilibria

For vector quasivariational inequalities involving multifunctions in topological vector spaces, an existence result is obtained without a monotonicity assumption and with a convergence assumption weaker than semicontinuity. A new type of quasivariational inequality is proposed. Applications to quasicomplementarity problems and traffic network equilibria are considered. In particular, definitions of weak and strong Wardrop equilibria are introduced for the case of multivalued cost functions.     

The canonical solution operator of $ {\bar \partial } $ on weighted spaces with holomorphic coefficients

On weighted spaces with strictly plurisubharmonic weightfunctions the canonical solution operator of and the ‐Neumann operator are bounded. In this paper we find a class of strictly plurisubharmonic weightfunctions with certain growth conditions, so that they are Hilbert‐Schmidt operators between weighted spaces with different weightfunctions, if they are restricted to forms with holomorphic coefficients. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

The long‐time behaviour of the thermoconvective flow in a porous medium

For the Boussinesq approximation of the equations of coupled heat and fluid flow in a porous medium we show that the corresponding system of partial differential equations possesses a global attractor. We give lower and upper bounds of the Hausdorff dimension of the attractor depending on a physical parameter of the system, namely the Rayleigh number of the flow. Numerical experiments confirm the theoretical findings and raise new questions on the structure of the solutions of the system. Copyright © 2004 John Wiley & Sons, Ltd.     

Existence and uniform decay for Euler–Bernoulli beam equation with memory term

In this article we prove the existence of the solution to the mixed problem for Euler–Bernoulli beam equation with memory term. The existence is proved by means of the Faedo–Galerkin method and the exponential decay is obtained by making use of the multiplier technique combined with integral inequalities due to Komornik. Copyright © 2004 John Wiley & Sons, Ltd.     

An algorithm for the divisors of monic polynomials over a commutative ring

Gilmer and Heinzer proved that given a reduced ring R, a polynomial f divides a monic polynomial in R[X] if and only if there exists a direct sum decomposition of R = R₀ ⊕ … ⊕ R_m (m ≤ deg f), associated to a fundamental system of idempotents e₀, … , e_m, such that the component of f in each R_i[X] has degree coefficient which is a unit of R_i. We propose to give an algorithm to explicitly find such a decomposition. Moreover, we extend this result to divisors of doubly monic Laurent polynomials.     

Two-Frequency Autowave Processes in the Complex Ginzburg–Landau Equation

We study the complex Ginzburg–Landau equation with zero Neumann boundary conditions on a finite interval and establish that this boundary problem (with suitably chosen parameters) has countably many stable two-dimensional self-similar tori. The case of periodic boundary conditions is also investigated.     

匹配问题实例空间和解空间结构

本文通过研究匹配问题的实例空间，匈牙利算法和解空间三者之间的关系，指出S实例空间的数目与问题复杂度之间的关系既不是充分也不是必要的，而如何对问题的解空间进行合理的分解才能是问题的关键。     

具脉冲效应的时滞周期捕食与被捕食系统正周期解的存在性

本文研究一类具脉冲效应的时滞周期捕食与被捕食系统，利用重合度理论中的方法，获得该系统至少存在一个正周期解的充分条件。