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51.
Nikolai Yu. Bakaev 《BIT Numerical Mathematics》1998,38(3):462-485
We consider a Cauchy problem for the sectorial evolution equation with generally variable operator in a Banach space. Variable
stepsize discretizations of this problem by means of a strongly A(φ)-stable Runge-Kutta method are studied. The stability
and error estimates of the discrete solutions are derived for wider families of nonuniform grids than quasiuniform ones (in
particular, if the operator in question is constant or Lipschitz-continuous, for arbitrary grids). 相似文献
52.
53.
Xingping Qiu Svetlana A. Sukhishvili 《Journal of polymer science. Part A, Polymer chemistry》2006,44(1):183-191
Free‐radical copolymerizations of N‐vinylcaprolactam (VCL) and glycidyl methacrylate (GMA) were investigated to synthesize temperature‐responsive reactive copolymers with minimized compositional heterogeneity. The average copolymer composition was determined by Fourier transform infrared and nuclear magnetic resonance techniques. The reactivity ratios for VCL and GMA were found to be 0.0365 ± 0.0009 and 6.44 ± 0.36 by the Fineman–Ross method and 0.039 ± 0.006 and 6.75 ± 0.29 by the Kelen–Tudos method, respectively. When prepared by batch polymerization, VCL–GMA copolymers had a highly heterogeneous composition and fractions of different solubilities in water. The use of a gradual feeding technique, which included the sequential addition of more reactive GMA monomer into the reaction, yielded copolymers with much more homogeneous composition. The produced copolymers with 0.9 and 0.11 fractional GMA contents preserved their temperature‐responsive properties and precipitated from aqueous solutions when the temperature exceeded 31 °C. The GMA units in the VCL–GMA copolymers were capable of reacting with amino end‐functionalized poly(ethylene oxide) at room temperature to produce poly(N‐vinylcaprolactam)–poly(ethylene oxide) graft copolymers. © 2005 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 44: 183–191, 2006 相似文献
54.
Mana Ito Takashi Ishizone 《Journal of polymer science. Part A, Polymer chemistry》2006,44(16):4832-4845
Anionic polymerization of N‐methoxymethyl‐N‐isopropylacrylamide ( 1 ) was carried out with 1,1‐diphenyl‐3‐methylpentyllithium and diphenylmethyllithium, ‐potassium, and ‐cesium in THF at ?78 °C for 2 h in the presence of Et2Zn. The poly( 1 )s were quantitatively obtained and possessed the predicted molecular weights based on the feed molar ratios between monomer to initiators and narrow molecular weight distributions (Mw/Mn = 1.1). The living character of propagating carbanion of poly( 1 ) either at 0 or ?78 °C was confirmed by the quantitative efficiency of the sequential block copolymerization using N,N‐diethylacrylamide as a second monomer. The methoxymethyl group of the resulting poly( 1 ) was completely removed to give a well‐defined poly(N‐isopropylacrylamide), poly(NIPAM), via the acidic hydrolysis. The racemo diad contents in the poly(NIPAM)s could be widely changed from 15 to 83% by choosing the initiator systems for 1 . The poly(NIPAM)s obtained with Li+/Et2Zn initiator system possessed syndiotactic‐rich configurations (r = 75–83%), while either atactic (r = 50%) or isotactic poly(NIPAM) (r = 15–22%) was generated with K+/Et2Zn or Li+/LiCl initiator system, respectively. Atactic and syndiotactic poly(NIPAM)s (42 < r < 83%) were water‐soluble, whereas isotactic‐rich one (r < 31%) was insoluble in water. The cloud points of the aqueous solution of poly(NIPAM)s increased from 32 to 37 °C with the r‐contents. These indicated the significant effect of stereoregularity of the poly(NIPAM) on the water‐solubility and the cloud point in water © 2006 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 44: 4832–4845, 2006 相似文献
55.
T. Radul 《Topology and its Applications》2007,154(8):1794-1798
R. Pol has shown that for every countable ordinal number α there exists a universal space for separable metrizable spaces X with trindX?α. W. Olszewski has shown that for every countable limit ordinal number λ there is no universal space for separable metrizable space with trIndX?λ. T. Radul and M. Zarichnyi have proved that for every countable limit ordinal number there is no universal space for separable metrizable spaces with dimWX?α where dimW is a transfinite extension of covering dimension introduced by P. Borst. We prove the same result for another transfinite extension dimC of the covering dimension.As an application, we show that there is no absorbing sets (in the sense of Bestvina and Mogilski) for the classes of spaces X with dimCX?α belonging to some absolute Borel class. 相似文献
56.
57.
G. Choudury 《Numerische Mathematik》1990,57(1):179-203
Summary In this paper we study the convergence properties of a fully discrete Galerkin approximation with a backwark Euler time discretization scheme. An approach based on semigroup theory is used to deal with the nonsmooth Dirichlet boundary data which cannot be handled by standard techniques. This approach gives rise to optimal rates of convergence inL
p[O,T;L
2()] norms for boundary conditions inL
p[O,T;L
2()], 1p. 相似文献
58.
Junping Wang 《Numerische Mathematik》1989,55(4):401-430
Summary Asymptotic expansions for mixed finite element approximations of the second order elliptic problem are derived and Richardson extrapolation can be applied to increase the accuracy of the approximations. A new procedure, which is called the error corrected method, is presented as a further application of the asymptotic error expansion for the first order BDM approximation of the scalar field. The key point in deriving the asymptotic expansions for the error is an establishment ofL
1-error estimates for mixed finite element approximations for the regularized Green's functions. As another application of theL
1-error estimates for the regularized Green's functions, we shall present maximum norm error estimates for mixed finite element methods for second order elliptic problems. 相似文献
59.
Wilhelm Heinrichs 《Numerische Mathematik》1989,56(1):25-41
Summary Spectral methods employ global polynomials for approximation. Hence they give very accurate approximations for smooth solutions. Unfortunately, for Dirichlet problems the matrices involved are dense and have condition numbers growing asO(N
4) for polynomials of degree N in each variable. We propose a new spectral method for the Helmholtz equation with a symmetric and sparse matrix whose condition number grows only asO(N
2). Certain algebraic spectral multigrid methods can be efficiently used for solving the resulting system. Numerical results are presented which show that we have probably found the most effective solver for spectral systems. 相似文献
60.
Summary We consider a class of steady-state semilinear reaction-diffusion problems with non-differentiable kinetics. The analytical properties of these problems have received considerable attention in the literature. We take a first step in analyzing their numerical approximation. We present a finite element method and establish error bounds which are optimal for some of the problems. In addition, we also discuss a finite difference approach. Numerical experiments for one- and two-dimensional problems are reported.Dedicated to Ivo Babuka on his sixtieth birthdayResearch partially supported by the Air Force Office of Scientific Research, Air Force Systems Command, USAF under Grant Number AFOSR 85-0322 相似文献