On irreversibility of von Neumann additive cellular automata on grids

The von Neumann cellular automaton appears in many different settings in Operations Research varying from applications in Formal Languages to Biology. One of the major questions related to it is to find a general condition for irreversibility of a class of two-dimensional cellular automata on square grids (σ⁺-automata). This question is partially answered here with the proposal of a sufficient condition for the irreversibility of σ⁺-automata.     

非齐次微分方程两点边值问题正解的存在性及多重性

本文考虑一类非齐次微分方程的两点边值问题,得到了一些有关其正解存在性与多重性的精确条件．     

Error estimate for a stabilised domain decomposition method with nonmatching grids

Summary. In this paper, we analyse a stabilisation technique for the so-called three-field formulation for nonoverlapping domain decomposition methods. The stabilisation is based on boundary bubble functions in each subdomain which are then eliminated by static condensation. The discretisation grids in the subdomains can be chosen independently as well as the grid for the final interface problem. We present the analysis of the method and we construct a set of bubble functions which guarantees the optimal rate of convergence. Received May 12, 1998 / Revised version received November 21, 2000 / Published online June 7, 2001     

用各向异性介质构造的一维光子晶体的特性分析

本文根据单轴晶体的传输矩阵，研究了一种由各向异性介质周期排列构成的一维光子晶体，分析了在不同入射角度和折射率条件下，该周期结构的反射和偏振的光学特性。分析结果表明，各向异性介质在折射率比值较大或与高折射率同性介绍结合使用，可获得较宽的禁带，并可实现在可见光范围内的全偏振全角度反射。     

广义凸集的支撑函数

本文讨论了笔者在[1]中提出的伪凸集,拟凸集的支撑函数与障碍锥的性质,并通过这些性质得出了二个闭性准则。     

On the augmented system approach to sparse least-squares problems

Summary We study the augmented system approach for the solution of sparse linear least-squares problems. It is well known that this method has better numerical properties than the method based on the normal equations. We use recent work by Arioli et al. (1988) to introduce error bounds and estimates for the components of the solution of the augmented system. In particular, we find that, using iterative refinement, we obtain a very robust algorithm and our estimates of the error are accurate and cheap to compute. The final error and all our error estimates are much better than the classical or Skeel's error analysis (1979) indicates. Moreover, we prove that our error estimates are independent of the row scaling of the augmented system and we analyze the influence of the Björck scaling (1967) on these estimates. We illustrate this with runs both on large-scale practical problems and contrived examples, comparing the numerical behaviour of the augmented systems approach with a code using the normal equations. These experiments show that while the augmented system approach with iterative refinement can sometimes be less efficient than the normal equations approach, it is comparable or better when the least-squares matrix has a full row, and is, in any case, much more stable and robust.This author was visiting Harwell and was funded by a grant from the Italian National Council of Research (CNR), Istituto di Elaborazione dell'Informazione-CNR, via S. Maria 46, I-56100 Pisa, ItalyThis author was visiting Harwell from Faculty of Mathematics and Computer Science of the University of Amsterdam     

Atomistic packing models for experimentally investigated swelling states induced by CO2 in glassy polysulfone and poly(ether sulfone)

Atomistic packing models have been created, which help to better understand the experimentally observed swelling behavior of glassy polysulfone and poly (ether sulfone), under CO₂ gas pressures up to 50 bar at 308 K. The experimental characterization includes the measurement of the time‐dependent volume dilation of the polymer samples after a pressure step and the determination of the corresponding gas concentrations by gravimetric gas‐sorption measurements. The models obtained by force‐field‐based molecular mechanics and molecular dynamics methods allow a detailed atomistic analysis of representative swelling states of polymer/gas systems, with respect to the dilation of the matrix. Also, changes of free volume distribution and backbone mobility are accessible. The behavior of gas molecules in unswollen and swollen polymer matrices is characterized in terms of sorption, diffusion, and plasticization. © 2006 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 44: 1874–1897, 2006     

Limits of parallelism in explicit ODE methods

Numerical methods for ordinary initial value problems that do not depend on special properties of the system are usually found in the class of linear multistage multivalue methods, first formulated by J.C. Butcher. Among these the explicit methods are easiest to implement. For these reasons there has been considerable research activity devoted to generating methods of this class which utilize independent function evaluations that can be performed in parallel. Each such group of concurrent function evaluations can be regarded as a stage of the method. However, it turns out that parallelism affords only limited opportunity for reducing the computing time with such methods. This is most evident for the simple linear homogeneous constant-coefficient test problem, whose solution is essentially a matter of approximating the exponential by an algebraic function. For a given number of stages and a given number of saved values, parallelism offers a somewhat enlarged set of algebraic functions from which to choose. However, there is absolutely no benefit in having the degree of parallelism (number of processors) exceed the number of saved values of the method. Thus, in particular, parallel one-step methods offer no speedup over serial one-step methods for the standard linear test problem. Although the implication of this result for general nonlinear problems is unclear, there are indications that dramatic speedups are not possible in general. Also given are some results relevant to the construction of methods.Work supported in part by National Science Foundation grants DMS 89 11410 and DMS 90 15533 and by US Department of Energy grant DOE DEFG02-87ER25026. Work of the second author was completed while at the University of Illinois.     

Martin Boundaries of Elliptic Skew Products, Semismall Perturbations, and Fundamental Solutions of Parabolic Equations

We consider positive solutions of elliptic partial differential equations on non-compact domains of Riemannian manifolds. We explicitly determine Martin boundaries and Martin kernels for a class of elliptic equations in skew product form by exploiting and developing perturbation theory for elliptic equations and short/long-time estimates for fundamental solutions of parabolic equations.     

中心—焦点区分问题的I l'yashenko算法

对二维平面系统的二维系统的中心焦点区分问题 ,I l'yashenko曾建议一个算法 ,本文给出此法的详细证明 .据此 ,我们讨论了区分问题在 Arnold意义下的代数可解性与不可解性