Application of Complexity Theory to an Information Processing Model in Science Education

The current work examines the role of working-memory capacity in problem solving in science education. It treats an information-processing model with tools of complexity theory. Nonlinear methods are used to correlate the subjects' achievement scores with working-memory capacity. Data have been taken from the achievement scores in simple organic-synthesis chemical problems. The subjects (N = 319) were in grade twelve (age 17–18). Problems of various Z-demands (that is the number of steps needed to solve the problem) from two to eight were used. Rank-order sequences of the subjects, according to their scores, were generated, and each score was then replaced by the value of subject's working memory capacity measured by the digit backward span test. Then the sequences were mapped onto a one-dimensional random walk model and when treated as dynamic flows were found to possess fractal geometry with characteristics depending on the Z-demand of the problem. The findings were interpreted using concepts from complexity theory, such as correlation exponents, fractal dimensions and entropy. The null hypothesis was tested with surrogate data.     

Strong approximation for the general Kesten-Spitzer random walk in independent random scenery

This paper is to prove that, if a one-dimensional random wa lkcan be approximated by a Brownian motion, then the related random walk in a g eneral independent scenery can be approximated by a Brownian motion in Brownian scenery.     

利率相依的离散时间保险风险模型的破产问题

本文对利率具有一阶自回归的离散时间风险模型进行了研究,得到了破产前最大盈余的分布,破产前盈余、破产后赤字与破产前最大盈余的联合分布以及首达某一水平x的时间分布的递推公式.     

两类非线性系统的全局稳定性

本文利用 Liapunov 函数方法和论证系统正半轨线有界的 Shimanov区域方法,给出了两类非线性系统的零解为全局稳定的充分条件,并讨论了一些低阶实例,得到了较好的结果.     

A complexity approach to sustainability – Stafford Beer revisited

There is wide acceptance of the need for a more holistic approach to sustainability. However, practical solutions remain elusive and tend to exhibit underlying conflicts between different paradigms and their associated methodologies. This paper argues the need to wield analytical tools that themselves embody the principles of systemic, ecological thinking. We present here a theoretical framework based on complexity science – focused on organisational and second order cybernetics – that highlights our understanding of the concept of sustainability. The paper goes on to reflect upon how current practice would benefit from such an approach.     

EXISTENCE OF PERIODIC SOLUTIONS TO A KIND OF HIGHER ORDER FUNCTIONAL DIFFERENTIAL EQUATION WITH TWO DEVIATING ARGUMENTS

In this paper, by the theory of Fourier series, Bernoulli number theory and continu-ation theorem of coincidence degree theory, we study a kind of higher order functional differential equation with two deviating arguments. Some new results on the existence of periodic solutions are obtained.     

On the duality problem of positive Dunford-Pettis operators on Banach lattices

We give some sufficient and necessary conditions for that a positive Dunford-Pettis operator admits a dual operator which is also Dunford-Pettis, and conversely.      

代数体函数的性质

本文研究了亚纯函数的几个性质推广到多值的代数体函数.利用代数体函数的循环加,循环乘运算及特征的性质,证明了代数体函数的级与下级的几个性质,并研究了两个代数体函数的公共a值点的度量,且得到代数体函数的两个唯一性定理.     

A multidomain integrated‐radial‐basis‐function collocation method for elliptic problems

This article is concerned with the use of integrated radial‐basis‐function networks (IRBFNs) and nonoverlapping domain decompositions (DDs) for numerically solving one‐ and two‐dimensional elliptic problems. A substructuring technique is adopted, where subproblems are discretized by means of one‐dimensional IRBFNs. A distinguishing feature of the present DD technique is that the continuity of the RBF solution across the interfaces is enforced with one order higher than with conventional DD techniques. Several test problems governed by second‐ and fourth‐order differential equations are considered to investigate the accuracy of the proposed technique. © 2008 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 2008     

On tracial approximation

Let C be a class of unital C*-algebras. The class TAC of C*-algebras which can be tracially approximated (in the Egorov-like sense first considered by Lin) by the C*-algebras in C is studied (Lin considered the case that C consists of finite-dimensional C*-algebras or the tensor products of such with C([0,1])). In particular, the question is considered whether, for any simple separable A∈TAC, there is a C*-algebra B which is a simple inductive limit of certain basic homogeneous C*-algebras together with C*-algebras in C, such that the Elliott invariant of A is isomorphic to the Elliott invariant of B. An interesting case of this question is answered. In the final part of the paper, the question is also considered which properties of C*-algebras are inherited by tracial approximation. (Results of this kind are obtained which are used in the proof of the main theorem of the paper, and also in the proof of the classification theorem of the second author given in [Z. Niu, A classification of tracially approximately splitting tree algebra, in preparation] and [Z. Niu, A classification of certain tracially approximately subhomogeneous C*-algebras, PhD thesis, University of Toronto, 2005]—which also uses the main result of the present paper.)