Making statistical thinking more productive

The use of the concept of plausibility is proposed for the comparison of psychological or physical images of an object with extremely complex structure. This concept helps the process of developing new image of an object that is not captured by the past observational data. It is argued that this process is the essential aspect of statistical thinking developed by original thinkers in various fields of scientific research with the aid of a model. The use of plausibility helps this process of thinking. A practical example is given by the analysis of golf swing motion.     

Adaptive version of Simpler GMRES

In this paper we propose a stable variant of Simpler GMRES. It is based on the adaptive choice of the Krylov subspace basis at a given iteration step using the intermediate residual norm decrease criterion. The new direction vector is chosen as in the original implementation of Simpler GMRES or it is equal to the normalized residual vector as in the GCR method. We show that such an adaptive strategy leads to a well-conditioned basis of the Krylov subspace and we support our theoretical results with illustrative numerical examples.     

Simpler Tests for Semisparse Subgroups

The main results of this article facilitate the search for quotients of regular abstract polytopes. A common approach in the study of abstract polytopes is to construct polytopes with specified facets and vertex figures. Any nonregular polytope may be constructed as a quotient of a regular polytope by a (so-called) semisparse subgroup of its automorphism group W (which will be a string C-group). It becomes important, therefore, to be able to identify whether or not a given subgroup N of a string C-group W is semisparse. This article proves a number of properties of semisparse subgroups. These properties may be used to test for semisparseness in a way which is computationally more efficient than previous methods. The methods are used to find an example of a section regular polytope of type {6, 3, 3} whose facets are Klein bottles. Received February 15, 2005     

添加近似误差的重新启动的simpler GMRES方法

本文给出了重新启动的LGMRES方法的一种代价更小的实现方式.这种做法基于消除以下减慢收敛速度的现象:重新启动的simpler GMRES的每次循环结束时得到的残向量经常交替方向,与重新启动的GMRES的情形类似.这种新的变形的方法的优点是它比重新启动的LGMRES所需要的计算量要少.大量的例子表明该方法计算速度更快.     

Simpler Polynomial Solutions in Control and Filtering

Kuera's completely algebraic method is used to derive a polynomialsolution with only one Diophantine equation for least-squaresdeterministic control in discrete-time. The same method is used,again involving only one Diophantine equation, to derive themultivariable discrete-time Wiener filter. This paper was presented at the IMA Symposium on Control Theory,Somerville College,Oxford, September 1986.     

Coincidences of Nonself Operators by a Simpler Algorithm

Abstract

In this article, we introduce a new class of contractive mappings and study analytical and computational aspects of a special case of Jungck-Khan iterative algorithm generated by this class of mappings. In particular, we improve upon strong convergence, rate of convergence and data dependence results existing in the current literature. Analytical as well numerical illustrative examples are given to support the new results.     

Simpler counterexamples to the edge-reconstruction conjecture for infinite graphs

A nonisomorphic, edge-hypomorphic pair of countable forests is constructed, hereby providing a counterexample to the edge-reconstruction conjecture for infinite graphs that is simpler than the counterexamples previously given by C. Thomassen. In addition, to answer the questions posed by C. Thomassen in a previous paper, it is shown that there is a countable forest that is vertex-reconstructible but not edge-reconstructible, and that there is a countable, connected graph with these properties.     

Properties that are productive,closed-hereditary and surjective

We obtain a characterization of all those topological properties of regular Hausdorff spaces, that are preserved under the formation of arbitrary products, closed subspaces and continuous surjections.     

On a Simpler Basis for the Pseudovariety EDS

A basis for the pseudovariety EDS which involves two distinct variables is computed. This improves upon a presently known basis for EDS that involves three distinct variables.     

BSHM meetings

In a deliberately provocative first part to this paper, I argue that nineteenth-century British mathematicians had an unduly high opinion of themselves and a striking lack of appreciation for contemporary continental developments. I argue that this failure was rooted in the institutions that supported mathematics, and was only remedied towards the end of the century. In the more sober second half of the paper I ask if historians of mathematics have subscribed to this overestimate, and explore some related questions, among them what are historians doing when they write history: telling it as it was, or righting or defending the record? Historians of mathematics also need to consider British priorities for research in the nineteenth century, and a comparison with other minor players (such as Japan, Portugal, or Poland) might be illuminating.     

Other meetings

Although the Victorian era was characterized by the dominance of Great Britain both militarily and economically, the achievements of the British in mathematics were considerably less spectacular. Nevertheless, significant contributions were made by British mathematicians, several of whose names are still well known today. This paper highlights the principal mathematical developments in Britain during this time, closing with some observations on the weaknesses and limitations of Victorian British mathematics.     

Decomposing Hitting Times of Walks on Graphs into Simpler Ones

Using the electric approach, we derive a formula that expresses an expected hitting time of a random walk between two vertices a and b of a graph G as a convex linear combination of expected hitting times of walks between a and b on subgraphs of G, provided certain condition on a and b is satisfied. Then we use this formula in several applications.     

一类函数不定积分的另一种求法

利用导数的运算法则及莱布尼兹定理的变形,推导出高阶导数公式的一个公式,从而导出一类不定积分的简便求解方法。