An oscillatory bifurcation from infinity, and from zero

The problem (where B is a unit ball in R ⁿ )

FREE BOUNDARY PROBLEM ARISING FROM EVAPORATION FROM POROUS MEDIUM

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Estimates from above and from below for the homogenized coefficients

Summary The computation of the homogenized coefficients involves the solution of a minimum problem for a quadratic functional. The use of conforming finite elements provides estimates from above. In this paper we prove that, under realistic assumptions, the use of linear non-conforming finite elements provides estimates from below. Hence, a-posteriori error estimates for the homogenized coefficients can be obtained.     

Complexes from Complexes

Foundations of Computational Mathematics - This paper is concerned with the derivation and properties of differential complexes arising from a variety of problems in differential equations, with...     

Reconstruction from vertex-switching

Let X be a graph with vertices x₁ ,…, x_n. Let X_i be the graph obtained by removing all edges {x_i, x_j} of X and inserting all nonedges {x_i, x_k}. If n ? 0 (mod 4), then X can be uniquely reconstructed from the unlabeled graphs X₁.…, X_n. If n = 4 the result is false, while for n = 4m≥8 the result remains open. The proof uses linear algebra and does not explicitly describe the reconstructed graph X.     

Learning from comparing

The article reviews five qualitative comparative studies in order to reflect on methods and methology of international comparative research within a qualitative paradigm. The goals, methodologies and theoretical perspectives of these studies are described and compared. Issues such as the different uses of the notion ‘culture’, and the purpose of comparison, are raised and discussed. The question of how comparative research can contribute to better a understanding of the ‘covert culture’ that shapes the mathematics education in different contexts is raised.     

Algorithms from algebra

The rules of algebra are rules about classes of objects. In many cases, algebra can be viewed as algorithmic in nature. By specifically defining the class for which a rule applies and then the general outline of the rule, the guesswork can be removed from the process. Thus the student has a clearer understanding of when and how a particular rule applies. The paper describes this approach to the solution of algebraic expressions and the simplification of rational expressions.     

Clones from creatures

We show that (consistently) there is a clone on a countable set such that the interval of clones above is linearly ordered and has no coatoms.

     

Factors from trees

We construct factors of type for , from group actions on homogeneous trees and their boundaries. Our result is a discrete analogue of a result of R.J Spatzier, where the hyperfinite factor of type is constructed from a group action on the boundary of the universal cover of a manifold.

     

Learning from projects

The ‘learning organisation’ is frequently emphasised in the literature and in practice, and this is particularly important for project-oriented organisations. However, experience tells us that organisations tend not to learn adequately from project experiences. This paper reviews some of the work seeking to model and explain the behaviour of complex projects, which explains why lessons are difficult to learn from such projects—not the easy and obvious lessons but the lessons about complex non-intuitive project behaviours. From there it looks at why projects are frequently not reviewed, and seeks to offer practical proposals for carrying out reviews, using small models to enable lessons to be learned that provide understanding (rather than simply data), and distributing that learning around the organisation.