is that, after controlling for these aggregate determinants, the systematic movement of credit spread changes still remains, and indeed, is the dominant factor. Brown The rest of the paper is organized as follows. In Section I, we examine the theoretical determinants of credit spread changes from a

representations of number notations. The neural and cognitive organization of those representations can explain why some mathematical concepts are intuitive, while others are so difficult to grasp. Thus, the ultimate foundations of mathematics rests on core representations that have been internalized in our

between give spaces. Thus the mathematics prima-facie requires variable types X;Y; : : : to represent talk about arbitrary spaces (of the kinds indicated) and highertype constructions such as of the type X ! Y of all functions from X to Y , from which function spaces are constructed. It happens

We present here the mathematical foundations of the wavelet transform, multiresolution analysis and discrete-time transforms and algorithms. This article serves as background material for the rest of the special issue. 1 Introduction When we deal with a given physical object, we encounter many

of mathematics. A consequence is that the criticism that radical constructivism is necessarily solipsistic is overcome. It is widely recognised that all practice and theories of learning and teaching rest on an epistemology, whether articulated or not. As Rene Thom puts it, for mathematics: "In fact

.g. movement of bacteria or movement of proteins in the cell nucleus). In this paper we consider a general model from a mathematical point of view. This provides general insight into the features of these models, which in turn is useful in the modelling process. We consider a singular perturbation expansion

Whenever a subject is organized systematically for expository or foundational purposes (or both), one must deal with the question: What rests on what? The way in which this is answered in the case of mathematics depends on whether one is considering it informally or formally, i.e. from the point

The independent sizing of the redox system's power and storage capacity makes it particularly attractive for long term electricity storage in remote areas where solar arrays or wind generators have been installed. An at-tractive feature of the vanadium redox battery is that since there is no solution contaminat ion due to cross-mixing, after the original capital investment, there would be negligible running and maintenance costs. Since the cell can be completely discharged without any deterioration i performance, it would be ideally suited for large scale energy storage in load leveling applica-tions. A larger scale five-cell battery unit is currently under construction so that the system performance can be fur-ther tested before scaling up to a 1 kW unit. Acknowledgments Support for this project was provided under the Na-

on the ability to control these interactions. An ongoing challenge is to explain the underlying physics of the motion of a contact line, a triple juncture of the solid/air, solid/liquid, and liquid/air interfaces. When the system is at rest, the three interfacial energies, determined by the energy per unit area

for speeding up queries and lowering the memory usage. We detail our experience in applying two known streaming algorithms: the SpaceSaving algorithm [4] that has favorable math-ematical guarantees [1], and HyperLogLog [2, 3], to data at rest. The first algorithm is normally used for finding the most frequent