Finnish mathematics teaching: a case of uniquely implicit didactics: Keynote presentation. This paper reports on a qualitative analysis of video-taped mathematics lessons taught by four case study teachers, defined locally as effective, in a provincial university city in Finland. The aim was to examine how teachers conceptualise and present mathematics to their learners and, in so doing, unders...

Digital signal processors (DSPs) are very important in various engineering disciplines. Fast multiplication is very important in DSPs for convolution, Fourier transforms, etc. A fast method for multiplication based on ancient Indian Vedic mathematics is proposed in this paper. The whole of Vedic mathematics is based on 16 sutras (word formulae) and manifests a unified structure of mathematics. ...

A method is presented for convergence acceleration of the generalized hypergeometric series 3F2 with the argument ±1 , using analytic properties of their terms. Iterated transformation of the series is performed analytically, which results in obtaining new fast converging expansions for some special functions and mathematical constants.

On purpose to extract trend and cycle from a time series many competing techniques have been developed. The probably most prevalent is the Hodrick Prescott filter. However this filter suffers from diverse shortcomings, especially the subjective choice of its penalization parameter. To this point penalized splines within a mixed model framework offer the advantage of a data driven derivation of ...

This paper describes a novel approach to representing experimental biological data in metabolic networks. The aim is to allow biologists to visualise and analyse the data in the context of the underlying processes. Biological networks can be modelled as graphs and visualised using graph drawing methods. We present a general method for mapping experimental data onto nodes and edges of a graph an...

An excellent introduction to the theory of automorphic representations and the relations with number theory is the Corvallis proceedings, Automorphic Forms, Representations and L-Functions, Parts 1 and 2, Proc. Sympos. Pure Math., vol. 33, 1979. Although composed mainly of survey articles, the proceedings are already rather formidable. They are a measure of the breadth of the field. They will b...

An efficient method for pattern discovery from discrete time series is introduced in this paper. The method utilizes two parallel streams of data, a discrete unit time-series and a set of labeled events, From these inputs it builds associative models between systematically co-occurring structures existing in both streams. The models are based on transitional probabilities of events at several d...

We state a qualitative form of strong multiplicity one for GL1. We derive refinements of strong multiplicity one for automorphic representations arising from Eisenstein series associated to a Borel subgroup on GL(n), and for the cuspidal representations on GL(n) induced from idele class characters of cyclic extensions of prime degree. These results are in accordance with a conjecture of D. Rama...