Search results for "General Mathematics"

Kurzweil-Henstock type integral on zero-dimensional group and some of its application

2008

A Kurzweil-Henstock type integral on a zero-dimensional abelian group is used to recover by generalized Fourier formulas the coefficients of the series with respect to the characters of such groups, in the compact case, and to obtain an inversion formula for multiplicative integral transforms, in the locally compact case.

A note on a generalization of Françoise's algorithm for calculating higher order Melnikov functions

2004

In [J. Differential Equations 146 (2) (1998) 320–335], Françoise gives an algorithm for calculating the first nonvanishing Melnikov function M of a small polynomial perturbation of a Hamiltonian vector field and shows that M is given by an Abelian integral. This is done under the condition that vanishing of an Abelian integral of any polynomial form ω on the family of cycles implies that the form is algebraically relatively exact. We study here a simple example where Françoise’s condition is not verified. We generalize Françoise’s algorithm to this case and we show that M belongs to the C[log t, t, 1/t] module above the Abelian integrals. We also establish the linear differential system ver…

A generalization of Françoise's algorithm for calculating higher order Melnikov functions

2002

Abstract In [J. Differential Equations 146 (2) (1998) 320–335], Francoise gives an algorithm for calculating the first nonvanishing Melnikov function Ml of a small polynomial perturbation of a Hamiltonian vector field and shows that Ml is given by an Abelian integral. This is done under the condition that vanishing of an Abelian integral of any polynomial form ω on the family of cycles implies that the form is algebraically relatively exact. We study here a simple example where Francoise's condition is not verified. We generalize Francoise's algorithm to this case and we show that Ml belongs to the C [ log t,t,1/t] module above the Abelian integrals. We also establish the linear differentia…

Smooth structures on algebraic surfaces with cyclic fundamental group

1988

Non-archimedean hyperbolicity and applications

2018

Inspired by the work of Cherry, we introduce and study a new notion of Brody hyperbolicity for rigid analytic varieties over a non-archimedean field $K$ of characteristic zero. We use this notion of hyperbolicity to show the following algebraic statement: if a projective variety admits a non-constant morphism from an abelian variety, then so does any specialization of it. As an application of this result, we show that the moduli space of abelian varieties is $K$-analytically Brody hyperbolic in equal characteristic zero. These two results are predicted by the Green-Griffiths-Lang conjecture on hyperbolic varieties and its natural analogues for non-archimedean hyperbolicity. Finally, we use …

From Graz to Göttingen: Neugebauer’s Early Intellectual Journey

2016

Otto Neugebauer’s early academic career was marked by a series of transitions. His interests shifted from physics to mathematics, and finally to the history of ancient mathematics and exact sciences. Yet even from his early years in Graz, Neugebauer was strongly attracted to the mathematical culture of Gottingen. When he arrived there in 1922, he quickly established a strong personal friendship with Richard Courant, the newly appointed Director of the Mathematics Institute. Neugebauer and Courant worked together closely up until 1933, when the Nazi government decimated the Gottingen scientific community. In this essay, Neugebauer’s historical work and his vision for a new approach to the st…

Archetypal analysis: an alternative to clustering for unsupervised texture segmentation

2019

Texture segmentation is one of the main tasks in image applications, specifically in remote sensing, where the objective is to segment high-resolution images of natural landscapes into different cover types. Often the focus is on the selection of discriminant textural features, and although these are really fundamental, there is another part of the process that is also influential, partitioning different homogeneous textures into groups. A methodology based on archetype analysis (AA) of the local textural measurements is proposed. AA seeks the purest textures in the image and it can find the borders between pure textures, as those regions composed of mixtures of several archetypes. The prop…

Automatic detection and classification of retinal vascular landmarks

2014

The main contribution of this paper is introducing a method to distinguish between different landmarks of the retina: bifurcations and crossings. The methodology may help in differentiating between arteries and veins and is useful in identifying diseases and other special pathologies, too. The method does not need any special skills, thus it can be assimilated to an automatic way for pinpointing landmarks; moreover it gives good responses for very small vessels. A skeletonized representation, taken out from the segmented binary image (obtained through a preprocessing step), is used to identify pixels with three or more neighbors. Then, the junction points are classified into bifurcations or…

Estimation of fibre orientation from digital images

2001

In this paper, estimation of fibre orientation is studied for fibre systems observable as a blurred greyscale image. The estimation method is based on scaled variograms observed along a set of sampling lines in different directions. The parameters of the orientation distribution are obtained numerically. Simulated data are used to study the statistical properties of the method.

Mediated action in teachers’ discussions about mathematics tasks

2012

Published version of an article in the journal: ZDM. Also available from the publisher at: http://dx.doi.org/10.1007/s11858-012-0423-0 This paper presents analyses of teachers’ discussions within mathematics teaching developmental research projects, taking mediation as the central construct. The relations in the so-called ‘didactic triangle’ form the basic framework for the analysis of two episodes in which upper secondary school teachers discuss and prepare tasks for classroom use. The analysis leads to the suggestion that the focus on tasks places an emphasis on the task as object and its resolution as goal; mathematics has the role of a mediating artefact. Subject content in the didactic…