201 research outputs found
-right equivalence of analytic functions
Let be analytic functions.
We will show that if and then and
are -right equivalent, where denote ideal generated by and .Comment: 9 pages. Main result has been significantly improve
On quadratic polynomial mappings from the plane into the dimensional space
We show that, up to linear equivalence, there are only finitely many
polynomial quadratic mappings and
. We list all possibilities.Comment: 22 page
Stability of implicit neural networks for long-term forecasting in dynamical systems
Forecasting physical signals in long time range is among the most challenging
tasks in Partial Differential Equations (PDEs) research. To circumvent
limitations of traditional solvers, many different Deep Learning methods have
been proposed. They are all based on auto-regressive methods and exhibit
stability issues. Drawing inspiration from the stability property of implicit
numerical schemes, we introduce a stable auto-regressive implicit neural
network. We develop a theory based on the stability definition of schemes to
ensure the stability in forecasting of this network. It leads us to introduce
hard constraints on its weights and propagate the dynamics in the latent space.
Our experimental results validate our stability property, and show improved
results at long-term forecasting for two transports PDEs.Comment: ICLR 2023 Workshop on Physics for Machine Learnin
Clustering polar curves
This essay builds on the idea of grouping the polar curves of 2-variable
function germs into polar clusters. In the topological category, one obtains a
bijective correspondence between certain partitions of the polar quotients of
two topologically equivalent function germs. We explain how this bijective
correspondence may be refined in the Lipschitz category in terms of the
associated gradient canyons.Comment: updated, revised versio
Computer-aided machine design with regard to new technologies and materials
The aim of the paper is to present the issue of using computer-aided methods as well as 3D printing technologies and not typical materials connected with it. Selected problems that can occur while applying computer-aided methods and their solutions have also been described
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