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Data probes, vertical trajectories and classification: a tentative study

100%
Pearson D. W.
International Journal of Applied Mathematics and Computer Science
|
2007
|
tom 17
|
nr 1
107-112
EN
In this paper we introduce a method of classification based on data probes. Data points are considered as point masses in space and a probe is simply a particle that is launched into the space. As the probe passes by data clusters, its trajectory will be influenced by the point masses. We use this information to help us to find vertical trajectories. These are trajectories in the input space that are mapped onto the same value in the output space and correspond to the data classes.
2
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Automatic control of mechatronic systems

88%
Schlacher K., Kugi A.
International Journal of Applied Mathematics and Computer Science
|
2001
|
tom 11
|
nr 1
131-164
EN
This contribution deals with different concepts of nonlinear control for mechatronic systems. Since most physical systems are nonlinear in nature, it is quite obvious that an improvement in the performance of the closed loop can often be achieved only by means of control techniques that take the essential nonlinearities into consideration. Nevertheless, it can be observed that industry often hesitates to implement these nonlinear controllers, despite all advantages existing from the theoretical point of view. On the basis of three different applications, a PWM-controlled dc-to-dc converter, namely the 'Cuk-converter, the problem of hydraulic gap control in steel rolling, and the design of smart structures with piezolelectric sensor and actuator layers, we will demonstrate how one can overcome these problems by exploiting the physical structure of the mathematical models of the considered plants.
3
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Isometric Embeddings of Pro-Euclidean Spaces

75%
Minemyer B.
Analysis and Geometry in Metric Spaces
|
2015
|
tom 3
|
nr 1
EN
In [12] Petrunin proves that a compact metric space X admits an intrinsic isometry into En if and only if X is a pro-Euclidean space of rank at most n, meaning that X can be written as a “nice” inverse limit of polyhedra. He also shows that either case implies that X has covering dimension at most n. The purpose of this paper is to extend these results to include both embeddings and spaces which are proper instead of compact. The main result of this paper is that any pro-Euclidean space of rank at most n is proper and admits an intrinsic isometric embedding into E2n+1. Since every n-dimensional Riemannian manifold is a pro-Euclidean space of rank at most n, this result is a partial generalization of (the C0 version of) the famous Nash isometric embedding theorem from [10].
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