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1

Some families of sublinear correspondences

Najmadi Parvaneh, Aghajani Masoumeh

Journal of Applied Analysis

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2019

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Vol. 25, nr 1

91--95

EN

Let K be a closed convex cone in a real Banach space, H: K → cc(K) a continuous sublinear correspondence with nonempty, convex and compact values in K, and let f : ℝ → ℝ be defined by f(t) = Σ∞n =0 antn, where t ∈ ℝ, an ≥ 0, n ∈ ℕ.We show that the correspondence Ft(x) := Σ∞n =0 an tnHn(x), (x ∈ K) is continuous and sublinear for every t ≥ 0 and Ft ∘ Fs(x) ⊆ Σ∞n=0 cnHn(x), x ∈ K, where cn = Σ>sup>nk = 0 akan−k tksn−k, t, s ≥ 0.

2

Wykorzystanie metody asynchronicznego próbkowania z linią opóźniającą oraz metryki Hausdorff'a do monitorowania systemów teletransmisji światłowodowej

Walewski P., Perlicki K., Siergiejczyk M.

Pomiary Automatyka Kontrola

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2014

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R. 60, nr 9

776--779

PL

W artykule przedstawiono metodę asynchronicznego próbkowania z liną opóźniającą ang. Asynchronous Delay Tap Sampling (ADTS) służącą do monitorowania jakości pracy systemów telekomunikacji światłowodowej. Przedstawiono analizę jednoczesnego wpływu zjawisk dyspersji chromatycznej i polaryzacyjnej oraz optycznego stosunku sygnału do szumu na wyniki metody ADTS. Do wyznaczania wartości liczbowych monitorowanych parametrów użyto metryki Hausdorff’a. Przy jednoczesnym wpływie wyżej wymienionych można monitorować dyspersję chromatyczną z błędem ±15 ps/nm, dyspersję polaryzacyjną z błędem ±1 ps oraz OSNR z błędem ±0,5 dB, co wykazały symulacje.

EN

Nowadays the development of optical fiber networks makes the requirements for them even higher. Not only public networks but also the specific corporate networks are being developed. Therefore there is a great need for complex Optical Performance Monitoring (OPM) methods. In the first three sections we discuss the needs of corporate optical networks and the limitations of OPM techniques. Then we present an application of the Asynchronous Delay Tap Sampling (ADTS) method for Optical Performance Monitoring. The way of sampling (Fig. 1), representation of samples on a scatter plot (Fig. 2) and representation of the sampled bit sequences (Fig. 3) are explained. We discuss and present the simultaneous influence of chromatic dispersion (CD), polarization mode dispersion (PMD) and optical signal to noise ratio (OSNR) on ADTS method results (Fig. 4). The simulations of 10 Gbit/s, Non-Return-to-Zero and On-Off Keying signal were made using OptSim 4.0 software. Hausdorff metric was used to evaluate the numerical value of simulated impairments (CD, PDM, OSNR). The relationship between those impairments and the Hausdorff metric was also defined (Figs. 5, 6 and 7). The evaluation of one impairment can be done when other impairments are limited. It was also determined. It was proved that chromatic dispersion could be evaluated with an error ±15 ps/nm, polarization mode dispersion ±1 ps and optical signal to noise ratio ±0,5 dB.

3

Invariant Levenstein Distance as an example of the Hausdorff Distance

Bartyzel K.

Journal of Applied Computer Science

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2014

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Vol. 22, nr 2

7--17

EN

The properties and applications of chain codes are studied around the world for many years. One of the most important uses is the ability to use them (chain codes) to describe objects contours and therefore for the comparison of objects. In previous work author presented Levenstein distance modification which allows to compare Brownian strings. In this paper, author focuses on expanding studies on developed distance and confirmation that the obtained measure is truly the mathematical metric.

4

Rozpoznawanie gestów wykonywanych dłońmi na podstawie pojedynczych obrazów

Koszowski G.

Studia Informatica

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2013

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Vol. 34, nr 2A

379--392

PL

Artykuł zawiera wyniki 3 grup algorytmów stosowanych do rozpoznawania gestów wykonywanych dłońmi na podstawie pojedynczych obrazów. Algorytmy te opierają się na: dopasowaniu szablonów masek binarnych obrazów, metodach opartych na konturach dłoni w obrazie oraz detekcji reprezentantów punktów reprezentujących krzywizny konturów dłoni. Wyniki uzyskano na podstawie 3 baz danych, w których obrazy zostały podzielone na bazę testową i referencyjną. Jedna baza referencyjna została wygenerowana na podstawie modelu 3D.

EN

This Paper include results of 3 groups of algorithms used to hand pose gesture recognition based on single images. Those algorithms base on: Template Matching of binary masks from images, methods based on hand contours in image and the Points representing points from curvatures detection. Results were obtained with 3 databases, which images were split for test and reference database. One of reference databases was generated from the 3D model.

5

The completion of the space of convex, bounded sets with respect to the Demyanov metric

Grzybowski J., Leśniewski A., Rzeżuchowski T.

Demonstratio Mathematica

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2013

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Vol. 46, nr 1

191--196

EN

The Demyanov metric in the family of convex, compact sets in finite dimensional spaces has been recently extended to the family of convex, bounded sets – not necessarily closed. In this note it is shown that these spaces are not complete and a model for the completion is proposed. A full answer is given in R2 and the situation in higher dimensions is discussed.

6

Spaces of upper semi-continuous multi-valued functions which are absolute retracts

Uehara S.

Bulletin of the Polish Academy of Sciences. Mathematics

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2003

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Vol. 51, no 3

319-328

EN

Let X = (X, d] be a metric space. We endow the hyperspace S^X x R consisting of non-empty closed subsets of X x R with the topology induced by d_H defined by d_H(E,F) = inf{epsilon is an element of (0,infinity] | N(E,epsilon) is a subset of F and N(F,epsilon) is a subset E}. Let USCC(X) be a space of upper semi-continuous multi-valued functions phi : X --> R such that phi (x) is a closed interval for every x is an element of X. Identifying those functions with their graphs, we consider USCC(X) as a subspace of 2^X x R. We give a necessary and sufficient condition on X is order that USCC(X) is closed in 2^X x R. In case X is complete, we also give a necessary and sufficient condition on USCC_B(X) to be an AR, where USCC_B(X) is a subspace of USCC(X) consisting of all bounded functions. As a corollary, we find that USCC(X) is an AR if X is compact.