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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

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.

4

Dimensionality reduction of dynamic mesh animations using HO-SVD

Romaszewski M., Gawron P., Opozda S.

Journal of Artificial Intelligence and Soft Computing Research

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2013

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Vol. 3, No. 4

277--289

EN

This work presents an analysis of Higher Order Singular Value Decomposition (HOSVD) applied to reduction of dimensionality of 3D mesh animations. Compression error is measured using three metrics (MSE, Hausdorff, MSDM). Results are compared with a method based on Principal Component Analysis (PCA) and presented on a set of animations with typical mesh deformations.

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

On unbounded almost periodic functions in Hausdorff metric

Stoiński S.

Commentationes Mathematicae

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2013

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Vol 53, No. 1

17--22

EN

In this article we give the definition and some properties of unbounded almost periodic functions in Hausdorff metric. Moreover, we examine almost periodicity of the inverse of a generalized trigonometric polynomial of constant sign.

7

The Demyanov metric and measurable multifunctions

Leśniewski A.

Journal of Mathematics and Applications

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2010

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Vol. 33

61-65

EN

We present in this paper measurability multifunctions in the family of all convex, bounded sets which need not be closed. The Demyanov metric is discussed.

8

On the continuity of the integrable multifunctions

Piątek B.

Opuscula Mathematica

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2009

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Vol. 29, no. 1

81-88

EN

The generalization of the Polovinkin theorem is studied.

9

On the Lifshits constant for hyperspaces

Leśniak K.

Bulletin of the Polish Academy of Sciences. Mathematics

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2007

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Vol. 55, no 2

155-160

EN

The Lifshits theorem states that any k-uniformly Lipschitz map with a bounded orbit on a complete metric space X has a fixed point provided k < x(X] where x(X) is the so-called Lifshits constant of X. For many spaces we have x(X) > 1. It is interesting whether we can use the Lifshits theorem in the theory of iterated function systems. Therefore we investigate the value of the Lifshits constant for several classes of hyperspaces.

10

When lines go bad in hyperspace

Bay C., Lembcke A., Schlicker S.

Demonstratio Mathematica

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2005

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Vol. 38, nr 3

689--701

EN

Let H(Rn) denote the hyperspace of all non-empty compact subsets of Rn. The Hausdorff metric h provides a way to measure distances between two elements of H(Rn) and generates the complete metric space (H(Rn),h)). In this paper, we examine geometric properties of lines in H(Rn), as determined by the Hausdorff metric, and compare and contrast the properties of these lines with Euclidean lines in Rn. Several surprising properties of these objects will be highlighted.

11

Hyperspaces of finite sets in universal spaces for absolute Borel classes

Mine K., Sakai K., Yaguchi M.

Bulletin of the Polish Academy of Sciences. Mathematics

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2005

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Vol. 53, no 4

409-419

EN

By Fin(X) (resp. Fink (X)), we denote the hyperspace of all non-empty finite subsets of X (resp. consisting of at most k points) with the Vietoris topology. Let ℓ2 (τ) be the Hilbert space with weight τ and ℓf2 (τ) the linear span of the canonical orthonormal basis of ℓ2 (τ). It is shown that if E = ℓf2 (τ) or E is an absorbing set in ℓ2 (τ) for one of the absolute Borel classes aα (τ) and Mα (τ) of weight ≤ τ (α > 0) then Fin(E) and each Fink (E) are homeomorphic to E. More generally, if X is a connected E-manifold then Fin(X) is homeomorphic to E and each Fink (X) is a connected E-manifold.

12

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.

13

The Hausdorff metric and its extensions

Moshokoa S. P.

Demonstratio Mathematica

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2002

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Vol. 35, nr 2

233-241

EN

We consider a complete metric space (X,p) such that closed balls are compact. The paper is devoted to the Hausdorff distance d denned on 5R, the space of all nonempty compact subsets of X.

14

Hausdorff convergence of domains and their boundaries for shape optimal design

Holzleitner L.

Control and Cybernetics

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2001

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Vol. 30, no 1

23-44

EN

A question, which arises frequently in shape optimal design, is the convergence of domains. If the objective function is defined by using the solution of a PDE with boundary conditions, then also the convergence of the boundary is of importance. In this paper a criterion for a set of domains is defined, such that from [Omega_n] --> Omega follows [Gamma_n] --> Gamma if one is restricting to this set of domains. Moreover it is proved that this criterion is sharp, meaning that if [Omega_n] --> Omega implies [Gamma_n] --> Gamma holds for any sequence of this set, then this criterion has to be fulfilled. A similar criterion for the convergence of the Lebesgue measure of the boundaries my(Gamma_n) --> my(Gamma) is given.

15

On the indefinite integral and approximation of H-almost periodic functions

Stoiński S.

Fasciculi Mathematici

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1999

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Nr 29

133-137

EN

The paper gives a theorem on the indefinite integral of H-almost periodic function and a theorem on approximation of an H-almost periodic function by means Steklov functions.