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1
Content available On the lattice of tolerances for a finite chain
Górnicka A., Grygiel J., Tyrala I.
Scientific Issues of Jan Długosz University in Częstochowa. Mathematics
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2016
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Vol. 21
25--30
EN
We provide some description of the lattice of tolerances for a finite chain, pointing to the skeleton tolerance as a special element of this lattice. In particular, we prove that the lattice of all glued tolerances of an n-element chain is isomorphic to the lattice of all tolerances of an n- 1-element chain nad at the same time is a principal filter of the lattice of an n-element chain.
2
Content available Sparingly glued tolerances
Górnicka A., Grygiel J., Tyrala I.
Scientific Issues of Jan Długosz University in Częstochowa. Mathematics
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2015
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Vol. 20
49--54
EN
We introduce the notion of sparingly glued tolerances for lattices and then count their numbers in case of finite chains. We also estimate the density of sparingly glued tolerances among all glued tolerances on finite chains.
3
Content available remote Application of Mel Cepstral Representation of Voice Recordings for Diagnosing Vocal Disorders
Grygiel J., Strumiłło P., Niebudek-Bogusz E.
Przegląd Elektrotechniczny
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2012
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R. 88, nr 6
8-11
EN
The aim of this study was to assess the applicability of Mel Frequency Cepstral Coefficients (MFCC) of voice samples in diagnosing vocal nodules and polyps. Patients’ voice samples were analysed acoustically with the measurement of MFCC and values of the first three formants. Classification of mel coefficients was performed by applying the Sammon Mapping and Support Vector Machines. For the tests conducted on 95 patients, voice disorders were detected with accuracy reaching approx. 80%.
PL
Celem niniejszej pracy była ocena możliwości zastosowania analizy tzw. współczynników cepstralnych (ang. Mel Cepstral Coefficients (MFCC)) dla próbek rejestrowanego głosu pacjentów we wspomaganiu diagnozy guzów i polipów. Rejestracje mowy pacjentów poddane zostały analizie akustycznej, w której zastosowano parametry MFCC oraz wartości trzech pierwszych formantów. Do klasyfikacji współczynników cepstralnych zastosowano odwzorowanie Sammona oraz tzw. Maszynę Wektorów Nośnych. W testach wykonanych dla 95 rejestracji mowy pacjentów, zaburzenia głosu zostały wykryte z ok. 80% dokładnością.
4
Content available Some counting formulas for finite distributive lattices
Grygiel J.
Scientific Issues of Jan Długosz University in Częstochowa. Mathematics
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2010
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Vol. 15
43--48
EN
In the paper we show that the weighted double skeleton of a finite distributive lattice is a suffcient structure to characterize the lattice numerically. We prove some combinatorial formulas for the number of all elements of a finite distributive lattice with the given weighted double skeleton, all its elements with exactly k lower covers and all its covering pairs. Introducing some simple examples, we show how the formulas work.
5
Content available remote W-irreducible Lattices
Grygiel J.
Scientific Issues of Jan Długosz University in Częstochowa. Mathematics
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2005
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Vol. 10
77--81
EN
A finite lattice is W-irreducible if it cannot be split into two overlapping lattices, one of them being an ideal and the other a filter of the lattice. We give some characterization of finite W-irreducible lattices.
6
Content available remote Application of the Cantor-Bendixon construction to the problem of freely generated filters
Grygiel J.
Reports on Mathematical Logic
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2004
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Nr 38
49-59
EN
In this paper we prove that using the Cantor-Bendixon construction, we can reduce the problem of existence of an independent se of generators of a filter in a Boolean algebra to the same problem in an atomless algebra.
7
Content available remote Boolean constructions of independent sets of generators for filters
Grygiel J.
Reports on Mathematical Logic
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2001
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No. 35
75-85
EN
Let F be a filter in a Boolean algebra. We consider the problem if it possible to construct an independent set of generators for F from any its set of generators. It turns out that the answer to this question depends on the minimal cardinality of the set of generators of F.
8
Content available remote The Sum Operation and Llink Lattices
Grygiel J., Wojtylak P.
Scientific Issues of Jan Długosz University in Częstochowa. Mathematics
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1999
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Vol. 6
23--28
EN
The sum operation, as introduced by Andrzej Wroński, is used to decompose any finite distributive lattice into its Boolean fragments. The decomposition is not unique but its maximal components are uniquely determined. We define an ordering relation between these maximal Boolean fragments of a given lattice and use this link ordering to describe the structure of the lattice.
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