Wyniki wyszukiwania - Biblioteka Nauki

1

The density Turan problem for 3-uniform linear hypertrees. An efficient testing algorithm

100%

Bielak H. , Powroźnik K.

Annales Universitatis Mariae Curie-Skłodowska, sectio A – Mathematica

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2018

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tom 72

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nr 2

EN

Let \(\mathcal{T}=(V,\mathcal{E})\) be a 3-uniform linear hypertree. We consider a blow-up hypergraph \(\mathcal{B}[\mathcal{T}]\). We are interested in the following problem. We have to decide whether there exists a blow-up hypergraph \(\mathcal{B}[\mathcal{T}]\) of the hypertree \(\mathcal{T}\), with hyperedge densities satisfying some conditions, such that the hypertree \(\mathcal{T}\) does not appear in a blow-up hypergraph as a transversal. We present an efficient algorithm to decide whether a given set of hyperedge densities ensures the existence of a 3-uniform linear hypertree \(\mathcal{T}\) in a blow-up hypergraph \(\mathcal{B}[\mathcal{T}]\).

2

A Characterization of Hypergraphs with Large Domination Number

100%

Henning M. A. , Löwenstein C.

Discussiones Mathematicae Graph Theory

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2016

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tom 36

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nr 2

427-438

EN

Let H = (V, E) be a hypergraph with vertex set V and edge set E. A dominating set in H is a subset of vertices D ⊆ V such that for every vertex v ∈ V \ D there exists an edge e ∈ E for which v ∈ e and e ∩ D ≠ ∅. The domination number γ(H) is the minimum cardinality of a dominating set in H. It is known [Cs. Bujtás, M.A. Henning and Zs. Tuza, Transversals and domination in uniform hypergraphs, European J. Combin. 33 (2012) 62-71] that for k ≥ 5, if H is a hypergraph of order n and size m with all edges of size at least k and with no isolated vertex, then γ(H) ≤ (n + ⌊(k − 3)/2⌋m)/(⌊3(k − 1)/2⌋). In this paper, we apply a recent result of the authors on hypergraphs with large transversal number [M.A. Henning and C. Löwenstein, A characterization of hypergraphs that achieve equality in the Chvátal-McDiarmid Theorem, Discrete Math. 323 (2014) 69-75] to characterize the hypergraphs achieving equality in this bound.

3

Generic saddle-node bifurcation for cascade second order ODEs on manifolds

88%

Medveď M.

Annales Polonici Mathematici

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1998

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tom 68

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nr 3

211-225

EN

Cascade second order ODEs on manifolds are defined. These objects are locally represented by coupled second order ODEs such that any solution of one of them can represent an external force for the other one. A generic saddle-node bifurcation theorem for 1-parameter families of cascade second order ODEs is proved.

4

Limitation of Cauchy function method in analysis for double estimators of free transversal vibration of cantilever tapered shafts

88%

Jaroszewicz J. , Dragun Ł.

Technical Sciences / University of Warmia and Mazury in Olsztyn

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2013

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tom nr 16(2)

131--146

EN

In this paper the Bernstein-Kieropian simplest Dunkerly estimators of natural frequencies of cantilever shafts with power variable flexural rigidity and attached concentrated mass were analyzed in a theoretical approach. The approximate solution of boundary value problem of transversal vibrations by means of Cauchy function and characteristic series method has gave getting functional dependence between natural frequency and variable parameters of shafts. Particular attention has been given to a singularity arising from the uncertainty of estimates of Bernstein-Kieropian. Limitation of Cauchy function method in analysis double estimators of natural frequencies of transversal vibration of cantilever tapered shafts exude to exact theoretical selection using by Bessel’s function and experimental result received by Panuszka R., Uhl T.

5

Analiza tablic decyzyjnych z wykorzystaniem monotonicznego rachunku sekwensów

63%

Tkacz J. , Adamski M.

Przegląd Elektrotechniczny

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2013

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tom R. 89, nr 6

256--259

PL

W artykule przedstawiono nowatorski sposób analizy systemów regułowych z wykorzystaniem symbolicznego wnioskowania w monotonicznej logice sekwentów Gentzena. Badany system dyskretny jest opisywany w postaci tablicy decyzyjnej. Celem analizy systemu jest usunięcie zbytecznych kolumn w tablicy decyzyjnej oraz nieistotnych symboli zmiennych logicznych w jej poszczególnych wierszach. Efektywny aparat wnioskowania w logice formalnej umożliwia sprawne wyznaczanie transwersal krawędzi hipergrafu rozróżnialności.

EN

The paper presents a new methodology for symbolic reduction of multivalued decision tables, currently intensively used for compact behavioral specifications of logic controllers. As an example the well known problem of simplification of a set of several logic rules with many variables is chosen. As a completely new, original solution, the formal automated reasoning based on Gentzen propositional calculus together with hypergraph theory are jointly used. The clique-transversal symbolic calculation is performed by means of effective reasoning in Gentzen calculus.

6

Wyznaczanie SM - pokrycia bezpiecznej sieci Petriego metodą komputerowego wnioskowania

63%

Tkacz J. , Adamski M.

Pomiary Automatyka Kontrola

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2011

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tom R. 57, nr 11

1397-1400

PL

W artykule przedstawiono nowy sposób pokrywania bezpiecznej sieci Petriego minimalną liczbą podsieci automatowych. Metoda symboliczna polega na wczesnej selekcji odpowiednich transwersali, stopniowo wyznaczanych dla rodziny maksymalnych podzbiorów współbieżnych miejsc sieci. W przypadku bezpiecznej sterującej sieci Petriego, miejsca traktowane są jako stany lokalne, natomiast ich dopuszczalne konfiguracje określają jej stany globalne. Transwersale wyróżniają podzbiory miejsc niewspółbieżnych, przypisanych do odpowiednich SM-podsieci. Komputerowe wnioskowanie odbywa się w monotonicznym rachunku sekwentów Gentzena. Rezultaty wykorzystywane są podczas syntezy cyfrowych, konfigurowanych sterowników logicznych z zastosowaniem komercjalnego oprogramowania i języków opisu sprzętu.

EN

The paper presents a way of finding a suitable Petri net cover by means of a minimal number of maximal State Machine subnets (SM-components). A new symbolic method of Petri net parallel decomposition is based on early selection of proper minimal transversals, taken from family of all global Petri net states. Global states are given in advance as maximal subsets, formed from mutually concurrent places. They can be found as reachable global states of Petri net. During digital design of a logic controller, the places of the safe Petri net are treated as local internal states of Concurrent State Machine, implemented in a reconfigurable logic device (FPGA). The minimal number of selected transversals, which characterizes subsets of sequentially related places, is assigned to separate State Machine subnets. The computer based reasoning is searching a logic expression describing transversals in Gentzen sequent logic. The obtained decomposition (or cover) is used for state encoding of configurable array based embedded logic controllers, implemented as microsystems.

7

Algorytm selekcji wykorzystujący teorię hipergrafów

51%

Stefanowicz Ł. , Wiśniewski R. , Adamski M.

Pomiary Automatyka Kontrola

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2014

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tom R. 60, nr 7

516--518

PL

Artykuł porusza kwestię selekcji określonych elementów zbioru z wykorzystaniem teorii hipergrafów. Przedstawiona została idea wspólnego algorytmu selekcji, w przypadku takich problemów, jak selekcja podsieci automatowych w dekompozycji sieci Petriego, a także selekcja implikantów prostych w procesie miminalizacji funkcji logicznych. Jako bazowy algorytm, wykorzystano metodę transwersal dokładnych, jednocześnie usprawniając ją o alternatywną scieżkę w przypadku, kiedy dany hipergraf selekcji nie należy do klasy hipergrafu transwersal dokładnych. Jak pokazują badania, metoda może być dobrą alternatywą obok wykorzystywanych metod tradycyjnych.

EN

The paper deals with the selection problem based on the hypergraph theory. There is presented an idea of a common selection algorithm for selection of State Machine Components and Prime Implicants. The exact transversal method was used as a baseline algorithm. It was improved by supporting it with an optional path when a given selection hypergraph did not belong to the xt-class (class of the exact transversal hypergraph). In this case, the exact transversal was searched. When it was unsuccessful, the regular transversal was searched. The studies prove that the method allows obtaining the exact solution when the selection hypergraph does not belong to the xt-class, but has an exact transversal. The presented results show that a hypergraph which does not belong to the xt-class may have an exact transversal enabling obtaining a solution which would be as good as the one obtained with the backtracking method. The exact solution was also obtained with the use of an ordinary transversal, which de facto indicated that the regular transversals allowed, in certain cases, obtaining the exact solution. It seems to confirm the aptly determined class of solutions of the proposed improvements. In some cases, the solution contained one extra subnet, but in one tested case, the solution turned out to be much worse than the exact one.