Wyniki wyszukiwania - BazTech

1

Kraty dystrybutywne w problemach analizy systemów elektroenergetycznych

Grishkevich Andrey

Przegląd Elektrotechniczny

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2025

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R. 101, nr 1

152--155

PL

Zbiór minimalnych przekrojów z wprowadzonymi na nim operacjami binarnymi jest kratą dystrybutywną. Zestaw minimalnych przekrojów w kracie dystrybutywnej minimalnych przekrojów można opisać analitycznie na podstawie podzbioru nierozkładalnych minimalnych przekrojów. Proponowane jest kodowanie kraty dystrybutywnej w celu efektywnej realizacji operacji na przekrojach.

EN

The set of minimal cuts with binary operations introduced on it is a distributive lattice. A set of minimal cuts in a distributive minimal cut lattice can be described analytically from a subset of indecomposable minimal cuts. We propose a coding of a distributive lattice for the efficient implementation of operations on cuts.

2

Optimization of computer ontologies for e-courses in information and communication technologies

Sabitova Nazym, Tikhonov Yuriy, Lakhno Valerii, Makulov Kariyrbek, Kryvoruchko Olena, Chubaievskyi Vitalyi, Desiatko Alona, Zhumadilova Mereke

International Journal of Electronics and Telecommunications

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2024

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Vol. 70, No. 1

191--197

EN

A methodology is proposed for modifying computer ontologies (CO) for electronic courses (EC) in the field of information and communication technologies (ICT) for universities, schools, extracurricular institutions, as well as for the professional retraining of specialists. The methodology includes the modification of CO by representing the formal ontograph of CO in the form of a graph and using techniques for working with the graph to find optimal paths on the graph using applied software (SW). A genetic algorithm (GA) is involved in the search for the optimal CO. This will lead to the division of the ontograph into branches and the ability to calculate the best trajectory in a certain sense through the EC educational material, taking into account the syllabus. An example is considered for the ICT course syllabus in terms of a specific topic covering the design and use of databases. It is concluded that for the full implementation of this methodology, a tool is needed that automates this procedure for developing EC and/or electronic textbooks. An algorithm and a prototype of software tools are also proposed, integrating machine methods of working with CO and graphs.

3

Two sufficient conditions for graphs to admit path factors

Zhou Sizhong, Wu Jiancheng

Fundamenta Informaticae

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2024

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Vol. 191, nr 1

67--77

EN

Let A be a set of connected graphs. Then a spanning subgraph A of G is called an A-factor if each component of A is isomorphic to some member of A. Especially, when every graph in A is a path, A is a path factor. For a positive integer d ≥ 2, we write P≥d = {Pi|i ≥ d}. Then a P≥d-factor means a path factor in which every component admits at least d vertices. A graph G is called a (P≥d, m)-factor deleted graph if G − E′ admits a P≥d-factor for any E′ ⊆ E(G) with |E′| = m. A graph G is called a (P≥d, k)-factor critical graph if G − Q has a P≥d-factor for any Q ⊆ V (G) with |Q| = k. In this paper, we present two degree conditions for graphs to be (P≥3, m)-factor deleted graphs and (P≥3, k)-factor critical graphs. Furthermore, we show that the two results are best possible in some sense.

4

Periodic and fixed points for mappings in extended b-gauge spaces equipped with a graph

Zikria Nosheen, Samreen Maria, Savas Ekrem, Sen Manuel De la, Kamran Tayyab

Demonstratio Mathematica

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2024

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Vol. 57, nr 1

art. no. 20240016

EN

This article presents the notions of extended b-gauge space (U, Qφ;Ω) and extended Jφ;Ω-families of generalized extended pseudo-b-distances on U. Furthermore, we look at these extended Jφ;Ω-families on U and define the extended Jφ;Ω-sequential completeness. We also look into some fixed and periodic point theorems for set-valued mappings in the new space with a graph that does not meet the completeness condition of the space. Additionally, this article includes some examples to explain the corresponding results and highlights some important consequences of our obtained results.

5

Edge coloring of small signed graphs

Janczewski Robert, Turowski Krzysztof, Wróblewski Bartłomiej

TASK Quarterly : scientific bulletin of Academic Computer Centre in Gdansk

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2023

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Vol. 27, No 2

1--9

EN

In 2020, Behr [1] introduced the problem of edge coloring of signed graphs and proved that every signed graph (G, σ) can be colored using ∆(G) or ∆(G) +1colors, where ∆(G) denotes the maximum degree of G. Three years later, Janczewski et al. [2] introduced a notion of signed class 1, such that a graph G is of signed class 1 if and only if everysigned graph (G, σ) can be colored using ∆(G) colors. It is a well-known fact [3] that almost all graphs are of class 1. In this paper, we conjecture that a similar fact is true for signed class 1, that almost all graphs are of signed class 1. To support the hypothesis we implemented an application that colored all the signed graphs with at most 8 vertices. We describe an algorithm behind the application and discuss the results of conducted experiments.

6

The crossing numbers of join products of four graphs of order five with paths and cycles

Staš Michal, Timková Mária

Opuscula Mathematica

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2023

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Vol. 43, no. 6

865--883

EN

The crossing number cr(G) of a graph G is the minimum number of edge crossings over all drawings of G in the plane. In the paper, we extend known results concerning crossing numbers of join products of four small graphs with paths and cycles. The crossing numbers of the join products G∗ + Pn and G∗ + Cn for the disconnected graph G∗ consisting of the complete tripartite graph K1,1,2 and one isolated vertex are given, where Pn and Cn are the path and the cycle on n vertices, respectively. In the paper also the crossing numbers of H∗ + Pn and H∗ + Cn are determined, where H∗ is isomorphic to the complete tripartite graph K1,1,3. Finally, by adding new edges to the graphs G∗ and H∗, we are able to obtain crossing numbers of join products of two other graphs G1 and H1 with paths and cycles.

7

Lopa i graf ryzyka dla wymagań SIL w obiektach przemysłowych

Hejke Igor

Chemia Przemysłowa

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2023

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Nr 1

128--129

PL

W nowoczesnym przemyśle skomplikowane systemy zabezpieczeń chronią przed powstaniem zdarzeń niebezpiecznych, np. przekroczeniem parametrów dopuszczalnych urządzeń ciśnieniowych, uwolnieniem substancji niebezpiecznej lub wytworzeniem atmosfery wybuchowej.

8

Upper bounds on distance vertex irregularity strength of some families of graphs

Cichacz Sylwia, Görlich Agnieszka, Semaničová-Feňovčíková Andrea

Opuscula Mathematica

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2022

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Vol. 42, no. 4

561--571

EN

For a graph G its distance vertex irregularity strength is the smallest integer k for which one can find a labeling f : V (G) → {1, 2, . . . , k} such that [formula] for all vertices u, v of G, where N(v) is the open neighborhood of v. In this paper we present some upper bounds on distance vertex irregularity strength of general graphs. Moreover, we give upper bounds on distance vertex irregularity strength of hypercubes and trees.

9

The crossing numbers of join products of paths with three graphs of order five

Staš Michal, Švecová Mária

Opuscula Mathematica

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2022

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Vol. 42, no. 4

635--651

EN

The main aim of this paper is to give the crossing number of the join product G∗ + Pn for the disconnected graph G∗ of order five consisting of the complete graph K4 and one isolated vertex, where Pn is the path on n vertices. The proofs are done with the help of a lot of well-known exact values for the crossing numbers of the join products of subgraphs of the graph G∗ with the paths. Finally, by adding new edges to the graph G∗, we are able to obtain the crossing numbers of the join products of two other graphs with the path Pn.

10

Analiza i implementacja algorytmów odnajdywania ścieżki do zastosowania w grach przeglądarkowych

Laszkiewicz Beata, Sobczak Tomasz

Biuletyn Naukowy Wrocławskiej Wyższej Szkoły Informatyki Stosowanej. Informatyka

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2022

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vol. 9, nr 1

16--24

PL

Celem tego artykułu jest przedstawienie, porównanie oraz implementacja algorytmów odnajdywania ścieżki do zastosowania w grach przeglądarkowych z wykorzystaniem ogólnodostępnych, darmowych technologii internetowych. Pokazano również możliwość wykorzystania najlepszego algorytmu w grze przeglądarkowej

EN

The goal of this article is to present, compare and implement path finding algorithms for use in browser games, using public, free internet technologies. The possibility of using the best algorithm in a browser game is also shown.

11

Modelling computer networks for further security research

Bederna Zsolt, Szádeczky Tamás

Security and Defence Quarterly

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2021

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Vol. 36, No. 4

51--66

EN

Computer networks are usually modelled from one aspect, e.g., the physical layer of the network, although this does not allow the researcher to understand all usage of that device. We aim to develop a model which leverages all aspects of a networked computer and, therefore, provides complete information to the scientist for all further security research, especially that related to the social sciences. Network science is about the analysis of any network, from social to protein. It is much easier to analyse computer networks with technical tools than protein networks. It is, therefore, a straightforward way to crawl the web as Albert-Laszlo Barabasi did to model its connections, nodes, and links in graph theory to analyse its internal connections. His analysis was based solely on the network layer. Our methodology uses graph theory and network science and integrates all ISO/OSI (computer networking) layers into the model. Each layer of the ISO/OSI model has its topology separately, but all of them also work as part of the complex system to operate the network. It therefore creates a multipartite graph of the network under analysis. Furthermore, the virtual private networks (VPNs) and application usage are also integrated as nodes and links. With this model, the computer network infrastructure and usage data can be used for further non-computing related research, e.g., social science research, as it includes the usage patterns of the network users.

12

Network connectivity dynamic modelling

Eid Mohamed

Safety and Reliability of Systems and Processes

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2021

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Summer Safety and Reliability Seminar 2021

117--127

EN

The chapter presents an approach based on basic notions issued from the graph theory and from the system reliability theory. The approach seeks to describe the transitions in the connectivity state of non-directional graphs induced by systemic losses of nodes and edges. Each component loss (node or edge) represents a transition and results in a connectivity degradation. Some of the transitions are classified as non-critical while others are critical. Degradations are measured using the notion of topological graph diameter issued from the graph theory. The critical transition notion is issued from the system reliability theory. The approach determines the degraded graph diameter corresponding to each possible transition and subsequently the criticality of the transition. The criticality threshold is determined by the highest acceptable connectivity order which is a function of the degraded graph diameter. A network with 9 nodes and 15 edges is used as an academic study case to illustrate the applicability of the approach. Nodes are supposed to be identical, as well as the edges. All network components (nodes and edges) are mutually independent. These precedent hypotheses are intended to evacuate all sources of numerical useless complexity. As our main objective is to highlight the original characteristic of the proposed approach.

13

Search for the optimal band of a given width in a simply connected region

Grishkevich Andrey

Przegląd Elektrotechniczny

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2021

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R. 97, nr 12

109--112

EN

An original method for finding the optimal band of a given width based on the algorithms for the maximum flow / minimum cut construction is proposed. An example of the presented algorithm work is given.

PL

Zaproponowano oryginalną metodę znajdowania optymalnego pasa o danej szerokości w oparciu o algorytmy konstruowania maksymalnego przepływu / minimalnego przekroju. Podano przykład działania prezentowanego algorytmu.

14

On the crossing numbers of join products of W4 + Pn and W4 + Cn

Stas Michal, Valiska Juraj

Opuscula Mathematica

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2021

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Vol. 41, no. 1

95-112

EN

The crossing number cr(G) of a graph G is the minimum number of edge crossings over all drawings of G in the plane. The main aim of the paper is to give the crossing number of the join product W4 + Pn and W4 + Cn for the wheel W4 on five vertices, where Pn and Cn are the path and the cycle on n vertices, respectively. Yue et al. conjectured that the crossing number of Wm + Cn is equal to [formula], for all m,n ≥ 3, and where the Zarankiewicz’s number[formula] is defined for n ≥ 1. Recently, this conjecture was proved for W3 + Cn by Klesc. We establish the validity of this conjecture for W4 + Cn and we also offer a new conjecture for the crossing number of the join product Wm + Pn for m ≥ 3 and n ≥ 2.

15

On the crossing numbers of join products of five graphs of order six with the discrete graph

Stas Michal

Opuscula Mathematica

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2020

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Vol. 40, no. 3

383--397

EN

The main purpose of this article is broaden known results concerning crossing numbers for join of graphs of order six. We give the crossing number of the join product G* + Dn, where the disconnected graph G* of order six consists of one isolated vertex and of one edge joining two nonadjacent vertices of the 5-cycle. In our proof, the idea of cyclic permutations and their combinatorial properties will be used. Finally, by adding new edges to the graph G*, the crossing numbers of Gi + Dn for four other graphs Gi of order six will be also established

16

Some results on graph associated to co-ideals of commutative semirings

Talebi Yahya, Darzi Atefeh

Fasciculi Mathematici

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2020

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nr 64

91--100

EN

For a commutative semiring R with non-zero identity, the graph Ω(R) of R, is the graph whose vertices are all elements of R and two distinct vertices x and y are adjacent if and only if the product of the co-ideals generated by x and y is R. In this paper, we study some properties of this graph such as planarity, domination number and connectivity.

17

On the Carrying Dimension of Occupation Measures for Self-Affine Random Fields

Kern Peter, Sönmez Ercan

Probability and Mathematical Statistics

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2019

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Vol. 39, Fasc. 2

459--479

EN

Hausdorff dimension results are a classical topic in the study of path properties of random fields. This article presents an alternative approach to Hausdorff dimension results for the sample functions of a large class of self-affine random fields. The aim is to demonstrate the following interesting relation to a series of articles by U. Zähle (1984, 1988, 1990, 1991). Under natural regularity assumptions, we prove that the Hausdorff dimension of the graph of self-affine fields coincides with the carrying dimension of the corresponding self-affine random occupation measure introduced by U. Zähle. As a remarkable consequence we obtain a general formula for the Hausdorff dimension given by means of the singular value function.

18

Correlation clustering: Let all the flowers bloom!

Aszalós László, Bakó Mária

Annals of Computer Science and Information Systems

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2019

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Vol. 20

21--28

EN

Correlation clustering is a NP-hard problem, and for large signed graphs finding even just a good approximation of the optimal solution is a hard task. In this article we examine the effect of ranking of the nodes and process them in order of ranks. We present that based on the rate of positive edges in the graph we should use different optimization methods. We show that all the building blocks of our methods are needed under certain circumstances.

19

Evaluation of the practicability of the decomposition and equivalent substitution method in the analysis of reliability of the sewage system

Kubala M., Królikowska J., Wawrentowicz D.

Technical Transactions

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2018

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Vol. 115, iss. 5

119--127

EN

The work compares the accuracy of calculations of the reliability parameters of the sewerage network using the Decomposition and Equivalent Replacement (MDE) method, proposed by Yu. A. Yermolin and M.I. Alekseev [3], definitely simpler and less onerous in relation to the graph method. Comparing the results of calculations with both methods, applied to a simple network, one can come to the conclusion that the MDE calculations in simple cases give satisfactory accuracy. However, it would be necessary to check whether, as the complexity increases, this accuracy is still satisfactory.

PL

W pracy porównano dokładność obliczeń parametrów niezawodnościowych sieci kanalizacyjnej metodą dekompozycji i ekwiwalentnej zamiany (MDE), zaproponowaną przez Ju. A. Jermolina i M.I. Alieksjejewa [3], zdecydowanie prostszą i mniej uciążliwą w stosunku do metody grafów. Porównując wyniki obliczeń obiema metodami, zastosowane do prostej sieci, można dojść do wniosku, że obliczenia metodą MDE w prostych przypadkach dają zadowalającą dokładność. Należałoby jednak sprawdzić, czy w miarę wzrostu złożoności, dokładność ta jest nadal zadowalająca.

20

The least eigenvalue of the graphs whose complements are connected and have pendent paths

Wang C., Yu G., Sun W., Cao J.

Journal of Artificial Intelligence and Soft Computing Research

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2018

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Vol. 8, No. 4

303--308

EN

The adjacency matrix of a graph is a matrix which represents adjacent relation between the vertices of the graph. Its minimum eigenvalue is defined as the least eigenvalue of the graph. Let Gn be the set of the graphs of order n, whose complements are connected and have pendent paths. This paper investigates the least eigenvalue of the graphs and characterizes the unique graph which has the minimum least eigenvalue in Gn.