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Wyświetlanie 1-5 z 5
Tytuł:
Optimal Locating-Total Dominating Sets in Strips of Height 3
Autorzy:
Junnila, Ville
Powiązania:
https://bibliotekanauki.pl/articles/31339416.pdf
Data publikacji:
2015-08-01
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
locating-total dominating set
domination
square grid
strip
Opis:
A set C of vertices in a graph G = (V,E) is total dominating in G if all vertices of V are adjacent to a vertex of C. Furthermore, if a total dominating set C in G has the additional property that for any distinct vertices u, v ∈ V \ C the subsets formed by the vertices of C respectively adjacent to u and v are different, then we say that C is a locating-total dominating set in G. Previously, locating-total dominating sets in strips have been studied by Henning and Jafari Rad (2012). In particular, they have determined the sizes of the smallest locating-total dominating sets in the finite strips of height 2 for all lengths. Moreover, they state as open question the analogous problem for the strips of height 3. In this paper, we answer the proposed question by determining the smallest sizes of locating-total dominating sets in the finite strips of height 3 as well as the smallest density in the infinite strip of height 3.
Źródło:
Discussiones Mathematicae Graph Theory; 2015, 35, 3; 447-462
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
On the 12-Representability of Induced Subgraphs of a Grid Graph
Autorzy:
Chen, Joanna N.
Kitaev, Sergey
Powiązania:
https://bibliotekanauki.pl/articles/32361728.pdf
Data publikacji:
2022-05-01
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
graph representation
12-representable graph
grid graph
forbidden subgraph
square grid graph
line grid graph
Opis:
The notion of a 12-representable graph was introduced by Jones, Kitaev, Pyatkin and Remmel in [Representing graphs via pattern avoiding words, Electron. J. Combin. 22 (2015) #P2.53]. This notion generalizes the notions of the much studied permutation graphs and co-interval graphs. It is known that any 12-representable graph is a comparability graph, and also that a tree is 12-representable if and only if it is a double caterpillar. Moreover, Jones et al. initiated the study of 12- representability of induced subgraphs of a grid graph, and asked whether it is possible to characterize such graphs. This question of Jones et al. is meant to be about induced subgraphs of a grid graph that consist of squares, which we call square grid graphs. However, an induced subgraph in a grid graph does not have to contain entire squares, and we call such graphs line grid graphs. In this paper we answer the question of Jones et al. by providing a complete characterization of 12-representable square grid graphs in terms of forbidden induced subgraphs. Moreover, we conjecture such a characterization for the line grid graphs and give a number of results towards solving this challenging conjecture. Our results are a major step in the direction of characterization of all 12-representable graphs since beyond our characterization, we also discuss relations between graph labelings and 12-representability, one of the key open questions in the area.
Źródło:
Discussiones Mathematicae Graph Theory; 2022, 42, 2; 383-403
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Square Grids in the Tomb of Akhethotep – Questions and Doubts
Autorzy:
Radtke, Krzysztof
Powiązania:
https://bibliotekanauki.pl/articles/1181982.pdf
Data publikacji:
2020
Wydawca:
Polska Akademia Nauk. Instytut Kultur Śródziemnomorskich i Orientalnych PAN
Tematy:
reliefs
human proportion in art
hypothetical square grid
guidelines
Akhethotep
Old Kingdom Egypt
Opis:
The proportions of the human figure in Egyptian art were determined on the basis of simple and rarely changing rules. The oldest preserved guidelines used for this purpose come from the times of the Fifth Dynasty, and the square grids from the mid-Twelfth Dynasty. The objective of this article is to interpret the guidelines from the chapel of vizier Akhethotep, dated to the Fifth Dynasty, and answer the following questions: when were they made and what rules were used to determine the proportions of the vizier’s body? To do this, the author proposes employment of a measuring method which uses square grids as the main tool and the smallest element of the grid, that is, the square module as the basic measurement unit.
Źródło:
Études et Travaux (Institut des Cultures Méditerranéennes et Orientales de l’Académie Polonaise des Sciences); 2020, 33; 163-178
2084-6762
2449-9579
Pojawia się w:
Études et Travaux (Institut des Cultures Méditerranéennes et Orientales de l’Académie Polonaise des Sciences)
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
A fault diagnosis method for substation grounding grid based on the square-wave frequency domain model
Autorzy:
Zhang, P.-H.
He, J.-J.
Zhang, D.-D.
Wu, L.-M.
Powiązania:
https://bibliotekanauki.pl/articles/221635.pdf
Data publikacji:
2012
Wydawca:
Polska Akademia Nauk. Czytelnia Czasopism PAN
Tematy:
square-wave
frequency characteristics
grounding grid
fault diagnosis
Opis:
Current methods of fault diagnosis for the grounding grid using DC or AC are limited in accuracy and cannot be used to identify the locations of the faults. In this study, a new method of fault diagnosis for substation grounding grids is proposed using a square-wave. A frequency model of the grounding system is constructed by analyzing the frequency characteristics of the soil and the grounding conductors into which two different frequency square-wave sources are injected. By analyzing and comparing the corresponding information of the surface potentials of the output signals, the faults of the grounding grid can be diagnosed and located. Our method is verified by software simulation, scale model experiments and field experiments.
Źródło:
Metrology and Measurement Systems; 2012, 19, 1; 63-71
0860-8229
Pojawia się w:
Metrology and Measurement Systems
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Формирование понятия площади плоского геометрического тела
Development of concept of square of the flat geometric body
Autorzy:
Снигур, Татьяна
Швец, Василий
Powiązania:
https://bibliotekanauki.pl/articles/442259.pdf
Data publikacji:
2016-06-30
Wydawca:
Towarzystwo Wiedzy Powszechnej w Szczecinie
Tematy:
Геометрическое тело
площадь плоского геометрического тела
измерение площади фигуры
единицы измерения
народные меры
палетка
geometric body
square of the flat geometric body
measurement of square of figures
units of measurement
national measures
measuring grid
Opis:
В статье рассмотрено формирование понятия площади как функции на множестве плоских геометрических тел. Сначала рекомендуем познакомить учащихся с историческими сведениями, фактами, связанными с вычислением площади фигуры, народными задачами, мерами и способами измерения. Это будет способствовать положительной мотивации, развитию интереса к изучению темы «Многоугольники. Площади многоугольников». Раскрытие понятия площади плоского геометрического тела предлагаем начать с практических упражнений на измерение площади с помощью палетки (для небольших по размеру геометрических плоских тел), а также задач на нахождение и сравнение площади земельных участков, квартиры, государства и т.д. После обсуждения и обобщения результатов рассмотренных задач от физических плоских объектов следует перейти к рассмотрению плоских геометрических тел: прямоугольника, параллелограмма, треугольника, ромба, трапеции, круга, которые являются математическими моделями плоских физических объектов. Только теперь можно выяснять, что понимать под площадью плоского геометрического тела и какими свойствами обладает данная геометрическая величина.
In the article we considered methodical recommendations in relation to forming for the students the concept of area of flat geometrical body as function on the plural of flat bodies. The article also shows the historical and mathematical details that contribute to the positive motivation, the development of interest in the study of the geometrical magnitude.
Źródło:
Edukacja Humanistyczna; 2016, 1; 151-159
1507-4943
Pojawia się w:
Edukacja Humanistyczna
Dostawca treści:
Biblioteka Nauki
Artykuł
    Wyświetlanie 1-5 z 5

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