Weak signed Roman k-domination in digraphs Volkmann, Lutz
Rocznik Akademii Górniczo-Hutniczej im. Stanisława Staszica. Opuscula Mathematica,
2024, Letnik:
44, Številka:
2
Journal Article
Recenzirano
Odprti dostop
Let \(k\geq 1\) be an integer, and let \(D\) be a finite and simple digraph with vertex set \(V(D)\). A weak signed Roman \(k\)-dominating function (WSRkDF) on a digraph \(D\) is a function \(f ...\colon V(D)\rightarrow \{-1,1,2\}\) satisfying the condition that \(\sum_{x \in N^-v}f(x)\geq k\) for each \(v\in V(D)\), where \(N^-v\) consists of \(v\) and all vertices of \(D\) from which arcs go into \(v\). The weight of a WSRkDF \(f\) is \(w(f)=\sum_{v\in V(D)}f(v)\). The weak signed Roman \(k\)-domination number \(\gamma_{wsR}^k(D)\) is the minimum weight of a WSRkDF on \(D\). In this paper we initiate the study of the weak signed Roman \(k\)-domination number of digraphs, and we present different bounds on \(\gamma_{wsR}^k(D)\). In addition, we determine the weak signed Roman \(k\)-domination number of some classes of digraphs. Some of our results are extensions of well-known properties of the weak signed Roman domination number \(\gamma_{wsR}(D)=\gamma_{wsR}^1(D)\) and the signed Roman \(k\)-domination number \(\gamma_{sR}^k(D).\)
Augustin Bea war nicht nur das ökumenische Gesicht des Zweiten Vatikanums, sondern eine der prägenden Gestalten der katholischen Bibelwissenschaft seiner Zeit. Das wissenschaftliche und ...kirchenpolitische Handeln des deutschen Jesuiten ermöglicht Einblicke in die wechselvolle Geschichte römischer Bibelexegese im Schatten des Vatikans. Beas Ringen mit Tradition und Moderne bestimmte den kirchlichen Kurs: Wie begegnete der Alttestamentler historischer und naturwissenschaftlicher Kritik an der Bibel? Welche Rolle spielte er bei der kirchlichen Buchzensur? Ermöglichte ihm seine Tätigkeit Kontakte über den katholischen Binnenraum hinaus? Und was verleitete Pius XII. dazu, mitten im Krieg die Bibelenzyklika „Divino afflante Spiritu“ zu veröffentlichen? Diesen Fragen geht Michael Pfister auf der Grundlage bisher unbekannter Dokumente nach und wirft ein neues Licht auf den späteren „Kardinal der Einheit“.
Upon its publication in 1871, Charles Darwin'sThe Descent of Man and Selection in Relation to Sexsent shock waves through the scientific community and the public at large. In an original and ...persuasive study, Bert Bender demonstrates that it is this treatise on sexual selection, rather than any of Darwin's earlier works on evolution, that provoked the most immediate and vigorous response from American fiction writers. These authors embraced and incorporated Darwin's theories, insights, and language, creating an increasingly dark and violent view of sexual love in American realist literature.
InThe Descent of Love, Bender carefully rereads the works of William Dean Howells, Henry James, Elizabeth Stuart Phelps, Sarah Orne Jewett, Kate Chopin, Harold Frederic, Charles W. Chesnutt, Edith Wharton, and Ernest Hemingway, teasing from them a startling but utterly convincing preoccupation with questions of sexual selection. Competing for readership as novelists who best grasped the "real" nature of human love, these writers also participated in a heated social debate over racial and sexual differences and the nature of sex itself. Influenced more byThe Descent of Manthan by theOrigin of Species, Bender's novelists built upon Darwin's anthropological and zoological materials to anatomize their character's courtship behavior, returning consistently to concerns with physical beauty, natural dominance, and the power to select a mate.
Bringing the resources of the history of science and intellectual history to this, the first full-length study of the impact of Darwin's theories in American literature, Bender revises accepted views of social Darwinism, American literary realism, and modernism in American literature, forever changing our perceptions of courtship and sexual interaction in American fiction from 1871 to 1926 and beyond.
What were the eating and drinking habits of the inhabitants of Britain during the Roman period? Drawing on evidence from a large number of archaeological excavations, this fascinating study shows how ...varied these habits were in different regions and amongst different communities and challenges the idea that there was any one single way of being Roman or native. Integrating a range of archaeological sources, including pottery, metalwork and environmental evidence such as animal bone and seeds, this book illuminates eating and drinking choices, providing invaluable insights into how those communities regarded their world. The book contains sections on the nature of the different types of evidence used and how this can be analysed. It will be a useful guide to all archaeologists and those who wish to learn about the strength and weaknesses of this material and how best to use it.
Triple Roman domination in graphs Abdollahzadeh Ahangar, H.; Álvarez, M.P.; Chellali, M. ...
Applied mathematics and computation,
02/2021, Letnik:
391
Journal Article
Recenzirano
The Roman domination in graphs is well-studied in graph theory. The topic is related to a defensive strategy problem in which the Roman legions are settled in some secure cities of the Roman Empire. ...The deployment of the legions around the Empire is designed in such a way that a sudden attack to any undefended city could be quelled by a legion from a strong neighbour. There is an additional condition: no legion can move if doing so leaves its base city defenceless. In this manuscript we start the study of a variant of Roman domination in graphs: the triple Roman domination. We consider that any city of the Roman Empire must be able to be defended by at least three legions. These legions should be either in the attacked city or in one of its neighbours. We determine various bounds on the triple Roman domination number for general graphs, and we give exact values for some graph families. Moreover, complexity results are also obtained.
On the double Roman domination in graphs Abdollahzadeh Ahangar, Hossein; Chellali, Mustapha; Sheikholeslami, Seyed Mahmoud
Discrete Applied Mathematics,
12/2017, Letnik:
232
Journal Article
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A double Roman dominating function (DRDF) on a graph G=(V,E) is a function f:V(G)→{0,1,2,3} having the property that if f(v)=0, then vertex v has at least two neighbors assigned 2 under f or one ...neighbor w with f(w)=3, and if f(v)=1, then vertex v must have at least one neighbor w with f(w)≥2. The weight of a DRDF is the value f(V(G))=∑u∈V(G)f(u). The double Roman domination number γdR(G) is the minimum weight of a DRDF on G. First we show that the decision problem associated with γdR(G) is NP-complete for bipartite and chordal graphs. Then we present some sharp bounds on the double Roman domination number which partially answer an open question posed by Beeler et al. (2016) in their introductory paper on double Roman domination. Moreover, a characterization of graphs G with small γdR(G) is provided.
The one vs. the many Woloch, Alex; Woloch, Alex
2003., 20090209, 2009, 2003, c2003.
eBook
Does a novel focus on one life or many? Alex Woloch uses this simple question to develop a powerful new theory of the realist novel, based on how narratives distribute limited attention among a ...crowded field of characters. His argument has important implications for both literary studies and narrative theory. Characterization has long been a troubled and neglected problem within literary theory. Through close readings of such novels as Pride and Prejudice, Great Expectations, and Le Pre Goriot, Woloch demonstrates that the representation of any character takes place within a shifting field of narrative attention and obscurity. Each individual--whether the central figure or a radically subordinated one--emerges as a character only through his or her distinct and contingent space within the narrative as a whole. The "character-space," as Woloch defines it, marks the dramatic interaction between an implied person and his or her delimited position within a narrative structure. The organization of, and clashes between, many character-spaces within a single narrative totality is essential to the novel’s very achievement and concerns, striking at issues central to narrative poetics, the aesthetics of realism, and the dynamics of literary representation.
Almost fifteen per cent of the world's population today experiences some form of mental or physical disability and society tries to accommodate their needs. But what was the situation in the Roman ...world? Was there a concept of disability? How were the disabled treated? How did they manage in their daily lives? What answers did medical doctors, philosophers and patristic writers give for their problems? This book, the first monograph on the subject in English, explores the medical and material contexts for disability in the ancient world, and discusses the chances of survival for those who were born with a handicap. It covers the various sorts of disability: mental problems, blindness, deafness and deaf-muteness, speech impairment and mobility impairment, and includes discussions of famous instances of disability from the ancient world, such as the madness of Emperor Caligula, the stuttering of Emperor Claudius and the blindness of Homer.
Roman law as a field of study is rapidly evolving to reflect new perspectives and approaches in research. Scholars who work on the subject are increasingly being asked to conduct research in an ...interdisciplinary manner whereby Roman law is not merely seen as a set of abstract concepts devoid of any background, but as a body of law which operated in a specific social, economic and cultural context. This "context-based" approach to the study of Roman law is an exciting new field which legal historians must address. Since the mid-1960s, a new academic movement has advocated a "law and society" approach to the study of Roman law instead of the prevailing dogmatic methodology employed in many Faculties of law.
Roman imagery and iconography are typically studied under the more general umbrella of Roman art and in broader, medium-specific studies. This handbook focuses primarily on visual imagery in the ...Roman world, examined by context and period, and the evolving scholarly traditions of iconographic analysis and visual semiotics that have framed the modern study of these images. As such topics—or, more directly, the isolation of these topics from medium-specific or strictly temporal evaluations of Roman art—are uncommon in monograph-length studies, our goal is that this handbook will be an important reference for both the communicative value of images in the Roman world and the tradition of iconographical analysis. The chapters herein represent contributions from a number of leading and emerging authorities on Roman imagery and iconography from across the world, representing a variety of academic traditions and methods of image analysis.
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