The legendary overland silk road was not the only way to reach Asia for ancient travelers from the Mediterranean. During the Roman Empire’s heyday, equally important maritime routes reached from the ...Egyptian Red Sea across the Indian Ocean. The ancient city of Berenike, located approximately 500 miles south of today’s Suez Canal, was a significant port among these conduits. In this book, Steven E. Sidebotham, the archaeologist who excavated Berenike, uncovers the role the city played in the regional, local, and “global” economies during the eight centuries of its existence. Sidebotham analyzes many of the artifacts, botanical and faunal remains, and hundreds of the texts he and his team found in excavations, providing a profoundly intimate glimpse of the people who lived, worked, and died in this emporium between the classical Mediterranean world and Asia.
Outer independent double Roman domination Abdollahzadeh Ahangar, H.; Chellali, M.; Sheikholeslami, S.M.
Applied mathematics and computation,
01/2020, Volume:
364
Journal Article
Peer reviewed
An outer independent double Roman dominating function (OIDRDF) of a graph G is a function h from V(G) to {0, 1, 2, 3} for which each vertex with label 0 is adjacent to a vertex with label 3 or at ...least two vertices with label 2, and each vertex with label 1, is adjacent to a vertex with label greater than 1; and all vertices labeled by 0 is independent. The weight of an OIDRDF h is ∑w ∈ V(G)h(w), and the outer independent double Roman domination number γoidR(G) is the minimum weight of an OIDRDF on G. In this article, we provide various bounds on γoidR(G) and we show that its determining is NP-complete on chordal and bipartite graphs. Moreover, we establish Nordhaus–Gaddum bounds for γoidR(G)+γoidR(G¯).
This is a ground-breaking philosophical-historical study of the work of Galen of Pergamum. It contains four case-studies on (1) Galen’s remarkable and original thoughts on the relation between body ...and soul, (2) his notion of human nature, (3) his engagement with Plato’s Timaeus, (4) and black bile and melancholy. It shows that Galen develops an innovative view of human nature that problematizes the distinction between body and soul.
The present volume contains papers on Origen and the history of his reception which were presented at a series of workshops at the Eighteenth International Conference on Patristic Studies held at ...Oxford in August 2019. They provide multifarious insights into various aspects of Origen’s thought and his impact on different topics of theology, exegesis and philosophy from Late Antiquity to Early Modern Times. By connecting the Alexandrian’s legacy with recent developments in Patristics and Classics, they open up new perspectives for Origen scholarship in the new millenium. Research on Origen can be connected with studies, e.g., on rhetoric and power, on individuality and diversity, on gender and equality issues, on determinism and freedom and on questions of cultural transfer and transformation. The contributions to this volume can thus be taken as starting points for future studies on Origen within the broader context of contemporary research in science and the humanities.
In this book, Andrew Riggsby offers a survey of the main areas of Roman law, both substantive and procedural, and how the legal world interacted with the rest of Roman life. Emphasising basic ...concepts, he recounts its historical development and focuses in particular on the later Republic and early centuries of the Roman Empire. The volume is designed as an introductory work, with brief chapters that will be accessible to college students with little knowledge of legal matters or Roman antiquity. The text is also free of technical language and Latin terminology. It can be used in courses on Roman law, Roman history, or comparative law, but it will also serve as a useful reference for more advanced students and scholars.
The fourteen chapters of this e-book examine Roman dance by looking at its role in Roman religion, by following it into the theatre and the banquet hall, and by tracing its (metaphorical) presence in ...a variety of literary contexts, including rhetorical treatises, biography, and lyric poetry. These different approaches, which draw on literary texts, inscriptions, documentary papyri, the visual record, and modern reperformances, converge in illustrating a rich and vibrant dance culture which prided itself on indigenous dances no less than on its capacity to absorb, transform, or revive the dance traditions of their Etruscan or Greek neighbours. Dance was a cultural practice which was able to affirm Romanness, for instance in the case of the Salian priests, but also to raise the question of what was Roman in the first place, for instance when the originally Greek pantomime was embraced by Augustus and came to be known as "Italian style of dancing". Together the fourteen case studies offer fresh perspectives on an underexplored topic, shedding light on the manifold contexts, functions, practitioners, and appreciations of Roman dance.
Nigeria is a country shaped by internal diversity and transnational connections, past and present. Leading Nigerian writers from Chinua Achebe, Amos Tutuola and Wole Soyinka to Chimamanda Ngozi ...Adichie and Teju Cole have portrayed these Nigerian issues, and have also written about some of the momentous events in Nigerian history. Afropolitan Horizons discusses their work alongside other novelists and commentators, as well as describing the ways in which Nigeria has appeared in foreign news reporting. It is all interwoven with the author’s own anthropological field research in a town in Central Nigeria.
Maximal double Roman domination in graphs Abdollahzadeh Ahangar, H.; Chellali, M.; Sheikholeslami, S.M. ...
Applied mathematics and computation,
02/2022, Volume:
414
Journal Article
Peer reviewed
•We introduce maximal double Roman dominating functions in graphs and study the corresponding parameter γdRm(G).•We show that the problem of determining γdRm(G) is NP-complete for bipartite, chordal ...and planar graphs. But it is solvable in linear time for bounded clique-width graphs including trees, cographs and distance-hereditary graphs.•We establish various relationships relating γdRm(G) to some domination parameters.•For the class of trees, we show that for every tree T of order n≥4,γdRm(T)≤54n and we characterize all trees attaining the bound.•Finally, the exact values of γdRm(G) are given for paths and cycles.
A maximal double Roman dominating function (MDRDF) on a graph G=(V,E) is a function f:V(G)→{0,1,2,3} such that (i) every vertex v with f(v)=0 is adjacent to least two vertices assigned 2 or to at least one vertex assigned 3, (ii) every vertex v with f(v)=1 is adjacent to at least one vertex assigned 2 or 3 and (iii) the set {w∈V|f(w)=0} is not a dominating set of G. The weight of a MDRDF is the sum of its function values over all vertices, and the maximal double Roman domination number γdRm(G) is the minimum weight of an MDRDF on G. In this paper, we initiate the study of maximal double Roman domination. We first show that the problem of determining γdRm(G) is NP-complete for bipartite, chordal and planar graphs. But it is solvable in linear time for bounded clique-width graphs including trees, cographs and distance-hereditary graphs. Moreover, we establish various relationships relating γdRm(G) to some domination parameters. For the class of trees, we show that for every tree T of order n≥4,γdRm(T)≤54n and we characterize all trees attaining the bound. Finally, the exact values of γdRm(G) are given for paths and cycles.
Double Roman domination Beeler, Robert A.; Haynes, Teresa W.; Hedetniemi, Stephen T.
Discrete Applied Mathematics,
10/2016, Volume:
211
Journal Article
Peer reviewed
Open access
For a graph G=(V,E), a double Roman dominating function is a function f:V→{0,1,2,3} having the property that if f(v)=0, then vertex v must have at least two neighbors assigned 2 under f or one ...neighbor with f(w)=3, and if f(v)=1, then vertex v must have at least one neighbor with f(w)≥2. The weight of a double Roman dominating function f is the sum f(V)=∑v∈Vf(v), and the minimum weight of a double Roman dominating function on G is the double Roman domination number of G. We initiate the study of double Roman domination and show its relationship to both domination and Roman domination. Finally, we present an upper bound on the double Roman domination number of a connected graph G in terms of the order of G and characterize the graphs attaining this bound.
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