This paper considers the following three Roman domination graph invariants on
Kneser graphs:
Roman domination, total Roman domination, and signed Roman domination.
For Kneser graph $K_{n,k}$, we ...present exact values for Roman domination
number $\gamma_{R}(K_{n,k})$ and total Roman domination number
$\gamma_{tR}(K_{n,k})$ proving that for $n\geqslant k(k+1)$,
$\gamma_{R}(K_{n,k}) =\gamma_{tR}(K_{n,k}) = 2(k+1)$. For signed Roman
domination number $\gamma_{sR}(K_{n,k})$, the new lower and upper bounds for
$K_{n,2}$ are provided: we prove that for $n\geqslant 12$, the lower bound is
equal to 2, while the upper bound depends on the parity of $n$ and is equal to
3 if $n$ is odd, and equal to $5$ if $n$ is even. For graphs of smaller
dimensions, exact values are found by applying exact methods from literature.
This paper examines the evidence for climatic changes in the Eastern Mediterranean for the period 200–800 AD and offers hypotheses on the role of climatic fluctuations in the societal developments ...that occurred in this region at the end of Antiquity. The geographical focus of the paper includes Anatolia and the Levant, two major regions of the Eastern Roman Empire that are rich in environmental, historical and archaeological data. The paper starts with the review of current research on the economic, settlement and vegetation history of the Eastern Mediterranean in Late Antiquity, which provides the necessary framework for the study of potential climate impacts. The core of the article is devoted to the analysis of the palaeoclimatic evidence, which is divided in two groups. The first one encompasses the direct evidence, that is palaeoclimate proxies and the textual record of extreme weather events, while the second includes indirect information on climate, in particular multi-proxy studies that include pollen analysis, archaeological evidence, and the historical evidence of subsistence crises. We conclude that during our study period there occurred three periods of substantially different climatic conditions. A late Roman drought ∼350–470 AD was followed by a dramatic shift to much wetter climatic conditions. These in turn changed into increasing dryness after ∼730 AD in Anatolia and ∼670 AD in the Levant. The lack of chronological precision in the dating of the archaeological evidence and of some climatic records makes it impossible at present to make conclusive observations regarding the societal responses to these climatic fluctuations. Nonetheless in all probability, the extended and – in some areas - severe late Roman drought did not cause any major social upheaval or economic decline in Anatolia or the Levant, although it appears to have contributed to a change in patterns of water use in the cities. In contrast, the increased availability of moisture after ∼470 AD does appear to have contributed to the expansion of rural settlement and agriculture into environmentally marginal terrain, including semi-arid areas such as the Negev. In this way climate probably contributed to the general economic prosperity of the late Roman Empire in the east of the Mediterranean basin. The end of this late Roman world system came about finally in mid-7th c. and, at least in Anatolia, is not directly associated with any shift in climatic conditions. Aridity during early Medieval times may be one of the main factors behind the gradual long-term decline of settlement on the marginal lands in the Levant following Islamic conquest.
•We review different types of evidence for climate change in Anatolia and the Levant.•A drought (~350–470AD) contributed to local famines and a change in urban water use.•A wetter period after ~470 AD correlates with settlement expansion in arid lands.•Another drier phase occurred already after the crisis caused by the Arab invasions.•It contributed to the long-term settlement decline in some parts of the region.
La moneda romana presenta una gran variedad de mensajes iconográficos que muestran la gran relación que hubo entre la religión tradicional, la transmisión de mensajes por parte del Estado y la ...moneda. En este artículo se analizan algunos de estos mensajes y la vinculación existente entre la moneda y el sacrilegio. Para ello se han seleccionado piezas clave dentro de la amonedación romana tardorrepublicana y altoimperial, abarcando un marco cronológico que data, de manera aproximada entre el 133 a.C. y el 192 d.C. y se ha estudiado la vinculación existente entre los tipos expuestos y su contexto sociopolítico.
Egypt under the Romans (30 BCE–3rd century CE) was a period when local deserts experienced an unprecedented flurry of activity. In the Eastern Desert, a marked increase in desert traffic came from ...imperial prospecting/quarrying activities and caravans transporting wares to and from the Red Sea ports. In the Western Desert, resilient camels slowly became primary beasts of burden in desert travel, enabling caravaneers to lengthen daily marching distances across previously inhospitable dunes. Desert road archaeology has used satellite imaging, landscape studies and network analysis to plot desert trail networks with greater accuracy; however, it is often difficult to date roadside installations and thus assess how these networks evolved in scope and density in reaction to climatic, social and technological change. Roads in the Deserts of Roman Egypt examines evidence for desert roads in Roman Egypt and assesses Roman influence on the road density in two select desert areas: the central and southern section of the Eastern Desert and the central Marmarican Plateau and discusses geographical and social factors influencing road use in the period, demonstrating that Roman overseers of these lands adapted remarkably well to local desert conditions, improving roads and developing the trail network. Crucially, the author reconceptualises desert trails as linear corridor structures that follow expedient routes in the desert landscape, passing through at least two functional nodes attracting human traffic, be those water sources, farmlands, mines/quarries, trade hubs, military installations or actual settlements. The ‘route of least resistance’ across the desert varied from period to period according to the available road infrastructure and beasts of burden employed. Roman administration in Egypt not only increased the density of local desert ‘node’ networks, but also facilitated internodal connections with camel caravans and transformed the Sahara by establishing new, or embellishing existing, nodes, effectively funnelling desert traffic into discernible corridors.Significantly, not all desert areas of Egypt are equally suited for anthropogenic development, but almost all have been optimised in one way or another, with road installations built for added comfort and safety of travellers. Accordingly, the study of how Romans successfully adapted to desert travel is of wider significance to the study of deserts and ongoing expansion due to global warming.
For over thirty years, David F. Kelly has worked with medical practitioners, students, families, and the sick and dying to confront the difficult and often painful issues that concern medical ...treatment at the end of life. In this short and practical book, Kelly shares his vast experience, providing a rich resource for thinking about life's most painful decisions. Kelly outlines eight major issues regarding end-of-life care as seen through the lens of the Catholic medical ethics tradition. He looks at the distinction between ordinary and extraordinary means; the difference between killing and allowing to die; criteria of patient competence; what to do in the case of incompetent patients; the meaning and use of advance directives; the morality of hydration and nutrition; physician-assisted suicide and euthanasia; and medical futility. Kelly's analysis is sprinkled with significant legal decisions and, throughout, elaborations on how the Catholic medical ethics tradition-as well as teachings of bishops and popes-understands each issue. He provides a helpful glossary to supplement his introduction to the terminology used by philosophical health care ethics. Included in Kelly's discussion is his lucid description of why the Catholic tradition supports the discontinuation of medical care in the Terry Schiavo case. He also explores John Paul II's controversial papal allocution concerning hydration and nutrition for unconscious patients, arguing that the Catholic tradition does not require feeding the permanently unconscious.Medical Care at the End of Lifeaddresses the major issues that inform this last stage of caregiving. It offers a critical guide to understanding the medical ethics and relevant legal cases needed for clear thinking when individuals are faced with those crucial decisions.
The responsibilities related to public religion in Rome – and more precisely to the sacra publica – are carried out by different actors. Magistrates – especially consuls – play an essential role as ...actors of the rites and also because they bring the Senate together to discuss religious issues and are thus at the origin of major religious initiatives and decisions. As for the priests of the major colleges, they also celebrate certain festivals and assist magistrates in their religious functions, but they mainly exercise a specific competence in sacred law jurisprudence.
Let G be a graph with vertex set V(G). A Roman dominating function (RDF) on a graph G is a function f:V(G)⟶{0,1,2} satisfying the condition that each vertex u with f(u)=0 has a neighbor v with ...f(v)=2. An Italian dominating function (IDF) is a function f:V(G)⟶{0,1,2} having the property that f(N(u))≥2 for every vertex u with f(u)=0, where N(u) is the neighborhood of u. If f is an RDF or an IDF on G, then let V0={v∈V(G):f(v)=0}. A restrained Roman (Italian) dominating function is an RDF (IDF) f having the property that the subgraph induced by V0 does not have an isolated vertex. A set {f1,f2,…,fd} of distinct restrained Roman (Italian) dominating functions on G with the property that ∑i=1dfi(v)≤2 for each v∈V(G) is called a restrained Roman (Italian) dominating family (of functions) on G. The maximum number of functions in a restrained Roman (Italian) dominating family on G is the restrained Roman (Italian) domatic number of G, denoted by drR(G) (drI(G)). We initiate the study of the restrained Roman (Italian) domatic numbers, and we present different sharp bounds on drR(G) and drI(G). In addition, we determine these parameters for some classes of graphs.
This volume, authored by outstanding papyrologists and historians of ancient medicine, deals with topics focused on the papyrological evidence of ancient medical texts and contexts. The first part ...contains some new reflections on important sources such as the Anonymus Londinensis and the Hippocratic corpus, the second part collects papers about the “doctors’ context”, and the final part is focused on the digitisation of the medical papyri.
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