Rank numbers for graphs with paths and cycles

A coloring of a graph, G, is an assignment of positive integers to the vertices of the graph with one number assigned to each vertex, so that adjacent vertices are assigned different numbers. A k-ranking of a graph is a coloring that uses {1, 2, ..., k} with the requirement that every path between any two vertices labeled with the same number contains a vertex with a higher label. The rank number of a graph, denoted [chi]r(G), is the smallest k such that G has a k-ranking. In this paper we seek rank numbers for four specific families of graphs. Each of these families of graphs contains at least one cycle as a subgraph

Bleeding flowers and waning moons : a history of menstruation in France, c. 1495-1761

This thesis explores early modem perceptions of menstrual bleeding, demonstrating that attempts to understand menstrual bleeding extended beyond the early modem medical world and captured the imagination of an entire cross-section of French society revealing culturally- embedded concerns about marriage, progeny, the family, patrilineage and state formation. The thesis draws on diverse sources including medical, casuistic and judicial texts, court records and private documents. Chapter One outlines the database of medical texts which forms a cornerstone of the thesis. The database includes texts printed between 1495, with the French edition of a medieval Latin work by Bernard de Gordon, and 1761, with Montpellier physician Jean Astruc's treatise on women's diseases which introduced the term 'menstruation' into French medical vocabulary. Chapter Two examines medical notions of menstrual bleeding within the context of attitudes to blood, blood-related fluids and the humoral and mechanical bodies. Sixteenth-century casuistic interpretations of Biblical taboos surrounding sex during menstrual bleeding and notions of menses as polluting are cross-referenced with medical notions of the relationship of menses to conception demonstrating the overriding concern for healthy progeny. Chapter Three explores the significance of concepts of time and periodicity, in the context of the merging of blood-related fluids in the humoral body, as a key to early modem perceptions of menstrual bleeding. Chapter Four examines early modern debates on the length of gestation and the calculation of a woman's time on the basis of the monthly menstrual cycle relating these to Sarah Hanley's model of the 'marital regime'. In Chapter Five, the ambivalent nature of menstrual bleeding in the medico-legal arena is investigated and the different cultural meanings ascribed to various bloody discharges emanating from the living female body are analysed. In the sixth and final chapter the role of menstrual bleeding in issues of sexual difference and hermaphroditism is discussed

Bleeding flowers and waning moons : a history of menstruation in France, c. 1495-1761

This thesis explores early modem perceptions of menstrual bleeding, demonstrating that attempts to understand menstrual bleeding extended beyond the early modem medical world and captured the imagination of an entire cross-section of French society revealing culturally- embedded concerns about marriage, progeny, the family, patrilineage and state formation. The thesis draws on diverse sources including medical, casuistic and judicial texts, court records and private documents. Chapter One outlines the database of medical texts which forms a cornerstone of the thesis. The database includes texts printed between 1495, with the French edition of a medieval Latin work by Bernard de Gordon, and 1761, with Montpellier physician Jean Astruc's treatise on women's diseases which introduced the term 'menstruation' into French medical vocabulary. Chapter Two examines medical notions of menstrual bleeding within the context of attitudes to blood, blood-related fluids and the humoral and mechanical bodies. Sixteenth-century casuistic interpretations of Biblical taboos surrounding sex during menstrual bleeding and notions of menses as polluting are cross-referenced with medical notions of the relationship of menses to conception demonstrating the overriding concern for healthy progeny. Chapter Three explores the significance of concepts of time and periodicity, in the context of the merging of blood-related fluids in the humoral body, as a key to early modem perceptions of menstrual bleeding. Chapter Four examines early modern debates on the length of gestation and the calculation of a woman's time on the basis of the monthly menstrual cycle relating these to Sarah Hanley's model of the 'marital regime'. In Chapter Five, the ambivalent nature of menstrual bleeding in the medico-legal arena is investigated and the different cultural meanings ascribed to various bloody discharges emanating from the living female body are analysed. In the sixth and final chapter the role of menstrual bleeding in issues of sexual difference and hermaphroditism is discussed.EThOS - Electronic Theses Online ServiceArts and Humanities Research Board (Great Britain) (AHRB)France. Ambassade (Great Britain)Society for the Study of French HistorySociety for the Social History of MedicineGBUnited Kingdo

Women at the Centre: Medical Entrepreneurialism and 'La Grande Medicine' in Eighteenth-Century Lyon

We draw on Colin Jones’ framing of the Sisters of Charity as medical practitioners rather than charitable carers (1989) to centre the entrepreneurialism of Marie Grand and Marie Fiansons’ medical practice in eighteenth-century Lyon. Although historians recognize the significance of early modern European women’s (medical) work, they often assume such work existed in the shadows of the medical marketplace. Archival erasures and gendered narratives obscure the flexibility of women’s medical practices. Grand and Fiansons’ documents, analysed alongside adverts for local medical services, elucidate working women’s medical practices. As silk-workers and self-defined ‘chymists’ and herbalists, Grand and Fiansons were at the centre of healthcare and medicine. The breadth of their practice and networks emerges through the exceptional survival of their ‘counter-archive’ in the consular court archives. Their story reveals the fluidity and porousness of boundaries between domestic and occupational medicine, precarity and commodified care work, and charity and entrepreneurialism

Supplemental Online Learning Tools (SOLTs) to Support Deaf and Hard of Hearing Students in Introductory Statistics Courses

Research in most Science, Technology, Engineering, and Mathematics (STEM) disciplines uses statistical methods. Thus as students develop into research scientists, introductory statistics serves as a gateway course. If students struggle to incorporate statistics into their knowledge base, they may be effectively kept from careers that rely on statistics. DHH students learn differently and thus may lag behind their hearing counterparts in mainstream classrooms. In part, a gap in language knowledge can impede the understanding of statistics topics. What is a variable? What does it mean to have a distribution? With sign language interpreters and other support services, many mainstream instructors believe that DHH students have equal access to learning in their classrooms. Yet variations of instructional skill, interpreter knowledge of the discipline, and the lack of alternative representations of content often result in access that falls short of equal . This paper describes the work of a team of faculty and student researchers seeking best practices for creating supplemental online learning tools. Starting from a list of prioritized challenging topics in statistics, the team developed a number of strategies and produced a pilot set of instructional videos. Formative feedback led to revised videos, which provided a significant gain in knowledge for DHH students when shown in an experimental setting

Female Barrenness, Bodily Access and Aromatic Treatments in Seventeenth-Century England

This is an open access article under the terms of the Creative Commons Attribution-NonCommercial-NoDerivs License, CC BY-NC-ND 3.0 which permits use and distribution in any medium, provided the original work is properly cited, the use is non-commercial and no modifications or adaptations are made, see https://creativecommons.org/licenses/by-nc-nd/3.0/.Scholars examining medical practice in early modern England have often remarked upon the complexities of the relationship between male physicians and female patients. It has been noted that ideas of female modesty and concern about the potential erotic nature of contact between patients and practitioners could affect the treatment of certain disorders. This paper contributes to this on-going discussion by examining the use of pungent substances to diagnose and treat female barrenness. Diagnostic tests included in medical treatises could rely upon the woman’s ability to perceive a particular substance. These tests thus put women at the centre of the diagnosis of their disorders and allowed them to negotiate access to their reproductive bodies. Similarly medical practitioners included a range of treatments for infertility that involved the fumes of certain substances entering the womb or surrounding the body. These treatments may have allowed women, and perhaps their medical practitioners, to choose a method of remedy that did not involve the application of external lotions to the genitalia. Thus by considering the multi-sensory nature of medical treatment this paper will highlight that the diversity of remedies advocated in early modern medical texts would perhaps have allowed women to restrict access to their reproductive bodies, while still obtaining diagnosis and treatment.Peer reviewe