Presenting a Mathematical Programming Model for Discovering Eulerian Paths (EP) in Certain Specific Graphs

In the modern era, graph theory is considered a useful tool for quantification and simplification of various dynamic components in complex systems. By representing elements as nodes and their connections as edges, graph theory can transform anything from urban planning to computer data into a meaningful mathematical language. Nowadays, numerous practical applications have been designed and developed based on graph theory. Graph theory is a branch of discrete mathematics that aims to describe and solve problems with discrete structures using points and edges. One of the problems concerning graphs is the Eulerian path problem. This research demonstrates that this problem can also be investigated from the perspective of Operations Research (OR). In a more general sense, the Eulerian path problem is a routing problem. This paper presents a pure mathematical model to describe the relationship between the variables of the Eulerian path problem. One of the features of the proposed mathematical model is its solvability by most optimization software. Finally, several numerical examples are provided to enhance the understanding of this model, and they are solved using the proposed approach. All the analyses in this research are conducted using one of the most advanced optimization software, MATLAB. The proposed mathematical model provides a systematic and efficient approach to discover Eulerian paths in specific graphs, contributing to the advancement of graph theory and its practical applications

Proposing a Pure Binary Linear Programming(PBLP) Model to Discover Eulerian Circuits in Complete Graphs

Known as a branch of Discrete Mathematics (DM), Graph Theory (GT) describes and solves problems of discrete nature through nodes (i.e., vertices) and arcs (i.e., edges). In this regard, a prominent problem is to find the Eulerian circuits. This paper indicates that the problem can be analyzed through operations research methods. In more general terms, finding the Eulerian circuits could be considered a pathfinding problem. Hence, this paper proposes a pure binary mathematical model to describe the relationship between the variables employed to find the Eulerian circuits. All the analyses in this paper were performed in MATLAB. The proposed model can be solved by many optimization software applications. Finally, several numerical examples are presented and solved through the proposed method. All the analyses in this paper were performed in MATLAB. This paper indicated that the problem(Eulerian Circuits in Complete Graphs) could be studied and solved from the perspective of operations research

Scott, Chaucer, and Medieval Romance: A Study in Sir Walter Scott\u27s Indebtedness to the Literature of the Middle Ages

While the influence of Shakespeare on Sir Walter Scott has long been recognized, the importance of medieval literature in shaping his creative imagination has never before been examined in depth. Jerome Mitchell\u27s new book fills this significant gap through a wide-ranging study of Scott\u27s indebtedness to Chaucer and to medieval romance, especially the Middle English romances, for story-patterns, motifs, character types, style and structure, and detail. Mitchell establishes more completely and accurately than any previous critic the extent of Scott\u27s knowledge of medieval literature. His examination of Scott\u27s poetry, especially the long narrative poems, demonstrates their debt to Chaucer and medieval romance. The heart of the book is a detailed analysis of the Waverley Novels. Scott\u27s debt to medieval literature, Mitchell shows, was vast, profound, and elemental; it is the single most important source area for the Waverley Novels, their warp and woof. Moreover, it is probably the key to Scott\u27s immense appeal—the very dimension which enabled him to cast an everlasting spell on his contemporaries, even on such great men as Byron and Goethe, and which has charmed generations of readers to the present day. This pioneering book, based on extensive research in Scotland, including Sir Walter Scott\u27s personal library, sheds new light on the narrative substance and texture of Scott\u27s poems and novels. Both the general reader and the serious student will derive from it a more informed appreciation of Scott\u27s impressive achievement. Jerome Mitchell teaches English at the University of Georgia. His previous books include The Walter Scott Operas.https://uknowledge.uky.edu/upk_english_language_and_literature_british_isles/1044/thumbnail.jp

Sandspur, Vol 112, No 17, 2006

Rollins College student newspaper, written by the students and published at Rollins College. The Sandspur started as a literary journal.https://stars.library.ucf.edu/cfm-sandspur/3684/thumbnail.jp

The Trail, 2002-09-27

https://soundideas.pugetsound.edu/thetrail_all/2815/thumbnail.jp

1908-1909 Bulletin

https://soundideas.pugetsound.edu/bulletins/1014/thumbnail.jp

An evaluation of the internationalisation process in schools of management in France: the experience of four schools of management

A Thesis submitted for the degree of Doctorate in Business Administration of the University of BedfordshireDue to the globalisation of the corporate world, business and management education has to respond by internationalising itself in order to prepare young graduates for the employment market. This doctoral thesis examines how four small to medium sized business and management schools in France are reacting to an ever increasing globalisation process. Evidence suggests that these schools have been experiencing an increase in their internationalisation process at the dawn of the twenty-first century which can be considered as somewhat later than the more prestigious schools both in France and elsewhere. This is due to changing balance between the traditional rationales for internationalisation and also the emerging of new rationales such as customer satisfaction and survival. A case study approach was adopted to study four business schools in different regions of France, all of which were linked to and managed by the local Chamber of Commerce. The research reveals that the timing for this internationalisation process is due to several factors which have both pushed forward and prevented international development. Even when there is a clearly defined international strategy the development is not linear since the international strategy is only one strategy amongst others within the institution and at certain times other strategies may be more important and thus prevent international development. All four schools have clearly used alliances and networks to obtain the necessary resources to carry out their internationalisation; this is seen on an academic, economic and staffing levels. As regards approach, a clear pattern has emerged in all four schools observed in that they have adopted a transitional marginal approach where the internationalisation begins slowly from the outer or peripheral part of the institution and gradually moves inward to affect the institution as a whole. This approach has given rise to several outcomes that prove to be advantageous to the institution as a whole, such as an improvement in the quality of teaching, learning and research. This transitional marginal approach has also reduced the risk of the possible forces against change which are very often present especially in the world of higher education. However, the research suggests that this was not an intended outcome of the strategy but nevertheless it is seen as a possible recommendation for other organisations to take into consideration. The findings also reveal that in the future, this model may become circular or spiral in structure since one outcome related to internationalisation is the globalisation of the institutions themselves where they are beginning to be present in other countries. This again, is seen as a marginal activity