1,227 research outputs found

    Interpolation theorem for a continuous function on orientations of a simple graph

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    summary:Let GG be a simple graph. A function ff from the set of orientations of GG to the set of non-negative integers is called a continuous function on orientations of GG if, for any two orientations O1O_1 and O2O_2 of GG, f(O1)f(O2)1|f(O_1)-f(O_2)|\le 1 whenever O1O_1 and O2O_2 differ in the orientation of exactly one edge of GG. We show that any continuous function on orientations of a simple graph GG has the interpolation property as follows: If there are two orientations O1O_1 and O2O_2 of GG with f(O1)=pf(O_1)=p and f(O2)=qf(O_2)=q, where p<qp<q, then for any integer kk such that p<k<qp<k<q, there are at least mm orientations OO of GG satisfying f(O)=kf(O) = k, where mm equals the number of edges of GG. It follows that some useful invariants of digraphs including the connectivity, the arc-connectivity and the absorption number, etc., have the above interpolation property on the set of all orientations of GG

    Interpolation theorem for a continuous function on orientations of a simple graph

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    Let G be a simple graph. A function f from the set of orientations of G to the set of Iron-negative integers is called a continuous function on orientations of G if, for any two orientations O-1 and O-2 of G, \f(O-1) - f(O-2)\ less than or equal to 1 whenever O-1 and O-2 differ in the orientation of exactly one edge of G. We show that any continuous function on orientations of a simple graph G has the interpolation property as follows: If there are two orientations O-1 and O-2 of G with f(O-1) = p and f(O-2) = q, where p < q, then for any integer k such that p < k < q, there are at least m orientations O of G satisfying f(O) = k, where m equals the number of edges of G. It follows that some useful invariants of digraphs including the connectivity, the arc-connectivity and the absorption number, etc., have the above interpolation property on the set of all orientations of G

    Heritage Patterns—Representative Models

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    The Heritage Patterns—Representative Models issue of Heritage welcomed twelve articles that discussed traditional and contemporary methodologies, as well as scholars from different backgrounds who intended to seek patterns of tangible heritage and its underlying principles to understand the diversity of heritage approaches. The Special Issue aims to research the patterns in heritage and the underlying rules that define tangible heritage as a universal value in spatial coexistence, economics, urban life, and design via case studies and theoretical proposals that could be implemented in the future. The pattern language and the heritage phenomenon could act as a base of observation to deduct logic and create generative algorithms (generative design); to understand the importance of spatial connection with tangible heritage and urban forms (space syntax, urban morphology, and urban morphometrics) and its visibility; as well as archaeological, architectural, and urban heritage. Based on the UNESCO-ICOMOS doctrines and the examination of morphological regions, urban morphological research and its different layers (urban forms, structural components, built environment, urban tissue, and their interaction) act as a background and foundation for general urban heritage conservation and protection proposals, and also as the base of specific interventions in the built environment caused by natural disasters

    Montreal in evolution: historical acount of the development of Montreal's architecture and environment

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    Montreal in Evolution is an historical account of the development of Montrealfs architecture and environment, from the time of the first visits of- the Sieur de Champlain at Place Royale to today's metropolis. It is concerned with both popular and academic architecture, with the organic growth of the urban settlement as well as with the planned developments.However, this study does not limit itself to the description of the evolution of construction, or to the characteristic traits of the environment and architecture of certain periods. It attempts principally to isolate and analyze the forces and influences which generated changes in the configuration of the urban environment as well as in its architecture. These forces and influences have been divided into two categories: those dictated by the physical environment and those emanating from the activities of men, acting individually and.collectively within the environment, according to their needs, technologies and ideologies. For the purpose of placing all these forces in their global context and in the chronological order of their appearance in the development of the city, this study has been divided into four parts. The first part deals with the location and site of Montreal and with the characteristics of its soil, subtratum, and climate® The remaining three parts reflect the evolution of technological and economic forces, and of social and cultural influences.The exceptional geographical situation of the island of Montreal at the confluent of several rivers marked its destiny, first as a centre for the. fur -trade and ' later as a commercial, industrial and financial centre.. This privileged situation was further: enhanced by improved means of transport and communication during the industrial period. On a human level, this situation accounts for Montreal's cosmopolitan nature.The structure and the character of urban development were also to benefit from the island's situation and site at the crossroad of a communications' network and in the middle of a very fertile plain. Thus, the main concern of the first human settlement on the island and in the plain was to take advantage of this network of waterways and to protect it: this is reflected to this day in the: regional structure of the metropolis. In a like manner, the early industrial settlement was also partly oriented along the St.Lawrence River axis. The original occupation of this fertile island according to the system of "cotes" is reflected today in the orthogonal grid of streets which is characteristic of the city. Finally, the migration of man power from the rural countryside into the -city would determine the particular types of industries which were to settle in the city and would also be responsible to a large extent for the" topographical division of the city into rich and poor districts and into anglophone and francophone districts, where each ethnic group's environment reflected both its command over the economy and its sociocultural organisation.While the achievements of architecture and urbanisation reflected man's mastery over both economy and technology, Montreal's evolution revealed a strong dichotomy between academic architecture and urbanism on the one hand, and popular architecture and urbanism on the other hand. The former, as exemplified by Dollier de Casson's plan, by the plans for the Town of Mount-Royal, or by the architecture of Notre Dame church or Windsor station, reflect the hegemony of culture as well as the predominance of styles which, according to the period, were fashionable in France, in England or in the United States. Popular architecture and urbanism harboured no official pretentions and was therefore more authentic, reflecting more truly the interaction of prevailing forces and influences. The traditional Quebec house, the industrial type of housing and the early commercial and industrial architecture attest to this fact. Today, under the impact of spontaneous communications and improved means of urban transport, both the shape of the city and its architecture tend to fuse into standardized versions of the typical large North American city.From this broad picture of the evolution of Montreal's architecture and environment over the last three centuries, it appears that the true essence and identity of the Canadian metropolis originated in a morphological evolution, in the "dynamic perenniality" of structures which left their mark on the land at various periods of history. In conclusion, the future for the harmonious development of Montreal depends on sound regional planning for the community and each and everyone assuming his responsibility in the planning of the living environment

    Human experience in the natural and built environment : implications for research policy and practice

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    22nd IAPS conference. Edited book of abstracts. 427 pp. University of Strathclyde, Sheffield and West of Scotland Publication. ISBN: 978-0-94-764988-3

    HISTORY URBANISM RESILIENCE VOLUME 03:

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    The 17th conference (2016, Delft)&nbsp;of the International Planning History Society (IPHS) and its proceedings place presentations from different continents and on varied topics side by side, providing insight into state-of-the art research in the field of planning history and offering a glimpse of new approaches, themes, papers and books to come. VOLUME 03:&nbsp;Change and Responsive Plannin

    Modeling pollutant dispersion at the city and street scales: from wind tunnel experiments to complex network theory

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    L'abstract è presente nell'allegato / the abstract is in the attachmen
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