Frameworks, Tensegrities, and Symmetry

2022 ◽  
Author(s):  
Robert Connelly ◽  
Simon D. Guest

This introduction to the theory of rigid structures explains how to analyze the performance of built and natural structures under loads, paying special attention to the role of geometry. The book unifies the engineering and mathematical literatures by exploring different notions of rigidity - local, global, and universal - and how they are interrelated. Important results are stated formally, but also clarified with a wide range of revealing examples. An important generalization is to tensegrities, where fixed distances are replaced with 'cables' not allowed to increase in length and 'struts' not allowed to decrease in length. A special feature is the analysis of symmetric tensegrities, where the symmetry of the structure is used to simplify matters and allows the theory of group representations to be applied. Written for researchers and graduate students in structural engineering and mathematics, this work is also of interest to computer scientists and physicists.

Author(s):  
Анастасия Руднева ◽  
Anastasiya Rudneva

The textbook examines the essence, place and role of international trade in the system of modern world economic relations and in ensuring international economic security, as well as forms and methods of international trade. Particular attention is paid to the specifics of pricing and state regulation of this form of MEO, including in the framework of the world trade organization, as well as trends in the development of international trade in the context of the transformation of its geographical and commodity structure, taking into account modern challenges and threats. The textbook is intended for bachelors studying in the direction of "Economics", graduate students, teachers and a wide range of readers interested in the discipline.


2021 ◽  
Author(s):  
◽  
Loveday Jane Anastasia Kempthorne

<p>This doctoral thesis is an examination of the relationship between poetry and mathematics, centred on three twentieth-century case studies: the Polish poets Czesław Miłosz (1911-2004) and Zbigniew Herbert (1924-1998), and the Romanian mathematician and poet Dan Barbilian/Ion Barbu (1895-1961).  Part One of the thesis is a review of current scholarly literature, divided into two chapters. The first chapter looks at the nature of mathematics, outlining its historical developments and describing some major mathematical concepts as they pertain to the later case studies. This entails a focus on non-Euclidean geometries, modern algebra, and the foundations of mathematics in Europe; the nature of mathematical truth and language; and the modern historical evolution of mathematical schools in Poland and Romania. The second chapter examines some existing attempts to bring together mathematics and poetry, drawing on literature and science as an academic field; the role of the imagination and invention in the languages of both poetics and mathematics; the interest in mathematics among certain Symbolist poets, notably Mallarmé; and the experimental work of the French groups of mathematicians and mathematician-poets, Bourbaki and Oulipo. The role of metaphor is examined in particular.  Part Two of the thesis is the case studies. The first presents the ethical and moral stance of Czesław Miłosz, investigating his attitudes towards classical and later relativistic science, in the light of the Nazi occupation and the Marxist regimes in Poland, and how these are reflected in his poetry. The study of Zbigniew Herbert is structured around a wide selection of his poetic oeuvre, and identifying his treatment of evolving and increasingly more complex mathematical concepts. The third case study, on Dan Barbilian, who published his poetry under the name Ion Barbu, begins with an examination of the mathematical school at Göttingen in the 1920s, tracing the influence of Gauss, Riemann, Klein, Hilbert and Noether in Barbilian’s own mathematical work, particularly in the areas of metric spaces and axiomatic geometry. In the discussion, the critical analysis of the mathematician and linguist Solomon Marcus is examined. This study finishes with a close reading of seven of Barbu’s poems.  The relationship of mathematics and poetry has rarely been studied as a coherent academic field, and the relevant scholarship is often disconnected. A feature of this thesis is that it brings together a wide range of scholarly literature and discussion. Although primarily in English, a considerable amount of the academic literature collated here is in French, Romanian, Polish and some German. The poems themselves are presented in the original Polish and Romanian with both published and working translations appended in the footnotes. In the case of the two Polish poets, one a Nobel laureate and the other a multiple prize-winning figure highly regarded in Poland, this thesis is unusual in its concentration on mathematics as a feature of the poetry which is otherwise much-admired for its politically-engaged and lyrical qualities. In the case of the Romanian, Dan Barbilian, he is widely known in Romania as a mathematician, and most particularly as the published poet Ion Barbu, yet his work is little studied outside that country, and indeed much of it is not yet translated into English.  This thesis suggests at an array of both theoretical and specific starting points for examining the multi-stranded and intricate relationship between mathematics and poetry, pointing to a number of continuing avenues of further research.</p>


2021 ◽  
Author(s):  
◽  
Loveday Jane Anastasia Kempthorne

<p>This doctoral thesis is an examination of the relationship between poetry and mathematics, centred on three twentieth-century case studies: the Polish poets Czesław Miłosz (1911-2004) and Zbigniew Herbert (1924-1998), and the Romanian mathematician and poet Dan Barbilian/Ion Barbu (1895-1961).  Part One of the thesis is a review of current scholarly literature, divided into two chapters. The first chapter looks at the nature of mathematics, outlining its historical developments and describing some major mathematical concepts as they pertain to the later case studies. This entails a focus on non-Euclidean geometries, modern algebra, and the foundations of mathematics in Europe; the nature of mathematical truth and language; and the modern historical evolution of mathematical schools in Poland and Romania. The second chapter examines some existing attempts to bring together mathematics and poetry, drawing on literature and science as an academic field; the role of the imagination and invention in the languages of both poetics and mathematics; the interest in mathematics among certain Symbolist poets, notably Mallarmé; and the experimental work of the French groups of mathematicians and mathematician-poets, Bourbaki and Oulipo. The role of metaphor is examined in particular.  Part Two of the thesis is the case studies. The first presents the ethical and moral stance of Czesław Miłosz, investigating his attitudes towards classical and later relativistic science, in the light of the Nazi occupation and the Marxist regimes in Poland, and how these are reflected in his poetry. The study of Zbigniew Herbert is structured around a wide selection of his poetic oeuvre, and identifying his treatment of evolving and increasingly more complex mathematical concepts. The third case study, on Dan Barbilian, who published his poetry under the name Ion Barbu, begins with an examination of the mathematical school at Göttingen in the 1920s, tracing the influence of Gauss, Riemann, Klein, Hilbert and Noether in Barbilian’s own mathematical work, particularly in the areas of metric spaces and axiomatic geometry. In the discussion, the critical analysis of the mathematician and linguist Solomon Marcus is examined. This study finishes with a close reading of seven of Barbu’s poems.  The relationship of mathematics and poetry has rarely been studied as a coherent academic field, and the relevant scholarship is often disconnected. A feature of this thesis is that it brings together a wide range of scholarly literature and discussion. Although primarily in English, a considerable amount of the academic literature collated here is in French, Romanian, Polish and some German. The poems themselves are presented in the original Polish and Romanian with both published and working translations appended in the footnotes. In the case of the two Polish poets, one a Nobel laureate and the other a multiple prize-winning figure highly regarded in Poland, this thesis is unusual in its concentration on mathematics as a feature of the poetry which is otherwise much-admired for its politically-engaged and lyrical qualities. In the case of the Romanian, Dan Barbilian, he is widely known in Romania as a mathematician, and most particularly as the published poet Ion Barbu, yet his work is little studied outside that country, and indeed much of it is not yet translated into English.  This thesis suggests at an array of both theoretical and specific starting points for examining the multi-stranded and intricate relationship between mathematics and poetry, pointing to a number of continuing avenues of further research.</p>


2015 ◽  
Vol 223 (2) ◽  
pp. 102-109 ◽  
Author(s):  
Evelyn H. Kroesbergen ◽  
Marloes van Dijk

Recent research has pointed to two possible causes of mathematical (dis-)ability: working memory and number sense, although only few studies have compared the relations between working memory and mathematics and between number sense and mathematics. In this study, both constructs were studied in relation to mathematics in general, and to mathematical learning disabilities (MLD) in particular. The sample consisted of 154 children aged between 6 and 10 years, including 26 children with MLD. Children performing low on either number sense or visual-spatial working memory scored lower on math tests than children without such a weakness. Children with a double weakness scored the lowest. These results confirm the important role of both visual-spatial working memory and number sense in mathematical development.


2008 ◽  
pp. 61-76
Author(s):  
A. Porshakov ◽  
A. Ponomarenko

The role of monetary factor in generating inflationary processes in Russia has stimulated various debates in social and scientific circles for a relatively long time. The authors show that identification of the specificity of relationship between money and inflation requires a complex approach based on statistical modeling and involving a wide range of indicators relevant for the price changes in the economy. As a result a model of inflation for Russia implying the decomposition of inflation dynamics into demand-side and supply-side factors is suggested. The main conclusion drawn is that during the recent years the volume of inflationary pressures in the Russian economy has been determined by the deviation of money supply from money demand, rather than by money supply alone. At the same time, monetary factor has a long-run spread over time impact on inflation.


2018 ◽  
Vol 7 (2) ◽  
pp. 117-128 ◽  
Author(s):  
Erin Sullivan ◽  
Marie Louise Herzfeld-Schild

This introduction surveys the rise of the history of emotions as a field and the role of the arts in such developments. Reflecting on the foundational role of the arts in the early emotion-oriented histories of Johan Huizinga and Jacob Burkhardt, as well as the concerns about methodological impressionism that have sometimes arisen in response to such studies, the introduction considers how intensive engagements with the arts can open up new insights into past emotions while still being historically and theoretically rigorous. Drawing on a wide range of emotionally charged art works from different times and places—including the novels of Carson McCullers and Harriet Beecher-Stowe, the private poetry of neo-Confucian Chinese civil servants, the photojournalism of twentieth-century war correspondents, and music from Igor Stravinsky to the Beatles—the introduction proposes five ways in which art in all its forms contributes to emotional life and consequently to emotional histories: first, by incubating deep emotional experiences that contribute to formations of identity; second, by acting as a place for the expression of private or deviant emotions; third, by functioning as a barometer of wider cultural and attitudinal change; fourth, by serving as an engine of momentous historical change; and fifth, by working as a tool for emotional connection across communities, both within specific time periods but also across them. The introduction finishes by outlining how the special issue's five articles and review section address each of these categories, while also illustrating new methodological possibilities for the field.


Author(s):  
C. Claire Thomson

The first book-length study in English of a national corpus of state-sponsored informational film, this book traces how Danish shorts on topics including social welfare, industry, art and architecture were commissioned, funded, produced and reviewed from the inter-war period to the 1960s. For three decades, state-sponsored short filmmaking educated Danish citizens, promoted Denmark to the world, and shaped the careers of renowned directors like Carl Th. Dreyer. Examining the life cycle of a representative selection of films, and discussing their preservation and mediation in the digital age, this book presents a detailed case study of how informational cinema is shaped by, and indeed shapes, its cultural, political and technological contexts.The book combines close textual analysis of a broad range of films with detailed accounts of their commissioning, production, distribution and reception in Denmark and abroad, drawing on Actor-Network Theory to emphasise the role of a wide range of entities in these processes. It considers a broad range of genres and sub-genres, including industrial process films, public information films, art films, the city symphony, the essay film, and many more. It also maps international networks of informational and documentary films in the post-war period, and explores the role of informational film in Danish cultural and political history.


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