Thomas Koshy
- Published in print:
- 2008
- Published Online:
- January 2009
- ISBN:
- 9780195334548
- eISBN:
- 9780199868766
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780195334548.003.0012
- Subject:
- Mathematics, Combinatorics / Graph Theory / Discrete Mathematics
This chapter shows the various ways Catalan numbers can be extracted from Pascal's triangle. It includes discussion of nonisomorphic groups, Catalan polynomials, Touchard's recursive formula, and ...
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This chapter shows the various ways Catalan numbers can be extracted from Pascal's triangle. It includes discussion of nonisomorphic groups, Catalan polynomials, Touchard's recursive formula, and Jonah's theorem.Less
This chapter shows the various ways Catalan numbers can be extracted from Pascal's triangle. It includes discussion of nonisomorphic groups, Catalan polynomials, Touchard's recursive formula, and Jonah's theorem.
Thomas Koshy
- Published in print:
- 2008
- Published Online:
- January 2009
- ISBN:
- 9780195334548
- eISBN:
- 9780199868766
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780195334548.003.0014
- Subject:
- Mathematics, Combinatorics / Graph Theory / Discrete Mathematics
This chapter investigates an interesting triangular array that contains Catalan numbers and Cayley numbers.
This chapter investigates an interesting triangular array that contains Catalan numbers and Cayley numbers.
Liu Fei
David Kerr (ed.)
- Published in print:
- 2007
- Published Online:
- January 2012
- ISBN:
- 9780197264089
- eISBN:
- 9780191734809
- Item type:
- book
- Publisher:
- British Academy
- DOI:
- 10.5871/bacad/9780197264089.001.0001
- Subject:
- Political Science, International Relations and Politics
The European Union and China have emerged as new international actors. They have an increasingly diverse relationship covering the economy, politics, technology, culture and education; but beyond ...
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The European Union and China have emerged as new international actors. They have an increasingly diverse relationship covering the economy, politics, technology, culture and education; but beyond these two-way linkages EU–China development is also changing the international political environment. One noted US scholar, David Shambaugh, has pointed to a ‘Strategic Triangle’ between the US, the EU, and China. Several other major actors such as Japan, India and Russia are also interested in the ‘EU factor’ in their relations with China; or the ‘China factor’ in their EU relations. This volume presents contributions from scholars from Europe and China, which debate the nature, problems and potential of the emerging strategic relationship between the EU and China. Several papers develop theoretical approaches to regionalism and inter-regionalism. This book provides an overview of EU–China relations and the wider international context, and it will be of interest to anyone interested in international relations.Less
The European Union and China have emerged as new international actors. They have an increasingly diverse relationship covering the economy, politics, technology, culture and education; but beyond these two-way linkages EU–China development is also changing the international political environment. One noted US scholar, David Shambaugh, has pointed to a ‘Strategic Triangle’ between the US, the EU, and China. Several other major actors such as Japan, India and Russia are also interested in the ‘EU factor’ in their relations with China; or the ‘China factor’ in their EU relations. This volume presents contributions from scholars from Europe and China, which debate the nature, problems and potential of the emerging strategic relationship between the EU and China. Several papers develop theoretical approaches to regionalism and inter-regionalism. This book provides an overview of EU–China relations and the wider international context, and it will be of interest to anyone interested in international relations.
L. Weiskrantz
- Published in print:
- 1990
- Published Online:
- January 2008
- ISBN:
- 9780198521921
- eISBN:
- 9780191706226
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198521921.003.0014
- Subject:
- Psychology, Cognitive Neuroscience
Given the good discrimination in the blind field, the question arises as to whether it is processed differently than discriminations in the intact field. One way of addressing the question was to ...
More
Given the good discrimination in the blind field, the question arises as to whether it is processed differently than discriminations in the intact field. One way of addressing the question was to present stimuli to the two fields simultaneously and to ask D. B. to make a ‘ same-different’ judgment. Two types of stimuli were used: curved vs. straight triangles, and X vs. O. The tests with triangles were ambiguous, possibly because it was not an easy task even for the intact field. The results for X vs. O were clearer, especially when conditions were optimized by varying the size of the stimuli and their positions in the fields. But the cross-field comparison task was more tiring than a within-field task for the blind field alone. In any event, he showed unmistakable evidence of being able to do the matching task. His ability to perform discrimination within the blind field alone was better than across fields. With stimuli to the blind field alone, depending on the parameters, he might report seeing waves, but with the same parameters for the cross-field matching task, he reported seeing nothing in the blind field but something in the good field, even when he was performing at 99% accuracy. A question arises as to whether he carried out the cross-field test sequentially in each field independently, which might be pursued by the analysis of reaction times in the single vs. double field presentations.Less
Given the good discrimination in the blind field, the question arises as to whether it is processed differently than discriminations in the intact field. One way of addressing the question was to present stimuli to the two fields simultaneously and to ask D. B. to make a ‘ same-different’ judgment. Two types of stimuli were used: curved vs. straight triangles, and X vs. O. The tests with triangles were ambiguous, possibly because it was not an easy task even for the intact field. The results for X vs. O were clearer, especially when conditions were optimized by varying the size of the stimuli and their positions in the fields. But the cross-field comparison task was more tiring than a within-field task for the blind field alone. In any event, he showed unmistakable evidence of being able to do the matching task. His ability to perform discrimination within the blind field alone was better than across fields. With stimuli to the blind field alone, depending on the parameters, he might report seeing waves, but with the same parameters for the cross-field matching task, he reported seeing nothing in the blind field but something in the good field, even when he was performing at 99% accuracy. A question arises as to whether he carried out the cross-field test sequentially in each field independently, which might be pursued by the analysis of reaction times in the single vs. double field presentations.
Thomas Koshy
- Published in print:
- 2008
- Published Online:
- January 2009
- ISBN:
- 9780195334548
- eISBN:
- 9780199868766
- Item type:
- book
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780195334548.001.0001
- Subject:
- Mathematics, Combinatorics / Graph Theory / Discrete Mathematics
Fibonacci and Lucas sequences are “two shining stars in the vast array of integer sequences,” and because of their ubiquitousness, tendency to appear in quite unexpected and unrelated places, ...
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Fibonacci and Lucas sequences are “two shining stars in the vast array of integer sequences,” and because of their ubiquitousness, tendency to appear in quite unexpected and unrelated places, abundant applications, and intriguing properties, they have fascinated amateurs and mathematicians alike. However, Catalan numbers are even more fascinating. Like the North Star in the evening sky, they are a beautiful and bright light in the mathematical heavens. They continue to provide a fertile ground for number theorists, especially, Catalan enthusiasts and computer scientists. Since the publication of Euler's triangulation problem (1751) and Catalan's parenthesization problem (1838), over 400 articles and problems on Catalan numbers have appeared in various periodicals. As Martin Gardner noted, even though many amateurs and mathematicians may know the abc's of Catalan sequence, they may not be familiar with their myriad unexpected occurrences, delightful applications, properties, or the beautiful and surprising relationships among numerous examples. Like Fibonacci and Lucas numbers, Catalan numbers are also an excellent source of fun and excitement. They can be used to generate interesting dividends for students, such as intellectual curiosity, experimentation, pattern recognition, conjecturing, and problem-solving techniques. The central character in the nth Catalan number is the central binomial coefficient. So, Catalan numbers can be extracted from Pascal's triangle. In fact, there are a number of ways they can be read from Pascal's triangle; every one of them is described and exemplified. This brings Catalan numbers a step closer to number-theory enthusiasts, especially.Less
Fibonacci and Lucas sequences are “two shining stars in the vast array of integer sequences,” and because of their ubiquitousness, tendency to appear in quite unexpected and unrelated places, abundant applications, and intriguing properties, they have fascinated amateurs and mathematicians alike. However, Catalan numbers are even more fascinating. Like the North Star in the evening sky, they are a beautiful and bright light in the mathematical heavens. They continue to provide a fertile ground for number theorists, especially, Catalan enthusiasts and computer scientists. Since the publication of Euler's triangulation problem (1751) and Catalan's parenthesization problem (1838), over 400 articles and problems on Catalan numbers have appeared in various periodicals. As Martin Gardner noted, even though many amateurs and mathematicians may know the abc's of Catalan sequence, they may not be familiar with their myriad unexpected occurrences, delightful applications, properties, or the beautiful and surprising relationships among numerous examples. Like Fibonacci and Lucas numbers, Catalan numbers are also an excellent source of fun and excitement. They can be used to generate interesting dividends for students, such as intellectual curiosity, experimentation, pattern recognition, conjecturing, and problem-solving techniques. The central character in the nth Catalan number is the central binomial coefficient. So, Catalan numbers can be extracted from Pascal's triangle. In fact, there are a number of ways they can be read from Pascal's triangle; every one of them is described and exemplified. This brings Catalan numbers a step closer to number-theory enthusiasts, especially.
Thomas Koshy
- Published in print:
- 2008
- Published Online:
- January 2009
- ISBN:
- 9780195334548
- eISBN:
- 9780199868766
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780195334548.003.0001
- Subject:
- Mathematics, Combinatorics / Graph Theory / Discrete Mathematics
This chapter presents a brief introduction to binomial coefficients, the cornerstone of all the discussions in the book. Among the properties discussed are Hermite's divisibility properties. Catalan ...
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This chapter presents a brief introduction to binomial coefficients, the cornerstone of all the discussions in the book. Among the properties discussed are Hermite's divisibility properties. Catalan numbers Cn are introduced.Less
This chapter presents a brief introduction to binomial coefficients, the cornerstone of all the discussions in the book. Among the properties discussed are Hermite's divisibility properties. Catalan numbers Cn are introduced.
Thomas Koshy
- Published in print:
- 2008
- Published Online:
- January 2009
- ISBN:
- 9780195334548
- eISBN:
- 9780199868766
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780195334548.003.0008
- Subject:
- Mathematics, Combinatorics / Graph Theory / Discrete Mathematics
This chapter presents delightful occurrences of Catalan numbers in the theory of trees. They include binary trees, full binary trees, planted trivalent binary trees, triangulations and prefix ...
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This chapter presents delightful occurrences of Catalan numbers in the theory of trees. They include binary trees, full binary trees, planted trivalent binary trees, triangulations and prefix expressions, chessboard, ordered rooted trees, forest, and ordered forests.Less
This chapter presents delightful occurrences of Catalan numbers in the theory of trees. They include binary trees, full binary trees, planted trivalent binary trees, triangulations and prefix expressions, chessboard, ordered rooted trees, forest, and ordered forests.
Christel Lane and Jocelyn Probert
- Published in print:
- 2009
- Published Online:
- May 2009
- ISBN:
- 9780199214815
- eISBN:
- 9780191721779
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199214815.003.0006
- Subject:
- Business and Management, International Business, Political Economy
This chapter discusses first sub-regional economic activity and the use of so-called ‘triangle manufacturing’ in Asia as a response to the quota system. This practice explains the emergence of new ...
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This chapter discusses first sub-regional economic activity and the use of so-called ‘triangle manufacturing’ in Asia as a response to the quota system. This practice explains the emergence of new economic actors, the industry's large, mainly Asian firms engaged in the orchestration of transnational production networks and serving as agents for western buyer firms. The chapter then moves to an examination of actual shifts in sourcing patterns by US and European firms. It concludes with an analysis of the countries that could be regarded as ‘winners’ and ‘losers’ in the international hierarchy as the industry consolidates in the post-quota era.Less
This chapter discusses first sub-regional economic activity and the use of so-called ‘triangle manufacturing’ in Asia as a response to the quota system. This practice explains the emergence of new economic actors, the industry's large, mainly Asian firms engaged in the orchestration of transnational production networks and serving as agents for western buyer firms. The chapter then moves to an examination of actual shifts in sourcing patterns by US and European firms. It concludes with an analysis of the countries that could be regarded as ‘winners’ and ‘losers’ in the international hierarchy as the industry consolidates in the post-quota era.
Rosalind R. James
- Published in print:
- 2008
- Published Online:
- September 2008
- ISBN:
- 9780195316957
- eISBN:
- 9780199871575
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780195316957.003.0008
- Subject:
- Biology, Animal Biology, Plant Sciences and Forestry
When disease strikes a hive of bees, it can devastate the colony and spread to the entire beekeeping operation. All bees are susceptible to diseases, and when they are domesticated, their population ...
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When disease strikes a hive of bees, it can devastate the colony and spread to the entire beekeeping operation. All bees are susceptible to diseases, and when they are domesticated, their population densities increase to suit human needs, making them more susceptible. Most attempts at disease control have centered on either drug treatments or destroying affected colonies. This chapter discusses how disease control strategies could be improved by first developing a better understanding of the disease-cycle, and in particular, developing knowledge of the disease triangle, allowing researchers to identify that time and place in the management system for which the pathogen is most vulnerable, followed by targeting treatments to that stage.Less
When disease strikes a hive of bees, it can devastate the colony and spread to the entire beekeeping operation. All bees are susceptible to diseases, and when they are domesticated, their population densities increase to suit human needs, making them more susceptible. Most attempts at disease control have centered on either drug treatments or destroying affected colonies. This chapter discusses how disease control strategies could be improved by first developing a better understanding of the disease-cycle, and in particular, developing knowledge of the disease triangle, allowing researchers to identify that time and place in the management system for which the pathogen is most vulnerable, followed by targeting treatments to that stage.
Steve Awodey
- Published in print:
- 2006
- Published Online:
- September 2007
- ISBN:
- 9780198568612
- eISBN:
- 9780191717567
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198568612.003.0010
- Subject:
- Mathematics, Algebra
This chapter presents a third characterization of adjunctions. This one has the virtue of being entirely equational. Topics discussed include the triangle identities, monads and adjoints, algebras ...
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This chapter presents a third characterization of adjunctions. This one has the virtue of being entirely equational. Topics discussed include the triangle identities, monads and adjoints, algebras for a monad, comonads and coalgebras, and algebras for endofunctors. Exercises are given in the last part of the chapter.Less
This chapter presents a third characterization of adjunctions. This one has the virtue of being entirely equational. Topics discussed include the triangle identities, monads and adjoints, algebras for a monad, comonads and coalgebras, and algebras for endofunctors. Exercises are given in the last part of the chapter.
Michael Saward
- Published in print:
- 2010
- Published Online:
- September 2010
- ISBN:
- 9780199579389
- eISBN:
- 9780191722950
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199579389.003.0003
- Subject:
- Political Science, Political Theory
This chapter defines and elaborates a number of key aspects of the representative claim, underscoring the latter's distinctive utility as an analytical tool. After locating the representative claim ...
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This chapter defines and elaborates a number of key aspects of the representative claim, underscoring the latter's distinctive utility as an analytical tool. After locating the representative claim in the wider context of perspectives on representation as an event rather than a given presence, the chapter sets out and discusses in some detail the five‐part account of the elements of the representative claim. Representation has often been understood as three‐sided: a subject stands for an object which is in turn an account of a referent. The argument in the chapter shows that to understand multiple forms of political representation we need to add to this triangular conception the ideas of the maker (of claims) and the audience (for claims). The crucial notions of constituency and audience are elaborated, showing their dynamic and interlinked character. The account is designed both to capture the essence and to show the subtlety and reach of the representative claim approach.Less
This chapter defines and elaborates a number of key aspects of the representative claim, underscoring the latter's distinctive utility as an analytical tool. After locating the representative claim in the wider context of perspectives on representation as an event rather than a given presence, the chapter sets out and discusses in some detail the five‐part account of the elements of the representative claim. Representation has often been understood as three‐sided: a subject stands for an object which is in turn an account of a referent. The argument in the chapter shows that to understand multiple forms of political representation we need to add to this triangular conception the ideas of the maker (of claims) and the audience (for claims). The crucial notions of constituency and audience are elaborated, showing their dynamic and interlinked character. The account is designed both to capture the essence and to show the subtlety and reach of the representative claim approach.
L. Weiskrantz
- Published in print:
- 1990
- Published Online:
- January 2008
- ISBN:
- 9780198521921
- eISBN:
- 9780191706226
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198521921.003.0008
- Subject:
- Psychology, Cognitive Neuroscience
D. B.'s ability to discriminate shapes by forced-choice guessing was studied using various letters, rectangles vs. squares, and degrees of curvature of triangles. Both projected and back-illuminated ...
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D. B.'s ability to discriminate shapes by forced-choice guessing was studied using various letters, rectangles vs. squares, and degrees of curvature of triangles. Both projected and back-illuminated material were used. The original discrimination in early testing between X and O was repeated, but using a variety of sizes and positions in the blind field. His ability was excellent. With back-projected stimuli he reported complete absence of experience, but with projected higher contrast stimuli he sometimes reported odd experiences but did not ‘see’ anything. When we moved to X vs. triangles he was at chance. Similarity, his ability to discriminate curved from straight triangles was poor. The hypothesis emerged that he was only able to discriminate shapes when there were major differences in orientation of the major components. A test of this was the discrimination between squares and rectangles equated for area, but with different length and widths. He performed poorly except for square vs. the longest rectangle. The final test of reintroducing an orientation difference was for squares vs. rectangles, for which he performed excellently. Over the main range of shape discriminations, he reported no subjective experience. All tests in which he reported no subjective experience for shape and grating orientation tests are summarized in a series of tables.Less
D. B.'s ability to discriminate shapes by forced-choice guessing was studied using various letters, rectangles vs. squares, and degrees of curvature of triangles. Both projected and back-illuminated material were used. The original discrimination in early testing between X and O was repeated, but using a variety of sizes and positions in the blind field. His ability was excellent. With back-projected stimuli he reported complete absence of experience, but with projected higher contrast stimuli he sometimes reported odd experiences but did not ‘see’ anything. When we moved to X vs. triangles he was at chance. Similarity, his ability to discriminate curved from straight triangles was poor. The hypothesis emerged that he was only able to discriminate shapes when there were major differences in orientation of the major components. A test of this was the discrimination between squares and rectangles equated for area, but with different length and widths. He performed poorly except for square vs. the longest rectangle. The final test of reintroducing an orientation difference was for squares vs. rectangles, for which he performed excellently. Over the main range of shape discriminations, he reported no subjective experience. All tests in which he reported no subjective experience for shape and grating orientation tests are summarized in a series of tables.
L. Weiskrantz
- Published in print:
- 1990
- Published Online:
- January 2008
- ISBN:
- 9780198521921
- eISBN:
- 9780191706226
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198521921.003.0017
- Subject:
- Psychology, Cognitive Neuroscience
During the last few years of work with D. B., it became possible to test a number of subjects with visual field defects at the National Hospital in London using a standard set of visual tests. The ...
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During the last few years of work with D. B., it became possible to test a number of subjects with visual field defects at the National Hospital in London using a standard set of visual tests. The tests included flash detection, curved vs. straight triangles, discrimination of orientation, figure-ground clustering, threshold for movement, and reaching. The results of variations of all of these tasks with D. B., with the exception of figure-ground clustering, were described in the previous chapters of the book. For the figure-ground task, the results demonstrated that D. B. had only a relatively mild deficit in discriminating the degrees of clustering of spots on the display.Less
During the last few years of work with D. B., it became possible to test a number of subjects with visual field defects at the National Hospital in London using a standard set of visual tests. The tests included flash detection, curved vs. straight triangles, discrimination of orientation, figure-ground clustering, threshold for movement, and reaching. The results of variations of all of these tasks with D. B., with the exception of figure-ground clustering, were described in the previous chapters of the book. For the figure-ground task, the results demonstrated that D. B. had only a relatively mild deficit in discriminating the degrees of clustering of spots on the display.
Keith Gandal
- Published in print:
- 2008
- Published Online:
- September 2008
- ISBN:
- 9780195338911
- eISBN:
- 9780199867127
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780195338911.003.0006
- Subject:
- Literature, Criticism/Theory, American, 20th Century Literature
These three authors, although compulsively writing out of a distress engendered by their “mobilization wounds,” learned by the time of writing their twenties masterpieces to submerge and transfigure ...
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These three authors, although compulsively writing out of a distress engendered by their “mobilization wounds,” learned by the time of writing their twenties masterpieces to submerge and transfigure this pain so as not to embarrass themselves with the revelation of their sense of inadequacy. All three had produced previous texts that openly address Anglo characters' humiliations in the military and so come off as bitter. The high modernism of Gatsby, Sun, A Farewell to Arms, and Sound, with its symbolism and its sense of tragedy (as opposed to bitterness), is a result of these authors developing the devices that allow them to disguise their mobilization traumas and thus to continue to exorcise them, but now obliquely. In Hemingway's and Faulkner's novels, “objective” sexual obstacles (injury, incest taboo) stand in for the military rejection that emasculated these Anglo authors, disguising and transfiguring it. Hemingway and Faulkner dignified the suffering of their Anglo alter egos by making their true loves impossible; Fitzgerald's alternative strategy for dignifying his sense of rejection was to split himself between two alter egos — one Anglo American and one ethnic American — and to give the experience of social rejection to a tragic character based only minimally on himself, namely, Gatsby.Less
These three authors, although compulsively writing out of a distress engendered by their “mobilization wounds,” learned by the time of writing their twenties masterpieces to submerge and transfigure this pain so as not to embarrass themselves with the revelation of their sense of inadequacy. All three had produced previous texts that openly address Anglo characters' humiliations in the military and so come off as bitter. The high modernism of Gatsby, Sun, A Farewell to Arms, and Sound, with its symbolism and its sense of tragedy (as opposed to bitterness), is a result of these authors developing the devices that allow them to disguise their mobilization traumas and thus to continue to exorcise them, but now obliquely. In Hemingway's and Faulkner's novels, “objective” sexual obstacles (injury, incest taboo) stand in for the military rejection that emasculated these Anglo authors, disguising and transfiguring it. Hemingway and Faulkner dignified the suffering of their Anglo alter egos by making their true loves impossible; Fitzgerald's alternative strategy for dignifying his sense of rejection was to split himself between two alter egos — one Anglo American and one ethnic American — and to give the experience of social rejection to a tragic character based only minimally on himself, namely, Gatsby.
Volker R. Berghahn
- Published in print:
- 2014
- Published Online:
- October 2017
- ISBN:
- 9780691161099
- eISBN:
- 9781400850297
- Item type:
- chapter
- Publisher:
- Princeton University Press
- DOI:
- 10.23943/princeton/9780691161099.003.0005
- Subject:
- History, American History: 20th Century
This chapter deals with the period between the 1923 economic crisis and an even more severe economic breakdown in 1929. This period saw an engagement of the United States in Europe that had not been ...
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This chapter deals with the period between the 1923 economic crisis and an even more severe economic breakdown in 1929. This period saw an engagement of the United States in Europe that had not been possible in the immediate postwar years, generating a few years of relative stability and prosperity in which American manufacturing companies and banks played a major role. It was the phase in which the United States succeeded in deploying its superior industrial and financial power in an attempt to uplift the economies of Europe. During those five years it was not only American ideas and practices of rationalized mass production that came to Europe through massive foreign direct investments; rather Europe, again for the first time, got a taste of mass consumption, even if it was still quite limited in terms of affordable consumer durables.Less
This chapter deals with the period between the 1923 economic crisis and an even more severe economic breakdown in 1929. This period saw an engagement of the United States in Europe that had not been possible in the immediate postwar years, generating a few years of relative stability and prosperity in which American manufacturing companies and banks played a major role. It was the phase in which the United States succeeded in deploying its superior industrial and financial power in an attempt to uplift the economies of Europe. During those five years it was not only American ideas and practices of rationalized mass production that came to Europe through massive foreign direct investments; rather Europe, again for the first time, got a taste of mass consumption, even if it was still quite limited in terms of affordable consumer durables.
Paula Tretkoff
- Published in print:
- 2016
- Published Online:
- October 2017
- ISBN:
- 9780691144771
- eISBN:
- 9781400881253
- Item type:
- chapter
- Publisher:
- Princeton University Press
- DOI:
- 10.23943/princeton/9780691144771.003.0003
- Subject:
- Mathematics, Geometry / Topology
This chapter deals with Riemann surfaces, coverings, and hypergeometric functions. It first considers the genus and Euler number of a Riemann surface before discussing Möbius transformations and ...
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This chapter deals with Riemann surfaces, coverings, and hypergeometric functions. It first considers the genus and Euler number of a Riemann surface before discussing Möbius transformations and notes that an automorphism of a Riemann surface is a biholomorphic map of the Riemann surface onto itself. It then describes a Riemannian metric and the Gauss-Bonnet theorem, which can be interpreted as a relation between the Gaussian curvature of a compact Riemann surface X and its Euler characteristic. It also examines the behavior of the Euler number under finite covering, along with finite subgroups of the group of fractional linear transformations PSL(2, C). Finally, it presents some basic facts about the classical Gauss hypergeometric functions of one complex variable, triangle groups acting discontinuously on one of the simply connected Riemann surfaces, and the hypergeometric monodromy group.Less
This chapter deals with Riemann surfaces, coverings, and hypergeometric functions. It first considers the genus and Euler number of a Riemann surface before discussing Möbius transformations and notes that an automorphism of a Riemann surface is a biholomorphic map of the Riemann surface onto itself. It then describes a Riemannian metric and the Gauss-Bonnet theorem, which can be interpreted as a relation between the Gaussian curvature of a compact Riemann surface X and its Euler characteristic. It also examines the behavior of the Euler number under finite covering, along with finite subgroups of the group of fractional linear transformations PSL(2, C). Finally, it presents some basic facts about the classical Gauss hypergeometric functions of one complex variable, triangle groups acting discontinuously on one of the simply connected Riemann surfaces, and the hypergeometric monodromy group.
Volker R. Berghahn
- Published in print:
- 2014
- Published Online:
- October 2017
- ISBN:
- 9780691161099
- eISBN:
- 9781400850297
- Item type:
- chapter
- Publisher:
- Princeton University Press
- DOI:
- 10.23943/princeton/9780691161099.003.0002
- Subject:
- History, American History: 20th Century
This chapter begins the story of the American–British–German business and political relationship in the year 1900. It assesses the prevailing attitudes toward this transitional period in terms of ...
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This chapter begins the story of the American–British–German business and political relationship in the year 1900. It assesses the prevailing attitudes toward this transitional period in terms of press commentary, before considering political and economic relations in the age of late-nineteenth-century imperialism. While positive visions of the future tended to predominate, the papers also contained evidence of the conflicts that were smoldering within the societies of Britain, Germany, and the United States. From here, the chapter turns to a rich archival source for the extent of the European–American constellation in the form of accounts made by financial expert Frank Vanderflip as well as by journalist William Stead.Less
This chapter begins the story of the American–British–German business and political relationship in the year 1900. It assesses the prevailing attitudes toward this transitional period in terms of press commentary, before considering political and economic relations in the age of late-nineteenth-century imperialism. While positive visions of the future tended to predominate, the papers also contained evidence of the conflicts that were smoldering within the societies of Britain, Germany, and the United States. From here, the chapter turns to a rich archival source for the extent of the European–American constellation in the form of accounts made by financial expert Frank Vanderflip as well as by journalist William Stead.
Inge Kaul and Ronald U. Mendoza
- Published in print:
- 2003
- Published Online:
- November 2003
- ISBN:
- 9780195157406
- eISBN:
- 9780199832965
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/0195157400.003.0004
- Subject:
- Economics and Finance, Public and Welfare
Examines the implications of translating the concept of public goods, originally developed in the setting of a domestic national economy, to that of global public goods set within a transnational ...
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Examines the implications of translating the concept of public goods, originally developed in the setting of a domestic national economy, to that of global public goods set within a transnational global economy. This requires important adjustments to the concepts of ‘triangle of publicness’ (publicness of consumption, of benefits, and of decision‐making), as well as new typologies of public goods.Less
Examines the implications of translating the concept of public goods, originally developed in the setting of a domestic national economy, to that of global public goods set within a transnational global economy. This requires important adjustments to the concepts of ‘triangle of publicness’ (publicness of consumption, of benefits, and of decision‐making), as well as new typologies of public goods.
Kurt Smith
- Published in print:
- 2010
- Published Online:
- September 2010
- ISBN:
- 9780199583652
- eISBN:
- 9780191723155
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199583652.003.0013
- Subject:
- Philosophy, History of Philosophy, Metaphysics/Epistemology
This chapter shows how the combinatorial nature of bodies expresses the permutation group concept, the latter expressing the conditions underwriting a genuine mathematical system. The chapter ...
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This chapter shows how the combinatorial nature of bodies expresses the permutation group concept, the latter expressing the conditions underwriting a genuine mathematical system. The chapter explains how synthesis, or a synthetic system, is isomorphic to a permutation group. What is more, it is shown how analysis, or the system of concepts resulting from analysis, is isomorphic to a synthetic system. This, it is argued, establishes a sense in which analysis and synthesis are ‘flip sides’ of the same conceptual coin. Since an analytic‐synthetic system is a group, and a group is a genuine mathematical system, it is seen the important role that Descartes's enumeration played in establishing a ‘mathematized’ physics.Less
This chapter shows how the combinatorial nature of bodies expresses the permutation group concept, the latter expressing the conditions underwriting a genuine mathematical system. The chapter explains how synthesis, or a synthetic system, is isomorphic to a permutation group. What is more, it is shown how analysis, or the system of concepts resulting from analysis, is isomorphic to a synthetic system. This, it is argued, establishes a sense in which analysis and synthesis are ‘flip sides’ of the same conceptual coin. Since an analytic‐synthetic system is a group, and a group is a genuine mathematical system, it is seen the important role that Descartes's enumeration played in establishing a ‘mathematized’ physics.
Charles L. Hughes
- Published in print:
- 2015
- Published Online:
- January 2016
- ISBN:
- 9781469622439
- eISBN:
- 9781469623245
- Item type:
- book
- Publisher:
- University of North Carolina Press
- DOI:
- 10.5149/northcarolina/9781469622439.001.0001
- Subject:
- History, African-American History
In the sound of the 1960s and 1970s, nothing symbolized the rift between black and white America better than the seemingly divided genres of country and soul. Yet the music emerged from the same ...
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In the sound of the 1960s and 1970s, nothing symbolized the rift between black and white America better than the seemingly divided genres of country and soul. Yet the music emerged from the same songwriters, musicians, and producers in the recording studios of Memphis and Nashville, Tennessee, and Muscle Shoals, Alabama—what this book calls the “country-soul triangle.” In legendary studios like Stax and FAME, integrated groups of musicians like Booker T. and the MGs and the Muscle Shoals Rhythm Section produced music that both challenged and reconfirmed racial divisions in the United States. Working with artists from Aretha Franklin to Willie Nelson, these musicians became crucial contributors to the era's popular music and internationally recognized symbols of American racial politics in the turbulent years of civil rights protests, Black Power, and white backlash.Less
In the sound of the 1960s and 1970s, nothing symbolized the rift between black and white America better than the seemingly divided genres of country and soul. Yet the music emerged from the same songwriters, musicians, and producers in the recording studios of Memphis and Nashville, Tennessee, and Muscle Shoals, Alabama—what this book calls the “country-soul triangle.” In legendary studios like Stax and FAME, integrated groups of musicians like Booker T. and the MGs and the Muscle Shoals Rhythm Section produced music that both challenged and reconfirmed racial divisions in the United States. Working with artists from Aretha Franklin to Willie Nelson, these musicians became crucial contributors to the era's popular music and internationally recognized symbols of American racial politics in the turbulent years of civil rights protests, Black Power, and white backlash.
