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Books on the topic 'Varieties of sums of powers'

Author: Grafiati

Published: 14 March 2023

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Reznick, Bruce Arie. Sums of even powers of real linear forms. Providence, R.I: American Mathematical Society, 1992.

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Rodale Press. Shades of lavender: A guide to the healing powers, flavor, and lore of nature's most fragrant herb. [Emmaus, PA]: Rodale, 2000.

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1953-, Campillo Antonio, ed. Zeta functions in algebra and geometry: Second International Workshop on Zeta Functions in Algebra and Geometry, May 3-7, 2010, Universitat de Les Illes Balears, Palma de Mallorca, Spain. Providence, R.I: American Mathematical Society, 2012.

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Alta.) WIN (Conference) (2nd 2011 Banff. Women in Numbers 2: Research directions in number theory : BIRS Workshop, WIN2 - Women in Numbers 2, November 6-11, 2011, Banff International Research Station, Banff, Alberta, Canada. Edited by David Chantal 1964-, Lalín Matilde 1977-, and Manes Michelle 1970-. Providence, Rhode Island: American Mathematical Society, 2013.

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Alladi, Krishnaswami, Frank Garvan, and Ae Ja Yee. Ramanujan 125: International conference to commemorate the 125th anniversary of Ramanujan's birth, Ramanujan 125, November 5--7, 2012, University of Florida, Gainesville, Florida. Providence, Rhode Island: American Mathematical Society, 2014.

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Kleiman, S. L., Anthony Iarrobino, Vassil Kanev, and A. Iarrobino. Power Sums, Gorenstein Algebras, and Determinantal Loci. Springer London, Limited, 2006.

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Iarrobino, Anthony, Vassil Kanev, A. Iarrobino, and S. L. Kleiman. Power Sums, Gorenstein Algebras, and Determinantal Loci. Springer, 2000.

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Becker, E. Sums of Powers in Fields and Artin-Schreier Theory of Orderings of Higher Level (Modern Surveys in Mathematics Series). Springer-Verlag, 1995.

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Dawson, C. Bryan. Calculus Set Free. Oxford University Press, 2021. http://dx.doi.org/10.1093/oso/9780192895592.001.0001.

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Calculus Set Free: Infinitesimals to the Rescue is a single-variable calculus textbook that incorporates the use of infinitesimals, and more generally the hyperreal numbers. The infinitesimal methods and notation herein were developed with beginning calculus students in mind, resulting in exposition that is more intuitive as well as many calculational procedures that are easier to perform, as compared to both traditional calculus textbooks and earlier attempts at including infinitesimals in calculus. Arithmetic of hyperreal numbers, levels of hyperreal numbers, and approximation in the hyperreals lead to a definition of limit. Limit computations are based directly on that definition. Computation-style proofs of derivative rules use an approximation formula called the “local linearity formula.” The definite integral is developed through the idea of finding area using infinitely many subintervals and right-hand endpoints; the resulting “omega sums” are much easier than Riemann sums as a result of the “sum of powers approximation formula,” which also anticipates the Fundamental Theorem of Calculus by its resemblance to the antiderivative power rule. The limit comparison test is replaced by the “level comparison test,” which is so widely applicable and computationally simple that strategy for testing series is noticeably less difficult. Although infinitesimal methods are used for any mathematical process involving a limit, the remainder of the text uses the standard methods of calculus. Organization is similar to other college-level calculus texts. Features include ample marginal notes, examples, illustrations, and answers to odd-numbered exercises.

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Knobloch, Eberhard. Generality in Leibniz’s mathematics. Edited by Karine Chemla, Renaud Chorlay, and David Rabouin. Oxford University Press, 2017. http://dx.doi.org/10.1093/oxfordhb/9780198777267.013.3.

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This article discusses generality in Gottfried Leibniz’s mathematics. In principle, Leibnizian mathematics has a philosophical-theological basis. From the beginning everything that exists is to be found in an orderly relation. The general and inviolable laws of the world are an ontological a priori. The universal harmony of the world consists in the largest possible variety being given the largest possible order so that the largest possible perfection is involved. After considering the relationship between the value of generality and the harmonies that are at the center of Leibniz’s concern, this article explores his view that generality implies beauty as well as conciseness and simplicity. It also examines how the interest in generality relates to notations, taking the examples of determinants and sums of powers, and to utility and fecundity. Finally, it demonstrates how generality is connected with laws of formation.

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Börzel, Tanja A., and Soo Yeon Kim. The International Political Economy of Regionalism. Oxford University Press, 2017. http://dx.doi.org/10.1093/acrefore/9780190228637.013.173.

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Economic regionalism has been dominated by preferential trade agreements (PTAs). Not only have their numbers surged since the end of the Cold War, we also see different varieties of PTAs emerging. First, long-standing PTAs have evolved into deeper forms of economic regionalism, such as custom unions, common markets, or currency unions. Second, PTAs increasingly involve “behind-the-border” trade liberalization, such as the coordination of domestic trade–related regulatory standards. Third, many of the PTAs that were established over the past 25 years no longer only involve countries of the “Global North” but are formed by developing and developed countries (“North-South” PTAs) and between developing countries (“South-South” PTAs). Finally, a most recent development in economic regionalism concerns the building of so called “mega-PTAs,” such as the Trans-Pacific Partnership (TTP) and the Transatlantic Trade and Investment Partnership (TTIP), combining several PTAs.In order to explain the formation, proliferation, and evolution of these varieties of PTA, existing international political economy (IPE) approaches have to give more credit to political factors, such as the locking-in of domestic reforms or the preservation of regional stability. Moreover, IPE scholarship should engage more systematically with diffusion research, particularly to account for the spate of deeper regionalism. Finally, “rising powers” and “emerging markets” constitute an exciting new research area for IPE. These new players differ with regard to the importance they attribute to regionalism and the ways in which they have sought to use and shape it. Identifying and explaining variations in the link between rising powers and regionalism is a key challenge for future research

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Maggi, Mauro, and Paola Orsatti. From Old to New Persian. Edited by Anousha Sedighi and Pouneh Shabani-Jadidi. Oxford University Press, 2018. http://dx.doi.org/10.1093/oxfordhb/9780198736745.013.2.

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This chapter looks at the evolution of Persian, the only language to be substantially documented in all three periods of Old, Middle, and New Iranian on account of its close association with political centres over the centuries: Old and Middle Persian with the Achaemenids and the Sasanians, New Persian with Islamic powers. The chapter includes two parts, preceded by a survey of research on the three stages of Persian. The first part presents the documentation of Old and Middle Persian, discusses the innovations of Old Persian, and considers the transition from Old to Middle Persian. The second part deals with the rise of New Persian by taking into account Early Judaeo-Persian, Persian in Syriac script, Manichaean New Persian, and the early texts in Arabic script. It then discusses the main changes of the language in its literary and non-literary varieties until Contemporary New Persian.

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Haesemeyer, Christian, and Charles A. Weibel. The Norm Residue Theorem in Motivic Cohomology. Princeton University Press, 2019. http://dx.doi.org/10.23943/princeton/9780691191041.001.0001.

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This book presents the complete proof of the Bloch–Kato conjecture and several related conjectures of Beilinson and Lichtenbaum in algebraic geometry. Brought together here for the first time, these conjectures describe the structure of étale cohomology and its relation to motivic cohomology and Chow groups. Although the proof relies on the work of several people, it is credited primarily to Vladimir Voevodsky. The book draws on a multitude of published and unpublished sources to explain the large-scale structure of Voevodsky's proof and introduces the key figures behind its development. It proceeds to describe the highly innovative geometric constructions of Markus Rost, including the construction of norm varieties, which play a crucial role in the proof. It then addresses symmetric powers of motives and motivic cohomology operations. The book unites various components of the proof that until now were scattered across many sources of varying accessibility, often with differing hypotheses, definitions, and language.

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Edmonds III, Radcliffe G. Drawing Down the Moon. Princeton University Press, 2019. http://dx.doi.org/10.23943/princeton/9780691156934.001.0001.

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What did magic mean to the people of ancient Greece and Rome? How did Greeks and Romans not only imagine what magic could do, but also use it to try to influence the world around them? This book provides the most comprehensive account of the varieties of phenomena labeled as magic in classical antiquity. Exploring why certain practices, images, and ideas were labeled as “magic” and set apart from “normal” kinds of practices, the book gives insight into the shifting ideas of religion and the divine in the ancient past and in the later Western tradition. Using fresh approaches to the history of religions and the social contexts in which magic was exercised, the book delves into the archaeological record and classical literary traditions to examine images of witches, ghosts, and demons as well as the fantastic powers of metamorphosis, erotic attraction, and reversals of nature, such as the famous trick of drawing down the moon. From prayer and divination to astrology and alchemy, the book journeys through all manner of ancient magical rituals and paraphernalia. It considers the ways in which the Greco-Roman discourse of magic was formed amid the cultures of the ancient Mediterranean, including Egypt and the Near East.

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Schimmelfennig, Frank, Thomas Winzen, Tobias Lenz, Jofre Rocabert, Loriana Crasnic, Cristina Gherasimov, Jana Lipps, and Densua Mumford. The Rise of International Parliaments. Oxford University Press, 2020. http://dx.doi.org/10.1093/oso/9780198864974.001.0001.

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International parliamentary institutions (IPIs) are on the rise. Around the world, international organizations have increasingly established or affiliated parliamentary assemblies. At the same time, IPIs have generally remained powerless institutions with at best a consultative role in the decision-making process of international organizations. This book pursues the question why the member states of international organizations create IPIs but do not vest them with relevant institutional powers. It argues that neither the functional benefits of delegation nor the internalization of democratic norms provide convincing answers to this question. Rather, IPIs are an instrument of strategic legitimation. By establishing IPIs that mimic a highly esteemed domestic democratic institution, governments seek to ensure that audiences at home and in the wider international environment recognize their IOs as democratically legitimate. At the same time, they seek to avoid being effectively constrained by IPIs in international governance. In a statistical analysis covering the world’s most relevant international organizations and a series of case studies from diverse world regions, we find two major varieties of international parliamentarization. IOs with general purpose and high authority create and empower IPIs to legitimate their region-building projects domestically. Alternatively, IOs are induced to create parliamentary bodies by international diffusion.

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Helleiner, Eric. The Neomercantilists. Cornell University Press, 2021. http://dx.doi.org/10.7591/cornell/9781501760129.001.0001.

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At a time when critiques of free trade policies are gaining currency, this book helps make sense of the protectionist turn, providing the first intellectual history of the genealogy of neomercantilism. The book identifies many pioneers of this ideology between the late eighteenth and early twentieth centuries who backed strategic protectionism and other forms of government economic activism to promote state wealth and power. They included not just the famous Friedrich List, but also numerous lesser-known thinkers, many of whom came from outside of the West. The book's emphasis on neomercantilism's diverse origins challenges traditional Western-centric understandings of its history. It illuminates neglected local intellectual traditions and international flows of ideas that gave rise to distinctive varieties of the ideology around the globe, including in Latin America, the Caribbean, Africa, and Asia. This rich history left enduring intellectual legacies, including in the two dominant powers of the contemporary world economy: China and the United States. The result is an exceptional study of a set of profoundly influential economic ideas. While rooted in the past, it sheds light on the present moment. The book shows how we might construct more global approaches to the study of international political economy and intellectual history, devoting attention to thinkers from across the world, and to the cross-border circulation of thought.

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Wilson, Jessica M. Metaphysical Emergence. Oxford University Press, 2021. http://dx.doi.org/10.1093/oso/9780198823742.001.0001.

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The special sciences and ordinary experience present us with a world of macro-entities trees, birds, lakes, mountains, humans, houses, and sculptures, to name a few which materially depend on lower-level configurations, but which are also distinct from and distinctively efficacious as compared to these configurations. Such appearances give rise to two key questions. First, what is metaphysical emergence, more precisely? Second, is there actually any metaphysical emergence? In Metaphysical Emergence, Jessica Wilson provides clear, compelling, and systematic answers to these questions. Wilson argues that there are two and only two forms of metaphysical emergence making sense of the target cases: ‘Weak’ emergence, whereby a macro-entity or feature has a proper subset of the powers of its base-level configuration, and ‘Strong’ emergence, whereby a macro-entity or feature has a new power as compared to its base-level configuration. Weak emergence unifies and accommodates diverse accounts of realization (e.g., in terms of functional roles, constitutive mechanisms, and parthood) associated with varieties of nonreductive physicalism, whereas Strong emergence unifies and accommodates anti-physicalist views according to which there may be fundamentally novel features, forces, interactions, or laws at higher levels of compositional complexity. After defending each form of emergence against various objections, Wilson considers whether complex systems, ordinary objects, consciousness, and free will are actually either Weakly or Strongly metaphysically emergent. She argues that Weak emergence is quite common, and that Strong emergence, while in most cases at best an open empirical possibility, is instantiated for the important case of free will.

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