96 resultados para History of number theory


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This chapter outlines the history of the practice of strategy, predating the introduction of the term. It homes in on episodes of European history since Antiquity for which historians claim to have found evidence of the practice of strategy, defined by Kimberly Kagan as ‘the setting of a state’s objectives and of priorities among those objectives’ in order to allocate resources and choose the best means. While focusing only on Europe, this chapter covers case studies over nearly 2500 ranging from the wars of Ancient Greece, of the Romans to Medieval warfare (here with a focus on English history), the warfare of Philip II of Spain, Louis XIV of France, Frederick II of Prussia, the French Revolutionaries and Napoleon.

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How and when the Americas were populated remains contentious. Using ancient and modern genome-wide data, we found that the ancestors of all present-day Native Americans, including Athabascans and Amerindians, entered the Americas as a single migration wave from Siberia no earlier than 23 thousand years ago (ka) and after no more than an 8000-year isolation period in Beringia. After their arrival to the Americas, ancestral Native Americans diversified into two basal genetic branches around 13 ka, one that is now dispersed across North and South America and the other restricted to North America. Subsequent gene flow resulted in some Native Americans sharing ancestry with present-day East Asians (including Siberians) and, more distantly, Australo-Melanesians. Putative “Paleoamerican” relict populations, including the historical Mexican Pericúes and South American Fuego-Patagonians, are not directly related to modern Australo-Melanesians as suggested by the Paleoamerican Model.

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We extend the method of Cassels for computing the Cassels-Tate pairing on the 2-Selmer group of an elliptic curve, to the case of 3-Selmer groups. This requires significant modifications to both the local and global parts of the calculation. Our method is practical in sufficiently small examples, and can be used to improve the upper bound for the rank of an elliptic curve obtained by 3-descent.

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Alfred Chandler, the celebrated business historian, provided detailed descriptions of the reasons for failed human commitments and the managerial tools needed to prevent/remediate such failings in the context of large business firms. Chandler's historical narrative identifies three distinct “faces” of bounded reliability—opportunism, benevolent preference reversal, and identity-based discordance—as the main drivers of commitment failure. Adopting bounded reliability (BRel) as a micro-foundation in management studies will raise the quality and relevance of scholarly recommendations to improve managerial decision making and action, because analysis of BRel challenges closely mirrors the real-world problems facing practicing managers.