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Paperback. Zustand: New. Milliken's tree theorem is a deep result in combinatorics that generalizes a vast number of other results in the subject, most notably Ramsey's theorem and its many variants and consequences. In this sense, Milliken's tree theorem is paradigmatic of structural Ramsey theory, which seeks to identify the common combinatorial and logical features of partition results in general. Its investigation in this area has consequently been extensive.Motivated by a question of Dobrinen, we initiate the study of Milliken's tree theorem from the point of view of computability theory. The goal is to understand how close it is to being algorithmically solvable, and how computationally complex are the constructions needed to prove it. This kind of examination enjoys a long and rich history, and continues to be a highly active endeavor. Applied to combinatorial principles, particularly Ramsey's theorem, it constitutes one of the most fruitful research programs in computability theory as a whole. The challenge to studying Milliken's tree theorem using this framework is its unusually intricate proof, and more specifically, the proof of the Halpern-La¨uchli theorem, which is a key ingredient.Our advance here stems from a careful analysis of the Halpern-Läuchli theorem which shows that it can be carried out effectively (i.e., that it is computably true). We use this as the basis of a new inductive proof of Milliken's tree theorem that permits us to gauge its effectivity in turn. The key combinatorial tool we develop for the inductive step is a fast-growing computable function that can be used to obtain a finitary, or localized, version of Milliken's tree theorem. This enables us to build solutions to the full Milliken's tree theorem using effective forcing. The principal result of this is a full classification of the computable content of Milliken's tree theorem in terms of the jump hierarchy, stratified by the size of instance. As usual, this also translates into the parlance of reverse mathematics, yielding a complete understanding of the fragment of second-order arithmetic required to prove Milliken's tree theorem.We apply our analysis also to several well-known applications of Milliken's tree theorem, namely Devlin's theorem, a partition theorem for Rado graphs, and a generalized version of the so-called tree theorem of Chubb, Hirst, and McNicholl. These are all certain kinds of extensions of Ramsey's theorem for different structures, namely the rational numbers, the Rado graph, and perfect binary trees, respectively. We obtain a number of new results about how these principles relate to Milliken's tree theorem and to each other, in terms of both their computability-theoretic and combinatorial aspects. In particular, we establish new structural Ramsey-theoretic properties of the Rado graph theorem and the generalized Chubb-Hirst-McNicholl tree theorem using Zucker's notion of big Ramsey structure.

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Paperback. Zustand: New. Milliken's tree theorem is a deep result in combinatorics that generalizes a vast number of other results in the subject, most notably Ramsey's theorem and its many variants and consequences. In this sense, Milliken's tree theorem is paradigmatic of structural Ramsey theory, which seeks to identify the common combinatorial and logical features of partition results in general. Its investigation in this area has consequently been extensive.Motivated by a question of Dobrinen, we initiate the study of Milliken's tree theorem from the point of view of computability theory. The goal is to understand how close it is to being algorithmically solvable, and how computationally complex are the constructions needed to prove it. This kind of examination enjoys a long and rich history, and continues to be a highly active endeavor. Applied to combinatorial principles, particularly Ramsey's theorem, it constitutes one of the most fruitful research programs in computability theory as a whole. The challenge to studying Milliken's tree theorem using this framework is its unusually intricate proof, and more specifically, the proof of the Halpern-La¨uchli theorem, which is a key ingredient.Our advance here stems from a careful analysis of the Halpern-Läuchli theorem which shows that it can be carried out effectively (i.e., that it is computably true). We use this as the basis of a new inductive proof of Milliken's tree theorem that permits us to gauge its effectivity in turn. The key combinatorial tool we develop for the inductive step is a fast-growing computable function that can be used to obtain a finitary, or localized, version of Milliken's tree theorem. This enables us to build solutions to the full Milliken's tree theorem using effective forcing. The principal result of this is a full classification of the computable content of Milliken's tree theorem in terms of the jump hierarchy, stratified by the size of instance. As usual, this also translates into the parlance of reverse mathematics, yielding a complete understanding of the fragment of second-order arithmetic required to prove Milliken's tree theorem.We apply our analysis also to several well-known applications of Milliken's tree theorem, namely Devlin's theorem, a partition theorem for Rado graphs, and a generalized version of the so-called tree theorem of Chubb, Hirst, and McNicholl. These are all certain kinds of extensions of Ramsey's theorem for different structures, namely the rational numbers, the Rado graph, and perfect binary trees, respectively. We obtain a number of new results about how these principles relate to Milliken's tree theorem and to each other, in terms of both their computability-theoretic and combinatorial aspects. In particular, we establish new structural Ramsey-theoretic properties of the Rado graph theorem and the generalized Chubb-Hirst-McNicholl tree theorem using Zucker's notion of big Ramsey structure.

Buch. Zustand: Neu. Neuware - The thematic program Quantum and Kinetic Problems: Modeling, Analysis, Numerics and Applications was held at the Institute for Mathematical Sciences at the National University of Singapore, from September 2019 to March 2020. Leading experts presented tutorials and special lectures geared towards the participating graduate students and junior researchers.Readers will find in this significant volume four expanded lecture notes with self-contained tutorials on modeling and simulation for collective dynamics including individual and population approaches for population dynamics in mathematical biology, collective behaviors for Lohe type aggregation models, mean-field particle swarm optimization, and consensus-based optimization and ensemble Kalman inversion for global optimization problems with constraints.This volume serves to inspire graduate students and researchers who will embark into original research work in kinetic models for collective dynamics and their applications.

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Paperback. Zustand: Fair. Dutch Treur- en triomfzang voor gemengd koor en orkest van koperen speeltuigen (1886). Met een prachtige kopergravure van P. Verhaert (1883) op speciaal stevig papier. 35 Blz. Groot formaat. Zeer mooie grafische verzorging Röder-Leipzig. Uitgave van het Peter Benoit-fonds, Antwerpen. Tekst + muziek. Klavierpartituur. Zeer zeldzaam ! Met Nederlandse en Franse tekst. Portretgravure H. Conscience.

Antwerpen, Drukkerij J.E. Buschmann, 1885, in-12°, oblong formaat, 10,5 x 13,5 cm, 30 nn pp, gedrukt op recto zijde alleen, tekst in blauwgekleurde tyopografische kader, halflinnen uitgeversband met titel herhaald op het voorplat. Bandje verkleurd en met de tekst los in de band . Zeldzame getuigenis van een Vlaamse culturele bijdrage aan de eerste Wereldtentoonstelling georganiseerd te Antwerpen.

No binding. Zustand: Very Good. a drawing by I.B. Nattier after Peter Paul Rubens (illustrator). 'L' Accouchement de la Reine.'Original etching/engraving on hand laid paper. Sheet size: 45,8 x 61,8 cm. (18 x 24,3 inch). Image size: 34 x 50 cm. (13,4 x 19,7 inch).From: 'La Gallerie de Palais du Luxembourg ', published by Duchange in Paris 1710. This is the large series of engraving by Nattier after the famous series of paintings by Rubens, currently held in the Louvre, depicting the Marriage of Maria de' Medici with Henri IV. Reknown engravers contributed to this work which consists of a Title page, Advertisement page, an engraved portrait of Rubens and 24 large plates.Made by 'Benoit Audran I, the elder (1661-1721) was a French designer, etcher and engraver from Lyon. He was the brother of Jean Audran (1667-1756). He was taught the rudiments of engraving by his father (Germain Audran), and was later placed under the care of his' after 'a drawing by I.B. Nattier after Peter Paul Rubens'. Benoit Audran I, the elder (1661-1721) was a French designer, etcher and engraver from Lyon. He was the brother of Jean Audran (1667-1756). He was taught the rudiments of engraving by his father (Germain Audran), and was later placed under the care of his uncle Gerard Audran in Paris. Benoit Audran II was his nephew and the son of Jean Audran. He was appointed engraver to the king. He was active in Paris and his prints very well respected. Jean-Baptiste Nattier (1678-1726) was A French history painter from Paris. He was the eldest son of Marc Nattier the elder and Marie Courtois. Peter Paul Rubens (1577-1640) was a reknown Flemish Baroque painter, who ran a large studio in Antwerp.Condition: Very good, given age. Print attached to carrier. Edges reinforced on rear. Top left corner with some damage, but not nearly effecting image. General age-related toning and/or occasional minor defects from handling. Please study scan carefully.Keywords: ACCOUCHEMENT-BIRTH LOUIS XIII-DE MEDICIRT-B1-15.

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