Tag: Duality

Reconstruction of Wave-Particle Duality and its Implications for General Chemistry Textbooks


Free Download Reconstruction of Wave-Particle Duality and its Implications for General Chemistry Textbooks By Mansoor Niaz, Cecilia Marcano (auth.)
2012 | 46 Pages | ISBN: 9400743955 | PDF | 1 MB
It goes without saying that atomic structure, including its dual wave-particle nature, cannot be demonstrated in the classroom. Thus, for most science teachers, especially those in physics and chemistry, the textbook is their key resource and their students’ core source of information. Science education historiography recognizes the role played by the history and philosophy of science in developing the content of our textbooks, and with this in mind, the authors analyze more than 120 general chemistry textbooks published in the USA, based on criteria derived from a historical reconstruction of wave-particle duality.They come to some revealing conclusions, including the fact that very few textbooks discussed issues such as the suggestion, by both Einstein and de Broglie, and before conclusive experimental evidence was available, that wave-particle duality existed. Other large-scale omissions included de Broglie’s prescription for observing this duality, and the importance of the Davisson-Germer experiments, as well as the struggle to interpret the experimental data they were collecting. Also untouched was the background to the role played by Schrödinger in developing de Broglie’s ideas. The authors argue that rectifying these deficiencies will arouse students’ curiosity by giving them the opportunity to engage creatively with the content of science curricula. They also assert that it isn’t just the experimental data in science that matters, but the theoretical insights and unwonted inspirations, too. In addition, the controversies and discrepancies in the theoretical and experimental record are key drivers in understanding the development of science as we know it today.

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Farey Sequences Duality and Maps Between Subsequences


Free Download Andrey O. Matveev, "Farey Sequences: Duality and Maps Between Subsequences"
English | ISBN: 3110546620 | 2017 | 182 pages | EPUB | 20 MB
As a first comprehensive overview on Farey sequences and subsequences, this monograph is intended as a reference for anyone looking for specific material or formulas related to the subject. Duality of subsequences and maps between them are discussed and explicit proofs are shown in detail.

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Duality in Measure Theory


Free Download Duality in Measure Theory by Corneliu Constantinescu
English | PDF | 1980 | 202 Pages | ISBN : 3540099891 | 6.1 MB
The duality in measure theory may be seen as a method to introduce a kind of generalized functions needed in integration theory (with re- spect to real or vector valued measures).

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Duality in 19th and 20th Century Mathematical Thinking


Free Download Duality in 19th and 20th Century Mathematical Thinking by Ralf Krömer, Emmylou Haffner
English | PDF (True) | 2024 | 962 Pages | ISBN : 3031597966 | 21.2 MB
This volume brings together scholars across various domains of the history and philosophy of mathematics, investigating duality as a multi-faceted phenomenon. Encompassing both systematic analysis and historical examination, the book endeavors to elucidate the status, roles, and dynamics of duality within the realms of 19th and 20th-century mathematics. Eschewing a priori notions, the contributors embrace the diverse interpretations and manifestations of duality, thus presenting a nuanced and comprehensive perspective on this intricate subject.

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Linear Programming Duality An Introduction to Oriented Matroids


Free Download Linear Programming Duality: An Introduction to Oriented Matroids by Achim Bachem , Walter Kern
English | PDF | 1992 | 215 Pages | ISBN : 3540554173 | 15.4 MB
The main theorem of Linear Programming Duality, relating a "pri mal" Linear Programming problem to its "dual" and vice versa, can be seen as a statement about sign patterns of vectors in complemen tary subspaces of Rn. This observation, first made by R.T. Rockafellar in the late six ties, led to the introduction of certain systems of sign vectors, called "oriented matroids". Indeed, when oriented matroids came into being in the early seventies, one of the main issues was to study the fun damental principles underlying Linear Progra.mrning Duality in this abstract setting. In the present book we tried to follow this approach, i.e., rather than starting out from ordinary (unoriented) matroid theory, we pre ferred to develop oriented matroids directly as appropriate abstrac tions of linear subspaces. Thus, the way we introduce oriented ma troids makes clear that these structures are the most general -and hence, the most simple -ones in which Linear Programming Duality results can be stated and proved. We hope that this helps to get a better understanding of LP-Duality for those who have learned about it before und a good introduction for those who have not.

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