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Showing 1 to 7 of 7 for “"infinitesimals"”.
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Point symmetry methods for Itô Stochastic Differential Equations (SDE) with a finite jump process
… equations is discussed, by considering the infinitesimals of not only spatial and temporal variables but also infinitesimals of the Poisson process variable. This was later extended, in the second part, to define the symmetry of jumpdiffusion stochastic differential equations (i.e., …
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Internal Set Theory and Euler's Introductio in Analysin Infinitorum
… (1748), he readily used infinite numbers and infinitesimals in many of his proofs. We aim to reformulate a group of proofs from the <em>Introductio</em> using concepts and techniques from Abraham Robinson's celebrated Nonstandard Analysis (NSA); in particular, we will use Internal Set Theory, …
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A memória da água e outras hipóteses para compreensão do possível mecanismo de ação dos medicamentos homeopáticos : uma revisão
… and the principle of high dilutions or law of infinitesimals. Homeopathy has over 200 years of experience, based on advances in several areas of knowledge, and is moving forward on the path of science, through scientific research me thods. Led by Jacques Benveniste , using a classic …
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Infinitesimal Models of Algebraic Theories
… an infinitesimal structure based on nil-square infinitesimals. This gives us a good supply of infinitesimally affine spaces in every well-adapted model of Synthetic Differential Geometry. In particular, it shows that every smooth manifold is infinitesimally affine and that every smooth map …
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On folding and unfolding with linkages and origami
… working over a field R(e) that includes formal infinitesimals. Using this model and the powerful Tarski-Seidenberg "transfer" principle for real closed fields, we prove a self-touching version of the celebrated Expansive Carpenter's Rule Theorem. We switch to folding polyhedra in Chapter 4: we …
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Mathematics and Late Elizabethan Drama, 1587-1603
… God and the monarchy. Chapter 5, ‘Infinities and Infinitesimals’, considers how the infinitely large and infinitely small permeate the language and structure of Shakespeare’s Hamlet. It argues that the play is embroiled with the mathematical implications of Copernican cosmography and its Brunian …
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Hyperreal structures arising from an infinite base logarithm
This paper presents new concepts in the use of infinite and infinitesimal numbers in real analysis. theory is based upon the hyperreal number system developed by Abraham Robinson in the 1960's in his invention of "nonstandard analysis". paper begins with a short exposition of the construction of …