Search results for "calculus"
showing 10 items of 617 documents
Newton's Law of Universal Gravitation and Hume's Conception of Causality
2013
This article investigates the relationship between Hume’s causal philosophy and Newton’s philosophy of nature. I claim that Newton’s experimentalist methodology in gravity research is an important background for understanding Hume’s conception of causality: Hume sees the relation of cause and effect as not being founded on a priori reasoning, similar to the way that Newton criticized non-empirical hypotheses about the properties of gravity. However, according to Hume’s criteria of causal inference, the law of universal gravitation is not a complete causal law, since it does not include a reference either to contiguity or to temporal priority. It is still argued that because of the empirical…
Introduction: Purpose and Scope of this Volume, and Some General Comments
2002
In recent years the method of “computer simulation” has started something like a revolution of science: the old division of physics (as well as chemistry, biology, etc.) into “experimental” and “theoretical” branches is no longer really complete. Rather, “computer simulation” has become a third branch complementary to the first two traditional approaches.
Elementary Integration Theory
1998
This section begins with the definitions and elementary properties of real and extended-real functions.
An Approach to a Version of the S(M, g)-pseudo-differential Calculus on Manifolds
2003
For appropriate triples (M,g,M), where M is an (in general non-compact) manifold, g is a metric on T* M, and M is a weight function on T* M, we develop a pseudo-differential calculus on.A4 which is based on the S(M,g))-calculus of L. Hormander [27] in local models. In order to do so, we generalize the concept of E. Schrohe [41] of so-called SG-compatible manifolds. In the final section we give an outlook onto topological properties of the algebras of pseudo-differential operators. We state the existence of “order reducing operators” and that the algebra of operators of order zero is a submultiplicative Ψ*-algebra in the sense of B. Gramsch [18] in \( \mathcal{L}\left( {{L^2}\left( M \right)…
Plantinga’s Haecceitism and Simple Quantified Modal Logic
2017
In a series of papers Alvin Plantinga argued for a serious actualist modal semantics based on the notions of possible world, understood as maximal possible state of affairs, and of individual essence (haecceity). Plantinga’s actualism is known as haecceitism. In spite of the fact that haecceitism has been thought by Plantinga to require a Kripke-style semantics, the aim of this paper is to show that it is compatible with constant domains semantics and the simplest quantified modal logic. I will argue that not only does this approach have all the advantages of a greater simplicity in combining quantification and modalities, but also it better conforms to the actualist program.
A closed-form solution for natural frequencies of thin-walled cylinders with clamped edges
2016
Abstract This paper presents an approximate closed-form solution for the free-vibration problem of thin-walled clamped–clamped cylinders. The used indefinite equations of motion are classic. They derive from Reissner׳s version of Love׳s theory, properly modified with Donnell׳s assumptions, but an innovative approach has been used to find the equations of natural frequencies, based on a solving technique similar to Rayleigh׳s method, on the Hamilton׳s principle and on a proper constructions of the eigenfuctions. Thanks to the used approach, given the geometric and mechanical characteristics of the cylinder, the model provides the natural frequencies via a sequence of explicit algebraic equat…
Exploiting Numerical Behaviors in SPH.
2010
Smoothed Particle Hydrodynamics is a meshless particle method able to evaluate unknown field functions and relative differential operators. This evaluation is done by performing an integral representation based on a suitable smoothing kernel function which, in the discrete formulation, involves a set of particles scattered in the problem domain. Two fundamental aspects strongly characterizing the development of the method are the smoothing kernel function and the particle distribution. Their choice could lead to the so-called particle inconsistency problem causing a loose of accuracy in the approximation; several corrective strategies can be adopted to overcome this problem. This paper focu…
A new interpretation and practical aspects of the direct-methods modulus sum function. VIII
2001
Since the first publication of the direct-methods modulus sum function [Rius (1993). Acta Cryst. A49, 406-409], the application of this function to a variety of situations has been shown in a series of seven subsequent papers. In this way, much experience about this function and its practical use has been gained. It is thought by the authors that it is now the right moment to publish a more complete study of this function which also considers most of this practical knowledge. The first part of the study relates, thanks to a new interpretation, this function to other existing phase-refinement functions, while the second shows, with the help of test calculations on a selection of crystal stru…
The expansion $\star$ mod $\bar{o}(\hbar^4)$ and computer-assisted proof schemes in the Kontsevich deformation quantization
2019
The Kontsevich deformation quantization combines Poisson dynamics, noncommutative geometry, number theory, and calculus of oriented graphs. To manage the algebra and differential calculus of series of weighted graphs, we present software modules: these allow generating the Kontsevich graphs, expanding the noncommutative & x22c6;-product by using a priori undetermined coefficients, and deriving linear relations between the weights of graphs. Throughout this text we illustrate the assembly of the Kontsevich & x22c6;-product up to order 4 in the deformation parameter Already at this stage, the & x22c6;-product involves hundreds of graphs; expressing all their coefficients via 149 w…
Central Themes and Impact of Pieri’s Work
2021
The first book of this series, The Legacy of Mario Pieri in Geometry and Arithmetic (cited here as M&S 2007), presented an overview of Pieri’s life and research, and a deeper study of the background of his work in foundations of geometry and arithmetic.