Search results for "CALCULUS"
showing 10 items of 617 documents
Economic Globalization, Perceptions of the Room to Maneuver of National Governments and Individual Electoral Participation
2013
Recent macro-level research argues that economic globalisation has negative consequences for electoral turnout as globalisation would constrain the leeway of national governments and thereby render elections less meaningful to voters. This article constitutes the first attempt to analyse the link between perceptions of the national government’s room to manoeuvre and turnout on the individual level: Do individual perceptions that national governments enjoy less leeway under economic globalisation lead to a lower individual inclination to vote? The paper draws on the case of UK’s General Election in 2001 and, thus, a context in which the idea of a constraining effect of globalisation was made…
An Integral on a Complete Metric Measure Space
2015
We study a Henstock-Kurzweil type integral defined on a complete metric measure space \(X\) endowed with a Radon measure \(\mu\) and with a family of “cells” \(\mathcal{F}\) that satisfies the Vitali covering theorem with respect to \(\mu\). This integral encloses, in particular, the classical Henstock-Kurzweil integral on the real line, the dyadic Henstock-Kurzweil integral, the Mawhin’s integral [19], and the \(s\)-HK integral [4]. The main result of this paper is the extension of the usual descriptive characterizations of the Henstock-Kurzweil integral on the real line, in terms of \(ACG^*\) functions (Main Theorem 1) and in terms of variational measures (Main Theorem 2).
From Arithmetic to Logic based AI: A Comparative Analysis of Neural Networks and Tsetlin Machine
2020
Neural networks constitute a well-established design method for current and future generations of artificial intelligence. They depends on regressed arithmetic between perceptrons organized in multiple layers to derive a set of weights that can be used for classification or prediction. Over the past few decades, significant progress has been made in low-complexity designs enabled by powerful hardware/software ecosystems. Built on the foundations of finite-state automata and game theory, Tsetlin Machine is increasingly gaining momentum as an emerging artificial intelligence design method. It is fundamentally based on propositional logic based formulation using booleanized input features. Rec…
A discrete mechanical model of fractional hereditary materials
2013
Fractional hereditary materials are characterized for the presence, in the stress-strain relations, of fractional-order operators with order beta a[0,1]. In Di Paola and Zingales (J. Rheol. 56(5):983-1004, 2012) exact mechanical models of such materials have been extensively discussed obtaining two intervals for beta: (i) Elasto-Viscous (EV) materials for 0a parts per thousand currency sign beta a parts per thousand currency sign1/2; (ii) Visco-Elastic (VE) materials for 1/2a parts per thousand currency sign beta a parts per thousand currency sign1. These two ranges correspond to different continuous mechanical models. In this paper a discretization scheme based upon the continuous models p…
Exact mechanical models of fractional hereditary materials
2012
Fractional Viscoelasticity is referred to materials, whose constitutive law involves fractional derivatives of order β R such that 0 β 1. In this paper, two mechanical models with stress-strain relation exactly restituting fractional operators, respectively, in ranges 0 β 1 / 2 and 1 / 2 β 1 are presented. It is shown that, in the former case, the mechanical model is described by an ideal indefinite massless viscous fluid resting on a bed of independent springs (Winkler model), while, in the latter case it is a shear-type indefinite cantilever resting on a bed of independent viscous dashpots. The law of variation of all mechanical characteristics is of power-law type, strictly related to th…
Products of Bessel functions and associated polynomials
2013
The symbolic method is used to get explicit formulae for the products or powers of Bessel functions and for the relevant integrals.
Schubert calculus and singularity theory
2010
Abstract Schubert calculus has been in the intersection of several fast developing areas of mathematics for a long time. Originally invented as the description of the cohomology of homogeneous spaces, it has to be redesigned when applied to other generalized cohomology theories such as the equivariant, the quantum cohomology, K -theory, and cobordism. All this cohomology theories are different deformations of the ordinary cohomology. In this note, we show that there is, in some sense, the universal deformation of Schubert calculus which produces the above mentioned by specialization of the appropriate parameters. We build on the work of Lerche Vafa and Warner. The main conjecture these auth…
Critical reflections on asymptotically safe gravity
2020
Asymptotic safety is a theoretical proposal for the ultraviolet completion of quantum field theories, in particular for quantum gravity. Significant progress on this program has led to a first characterization of the Reuter fixed point. Further advancement in our understanding of the nature of quantum spacetime requires addressing a number of open questions and challenges. Here, we aim at providing a critical reflection on the state of the art in the asymptotic safety program, specifying and elaborating on open questions of both technical and conceptual nature. We also point out systematic pathways, in various stages of practical implementation, towards answering them. Finally, we also take…
Euclid’s Proof of the Infinitude of Primes: Distorted, Clarified, Made Obsolete, and Confirmed in Modern Mathematics
2014
Published version of an article in the journal: Mathematical Intelligencer. Also available from the publisher at: http://dx.doi.org/10.1007/s00283-014-9506-9
Path integral solution by fractional calculus
2008
In this paper, the Path Integral solution is developed in terms of complex moments. The method is applied to nonlinear systems excited by normal white noise. Crucial point of the proposed procedure is the representation of the probability density of a random variable in terms of complex moments, recently proposed by the first two authors. Advantage of this procedure is that complex moments do not exhibit hierarchy. Extension of the proposed method to the study of multi degree of freedom systems is also discussed.