Search results for "Calculus"
showing 10 items of 617 documents
Basics of Post-quantum Calculus
2018
Entropies and Equilibria of Many-Particle Systems: An Essay on Recent Research
2004
International audience; .This essay is intended to present a fruitful collaboration which has developed among a group of people whose names are listed above: entropy methods have proved over the last years to be an efficient tool for the understanding of the qualitative properties of physically sound models, for accurate numerics and for a more mathematical understanding of nonlinear PDEs. The goal of this essay is to sketch the historical development of the concept of entropy in connection with PDEs of continuum mechanics, to present recent results which have been obtained by the members of the group and to emphasize the most striking achievements of this research. The presentation is by n…
Multiple Solutions for Fractional Boundary Value Problems
2018
Variational methods and critical point theorems are used to discuss existence and multiplicity of solutions for fractional boundary value problem where Riemann–Liouville fractional derivatives and Caputo fractional derivatives are used. Some conditions to determinate nonnegative solutions are presented. An example is given to illustrate our results.
Vertical versus horizontal Sobolev spaces
2020
Let $\alpha \geq 0$, $1 < p < \infty$, and let $\mathbb{H}^{n}$ be the Heisenberg group. Folland in 1975 showed that if $f \colon \mathbb{H}^{n} \to \mathbb{R}$ is a function in the horizontal Sobolev space $S^{p}_{2\alpha}(\mathbb{H}^{n})$, then $\varphi f$ belongs to the Euclidean Sobolev space $S^{p}_{\alpha}(\mathbb{R}^{2n + 1})$ for any test function $\varphi$. In short, $S^{p}_{2\alpha}(\mathbb{H}^{n}) \subset S^{p}_{\alpha,\mathrm{loc}}(\mathbb{R}^{2n + 1})$. We show that the localisation can be omitted if one only cares for Sobolev regularity in the vertical direction: the horizontal Sobolev space $S_{2\alpha}^{p}(\mathbb{H}^{n})$ is continuously contained in the vertical Sobolev sp…
Contextuality-by-Default: A Brief Overview of Ideas, Concepts, and Terminology
2016
This paper is a brief overview of the concepts involved in measuring the degree of contextuality and detecting contextuality in systems of binary measurements of a finite number of objects. We discuss and clarify the main concepts and terminology of the theory called “contextuality-by-default,” and then discuss generalizations of the theory to arbitrary systems of arbitrary random variables.
Controlled time integration for the numerical simulation of meteor radar reflections
2016
We model meteoroids entering the Earth[U+05F3]s atmosphere as objects surrounded by non-magnetized plasma, and consider efficient numerical simulation of radar reflections from meteors in the time domain. Instead of the widely used finite difference time domain method (FDTD), we use more generalized finite differences by applying the discrete exterior calculus (DEC) and non-uniform leapfrog-style time discretization. The computational domain is presented by convex polyhedral elements. The convergence of the time integration is accelerated by the exact controllability method. The numerical experiments show that our code is efficiently parallelized. The DEC approach is compared to the volume …
Dental calculus indicates widespread plant use within the stable Neanderthal dietary niche.
2018
The ecology of Neanderthals is a pressing question in the study of hominin evolution. Diet appears to have played a prominent role in their adaptation to Eurasia. Based on isotope and zooarchaeological studies, Neanderthal diet has been reconstructed as heavily meat-based and generally similar across different environments. This image persists, despite recent studies suggesting more plant use and more variation. However, we have only a fragmentary picture of their dietary ecology, and how it may have varied among habitats, because we lack broad and environmentally representative information about their use of plants and other foods. To address the problem, we examined the plant microremains…
Dietary evidence from Central Asian Neanderthals: A combined isotope and plant microremains approach at Chagyrskaya Cave (Altai, Russia).
2021
Neanderthals are known primarily from their habitation of Western Eurasia, but they also populated large expanses of Northern Asia for thousands of years. Owing to a sparse archaeological record, relatively little is known about these eastern Neanderthal populations. Unlike in their western range, there are limited zooarchaeological and paleobotanical studies that inform us about the nature of their subsistence. Here, we perform a combined analysis of carbon and nitrogen stable isotopes on bone collagen and microbotanical remains in dental calculus to reconstruct the diet of eastern Neanderthals at Chagyrskaya Cave in the Altai Mountains of Southern Siberia, Russia. Stable isotopes identify…
The efficacy of whole human genome capture on ancient dental calculus and dentin
2019
Objectives Dental calculus is among the richest known sources of ancient DNA in the archaeological record. Although most DNA within calculus is microbial, it has been shown to contain sufficient human DNA for the targeted retrieval of whole mitochondrial genomes. Here, we explore whether calculus is also a viable substrate for whole human genome recovery using targeted enrichment techniques. Materials and methods Total DNA extracted from 24 paired archaeological human dentin and calculus samples was subjected to whole human genome enrichment using in-solution hybridization capture and high-throughput sequencing. Results Total DNA from calculus exceeded that of dentin in all cases, and altho…
Sliding solutions of second-order differential equations with discontinuous right-hand side
2017
We consider second-order ordinary differential equations with discontinuous right-hand side. We analyze the concept of solution of this kind of equations and determine analytical conditions that are satisfied by typical solutions. Moreover, the existence and uniqueness of solutions and sliding solutions are studied. Copyright © 2017 John Wiley & Sons, Ltd.