Nombre négatif

Résumé

vignette|Thermomètre indiquant une température négative en degrés Fahrenheit. Un nombre négatif est un nombre réel qui est inférieur à zéro, comme −3 ou −π . Histoire La première apparition connue des nombres négatifs est dans Les Neuf Chapitres sur l'art mathématique (Jiǔzhāng Suànshù), dont les versions qui nous sont parvenues datent du début de la dynastie Han (), sans qu'on puisse dater les versions originales, sans doute plus anciennes. Les Neuf Chapitres utilise des bâtons de numération rouges pour les nombres positifs et des noirs pour les négatifs. Cela permettait aux Chinois de résoudre un système d'équations linéaires à coefficients négatifs. En Inde, on formule des règles cohérentes pour les travailler, et on comprend leur signification (en même temps que celui du zéro) dans des situations telle que les emprunts et dettes, ainsi qu'en atteste le Brahmasphutasiddhanta de Brahmagupta (), mais ces concepts peuvent être antérieurs. Brahmagupta utilise les nombres né

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Electric Field Eect on Skyrmion phase in Chiral lattice Ferrimagnet Cu2OSeO3

Naman Agarwal

Insulator materials are the recent research interest in Spintronics because of the absence of joule heating. There has been continued interest in insulator material Cu2OSeO3 because it possesses the novel Skyrmion phase [1], specific type of spin vortices in the lattice, characterized by quantized topological number, near the paramagnetic phase boundary [2]. This Skyrmion phase can be harnessed for the switching applications in the data storage devices [3–6]. We study the effect of positive or negative DC electric field on the Skyrmion phase boundary of this material by magnetoelectric susceptibility(dM/dE)measurements, which is a sensitive technique for scanning phase boundary [7,8]. We scan out the phase diagram for positive, negative and zero DC electric fields and find that electric field effect is maximum at the phase boundaries and decreases inside the phase There is no cut-off for the electric field effect. Also, the electric field effect is maximum at upper skyrmion boundary compared to other phase boundaries. We also show the small expansion(contraction) of Skyrmion phase along temperature axis with the application of positive(negative) DC electric field.

2016

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Sign-Changing Solutions for a Class of Zero Mass Nonlocal Schrodinger Equations

We consider the following class of fractional Schrodinger equations: (-Delta)(alpha)u + V(x)u = K(x)f(u) in R-N, where alpha is an element of (0, 1), N > 2 alpha, (-Delta)(alpha) is the fractional Laplacian, V and K are positive continuous functions which vanish at infinity, and f is a continuous function. By using a minimization argument and a quantitative deformation lemma, we obtain the existence of a sign-changing solution. Furthermore, when f is odd, we prove that the above problem admits infinitely many nontrivial solutions. Our result extends to the fractional framework some well-known theorems proved for elliptic equations in the classical setting. With respect to these cases studied in the literature, the nonlocal one considered here presents some additional difficulties, such as the lack of decompositions involving positive and negative parts, and the non-differentiability of the Nehari Manifold, so that a careful analysis of the fractional spaces involved is necessary.

2019

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In the restricted Santa Claus problem we are given resources R and players P. Every resource j is an element of R. has a value v(j) and every player i is an element of P desires a set of resources R(i). We are interested in distributing the resources to players that desire them. The quality of a solution is measured by the least happy player, i.e., the lowest sum of resource values. This value should be maximized. The local search algorithm by Asadpour et al. [1] and its connection to the configuration LP has proved itself to be a very influential technique for this and related problems. Asadpour et al. used a local search to obtain a bound of 4 for the ratio of the fractional to the integral optimum of the configuration LP (the integrality gap). This bound is non-constructive, since the local search has not been shown to terminate in polynomial time. On the negative side, the worst instance known has an integrality gap of 2. Although much progress was made in this area, neither bound has been improved since. We present a better analysis that shows the integrality gap is not worse than 3 + 5/6 approximate to 3.8333. (C) 2020 Elsevier B.V. All rights reserved.

ELSEVIER2020

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