The System of Inequalities ars > xs−xr

Author(s):  
S. N. Afriat
1998 ◽  
Vol 53 (3-4) ◽  
pp. 171-177
Author(s):  
Hsing-Ya Li

Abstract A chemical reaction network can admit multiple positive steady states if and only if there exists a positive steady state having a zero eigenvalue with its eigenvector in the stoichiometric subspace. A zero eigenvalue analysis is proposed which provides a necessary and sufficient condition to determine the possibility of the existence of such a steady state. The condition forms a system of inequalities and equations. If a set of solutions for the system is found, then the network under study is able to admit multiple positive steady states for some positive rate constants. Otherwise, the network can exhibit at most one steady state, no matter what positive rate constants the system might have. The construction of a zero-eigenvalue positive steady state and a set of positive rate constants is also presented. The analysis is demonstrated by two examples.


2013 ◽  
Vol 107 (1) ◽  
pp. 123-138 ◽  
Author(s):  
JEFFREY EDWARD GREEN

This article aims to correct the widespread imbalance in contemporary liberal thought, which makes explicit appeal to the “least advantaged” without parallel attention to the “most advantaged” as a distinct group in need of regulatory attention. Rawls's influential theory of justice is perhaps the paradigmatic instance of this imbalance, but I show how a Rawlsian framework nonetheless provides three justifications for why implementers of liberal justice—above all, legislators—should regulate the economic prospects of a polity's richest citizens: as a heuristic device for ensuring that a system of inequalities not reach a level at which inequalities cease being mutually advantageous, as protection against excessive inequalities threatening civic liberty, and as redress for a liberal society's inability to fully realize fair equality of opportunity with regard to education and politics. Against the objection that such arguments amount to a defense of envy, insofar as they support policies that in certain instances impose economic costs on the most advantaged with negative or neutral economic impact on the rest of society, I attend to Rawls's often overlooked distinction between irrational and reasonable forms of envy, showing that any envy involved in the proposed regulation of the most advantaged falls within this latter category.


2017 ◽  
Vol 29 (2) ◽  
pp. 329-345 ◽  
Author(s):  
Aureliano M. Robles-Pérez ◽  
José Carlos Rosales

AbstractLet ${{\mathbb{N}}}$ be the set of nonnegative integers. A problem about how to transport profitably an organized group of persons leads us to study the set T formed by the integers n such that the system of inequalities, with nonnegative integer coefficients,$a_{1}x_{1}+\cdots+a_{p}x_{p}<n<b_{1}x_{1}+\cdots+b_{p}x_{p}$has at least one solution in ${{\mathbb{N}}^{p}}$. We will see that ${T\cup\{0\}}$ is a numerical semigroup. Moreover, we will show that a numerical semigroup S can be obtained in this way if and only if ${\{a+b-1,a+b+1\}\subseteq S}$, for all ${a,b\in S\setminus\{0\}}$. In addition, we will demonstrate that such numerical semigroups form a Frobenius variety and we will study this variety. Finally, we show an algorithmic process in order to compute T.


Author(s):  
Arthur Fine

Bell’s theorem is concerned with the outcomes of a special type of ‘correlation experiment’ in quantum mechanics. It shows that under certain conditions these outcomes would be restricted by a system of inequalities (the ‘Bell inequalities’) that contradict the predictions of quantum mechanics. Various experimental tests confirm the quantum predictions to a high degree and hence violate the Bell inequalities. Although these tests contain loopholes due to experimental inefficiencies, they do suggest that the assumptions behind the Bell inequalities are incompatible not only with quantum theory but also with nature. A central assumption used to derive the Bell inequalities is a species of no-action-at-a-distance, called ‘locality’: roughly, that the outcomes in one wing of the experiment cannot immediately be affected by measurements performed in another wing (spatially distant from the first). For this reason the Bell theorem is sometimes cited as showing that locality is incompatible with the quantum theory, and the experimental tests as demonstrating that nature is nonlocal. These claims have been contested.


2017 ◽  
Vol 24 (4) ◽  
Author(s):  
Justyna Ogorzaly

AbstractWe consider a model of a dynamic frictional contact between the body and the foundation. In this model the contact is bilateral. The behaviour of the material is described by the elastic-viscoplastic constitutive law with thermal effect. The variational formulation of this model leads to a system of two evolution hemivariational inequalities. The aim of this paper is to prove that this system of inequalities has a unique solution. The proof is based on the Banach fixed point theorem and some results for hemivariational inequalities.


2001 ◽  
Vol 94 (5) ◽  
pp. 362-364
Author(s):  
Miriam Amit ◽  
Michael N. Fried ◽  
Pavel Satianov

In studying algebra, a segment of the number line is inevitably related to a system of inequalities in one variable. Similarly, a convex region of the plane is inevitably related to a system of inequalities in two variables. Indeed, we drew this unsurprising conclusion from a questionnaire that we gave to a group of high school teachers and a large group of advanced twelfth graders. In the questionnaire, we simply asked what kind of mathematical expression is needed to determine the points in a line segment and in a triangular region.


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