Search results for "B25"

A mechanism for ejecting a horseshoe from a partially hyperbolic chain recurrence class

2022

We give a $C^1$-perturbation technique for ejecting an a priori given finite set of periodic points preserving a given finite set of homo/hetero-clinic intersections from a chain recurrence class of a periodic point. The technique is first stated under a simpler setting called Markov iterated function system, a two dimensional iterated function system in which the compositions are chosen in Markovian way. Then we apply the result to the setting of three dimensional partially hyperbolic diffeomorphisms.

A Dirichlet problem for the Laplace operator in a domain with a small hole close to the boundary

2016

We study the Dirichlet problem in a domain with a small hole close to the boundary. To do so, for each pair $\boldsymbol\varepsilon = (\varepsilon_1, \varepsilon_2 )$ of positive parameters, we consider a perforated domain $\Omega_{\boldsymbol\varepsilon}$ obtained by making a small hole of size $\varepsilon_1 \varepsilon_2 $ in an open regular subset $\Omega$ of $\mathbb{R}^n$ at distance $\varepsilon_1$ from the boundary $\partial\Omega$. As $\varepsilon_1 \to 0$, the perforation shrinks to a point and, at the same time, approaches the boundary. When $\boldsymbol\varepsilon \to (0,0)$, the size of the hole shrinks at a faster rate than its approach to the boundary. We denote by $u_{\bolds…

A Derivation of the Vlasov-Stokes System for Aerosol Flows from the Kinetic Theory of Binary Gas Mixtures

2016

In this short paper, we formally derive the thin spray equation for a steady Stokes gas, i.e. the equation consists in a coupling between a kinetic (Vlasov type) equation for the dispersed phase and a (steady) Stokes equation for the gas. Our starting point is a system of Boltzmann equations for a binary gas mixture. The derivation follows the procedure already outlined in [Bernard-Desvillettes-Golse-Ricci, arXiv:1608.00422 [math.AP]] where the evolution of the gas is governed by the Navier-Stokes equation.

Commutator anomalies and the Fock bundle

1990

We show that the anomalous finite gauge transformations can be realized as linear operators acting on sections of the bundle of fermionic Fock spaces parametrized by vector potentials, and more generally, by splittings of the fermionic one-particle space into a pair of complementary subspaces. On the Lie algebra level we show that the construction leads to the standard formula for the relevant commutator anomalies.

Frank H. Knight on social values in economic consumption: an archival note

2020

We reproduce an unpublished address on “Social Values in Economic Consumption” which Knight prepared for a SSRC Conference in June 1931. This material sheds new light on Knight in two respects. First, anticipating what is known as the relative income hypothesis, Knight indicated that a general increase in income, not only leaves the individual’s relative position in society unaltered but makes her/his situation worse off due to the peculiar characteristics of the market for “personal services.” Second, this address provides further evidence of how, in spite of some substantial methodological differences, Knight’s research interests converged with those of the institutionalists.

Weighted norm inequalities in a bounded domain by the sparse domination method

2019

AbstractWe prove a local two-weight Poincaré inequality for cubes using the sparse domination method that has been influential in harmonic analysis. The proof involves a localized version of the Fefferman–Stein inequality for the sharp maximal function. By establishing a local-to-global result in a bounded domain satisfying a Boman chain condition, we show a two-weight p-Poincaré inequality in such domains. As an application we show that certain nonnegative supersolutions of the p-Laplace equation and distance weights are p-admissible in a bounded domain, in the sense that they support versions of the p-Poincaré inequality.

Quasisymmetric maps and string theory

1994

The Institutionalists’ Reaction to Chamberlin’s 'Theory of Monopolistic Competition

2009

Edwin Chamberlin's The Theory of Monopolistic competition is often described as containing omportant traces of institutionalist influence. This is also confimred by Chamberlin himself who, repeadetly, referred to the work of Veblen, and John Maurice Clark among his inspirational sources. The aim of this paper is to analyse the institutionalist rection to the publication of the Theory of Monopolistic Competition. What will be argued is that the institutionalist response to Chamberlin was a mixed one, and involved some substantial criticisms of his analysis of market structures both on methodological and theoretical grounds. The paper is organized as follows. The first section presents a sket…

Local uniqueness of the solutions for a singularly perturbed nonlinear nonautonomous transmission problem

2020

Abstract We consider the Laplace equation in a domain of R n , n ≥ 3 , with a small inclusion of size ϵ . On the boundary of the inclusion we define a nonlinear nonautonomous transmission condition. For ϵ small enough one can prove that the problem has solutions. In this paper, we study the local uniqueness of such solutions.

A DERIVATION OF THE VLASOV-NAVIER-STOKES MODEL FOR AEROSOL FLOWS FROM KINETIC THEORY

2016

This article proposes a derivation of the Vlasov-Navier-Stokes system for spray/aerosol flows. The distribution function of the dispersed phase is governed by a Vlasov-equation, while the velocity field of the propellant satisfies the Navier-Stokes equations for incompressible fluids. The dynamics of the dispersed phase and of the propellant are coupled through the drag force exerted by the propellant on the dispersed phase. We present a formal derivation of this model from a multiphase Boltzmann system for a binary gaseous mixture, involving the droplets/dust particles in the dispersed phase as one species, and the gas molecules as the other species. Under suitable assumptions on the colli…