Search results for "Measure theory"

A theory of spatial general equilibrium in a fuzzy economy

1984

Let an economic space be characterized by the existence of a given distribution of locations, i.e. consumers' residential locations and producers' plants. It is equipped with a system of prices. The economy is fuzzy because the economic behaviors of agents are imprecise. In this context, spatial partial equilibria theories are applications of a fuzzy economic calculation model. The aim of the present paper is to study the conditions which must be fulfilled in order that the compatibility of consumers' equilibria and producers' equilibria be verified. Mathematical tools are Butnariu's theorems which extend the Brouwer's and Kakutani's theorems to the cases of fuzzy functions and fuzzy point-…

Accessible parts of boundary for simply connected domains

2018

For a bounded simply connected domain $\Omega\subset\mathbb{R}^2$, any point $z\in\Omega$ and any $0<\alpha<1$, we give a lower bound for the $\alpha$-dimensional Hausdorff content of the set of points in the boundary of $\Omega$ which can be joined to $z$ by a John curve with a suitable John constant depending only on $\alpha$, in terms of the distance of $z$ to $\partial\Omega$. In fact this set in the boundary contains the intersection $\partial\Omega_z\cap\partial\Omega$ of the boundary of a John sub-domain $\Omega_z$ of $\Omega$, centered at $z$, with the boundary of $\Omega$. This may be understood as a quantitative version of a result of Makarov. This estimate is then applied to obta…

Dynamical equivalence of impulsive quasilinear equations

2015

Abstract Using Green type map we can find sufficient conditions under which an impulsive quasilinear equation is dynamically equivalent to its corresponding linear equation. This result extends Grobman Hartman theorem for equations without ordinary dichotomy.

Curve packing and modulus estimates

2018

A family of planar curves is called a Moser family if it contains an isometric copy of every rectifiable curve in $\mathbb{R}^{2}$ of length one. The classical "worm problem" of L. Moser from 1966 asks for the least area covered by the curves in any Moser family. In 1979, J. M. Marstrand proved that the answer is not zero: the union of curves in a Moser family has always area at least $c$ for some small absolute constant $c &gt; 0$. We strengthen Marstrand's result by showing that for $p &gt; 3$, the $p$-modulus of a Moser family of curves is at least $c_{p} &gt; 0$.

The isoperimetric profile of a smooth Riemannian manifold for small volumes.

2009

On Upper Conical Density Results

2010

We report a recent development on the theory of upper conical densities. More precisely, we look at what can be said in this respect for other measures than just the Hausdorff measure. We illustrate the methods involved by proving a result for the packing measure and for a purely unrectifiable doubling measure.

A link between the residual-based gradient plasticity theory and the analogous theories based on the virtual work principle

2009

A link is shown to exist between the so-called residual-based strain gradient plasticity theory and the analogous theories based on the (extended) virtual work principle (VWP). To this aim, the former theory is reformulated and cast in a residual-free form, whereby the insulation condition and the (nonlocal) Clausius–Duhem inequality, on which the theory is grounded, are substituted with equivalent residual-free ingredients, namely the energy balance condition and the residual-free form of the Clausius–Duhem inequality. The equivalence of the residual-free formulation to the original one is shown, also in their ability to cope with energetic size effects and interfacial energy ones. It emer…

A recap on Linear Mixed Models and their hat-matrices

2017

This working paper has a twofold goal. On one hand, it provides a recap of Linear Mixed Models (LMMs): far from trying to be exhaustive, this first part of the working paper focusses on the derivation of theoretical results on estimation of LMMs that are scattered in the literature or whose mathematical derivation is sometimes missing or too quickly sketched. On the other hand, it discusses various definitions that are available in the literature for the hat-matrix of Linear Mixed Models, showing their limitations and proving their equivalence.

THE PARISI–SOURLAS MECHANISM IN YANG–MILLS THEORY?

1999

The Parisi-Sourlas mechanism is exhibited in pure Yang-Mills theory. Using the new scalar degrees of freedom derived from the non-linear gauge condition, we show that the non-perturbative sector of Yang-Mills theory is equivalent to a 4D O(1,3) sigma model in a random field. We then show that the leading term of this equivalent theory is invariant under supersymmetry transformations where (x^{2}+\thetabar\theta) is unchanged. This leads to dimensional reduction proving the equivalence of the non-perturbative sector of Yang-Mills theory to a 2D O(1,3) sigma model.

Determination of defect content and defect profile in semiconductor heterostructures

2011

In this article we present an overview of the technique to obtain the defects depth profile and width of a deposited layer and multilayer based on positron annihilation spectroscopy. In particular we apply the method to ZnO and ZnO/ZnCdO layers deposited on sapphire substrates. After introducing some terminology we first calculate the trend that the W/S parameters of the Doppler broadening measurements must follow, both in a qualitative and quantitative way. From this point we extend the results to calculate the width and defect profiles in deposited layer samples.