Stable Complete Intersections

A complete intersection of n polynomials in n indeterminates has only a finite number of zeros. In this paper we address the following question: how do the zeros change when the coefficients of the polynomials are perturbed? In the first part we show how to construct semi-algebraic sets in the parameter space over which all the complete intersection ideals share the same number of isolated real zeros. In the second part we show how to modify the complete intersection and get a new one which generates the same ideal but whose real zeros are more stable with respect to perturbations of the coefficients.Comment: 1 figur

Dissipative scale effects in strain-gradient plasticity: the case of simple shear

We analyze dissipative scale effects within a one-dimensional theory, developed in [L. Anand et al. (2005) J. Mech. Phys. Solids 53], which describes plastic flow in a thin strip undergoing simple shear. We give a variational characterization of the {\emph{ yield (shear) stress}} --- the threshold for the inset of plastic flow --- and we use this characterization, together with results from [M. Amar et al. (2011) J. Math. Anal. Appl. 397], to obtain an explicit relation between the yield stress and the height of the strip. The relation we obtain confirms that thinner specimens are stronger, in the sense that they display higher yield stress

Convergence of the regularized short pulse equation to the short pulse one

We consider the regularized short-pulse equation, which contains nonlinear dis- persive effects. We prove that as the diffusion parameter tends to zero, the solutions of the dispersive equation converge to discontinuous weak solutions of the short-pulse one. The proof relies on deriving suitable a priori estimates together with an application of the compensated compactness method in the Lp setting

Oleinik type estimates for the Ostrovsky-Hunter eequation

The Ostrovsky-Hunter equation provides a model for small-amplitude long waves in a rotating fluid of finite depth. It is a nonlinear evolution equation. In this paper we study the well-posedness for the Cauchy problem associated to this equation within a class of bounded discontinuous solutions. We show that we can replace the Kruzkov-type entropy inequalities by an Oleinik-type estimate and prove uniqueness via a nonlocal adjoint problem. An implication is that a shock wave in an entropy weak solution to the Ostrovsky-Hunter equation is admissible only if it jumps down in value (like the inviscid Burgers equation)

Wellposedness results for the short pulse equation

The short pulse equation provides a model for the propagation of ultra-short light pulses in silica optical fibers. It is a nonlinear evolution equation. In this paper the wellposedness of bounded solutions for the homogeneous initial boundary value problem and the Cauchy problem associated to this equation are studied.Comment: arXiv admin note: text overlap with arXiv:1310.701

Convergence of the Ostrovsky equation to the Ostrovsky-Hunter one

We consider the Ostrovsky equation, which contains nonlinear dispersive effects. We prove that as the diffusion parameter tend to zero, the solutions of the dispersive equation converge to discontinuous weak solutions of the Ostrovsky-Hunter equation. The proof relies on deriving suitable a priori estimates together with an application of the compensated compactness method in the L^p setting

Social Opportunities and Private Convenience of Choices at Farm Level: An Approach to the Links Between Farm Income and Sustainable GDP

This work proposes a method to identify and evaluate the links between the economic and environmental management of a farm, its income, and sustainable GDP. The approach is designed to link micro and macro economic aspects and is based on certain indicators, chosen from among those obtained from analysis of the farm accounts, suitable for representing socially desirable objectives. Three different types of farm accounts are employed. An MADM method of quantitative MCDM analysis was used to make a joint evaluation of various objective indicators in different types of farm management. The work only presents the most interesting result of the research, which was the method itself and does not include the results of a specific case study which was made. This method can be generally applied to connect macro and micro economic aspects and thus might be applicable to different contexts.Method, Farm, Society, Income, Environment, Well-being, Institutional and Behavioral Economics, Q1,