Fractional variational problems with the Riesz-Caputo derivative

In this paper we investigate optimality conditions for fractional variational problems, with a Lagrangian depending on the Riesz-Caputo derivative. First we prove a generalized Euler-Lagrange equation for the case when the interval of integration of the functional is different from the interval of the fractional derivative. Next we consider integral dynamic constraints on the problem, for several different cases. Finally, we determine optimality conditions for functionals depending not only on the admissible functions, but on time also, and we present a necessary condition for a pair function-time to be an optimal solution to the problem. © 2011 Elsevier Ltd. All rights reserved.FCTCIDM

A nonstandard characterization of regular surfaces

In the present work we approach the study of surfaces using Nonstandard Analysis, by providing first a nonstandard characterization of a surface. Further, the tangent space to a surface is defined as well.CEOCFCTFEDER/POCT

Connectedness and compactness on standard sets

We present a nonstandard characterization of connected compact sets. (C) 2010 WILEY-VCH Verlag GmbH & Co KGaA. WeinheimCEOCFCTFEDER/POCI 201

The return to firm investment in human capital

In this paper we estimate the rate of return to firm investments in human capital in the form of formal job training. We use a panel of large firms with unusually detailed information on the duration of training, the direct costs of training, and several firm characteristics such as their output, workforce characteristics and capital stock. Our estimates of the return to training vary substantially across firms. On average it is -7% for firms not providing training and 24% for those providing training. Formal job training is a good investment for many firms and the economy, possibly yielding higher returns than either investments in physical capital or investments in schooling. In spite of this, observed amounts of formal training are very small

Enforcement of regulation, informal labor and firm performance

This paper investigates how enforcement of labor regulation affects the firm’s use of informal labor and firm performance. Using firm level data on informal employment and firm performance, and administrative data on enforcement of regulation at the city level, we show that in areas where law enforcement is stricter firms employ a smaller amount of informal employment. Furthermore, by reducing the firm’s access to unregulated labor, stricter enforcement is also associated with lower labor productivity. We control for different regional and firm characteristics, and we instrument enforcement with a measure of the access of labor inspectors to firms. Taken together, our findings suggest that increased access to labor flexibility significantly improves firm performance

A strong form of almost differentiability

We present a uniformization of Reeken's macroscopic differentiability (see [5]), discuss its relations to uniform differentiability (see [6]) and classical continuous differentiability, prove the corresponding chain rule, Taylor's theorem, mean value theorem, and inverse mapping theorem. An attempt to compare it with the observability (see [1, 4]) is made too. © 2009 Springer Science+Business Media, Inc.CEOCFCTFEDER/POCT

Retroreflecting curves in nonstandard analysis

We present a direct construction of retroreflecting curves by means of Nonstandard Analysis. We construct non self-intersecting curves which are of class C(1), except for a hyper-finite set of values, such that the probability of a particle being reflected from the curve with the velocity opposite to the velocity of incidence, is infinitely close to 1. The constructed curves are of two kinds: a curve infinitely close to a straight line and a curve infinitely close to the boundary of a bounded convex set. We shall see that the latter curve is a solution of the problem: find the curve of maximum resistance infinitely close to a given curve.CEOCFCTFEDER/POCT