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

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

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

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

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

Fractional Euler-Lagrange differential equations via Caputo derivatives

We review some recent results of the fractional variational calculus. Necessary optimality conditions of Euler-Lagrange type for functionals with a Lagrangian containing left and right Caputo derivatives are given. Several problems are considered: with fixed or free boundary conditions, and in presence of integral constraints that also depend on Caputo derivatives.Comment: This is a preprint of a paper whose final and definite form will appear as Chapter 9 of the book Fractional Dynamics and Control, D. Baleanu et al. (eds.), Springer New York, 2012, DOI:10.1007/978-1-4614-0457-6_9, in pres