A survey on C 1,1 fuctions: theory, numerical methods and applications

In this paper we survey some notions of generalized derivative for C 1,1 functions. Furthermore some optimality conditions and numerical methods for nonlinear minimization problems involving C1,1 data are studied.

Mean value theorem for continuous vector functions by smooth approximations

In this note a mean value theorem for continuous vector functions is introduced by mollified derivatives and smooth approximations

C 1,1 functions and optimality conditions

In this work we provide a characterization of C 1,1 functions on Rn (that is, differentiable with locally Lipschitz partial derivatives) by means of second directional divided differences. In particular, we prove that the class of C 1,1 functions is equivalent to the class of functions with bounded second directional divided differences. From this result we deduce a Taylor's formula for this class of functions and some optimality conditions. The characterizations and the optimality conditions proved by Riemann derivatives can be useful to write minimization algorithms; in fact, only the values of the function are required to compute second order conditions.divided differences, Riemann derivatives, C 1,1 functions, nonlinear optimization, generalized derivatives

Fractals and Self-Similarity in Economics: the Case of a Stochastic Two-Sector Growth Model

We study a stochastic, discrete-time, two-sector optimal growth model in which the production of the homogeneous consumption good uses a Cobb-Douglas technology, combining physical capital and an endogenously determined share of human capital. Education is intensive in human capital as in Lucas (1988), but the marginal returns of the share of human capital employed in education are decreasing, as suggested by Rebelo (1991). Assuming that the exogenous shocks are i.i.d. and affect both physical and human capital, we build specific configurations for the primitives of the model so that the optimal dynamics for the state variables can be converted, through an appropriate log-transformation, into an Iterated Function System converging to an invariant distribution supported on a generalized Sierpinski gasket.fractals, iterated function system, self-similarity, Sierpinski gasket, stochastic growth

Second-order mollified derivatives and optimization

The class of strongly semicontinuous functions is considered. For these functions the notion of mollified derivatives, introduced by Ermoliev, Norkin and Wets, is extended to the second order. By means of a generalized Taylor's formula, second order necessary and sufficient conditions are proved for both unconstrained and constrained optimizationMollifiers, optimization, smooth approximations, strong semicontinuity

On the Presence of Green and Sustainable Software Engineering in Higher Education Curricula

Nowadays, software is pervasive in our everyday lives. Its sustainability and environmental impact have become major factors to be considered in the development of software systems. Millennials-the newer generation of university students-are particularly keen to learn about and contribute to a more sustainable and green society. The need for training on green and sustainable topics in software engineering has been reflected in a number of recent studies. The goal of this paper is to get a first understanding of what is the current state of teaching sustainability in the software engineering community, what are the motivations behind the current state of teaching, and what can be done to improve it. To this end, we report the findings from a targeted survey of 33 academics on the presence of green and sustainable software engineering in higher education. The major findings from the collected data suggest that sustainability is under-represented in the curricula, while the current focus of teaching is on energy efficiency delivered through a fact-based approach. The reasons vary from lack of awareness, teaching material and suitable technologies, to the high effort required to teach sustainability. Finally, we provide recommendations for educators willing to teach sustainability in software engineering that can help to suit millennial students needs.Comment: The paper will be presented at the 1st International Workshop on Software Engineering Curricula for Millennials (SECM2017

MINKOWSKI-ADDITIVE MULTIMEASURES, MONOTONICITY AND SELF-SIMILARITY

We discuss the main properties of positive multimeasures and we show how to define a notion of self-similarity based on a generalized Markov operator

A note on demographic shocks in a multi-sector growth model

We introduce demographic shocks in a multi-sector endogenous growth model, a-la Uzawa-Lucas. We show that an analytical solution of the stochastic problem can be found, under the restriction that the capital share equals both the inverse of the intertemporal elasticity of substitution and the degree of altruism. We show that uncertainty lowers the optimal levels of consumption and the physical capital stock, while they do not affect the share of human capital employed in production

Group-galaxy correlations in redshift space as a probe of the growth of structure

We investigate the use of the cross-correlation between galaxies and galaxy groups to measure redshift-space distortions (RSD) and thus probe the growth rate of cosmological structure. This is compared to the classical approach based on using galaxy auto-correlation. We make use of realistic simulated galaxy catalogues that have been constructed by populating simulated dark matter haloes with galaxies through halo occupation prescriptions. We adapt the classical RSD dispersion model to the case of the group-galaxy cross-correlation function and estimate the RSD parameter $\beta$ by fitting both the full anisotropic correlation function $\xi(r_p,\pi)$ and its multipole moments. In addition, we define a modified version of the latter statistics by truncating the multipole moments to exclude strongly non-linear distortions at small transverse scales. We fit these three observable quantities in our set of simulated galaxy catalogues and estimate statistical and systematic errors on $\beta$ for the case of galaxy-galaxy, group-group, and group-galaxy correlation functions. When ignoring off-diagonal elements of the covariance matrix in the fitting, the truncated multipole moments of the group-galaxy cross-correlation function provide the most accurate estimate, with systematic errors below 3% when fitting transverse scales larger than $10Mpc/h$. Including the full data covariance enlarges statistical errors but keep unchanged the level of systematic error. Although statistical errors are generally larger for groups, the use of group-galaxy cross-correlation can potentially allow the reduction of systematics while using simple linear or dispersion models.Comment: 18 pages, 16 figure