A Phragm\'en-Lindel\"of theorem via proximate orders, and the propagation of asymptotics

We prove that, for asymptotically bounded holomorphic functions in a sector in $\mathbb{C}$, an asymptotic expansion in a single direction towards the vertex with constraints in terms of a logarithmically convex sequence admitting a nonzero proximate order entails asymptotic expansion in the whole sector with control in terms of the same sequence. This generalizes a result by A. Fruchard and C. Zhang for Gevrey asymptotic expansions, and the proof strongly rests on a suitably refined version of the classical Phragm\'en-Lindel\"of theorem, here obtained for functions whose growth in a sector is specified by a nonzero proximate order in the sense of E. Lindel\"of and G. Valiron.Comment: 20 page

Indices of O-regular variation for weight functions and weight sequences

A plethora of spaces in Functional Analysis (Braun-Meise-Taylor and Carleman ultradifferentiable and ultraholomorphic classes; Orlicz, Besov, Lipschitz, Lebesque spaces, to cite the main ones) are defined by means of a weighted structure, obtained from a weight function or sequence subject to standard conditions entailing desirable properties (algebraic closure, stability under operators, interpolation, etc.) for the corresponding spaces. The aim of this paper is to stress or reveal the true nature of these diverse conditions imposed on weights, appearing in a scattered and disconnected way in the literature: they turn out to fall into the framework of O-regular variation, and many of them are equivalent formulations of one and the same feature. Moreover, we study several indices of regularity/growth for both functions and sequences, which allow for the rephrasing of qualitative properties in terms of quantitative statements.Comment: 37 page

The surjectivity of the Borel mapping in the mixed setting for ultradifferentiable ramification spaces

We consider r-ramification ultradifferentiable classes, introduced by J. Schmets and M. Valdivia in order to study the surjectivity of the Borel map, and later on also exploited by the authors in the ultraholomorphic context. We characterize quasianalyticity in such classes, extend the results of Schmets and Valdivia about the image of the Borel map in a mixed ultradifferentiable setting, and obtain a version of the Whitney extension theorem in this framework.Comment: 31 pages; this version has been accepted for publication in Monatsh. Mat

Probabilistic localization of gas emission areas with a mobile robot in indoor environments

This work deals with the problem of gas source localization by a mobile robot with gas-sensing capabilities. Particularly, we address the problem for the case of indoor environments, where the presence of obstacles and the possibly complex structure with multiple rooms, inlets and outlets provoke the chaotic dispersion of the gases. Under these challenging conditions, where traditional approaches based on tracking or mathematical modeling of the plume cannot be applied, we propose a two-stage methodology to split the search into coarse and fine localization. Focusing on the broad localization, we contribute with a novel approach to estimate, from a set of sparse observations, the likelihood of different regions in the environment to hold a gas source. Experiments demonstrate that our approach is suitable to locate gas emission sources.Universidad de Málaga. Campus de Excelencia Internacional Andalucía Tech

THE EFFECTS OF SPOT WATER MARKETS ON THE ECONOMIC RISK DERIVED FROM VARIABLE WATER SUPPLY

Water availability in semiarid regions commonly exhibits patterns of extreme variability. Even in basins with large infrastructure development, some users are subject to low levels of water reliability, incurring economic losses during periods of scarcity. More flexible instruments, such as voluntary exchanges of water among users, may help users reduce their risk exposure. Recent changes in the Spanish water Law have given an initial impulse to allow for lease-out contracts of water use rights. This paper analyses, from theoretical and empirical standpoints, the effect that establishing water markets has on the economic risk caused by water availability variations. The empirical study is performed on an irrigation district of the Guadalquivir Valley (Spain) with fair levels of average water availability but a high probability of periods of extreme scarcity. A non-linear programming model is used to simulate irrigators' behaviour and derive water demand functions. Another spatial equilibrium model is used to compute market exchange and equilibrium. These programming models are combined with statistical simulation techniques. It is shown that the probability distribution of profits for a representative irrigator is modified if water exchanges are authorised, resulting in unambiguous risk reductions. Results also suggests that if the market would be extended to several irrigation districts and users, each characterised by different hydrological risk exposure, the occurrence of extremely low benefits events would become more unlikely. In sum, it is shown that exchanging water in annual spot markets allows for the reduction of farmers' economic vulnerability caused by the variability of water supply across irrigation seasons.Resource /Energy Economics and Policy,

Modelling Spot Water Markets Under Uncertain Water Supply

Water availability in semiarid regions usually exhibits patterns of extreme variability. Even in intensively controlled basins, some users are subject to low levels of water reliability, and more vulnerable to periods of extreme scarcity. To reduce their risk exposure more flexible instruments, such as voluntary exchanges of water among users, are required. Recent changes in the Spanish water Law have given an initial impulse to allow for leases of water use rights. Properly designed and monitored, this instrument provides some flexibility to water management, and may increase the economic use efficiency as well as mitigate the adverse economic effects of droughts. This paper looks at the risks and uncertainty dimensions of water markets, which have not been paid much attention in the literature. It analyses, from theoretical and empirical standpoints, the role that uncertainty plays in market participants' decisions and its impact on gains from trade. Two models have been developed to carry out the empirical application. One is a stochastic and two-stage discreet programming model which simulates irrigators behaviour and the other is a spatial equilibrium model to compute market exchange and equilibrium. Water market price endogeneity is solved by an iterative process, which characterise price uncertainty from the results obtained from the spatial equilibrium model. Hydrological risk is characterised at the irrigation farm level through the variation of the water allowances served for irrigation. The application is performed on eleven irrigated farms in a district of the Guadalquivir Valley (Southern Spain. It is shown how water availability uncertainty reduces farmers' benefits because of the fact that they must take ex-ante decisions. However, if market participation is allowed once water allowances become known, even at an uncertain price, the benefit losses are partly mitigated. From a methodological standpoint, these results suggest that the agricultural water market benefits estimates found in the literature may be undervalued as a result of omitting the option to participate in the market in the mix of possible strategies. Exchanging water in annual spot markets allows for the reduction of farmers' economic vulnerability caused by the variability and uncertainty of water supply within an irrigation season.uncertainty, farm modelling, water markets, water supply, Resource /Energy Economics and Policy,

Modeling and analysis of random and stochastic input flows in the chemostat model

In this paper we study a new way to model noisy input flows in the chemostat model, based on the Ornstein-Uhlenbeck process. We introduce a parameter β as drift in the Langevin equation, that allows to bridge a gap between a pure Wiener process, which is a common way to model random disturbances, and no noise at all. The value of the parameter β is related to the amplitude of the deviations observed on the realizations. We show that this modeling approach is well suited to represent noise on an input variable that has to take non-negative values for almost any time.European Commission (EC). Fondo Europeo de Desarrollo Regional (FEDER)Ministerio de Economía y Competitividad (MINECO). EspañaJunta de Andalucí