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The increasing presence of non-programmable renewable energy plants increases the intermittency of the electricity supply and thus threatens the adequacy of a power system. Hydropower can solve this problem due to its flexibility. This paper applies statistical approaches to assess water availability in the context of hydropower generation and adequacy analysis on a seasonal basis for one site in Sicily and the other in Sardinia, where major hydroelectric plants are present. First, an empirical relationship between soil moisture content (SMC) and potential evapotranspiration (ET0) is evaluated through linear regression analysis. Then, precipitation trends over the last twenty years are analyzed to determine any effects of global warming on water availability. Finally, Monte Carlo algorithms are used for the stochastic generation of hourly precipitation, direct runoff profiles, and daily SMC profiles. Strong positive and negative correlations between ET0 and SMC (p < 0.05), and R2 ≥ 0.5 are found for both sites, except for summer, and R2 ≥ 0.5 is obtained. The cumulative pH-historical precipitation shows changes in seasonal trends, with evidence of a decrease at the annual level. The algorithms used to synthetically generate hourly precipitation and direct runoff profiles, as well as daily SMC profiles, effectively simulate the statistical variability of the historical profiles of these physical quantities.

The \oarpaf telescope is an $80\rm cm$-diameter optical telescope installed in the Antola Mount Regional Reserve, in Northern Italy. This work presents the results of the characterization of the site, as well as developments and interventions that have been implemented, with the goal of exploiting the facility for scientific and educational purposes. During the characterization of the site, an average background brightness of $22.40 \, m_{AB}$ ($B$ filter) -- $21.14 \, m_{AB}$ ($I$) per arcsecond squared, and a $1.5$--$3.0"$ seeing, have been measured. An estimate of the magnitude zero points for photometry is also reported. The material under commissioning includes 3 CCD detectors for which we provide the linearity range, gain, and dark current; a 31 orders \'echelle Northern Italy. This work presents the results of the characterization of the site, as well as developments andspectrograph with $R\sim 8500$--$15000$, and a dispersion of $n = 1.39\times 10^{-6}\rm px^{-1}\lambda + 1.45\times 10^{-4}\rm nm/px$, where $\lambda$ is expressed in $\rm nm$. The scientific and outreach potential of the facility is proven in different science cases, such as exoplanetary transits and active galactic nuclei variability. The determination of time delays of gravitationally lensed quasars, the microlensing phenomenon and the tracking and the study of asteroids are also discussed as prospective science cases., Comment: 21 pages, 12 figures. Published in Journal of Astronomical Telescopes, Instruments, and Systems

In a bounded open set of R n we consider the Dirichlet problem for nonlinear2m-order equations in divergence form with L 1 -right-hand sides. It is supposed that 2 6m 0 with respect to the derivatives of orderm of unknown function. We establish that under the condition p 6 2 -m/n for some L 1 -data the corresponding Dirichlet problem does not have W-solutions. RESUMEN

In a very recent paper, the authors proved the local boundedness of solutions for a class of degenerate nonlinear elliptic higher order equations with right-hand sides f(x) ∈ L 1(Ω). Now we give some sufficient conditions in order to have analogous results assuming that the data f(x) belongs to L m (Ω), with m close enough to 1 and not sufficient to consider the problem within the usual theory of monotone operators.

We consider the Dirichlet problem for a class of degenerate nonlinear elliptic high-order equations with a strengthened monotonicity and L 1-right-hand sides. We give sufficiently general conditions on the right-hand sides which guarantee the existence of W-solutions of the given problem belonging along with their derivatives to some limit Lebesgue spaces.

In this article, we shall study solvability and boundedness of solutions to the system of equations (1.1).

In this article, we shall study Holder regularity of weak solutions to the system of Equations (1.1). To this aim, we estimate the oscillation of solutions in a generic ball B(y, ρ), such that B(y, ρ) ⊂ Ω by ρ and a constant depending on known parameters and on d(y, ∂Ω).

We establish an inequality of the Nirenberg–Gagliardo kind for functions belonging to some degenerate Sobolev space with variable exponents.

Under non-standard growth conditions, following Moser’s iteration technique, we shall prove boundedness of solutions for an equation of fourth order of the following kind ∑ | α | = 1 , 2 ( − 1 ) | α | D α A α ( x , ∇ 2 u ) = f in Ω .

We deal with a class of degenerate nonlinear high-order equations with coefficients satisfying a strengthened monotonicity condition and L 1 -right-hand sides. Our main result describes functional multipliers with which solutions of the Dirichlet problem for equations of the given class and their derivatives belong to some limit Lebesgue spaces.

In this paper we study qualitative properties of minimizers for a class of integral functionals, defined in a weighted space. In particular we obtain boundedness and Holder regularity for the minimizers by using a modified Moser method with a special test function.

We consider the Dirichlet problem for a class of degenerate nonlinear elliptic fourth-order equations in divergence form. Coefficients of the equations satisfy a strengthened ellipticity condition involving two weighted functions. The right-hand sides F(x,u) of the equations depend on the unknown function u. Under some conditions, including Lm-regularity of F(⋅,0) with m close to 1, we establish that the problem under consideration has a W-solution bounded on the sets where the behaviour of the data of the problem is regular enough.

We prove local boundedness of solutions for a class of degenerate nonlinear elliptic higher-order equations with L(1)-data.

Under some hypotheses on weighted functions, using the interior regularity results established in (Kovalevsky, A. and Nicolosi, F., 2005, Existence and regularity of solutions to a system of degenerate nonlinear fourth-order equations. Nonlinear Analysis, 61, 281–307) and estimating the oscillation of solutions near the boundary of Ω, we establish results on regularity up to the boundary of a solutions of the system (1.1).

BACKGROUND: We recently developed a clinical decision support tool, capable of estimating the likelihood of survival at 3 and 12 months following surgery for patients with operable skeletal metastases. After making it publicly available on www.PATHFx.org , we attempted to externally validate it using independent, international data. METHODS: We collected data from patients treated at 13 Italian orthopaedic oncology referral centers between 2010 and 2013, then applied to PATHFx, which generated a probability of survival at three and 12-months for each patient. We assessed accuracy using the area under the receiver-operating characteristic curve (AUC), clinical utility using Decision Curve Analysis (DCA), and compared the Italian patient data to the training set (United States) and first external validation set (Scandinavia). RESULTS: The Italian dataset contained 287 records with at least 12 months follow-up information. The AUCs for the three-month and 12-month estimates was 0.80 and 0.77, respectively. There were missing data, including the surgeon's estimate of survival that was missing in the majority of records. Physiologically, Italian patients were similar to patients in the training and first validation sets. However notable differences were observed in the proportion of those surviving three and 12-months, suggesting differences in referral patterns and perhaps indications for surgery. CONCLUSIONS: PATHFx was successfully validated in an Italian dataset containing missing data. This study demonstrates its broad applicability to European patients, even in centers with differing treatment philosophies from those previously studied.

We consider a class of degenerate nonlinear elliptic fourth-order equations in divergence form. Coefficients of the equations satisfy a strengthened ellipticity condition involving two weighted functions. The right-hand side F (x, u) of the equations depends on the unknown function u. Under some conditions, including Lm -summability of F(·, 0) with m close to 1 and restrictions on the exponent σ of the growth of F (x, u) with respect to u, we establish existence of W-solutions of the Dirichlet problem for the given equations and describe the dependence of summability properties of these solutions on m and σ.

We consider a class of degenerate nonlinear elliptic fourth-order equations in divergence form. Coefficients of the equations satisfy a strengthened ellipticity condition involving two weighted functions. Existence of solutions of Dirichlet problem for equations of the given class in the case where these equations have L 1-right-hand sides depending on unknown function has been established in our recent article. In the present article we prove some results which show the improvement of summability of solutions of the same problem under additional conditions on right-hand sides of the equations under consideration.

We study Dirichlet problem for a class of degenerate anisotropic nonlinear elliptic fourth order equations with L 1 -right-hand sides. Anisotropic and degenerate character of the equations under consideration is expressed by the presence in their coefficients of different exponents and weighted functions associated to the first and second order derivatives of unknown function. Under some hypotheses on the involved exponents and weighted functions we prove existence of so-called H ν , μ -solution and H-solution of the given problem.

Here is a bounded open set of Rn; m?2; q?p?2; and are positive functions in ; ◦ W 1; q m;p( ; ; ) is the Banach space of all functions u : → R with the properties |u|q; |D u|q; |D u|p ∈ L1( ); | |=1; | |=m, and “zero” boundary values. Symbols and all through the paper denote n-dimensional multiindices, | |; | | are their lengths, mu= {D u: | | 6 m}. The class of operators under consideration is characterized by the following degenerate ellipticity condition for their coe>cients: ∑

This article deals with a class of degenerate nonlinear elliptic fourth-order equations with L 1 -right-hand sides. Equations of the given class have divergence form and their coefficients satisfy a strengthened ellipticity condition with two different weights associated, respectively, to the first- and the second-order derivatives of unknown function. Under suitable hypotheses on the weighted functions involved we establish solvability in a Sobolev space of Dirichlet problem for equations under consideration.

Sufficient conditions are obtained so that a weak subsolution of a class of quasilinear degenerate parabolic equations, bounded from above on theparabolic boundary of the cylinder Q, turns out to be bounded from above in Q.

We prove the existence of bounded solutions of some boundary value problems for degenerate elliptic equations of second order in divergence form. Our results cover also the unbounded domain case. We discuss also the uniqueness problem and asymptotic behaviour of the solutions of our equation.

We consider the nonnegative solutions to the nonlinear degenerate parabolic equation ut = (D(x, t)um − 1ux)x − b(x, t)up with m > 1, 0 < p < 1, and positive D(x, t), b(x, t). After obtaining the uniqueness and Hölder regularity results, we investigate the dependence of such phenomena as extinction in finite time and instantaneous shrinking of the support on the behaviour of D(x, t) and b(x, t).