Explicit methods for fractional differential equations and their stability properties

The use of explicit methods in the numerical treatment of differential equations of fractional order is an area not yet widely investigated. In this paper stability properties of some multistep methods of explicit type are investigated and new methods with larger intervals of stability are proposed. Some numerical experiments are presented in order to validate theoretical results.     

The Cohomology of the Universal Steenrod Algebra

The mod 2 universal Steenrod algebra Q is a homogeneous quadratic algebra closely related to the ordinary mod 2 Steenrod algebra and the Lambda algebra introduced in [1]. In this paper we show that Q is Koszul. It follows by [7] that its cohomology, being purely diagonal, is isomorphic to a completion of Q itself with respect to a suitable chain of two-sided ideals.     

A dynamic wind farm aggregate model for the simulation of power fluctuations due to wind turbulence

An important aspect related to wind energy integration into the electrical power system is the fluctuation of the generated power due to the stochastic variations of the wind speed across the area where wind turbines are installed. Simulation models are useful tools to evaluate the impact of the wind power on the power system stability and on the power quality. Aggregate models reduce the simulation time required by detailed dynamic models of multiturbine systems.In this paper, a new behavioral model representing the aggregate contribution of several variable-speed-pitch-controlled wind turbines is introduced. It is particularly suitable for the simulation of short term power fluctuations due to wind turbulence, where steady-state models are not applicable.The model relies on the output rescaling of a single turbine dynamic model. The single turbine output is divided into its steady state and dynamic components, which are then multiplied by different scaling factors. The smoothing effect due to wind incoherence at different locations inside a wind farm is taken into account by filtering the steady state power curve by means of a Gaussian filter as well as applying a proper damping on the dynamic part.The model has been developed to be one of the building-blocks of a model of a large electrical system, therefore a significant reduction of simulation time has been pursued. Comparison against a full model obtained by repeating a detailed single turbine model, shows that a proper trade-off between accuracy and computational speed has been achieved.     

Fracture and Fragmentation of Silicon Dies

Different failure modes of silicon are observed. Experimental results are not able to explain these variations clearly and therefore numerical simulations have been performed. In order to reduce high computational costs a simplified method to introduce weakened areas on silicon chips is presented. (© 2010 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Qualche criterio di esistenza per soluzioni di un sistema di equazioni differenziali

We give some solution existence and uniqueness theorems for the Volterra type equations systems (1) and (6).     

Density estimation using game theory

In this note we show that the mathematical tools of cooperative game theory allow a successful approach to the statistical problem of estimating a density function. Specifically, any random sample of an absolutely continuous random variable determines a transferable utility game, the Shapley value of which proves to be an estimator of the density function of binned kernel and WARPing types, with good computational and statistical properties.Authors acknowledge the financial support of Spanish Ministry for Science and Technology and FEDER through projects BFM2002-03213 and BEC2002-04102-C02-02 and of Xunta de Galicia through projects PGIDT00PXI20104PR and PGIDT03PXIC20701PN. They also thank the comments of two anonymous referees.     

Construction of a singular elliptic-harmonic measure

The authors study an example, suggested by E. De Giorgi, of a second-order uniformly elliptic partial differential operator in divergence form with continuous coefficients on a smooth domain in the plane such that the associated harmonic measure on the boundary is not absolutely continuous with respect to the ordinary surface measure.