On a Class of Functionals Whose Local Minima are Global

In this note we introduce a suitable class of functionals, including the class of integral functionals, and prove that any (strict) local minimum of a functional of this class, defined on a decomposable space, is a (strict) global minimum. So, the recent result obtained by Giner in [1] is specified and extended.     

Set-theoretic equivalence of extensive-form games

A new game-form, theset-theoretic form, is introduced and it is shown that a set-theoretic form can be associated with every extensive form. The map from extensive forms to set-theoretic forms is not one-to-one and this fact is used to define a notion of equivalence for extensive games. A transformation for extensive forms is then defined, called theinterchange of contiguous simultaneous moves, and it is shown that it is possible to move from one game to any other game in the same equivalence class by using this transformation a finite number of times and without ever leaving the equivalence class. This transformation is a generalization of Thompson's interchange of decision nodes. Thus given an extensive gameG there is a different extensive gameG that is equivalent toG if and only if there are moves inG that are simultaneous and the difference betweenG andG lies exactly in the fact that (some of) these moves are taken in a different temporal order in the two games.     

Radiation-driven hydrodynamics of high- hohlraums on the national ignition facility

The first hohlraum experiments on the National Ignition Facility (NIF) using the initial four laser beams tested radiation temperature limits imposed by plasma filling. For a variety of hohlraum sizes and pulse lengths, the measured x-ray flux shows signatures of filling that coincide with hard x-ray emission from plasma streaming out of the hohlraum. These observations agree with hydrodynamic simulations and with an analytical model that includes hydrodynamic and coronal radiative losses. The modeling predicts radiation temperature limits with full NIF (1.8 MJ), greater, and of longer duration than required for ignition hohlraums.     

Noether symmetry approach in matter-dominated cosmology with variable G and Λ

In the framework of renormalization-group improved cosmologies, we use the Noether symmetry approach to get exact and general integration of the matter-dominated cosmological equations. This is performed by using an expression of Λ = Λ (G) determined by the method itself. We also work out a comparison between such a model and the concordance ΛCDM model as to the magnitude–redshift relationship, hence showing that no appreciable differences occur.     

The national ignition facility: path to ignition in the laboratory

The National Ignition Facility (NIF) is a 192-beam laser facility presently under construction at LLNL. When completed, NIF will be a 1.8-MJ, 500-TW ultraviolet laser system. Its missions are to obtain fusion ignition and to perform high energy density experiments in support of the US nuclear weapons stockpile. Four of the NIF beams have been commissioned to demonstrate laser performance and to commission the target area including target and beam alignment and laser timing. During this time, NIF demonstrated on a single-beam basis that it will meet its performance goals and demonstrated its precision and flexibility for pulse shaping, pointing, timing and beam conditioning. It also performed four important experiments for Inertial Confinement Fusion and High Energy Density Science. Presently, the project is installing production hardware to complete the project in 2009 with the goal to begin ignition experiments in 2010. An integrated plan has been developed including the NIF operations, user equipment such as diagnostics and cryogenic target capability, and experiments and calculations to meet this goal. This talk will provide NIF status, the plan to complete NIF, and the path to ignition.     

Existence and multiplicity results to Neumann problems for elliptic equations involving the p-Laplacian

In this paper, existence results of positive solutions to a Neumann problem involving the p-Laplacian are established. Multiplicity results are also pointed out. The approach is based on variational methods.     

Analysis of the managing conditions of a linear-collector network of a solar power plant

Summary A model has been solved to evaluate the influence of different control options on the performances of a linear-collector solar power plant. The results represent a basis for the choice between the different options. This work has been performed in the framework of activities of the „Progetto Finalizzato Energetica” supported by the C.N.R.     

On the Logic of Common Belief

We investigate an axiomatization of the notion of common belief (knowledge) that makes use of no rules of inference (apart from Modus Ponens and Necessitation) and highlight the property of the set of accessibility relations that characterizes each axiom. Mathematics Subject Classification: 03B45, 68T25.