Large-Time Behaviour of Energy in Elasticity

This paper is concerned with the large-time behaviour of energy for the n-dimensional nonhomogeneous and anisotropic elastic system with a locally reacting boundary subject to small oscillations. Under reasonable assumptions, the polynomial decay for the energy of such a model has been established. Multiplicative techniques and the energy method are used.     

An efficient shrinkage bootstrap bias estimator for smooth functions of sample means

Summary  Since it is not always possible to calculate bootstrap estimators, they are usually approximated by simulation. In this article, we propose a bootstrap bias estimator for smooth functions of sample means that has less mean squared error, due to the simulation process, than the ordinary bootstrap. The estimator is based on shrinking the bootstrap mean towards the original sample mean. It can easily be implemented while demanding almost no additional computational effort.     

On the nuclear curvature energy

The curvature energy coefficient of the nuclear mass formulaa _c is first calculated for the model case of a Fermi gas bounded by an external Woods-Saxon potential. The semiclassical theory of Wigner and Kirkwood is used anda _c is found to be close to zero. It is, however, shown that this low value is due to the lack of selfconsistency of the potential. When available, the results of the model compare very well with quantal values and the extrapolation to the spherical cavity (billiard) checks with the value fora _c known from the Balian-Bloch theory. Second, the selfconsistent case is generalised to finite range forces. No indication is found that this modifies the fact that all theoretical values for a _c are larger than about 7 MeV which is an order of magnitude above the empirical value.     

The Foundations of Linear Stochastic Electrodynamics

An analysis is briefly presented of the possible causes of the failure of stochastic electrodynamics (SED) when applied to systems with nonlinear forces, on the basis that the main principles of the theory are correct. In light of this analysis, an alternative approach to the theory is discussed, whose postulates allow to establish contact with quantum mechanics in a natural way. The ensuing theory, linear SED, confirms the essential role of the vacuum–particle interaction as the source of quantum phenomena.     

Stabilization of the Furuta Pendulum Based on a Lyapunov Function

We propose a Lyapunov-function-based control for the stabilization of the under-actuated Furuta pendulum. Firstly, by a suitable partial feedback linearization that allows to linearize only the actuated coordinate of the system, we proceed to find a candidate Lyapunov function. Based on this candidate function, we derive a stabilizing controller, in such away that the closed-loop system is locally and asymptotically stable around the unstable vertical equilibrium rest, with a computable domain of attraction.     

Properties of C60 polymerized under high pressure and temperature

60 polymers. Pure and mixed phase polymeric samples were synthesized by simultaneously subjecting microcrystalline C₆₀ powder or pellets to various pressures () and temperatures (). The optical spectra of the orthorhombic, tetragonal, and rhombohedral C₆₀ polymer phases are observed to be quite distinct and rich. These spectra exhibit numerous lines and an overall downshift in frequency relative to C₆₀ is observed, consistent with a loss of double bonds from the fullerene cage. The LDMS spectra of a sample synthesized at under hydrostatic conditions and , exhibited a succession of clear peaks at mass numbers corresponding to , similar to the LDMS data on the C₆₀ photopolymer. This is taken as further evidence for interfullerene bonds in these high-pressure polymers. The XRD pattern of this sample indicates the presence of a strong texture in the sample. Received: 14 November 1996/Accepted: 8 January 1997     

An analysis of soft terms in Calabi-Yau compactifications

We perform an analysis of the soft supersymmetry-breaking terms arising in Calabi-Yau compactifications. The sigma-model contribution and the instanton correction to the Kähler potential are included in the computation. The existence of off-diagonal moduli and matter metrics gives rise to specific features as the possibility of having scalars heavier than gauginos or the presence of tachyons. Although non-universal soft terms is a natural situation, we point out that there is an interesting limit where universality is achieved. Finally, we compare these results with those of orbifold compactifications. Although they are qualitatively similar some features indeed change. For example, sum rules found in orbifold models which imply that on average the scalars are lighter than gauginos can be violated in Calabi-Yau manifolds.