Overcoming the boundary effects in surface spline interpolation

Surface spline interpolation when the domain is all of R^d isknown to converge much faster to the data function f than inthe case when the domain is the unit ball. This difference isunderstood to be due to boundary effects which, as will be shown,also affect the size of the surface spline's coefficients. Wepropose a modified form of surface spline interpolation which,to a great extent, overcomes these boundary effects. This modifiedsurface spline interpolant uses only the values of f at thegiven interpolation points.     

On a Fermat principle in general relativity. A Ljusternik-Schnirelmann theory for light rays

Summary In this paper existence and multiplicity results for lightlike geodesics joining a point with a timelike curve on a class of Lorentzian manifolds are proved under intrinsic assumptions. Such results are obtained using an extension to Lorentzian Geometry of the classical Fermat principle in optics. The results are proved using critical point theory on infinite dimensional manifolds. An application to the gravitational lens effect is presented.     

Geodesics on lorentzian manifolds with quasi-convex boundary

In this paper we study existence and multiplicity results of geodesics joining two given events in Lorentzian manifolds with lack of geodesic completeness. The considered Lorentzian manifolds are not necessarily static or stationary and satisfy a condition of convexity on the boundary. work supported by M.U.R.S.T. research founds 40%–60% 1992     

Study of the peak effect phenomenon in single crystals of 2H-NbSe2

The weakly pinned single crystals of the hexagonal 2H-NbSe₂ compound have emerged as prototypes for determining and characterizing the phase boundaries of the possible order-disorder transformations in the vortex matter. We present here a status report based on the ac and dc magnetization measurements of the peak effect phenomenon in three crystals of 2H-NbSe₂, in which the critical current densities vary over two orders of magnitude. We sketch the generic vortex phase diagram of a weakly pinned superconductor, which also utilizes theoretical proposals. We also establish the connection between the metastability effects and pinning.     

On the Finiteness of Light Rays Between a Source and an Observer on Conformally Stationary Space-Times

We use a convexity condition to prove the finiteness of the number of light rays joining a pointlike source with a pointlike observer in a stationary relativistic spacetime. The result is extended to the case of conformally stationary metrics under suitable boundedness assumptions on the conformal factor. We discuss our hypotheses in some explicit examples of standard static and stationary Lorentzian manifolds.     

A timelike extension of Fermat's principle in general relativity and applications

We define a variational problem based on the arrival time functional for timelike curves on a Lorentzian manifold parameterized by a fixed constant multiple of their proper time. Under a causality assumption for the manifold , we prove that the stationary points of our problem are geodesics, obtaining an extension of the Fermat's Principle for light rays proven in [14] (see also [2]). Moreover, we study the compactness pr operties of the arrival time functional by global variational techniques. Under intrinsic assumptions on the metric of we get results of existence and multiplicity for geodesics with a given energy between an event and an observer of .     

Genericity of Nondegeneracy for Light Rays in Stationary Spacetimes

Given a Lorentzian manifold (M, g), an event p and an observer U in M, then p and U are light conjugate if there exists a lightlike geodesic γ : [0, 1] → M joining p and U whose endpoints are conjugate along γ. Using functional analytical techniques, we prove that if one fixes p and U in a differentiable manifold M, then the set of stationary Lorentzian metrics in M for which p and U are not light conjugate is generic in a strong sense. The result is obtained by reduction to a Finsler geodesic problem via a second order Fermat principle for light rays, and using a transversality argument in an infinite dimensional Banach manifold setup.     

Carbon-13 EPR Hyperfine Interaction in the Complex [Rh(CN)6]in a KCl Host Lattice

The hyperfine interaction with¹³C in nonenriched [Rh(CN)₆]⁴⁻, in a KCl host lattice at 7 K, is measured by continuous-wave X- and Q-band electron paramagnetic resonance, allowing, for the first time, a comparative study of spin densities on the carbon of the axial cyanide in this complex and in the similar [Co(CN)₆]⁴⁻complex. From the experimental data corrected for dipolar interactions,A_iso= 79.80 × 10⁻⁴cm⁻¹andA_anis= 0.76 × 10⁻⁴cm⁻¹.     

Verification of a model to predict the influence of particle inertia and gravity on a decaying turbulent particle-laden flow

In an earlier publication some of the authors presented a theoretical model for the calculation of the influence of particle inertia and gravity on the turbulence in a stationary particle-laden flow. In the present publication the model is extended for application to a decaying suspension. Also a comparison is given between predictions made with the model and experimental data (own data and data reported in the literature) on a decaying turbulent flow with particles in a water tunnel or in a wind tunnel. For most of the experiments a prediction with reasonable accuracy and an interpretation is possible by means of the model.