Convergence estimates for the wavelet-Galerkin method: superconvergence at the node points

In this paper we consider a regular 1-periodic initial value problem and Galerkin approximate solutions in subspaces ν _t spanned by scaled translates of a basic function?. Our goal is to estimate the error when? is in a class of functions which we name . Herer is a regularity parameter andm is related with a property (the Strang and Fix condition) which determines the best order of accuracy in theL ²-norm of approximations from ν _h . Whenm=r, includes all scaling functions corresponding tor-regular multiresolution analyses ofL ²(?). We get the exact node values of the given initial condition as coefficients for the approximate initial data. With this procedure, the coefficients of the resulting Galerkin solution can give a very accurate approximation of the exact solution at the node points, provided that? has many vanishing moments. Since this property is not satisfied in general, we work with another modified basic function?* constructed from the integer translates of?. GlobalL ²-estimates are also obtained.     

Angular dependence of Bose-Einstein correlations in interactions of π+ andK + mesons with protons and nuclei at 250 GeV/c

The angular dependence of Bose-Einstein correlations is studied in interactions of ⁺ andK ⁺ mesons with protons and nuclei at 250 GeV/c. The pion source is found to be elongated along the interaction axis in the c.m.s., with the ratioa between transverse and longitudinal dimension equal to 0.55±0.06 for the case of proton, 0.53±0.13 for the case ofAl and 0.33±0.21 for the case ofAu target. For meson-proton interactions, indication for an increase of the elongation is found with increasing event multiplicity, pair momentum and particle transverse momentum.Now at UIA, Wilrijk, Belgium     

Second-order properties of the loss probability inM/M/s/s +c systems

The Erlang loss function, which gives the steady state loss probability in anM/M/s/s system, has been extensively studied in the literature. In this paper, we look at the similar loss probability inM/M/s/s + c systems and an extension of it to nonintegral number of servers and queue capacity. We study its monotonicity properties. We show that the loss probability is convex in the queue capacity, and that it is convex in the traffic intensity if is below some ^* and concave if is greater that ^*, for a broad range of number of servers and queue capacities. We prove that the one-server loss system is the onlyM/M/s/s +c system for which the loss probability is concave in the traffic intensity in all its range.Research supported by Grant BD/645/90-RM from Junta Nacional de Investigação Científica e Tecnológica.On leave from: Departamento de Matemática, Instituto Superior Técnico, Av. Rovisco Pais, 1096 Lisboa Codex, Portugal.     

On the cube problem of Las Vergnas

We prove a conjecture of Las Vergnas in dimensions d7: The matroid of the d-dimensional cube C ^d has a unique reorientation class. This extends a result of Las Vergnas, Roudneff and Salaün in dimension 4. Moreover, we determine the automorphism group G ^d of the matroid of the d-cube C ^d for arbitrary dimension d, and we discuss its relation to the Coxeter group of C ^d . We introduce matroid facets of the matroid of the d-cube in order to evaluate the order of G ^d . These matroid facets turn out to be arbitrary pairs of parallel subfacets of the cube. We show that the Euclidean automorphism group W ^d is a proper subgroup of the group G ^d of all matroid symmetries of the d-cube by describing genuine matroid symmetries for each Euclidean facet. A main theorem asserts that any one of these matroid symmetries together with the Euclidean Coxeter symmetries generate the full automorphism group G ^d . For the proof of Las Vergnas' conjecture we use essentially these symmetry results together with the fact that the reorientation class of an oriented matroid is determined by the labeled lower rank contractions of the oriented matroid. We also describe the Folkman-Lawrence representation of the vertex figure of the d-cube and a contraction of it. Finally, we apply our method of proof to show a result of Las Vergnas, Roudneff, and Salaün that the matroid of the 24-cell has a unique reorientation class, too.     

Hydrodynamic limit for a spin system on a multidimensional lattice

Summary The hydrodynamic limit for a Markov process of [0, )-valued spin fields on a periodic multidimensional lattice is studied. In the process a positive real number, called energy, is attached to each site of the lattice and each couple of adjacent sites exchange thier energy by random amounts at random times. The law of the exchange is such that the sum of the total energy is conserved, and that the process is reversible and of gradient type for the energy distribution. We show that under diffusion type scaling of space and time, the macroscopic energy distribution converges to a deterministic limit which is characterized by a non-linear diffusion equation /t=2^–1P(), whereP is an increasing function which in a typical case equals const·².     

Noncovalent functionalization of multi-walled carbon nanotubes by pyrene containing polymers

Multi-walled carbon nanotubes (MWNTs) have been solubilized in water and in various organic solvents by noncovalent side-wall functionalization by pyrene containing polymers.