The Banach envelopes of Besov and Triebel-Lizorkin spaces and applications to partial differential equations

With “hat” denoting the Banach envelope (of a quasi-Banach space) we prove that if 0<p<1, 0<q<1, ℝ, while if 0<p<1, 1≤q<+∞, ∝, and if 1≤p<+∞, 0<q<1, ℝ. Applications to questions regarding the global interior regularity of solutions to Poisson type problems for the three-dimensional Lamé system in Lipschitz domains are presented.     

Opérateur de Monge-Ampère et Tranchage des Courants Positifs Fermés

Sans résumé

---

     

Finite-dimensional approximation of the inverse frame operator

A frame in a Hilbert space allows every element in to be written as a linear combination of the frame elements, with coefficients called frame coefficients. Calculations of those coefficients and many other situations where frames occur, requires knowledge of the inverse frame operator. But usually it is hard to invert the frame operator if the underlying Hilbert space is infinite dimensional. In the present paper we introduce a method for approximation of the inverse frame operator using finite subsets of the frame. In particular this allows to approximate the frame coefficients (even inl ²) using finite-dimensional linear algebra. We show that the general method simplifies in the important cases of Weil-Heisenberg frames and wavelet frames.     

A characterization of wavelets on general lattices

In the context of a general lattice Γ in Rⁿ and a strictly expanding map M which preserves the lattice, we characterize all the wavelet families. This result generalizes the characterization of Frazier, Garrigós, Wang, and Weis about the wavelet families with Γ = Zⁿ and M = 21. In the second part of the paper, we characterize all the MSF wavelets. Moreover, we give a constructive method for the support of the Fourier transform of an MSF wavelet and apply this method by giving examples with particular attention to the quincunx lattice.     

On Two Theorems about Symplectic Reflection Algebras

We give a new proof and an improvement of two Theorems of J. Alev, M.A. Farinati, T. Lambre and A.L. Solotar [1] : the first one about Hochschild cohomology spaces of some twisted bimodules of the Weyl Algebra W, and the second one about Hochschild cohomology spaces of the smash product G * W (G a finite subgroup of SP (2n)) and, as a consequence, we then give a new proof of a Theorem of P. Etingof and V. Ginzburg (Invent Math 147:243–348, 2002), which shows that the Symplectic Reflection Algebras are deformations of G * W (and, in fact, all possible ones). Dedicated to my friend J.-C. Cortet.     

On the geometry of reduced cotangent bundles at zero momentum

We consider the problem of cotangent bundle reduction for proper non-free group actions at zero momentum. We show that in this context the symplectic stratification obtained by Sjamaar and Lerman refines in two ways: (i) each symplectic stratum admits a stratification which we call the secondary stratification with two distinct types of pieces, one of which is open and dense and symplectomorphic to a cotangent bundle; (ii) the reduced space at zero momentum admits a finer stratification than the symplectic one into pieces that are coisotropic in their respective symplectic strata.     

An orbifold relative index theorem

In this paper we prove a relative index theorem for pairs of generalized Dirac operators on orbifolds which are the same at infinity. This generalizes to orbifolds a celebrated theorem of Gromov and Lawson.     

Study of high-coercivity sintered NdFeB magnets

Magnetic powders for sintered NdFeB magnets have been prepared by using an advanced processing method including strip casting, hydrogen decrepitation, jet milling and rubber isotropic press. The effects of Dy, Ga and Co addition on the microstructure and magnetic properties of sintered magnets have been investigated. By adopting a suitable component ratio and adjusting proper technological parameters, we have prepared high-coercivity sintered NdFeB magnets with hard magnetic properties of _jH_c=25.6 kOe, B_r=13.2 kG and (BH)_max=39.9 MGOe. The temperature coefficient of coercivity of the magnets (between 20 and 150 °C) is –0.53%/°C. The magnetic properties at high temperature satisfy the needs of permanent magnet motors.     

Simulation of outdoor sound propagation with a transmission line matrix method

The present paper focusses on the application of the transmission line matrix method (TLM) for outdoor sound propagation simulations. It is shown how the reflection at the ground and vertical sound speed gradients can be taken into account. The comparison with calculations using finite differences in the time domain (FDTD), with calculations using parabolic equation and with analytical solutions showed all very good agreement. Thereby the computational effort of TLM is significantly lower compared to common FDTD calculation schemes.     

Synthesis and luminescent properties of Y6W2O15:Eu phosphors

In this paper, a novel phosphor, Y₆W₂O₁₅:Eu³⁺ was synthesized by thermal decomposition and phase transition of its decatungstate gel precursor. With stepwise increase of temperature to 750 °C, a crystalline phase of Y₆W₂O₁₅:Eu³⁺forms that gives intense red emission when excited at 466 nm, the emission is attributed to the Eu³⁺ ions transitions from ⁵D₀ excited states to ⁷F_J (J=0-4) ground states. The long excitation wavelength proves the Eu³⁺ transition follows the photoexcitation of the oxygen-metal (O→W lmct) charge transfer bands in yttrium tungstate. Some structural information regarding Y₆W₂O₁₅ provided by luminescence is in accord with that characterized by X-ray diffraction (XRD) and scanning electron microscope (SEM). The long-wavelength excitation properties of this material may find application in the production of red phosphors for white light-emitting diodes (LEDs).