Parabolic Capacity and Soft Measures for Nonlinear Equations

We first introduce, using a functional approach, the notion of capacity related to the parabolic p-Laplace operator. Then we prove a decomposition theorem for measures (in space and time) that do not charge the sets of null capacity. We apply this result to prove existence and uniqueness of renormalized solutions for nonlinear parabolic initial boundary-value problems with such measures as right-hand side.     

The bestL 2-approximation by finite sums of functions with separable variables

Summary We consider the problem of the best approximation of a given functionh L ² (X × Y) by sums _k=1 ⁿ f _k f _k, with a prescribed numbern of products of arbitrary functionsf _k L ² (X) andg _k L ² (Y). As a co-product we develop a new proof of the Hilbert—Schmidt decomposition theorem for functions lying inL ² (X × Y).     

The deformation of the neutron-rich isotopes102Mo and104Mo

The half-lives of low-lying levels of the neutron-rich isotopes¹⁰²Mo and¹⁰⁴Mo have been measured at the fission product separator Josef with the ß-- triple coincidence technique. Values of t_1/2= 126(4)ps and 0.72(4)ns have been obtained for the 2₁ ⁺ levels at 296 keV and 192 keV in¹⁰²Mo and¹⁰⁴Mo, respectively. Deformation parameters of ß_q=0.28(1) and 0.31(1), respectively, are deduced, which are smaller than those of the isotones of Sr and Zr. The interacting boson model accounts well for the trend of 2⁺ energies in the Mo isotopes but slightly overpredicts the B(E2) values at saturation. A smooth dependence of 2₁ ⁺ vs. E 2₁ ⁺ is found for the A 100 region in agreement with the hydrodynamical model.Dedicated to Prof. Dr. P. Kienle on the occasion of his 60th birthday     

Equivalent quasi-norms on Lorentz spaces

We give new characterizations of Lorentz spaces by means of certain quasi-norms which are shown to be equivalent to the classical ones.

     

Local automorphisms of operator algebras on Banach spaces

In this paper we extend a result of Semrl stating that every 2-local automorphism of the full operator algebra on a separable infinite dimensional Hilbert space is an automorphism. In fact, besides separable Hilbert spaces, we obtain the same conclusion for the much larger class of Banach spaces with Schauder bases. The proof rests on an analogous statement concerning the 2-local automorphisms of matrix algebras for which we present a short proof. The need to get such a proof was formulated in Semrl's paper.

     

Sound radiation around a flying fly

Many insects produce sounds during flight. These acoustic emissions result from the oscillation of the wings in air. To date, most studies have measured the frequency characteristics of flight sounds, leaving other acoustic characteristics--and their possible biological functions--unexplored. Here, using close-range acoustic recording, we describe both the directional radiation pattern and the detailed frequency composition of the sound produced by a tethered flying (Lucilia sericata). The flapping wings produce a sound wave consisting of a series of harmonics, the first harmonic occurring around 190 Hz. In the horizontal plane of the fly, the first harmonic shows a dipolelike amplitude distribution whereas the second harmonic shows a monopolelike radiation pattern. The first frequency component is dominant in front of the fly while the second harmonic is dominant at the sides. Sound with a broad frequency content, typical of that produced by wind, is also recorded at the back of the fly. This sound qualifies as pseudo-sound and results from the vortices generated during wing kinematics. Frequency and amplitude features may be used by flies in different behavioral contexts such as sexual communication, competitive communication, or navigation within the environment.