Vector weights and a Hardy-Littlewood maximal function

An analogue of the Hardy-Littlewood maximal function is introduced, for functions taking values in finite-dimensional Hilbert spaces. It is shown to be bounded with respect to weights in the class of Treil, thereby extending a theorem of Muckenhoupt from the scalar to the vector case.

     

Upper bounds for discrete moments of the derivatives of the riemann zeta-function on the critical line*

Assuming the Riemann hypothesis, we establish upper bounds for discrete moments of the Riemann zeta-function and its derivatives on the critical line. Moreover, we express continuous moments of the Riemann zeta-function and its derivatives in terms of these discrete moments. This allows us to give conditional upper bounds for $ {\int_0^T {\left| {{\zeta^{(l)}}\left( {{{1} \left/ {2} \right.} + {\text{i}}t} \right)} \right|}^{2k}}{\text{d}}t $ , where l and k are nonnegative integers.     

Absolutely continuous spectrum for one-dimensional Schrödinger operators with slowly decaying potentials: Some optimal results

The absolutely continuous spectrum of one-dimensional Schrödinger operators is proved to be stable under perturbation by potentials satisfying mild decay conditions. In particular, the absolutely continuous spectra of free and periodic Schrödinger operators are preserved under all perturbations satisfying This result is optimal in the power scale. Slightly more general classes of perturbing potentials are also treated. A general criterion for stability of the absolutely continuous spectrum of one-dimensional Schrödinger operators is established. In all cases analyzed, the main term of the asymptotic behavior of the generalized eigenfunctions is shown to have WKB form for almost all energies. The proofs rely on maximal function and norm estimates, and on almost everywhere convergence results for certain multilinear integral operators.

     

Centrality dependence of charged particle multiplicity in Au-Au collisions at square root of (s)NN = 130 GeV

We present results for the charged-particle multiplicity distribution at midrapidity in Au-Au collisions at square root of [s(NN)] = 130 GeV measured with the PHENIX detector at RHIC. For the 5% most central collisions we find dN(ch)/d eta(vertical line eta = 0) = 622+/-1(stat)+/-41(syst). The results, analyzed as a function of centrality, show a steady rise of the particle density per participating nucleon with centrality.     

Hearing thresholds of a harbor porpoise (Phocoena phocoena) for sweeps (1-2 kHz and 6-7 kHz bands) mimicking naval sonar signals

The distance at which active naval sonar signals can be heard by harbor porpoises depends, among other factors, on the hearing thresholds of the species for those signals. Therefore the hearing sensitivity of a harbor porpoise was determined for 1 s up-sweep and down-sweep signals, mimicking mid-frequency and low-frequency active sonar sweeps (MFAS, 6-7 kHz band; LFAS, 1-2 kHz band). The 1-2 kHz sweeps were also tested with harmonics, as sonars sometimes produce these as byproducts of the fundamental signal. The hearing thresholds for up-sweeps and down-sweeps within each sweep pair were similar. The 50% detection threshold sound pressure levels (broadband, averaged over the signal duration) of the 1-2 kHz and 6-7 kHz sweeps were 75 and 67 dB re 1 μPa(2), respectively. Harmonic deformation of the 1-2 kHz sweeps reduced the threshold to 59 dB re 1 μPa(2). This study shows that the presence of harmonics in sonar signals can increase the detectability of a signal by harbor porpoises, and that tonal audiograms may not accurately predict the audibility of sweeps. LFAS systems, when designed to produce signals without harmonics, can operate at higher source levels than MFAS systems, at similar audibility distances for porpoises.     

Synthesis of 2-(Perfluoroalkylether)- and -(Perfluoroaryl) Benzothiazoles(su1)

Benzothiazoles containing 2-perfluoroalkylether as well as perfluoroaryl substituents have been synthesized by two methods: (1) direct acylation of 2-aminobenzenethiol with perfluoroacyl halides, and (2) the reduction of N, Nt?-diacy1-2, 2t?-diaminodiphenyldisulfides followed by dehydrative cyclization. The intermediates formed in the direct acylation procedure are the N-acylaminobenzenethiols rather than the S-acyl derivatives.     

Hyperfine structure investigation on the (3d 4)3 G 4,5 levels of47Ti

Using two-step laser spectroscopy with the sideband technique the hyperfine structure (hfs) splittings of the levels (3d ⁴)³ G _4,5 in⁴⁷Ti have been measured. These are the first hfs measurements of the levels belonging to the 3d ^N+2 configuration of the system (3d+4s) ^N+2. The experimental results indicate a strong increase of the core polarization effect due to excitation of both 4s-electrons to the open 3d-shell.