Applications of Langlands' functorial lift of odd orthogonal groups

Together with Cogdell, Piatetski-Shapiro and Shahidi, we proved earlier the existence of a weak functorial lift of a generic cuspidal representation of to . Recently, Ginzburg, Rallis and Soudry obtained a more precise form of the lift using their integral representation technique, namely, the lift is an isobaric sum of cuspidal representations of (more precisely, cuspidal representations of such that the exterior square -functions have a pole at ). One purpose of this paper is to give a simpler proof of this fact in the case that a cuspidal representation has one supercuspidal component. In a separate paper, we prove it without any condition using a result on spherical unitary dual due to Barbasch and Moy. We give several applications of the functorial lift: First, we parametrize square integrable representations with generic supercuspidal support, which have been classified by Moeglin and Tadic. Second, we give a criterion for cuspidal reducibility of supercuspidal representations of . Third, we obtain a functorial lift from generic cuspidal representations of to automorphic representations of , corresponding to the -group homomorphism , given by the second fundamental weight.

     

Benefits of amplification for speech recognition in background noise

The purpose of the present study was to examine the benefits of providing audible speech to listeners with sensorineural hearing loss when the speech is presented in a background noise. Previous studies have shown that when listeners have a severe hearing loss in the higher frequencies, providing audible speech (in a quiet background) to these higher frequencies usually results in no improvement in speech recognition. In the present experiments, speech was presented in a background of multitalker babble to listeners with various severities of hearing loss. The signal was low-pass filtered at numerous cutoff frequencies and speech recognition was measured as additional high-frequency speech information was provided to the hearing-impaired listeners. It was found in all cases, regardless of hearing loss or frequency range, that providing audible speech resulted in an increase in recognition score. The change in recognition as the cutoff frequency was increased, along with the amount of audible speech information in each condition (articulation index), was used to calculate the "efficiency" of providing audible speech. Efficiencies were positive for all degrees of hearing loss. However, the gains in recognition were small, and the maximum score obtained by an listener was low, due to the noise background. An analysis of error patterns showed that due to the limited speech audibility in a noise background, even severely impaired listeners used additional speech audibility in the high frequencies to improve their perception of the "easier" features of speech including voicing.     

A modified approach to 2-(N-aryl)-1,3-oxazoles: application to the synthesis of the IMPDH inhibitor BMS-337197 and analogues

[structure: see text] A modified approach to the synthesis of 2-(N-aryl)-1,3-oxazoles, employing an optimized iminophosphorane/heterocumulene-mediated methodology, and its application to the synthesis of BMS-337197, a potent inhibitor of IMPDH, are described.     

The Floating Ball Paradox

In capillary theory there are two kinds of surface tension. There is the surface tension at the interface between two immiscible fluids. Thomas Young [9] also allowed for there to be a surface tension associated with a liquid-solid interface. He proceeded to use a balance of forces argument to derive the well-known contact angle condition along a liquid-liquid-solid intersection. The validity of this argument has recently been called into question by R. Finn [6]. A floating ball experiment discussed in that paper leads to an apparent paradox. We address this issue.      

Renormalised Steepest Descent in Hilbert Space Converges to a Two-Point Attractor

The result that for quadratic functions the classical steepest descent algorithm in R ^d converges locally to a two-point attractor was proved by Akaike. In this paper this result is proved for bounded quadratic operators in Hilbert space. The asymptotic rate of convergence is shown to depend on the starting point while, as expected, confirming the Kantorovich bounds. The introduction of a relaxation coefficient in the steepest-descent algorithm completely changes its behaviour, which may become chaotic. Different attractors are presented. We show that relaxation allows a significantly improved rate of convergence.     

A free-electron laser generated gamma-ray beam for nuclear physics

The High Intensity Gamma Ray Source (HIγS), a collaborative project between TUNL and the Duke Free Electron Laser Laboratory, is described. An initial experiment and plans for a future research program are discussed briefly.     

A Template‐Free Route to Polypyrrole Nanofibers

A template‐free method for the production of polypyrrole nanofibers is presented. By adding a small amount of bipyrrole into the oxidative polymerization of pyrrole, a drastic change in the morphology of the observed material is observed from large, granular particles to nanofibrils with an average diameter of 20 nm. This simple procedure allows for the production of polypyrrole nanofibers without the presence of surfactants or other structural directing agents. The polypyrrole nanofibers can form stable water dispersions which can be cast into films of sufficient quality to function as chemical sensors for analytes such as ammonia.