An estimate for the number of bound states of the Schrödinger operator in two dimensions

For the Schrödinger operator on let be the number of bound states. One obtains the following estimate:

where and ( is the Euler constant). This estimate holds for all potentials for which the previous integral is finite.

     

Frequency-place compression and expansion in cochlear implant listeners

In multichannel cochlear implants, low frequency information is delivered to apical cochlear locations while high frequency information is delivered to more basal locations, mimicking the normal acoustic tonotopic organization of the auditory nerves. In clinical practice, little attention has been paid to the distribution of acoustic input across the electrodes of an individual patient that might vary in terms of spacing and absolute tonotopic location. In normal-hearing listeners, Ba?kent and Shannon (J. Acoust. Soc. Am. 113, 2003) simulated implant signal processing conditions in which the frequency range assigned to the array was systematically made wider or narrower than the simulated stimulation range in the cochlea, resulting in frequency-place compression or expansion, respectively. In general, the best speech recognition was obtained when the input acoustic information was delivered to the matching tonotopic place in the cochlea with least frequency-place distortion. The present study measured phoneme and sentence recognition scores with similar frequency-place manipulations in six Med-El Combi 40+ implant subjects. Stimulation locations were estimated using the Greenwood mapping function based on the estimated electrode insertion depth. Results from frequency-place compression and expansion with implants were similar to simulation results, especially for postlingually deafened subjects, despite the uncertainty in the actual stimulation sites of the auditory nerves. The present study shows that frequency-place mapping is an important factor in implant performance and an individual implant patient's map could be optimized with functional tests using frequency-place manipulations.     

Molecular forces caused by the confinement of thermal noise

We have investigated spontaneous surface instabilities of very thin polymer films. Film stability and the wavelength of the dominating unstable mode were found to depend sensitively on the media adjacent to the film. Our experimental results cannot be explained by van der Waals interactions alone. To account for the presence of an additional destabilizing force, we propose that the geometrical confinement of thermally excited acoustic waves gives rise to a force that is strong enough to destabilize thin films. This thermoacoustic effect is of similar magnitude as van der Waals forces.     

Critical behavior of the disorder-induced Raman modes close to the lambda-phase transition in NH4Cl

This study gives our analysis of the disorder-induced Raman modes of v7 (93 cm(-1)) and v5 (144 cm(-1)) close to the lambda-phase transition (P = 0) in the NH4Cl crystal. We describe the critical behavior of the frequency shifts for those modes by a power-law formula and using our Raman data we obtain the value of 0.1 for the critical exponent which can also describe the critical behavior of the thermal expansivity and the specific heat of NH4Cl close to its lambda-phase transition (Tlambda = 242.9 K).     

On 2-almost contact tachibana manifolds

LeM be a (2m+2)-dimensional Riemannian manifold with two structure vector fieldsξ _r (r=2m+1, 2m+2) and letη ^r =ξ _r ^b be their corresponding covectors (or Pfaffians). These vector fields define onM a 2-almost contact structure. If the 2-formϕ=η ^2m+1∧η ^2m+2 is harmonic, then, following S. Tachibana [12],M is a Tachibana manifold and in this caseM is covered with 2 families of minimal submanifolds tangent toD ^⊥={ξ r} and its complementary orthogonal distributionD ^⊤. On such a manifold a canonical eigenfunction α of the Laplacian is associated. Since the corresponding eingenvalue is negative,M cannot be compact. Any horizontal vector fieldX orthogonal to α^# is a skew-symmetric Killing vector field (see [6]). Next, we assume that the Tachibana manifoldM under consideration is endowed with a framedf-structure defined by an endomorphism ϕ of the tangent bundleTM. Infinitesimal automorphisms of the symplectic form Ω _ϕ are obtained.     

On a class of Einstein hypersurfaces immersed in a Riemannian manifold

Let x:M→ be an isometric immersion of a hypersurface M into an (n+1)-dimensional Riemannian manifold and let ρ _i  (i∈{1,...,n}) be the principal curvatures of M. We denote by E and P the distinguished vector field and the curvature vector field of M, respectively, in the sense of [8].?If M is structured by a P-parallel connection [7], then it is Einsteinian. In this case, all the curvature 2-forms are exact and other properties induced by E and P are stated.?The principal curvatures ρ _i are isoparametric functions and the set (ρ₁,...,ρ _n ) defines an isoparametric system [10].?In the last section, we assume that, in addition, M is endowed with an almost symplectic structure. Then, the dual 1-form π=P ^♭ of P is symplectic harmonic. If M is compact, then its 2nd Betti number b ₂≥1. Received: April 7, 1999; in final form: January 7, 2000?Published online: May 10, 2001     

On the definition of viscosity solutions for parabolic equations

In this short note we suggest a refinement for the definition of viscosity solutions for parabolic equations. The new version of the definition is equivalent to the usual one and it better adapts to the properties of parabolic equations. The basic idea is to determine the admissibility of a test function based on its behavior prior to the given moment of time and ignore what happens at times after that.

     

RTL Investigation on the Radiochemical Oxidation of Polyolefins

High energy radiation causes deep modification of exposed polymers. In the irradiated polymers, the main macroscopic process is the formation of free radicals. The “cooled” electron distribution at the temperature of liquid nitrogen will develop the existence of various electron gaps with certain depths by smooth heating up to room temperature. In this paper, low density polyethylene, high density polyethylene and polypropylene were subjected to the action of gamma rays for causing structural modifications. The glow curves of quantum emission were recorded by slow heating from 106 to 286 K. The characteristic shoulders were obtained, which were ascribed to various electron traps consisting of unsaturation or carbonyl groups. For depicting the influence of molecular structures, the influence of CH₃ number/100 carbon atoms on the intensity of radiothermoluminescence (RTL) signal was studied on three types of LDPEs. A sharp decrease of maximum RTL intensity at advanced branching was pointed out. A mechanism of RTL emission is based on the present measurements.     

Swelling Behavior of N-t-butylacrylamide Copolymer and Terpolymers

Copolymers and terpolymers of N-t-butylacrylamide (TBA) with 2-acrylamido-2-methyl propane sulfonic acid (AMPS) and N-hydroxy methyl acrylamide (NHMAAM) were prepared by solution polymerization in a 1:1 (v/v) mixture of methanol and water at 50 °C keeping the TBA content in the feed constant at 60% based on mole ratio. The contents of AMPS or NHMAAM used for the preparation of TBA-AMPS and TBA-NHMAAM copolymers were 40 mole %. Molar percentages of AMPS and NHMAAM monomers in the feed for the preparation of TBA-AMPS-NHMAAM terpolymers were varied as 10:30, 20:20, and 30:10, respectively. The effects of temperature, AMPS and crosslinker contents, and the drying of swollen gels on the swelling behavior of ionic and non-ionic TBA gels were investigated in distilled water between 10–50 °C and in buffer solutions having various pHs (1.9, 3.1, 5.6, 7.1, and 9.8) with constant ionic strength of 0.08 M at 20 °C using both the dry and the swollen forms of gels. The chemical structures and microscopic morphologies of the polymers were investigated by FTIR and SEM, respectively.     

Analysis of optimality in singular control

The non-negativity, respectively, negativity conditions of the second variation of the performance index, give the sufficient optimality and non-optimality criteria for the singular control. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)