Asymptotics of generalized jacobi polynomials

Polynomialsp ₁,(z),p ₂ (z), of degreen are defined by the relation \(p_1 (z) + p_2 (z)\prod\nolimits_{i = 1}^3 {(z - b_l )^{v_1 } } = O(z^{ - n - 1} ),z \to \infty \) , where \(\sum\nolimits_{i = 1}^3 {v_i = 0} \) . We obtain the asymptotic behavior of these polynomials asn→∞ and show that it agrees with a previous conjecture.     

EPR and 1H and 13C dynamic nuclear polarization studies of a molecularly doped polymer: bisphenol A polycarbonate doped with trianisylamine and trianisylaminium perchlorate.

We have investigated the EPR and DNP behavior of a molecularly doped polymer modeling those used to transport electronic charge in electrophotography. The EPR spectra show no evidence of the superexchange reported for a closely related system based on tri-p-tolylamine. The difference may be due to larger charge-transfer matrix elements in the latter system. An unambiguous interpretation of the observed 1H DNP was rendered difficult by the unanticipated asymmetry of the EPR spectra. We report extensive data on the "three-spin" effect evident in the DNP-enhanced 13C NMR spectra, and comment on its potential for characterizing polymer interfaces.     

The mechanical waveform of the basilar membrane. IV. Tone and noise stimuli

Analysis of mechanical cochlear responses to wide bands of random noise clarifies many effects of cochlear nonlinearity. The previous paper [de Boer and Nuttall, J. Acoust. Soc. Am. 107, 1497-1507 (2000)] illustrates how closely results of computations in a nonlinear cochlear model agree with responses from physiological experiments. In the present paper results for tone stimuli are reported. It was found that the measured frequency response for pure tones differs little from the frequency response associated with a noise signal. For strong stimuli, well into the nonlinear region, tones have to be presented at a specific level with respect to the noise for this to be true. In this report the nonlinear cochlear model originally developed for noise analysis was modified to accommodate pure tones. For this purpose the efficiency with which outer hair cells modify the basilar-membrane response was made into a function of cochlear location based on local excitation. For each experiment, the modified model is able to account for the experimental findings, within 1 or 2 dB. Therefore, the model explains why the type of filtering that tones undergo in the cochlea is essentially the same as that for noise signals (provided the tones are presented at the appropriate level).     

The effects of cochlear hypothermia on compound action potential tuning

The effects of lowered cochlear temperature on eighth-nerve tuning were assessed by using forward masking of whole nerve action potential (AP) responses to generate AP tuning curves (APTCs) at cochlear temperatures ranging from 38.5 degrees to 30 degrees C for probe frequencies from 8 to 36 kHz. The data indicate that subnormal cochlear temperatures result in: broadened APTCs for probe frequencies above 10 kHz which are interpreted as resulting from reduced hair-cell frequency selectivity, lowered or more sensitive APTC tips where tone-burst thresholds are unchanged, and raised or less sensitive tips where thresholds to tone bursts were elevated. Increased tip sensitivity is explained in terms of enhanced eighth-nerve adaptation which occurred during hypothermia. Experiments directly addressing adaptation were performed, in which the masker-probe interval (delta t) was systematically lengthened. The normalized AP decrement versus delta t functions indicate an enhancement of both the amount and duration of adaptation during hypothermia. Functions relating the growth of response to the masker (AP decrement versus masker intensity functions) were reduced at low temperatures.     

The mechanical waveform of the basilar membrane. III. Intensity effects

Mechanical responses in the basal turn of the guinea-pig cochlea were measured with broad-band noise stimuli and expressed as input-output cross-correlation functions. The experiments were performed over the full range of stimulus intensities in order to try to understand the influence of cochlear nonlinearity on frequency selectivity, tuning, signal compression and the impulse response. The results are interpreted within the framework of a nonlinear, locally active, three-dimensional model of the cochlea. The data have been subjected to inverse analysis in order to recover the basilar-membrane (BM) impedance, a parameter function that, when inserted into the (linearized version of that) model, produces a model response that is similar to the measured response. This paper reports details about intensity effects for noise stimulation, in particular, the way the BM impedance varies with stimulus intensity. In terms of the underlying cochlear model, the decrease of the "activity component" in the BM impedance with increasing stimulus level is attributed to saturation of transduction in the outer hair cells. In the present paper this property is brought into a quantitative form. According to the theory [the EQ-NL theorem, de Boer, Audit. Neurosci. 3, 377-388 (1997)], the BM impedance is composed of two components, both intrinsically independent of stimulus level. One is the passive impedance Zpass and the other one is the "extra" impedance Zextra. The latter impedance is to be multiplied by a real factor gamma (0 < or = gamma < or = 1) that depends on stimulus level. This concept about the composition of the BM impedance is termed the "two-component theory of the BM impedance." In this work both impedances are entirely derived from experimental data. The dependence of the factor gamma on stimulus level can be derived by using a unified form of the outer-hair-cell transducer function. From an individual experiment, the two functions Zpass and Zextra are determined, and an approximation (Zpass + gamma Zextra) to the BM impedance constructed. Next, the model response (the "resynthesized" response) corresponding to this "artificial" impedance is computed. The same procedure is executed for several stimulus-level values. For all levels, the results show a close correspondence with the original experimental data; this includes correct prediction of the compression of response amplitudes, the reduction of frequency selectivity, the shift in peak frequency and, most importantly, the preservation of timing in the impulse response. All these findings illustrate the predictive power of the underlying model.     

Photorefractive two-beam coupling equations with multiple spatial–temporal features: an SVD approach

We analyze the evolution of multi-feature two-beam coupling, wherein each beam contains several spatial–temporal features (spatial patterns modulated by different signals), using a one-dimensional plane wave model to describe the evolution of paired components. This general scenario is of interest for analyzing signal-processing applications of photorefractives, such as source-separation by orthogonalization of source-modulated spatial patterns. We use singular-value decomposition (SVD) to express each beam as a simple superposition of modes that are both temporally uncorrelated and spatially orthogonal. We find a solution that is a natural matrix generalization of the scalar solution for simple two-beam coupling, and a test for its validity: the two operators that give the spatial overlap associated with the temporal basis signals in the two beams must commute. Equivalently, this means that the same set of signals must be modulating the SVD modes in the two beams. Then the SVD modes are preserved in the two-beam coupling evolution, with only their amplitudes changing. Dedicated to Prof. Dr. Eckard Kr?tzig on the occasion of his 60th birthday. Received: 10 November 1998 / Revised version: 13 January 1999 / Published online: 7 April 1999