Invertibility theory for Toeplitz plus Hankel operators and singular integral operators with flip

It is well known that a Toeplitz operator is invertible if and only if its symbols admits a canonical Wiener-Hopf factorization, where the factors satisfy certain conditions. A similar result holds also for singular integral operators. More generally, the dimension of the kernel and cokernel of Toeplitz or singular integral operators which and Fredholm operators can be expressed in terms of the partial indices of an associated Wiener-Hopf factorization problem.In this paper we establish corresponding results for Toeplitz plus Hankel operators and singular integral operators with flip under the assumption that the generating functions are sufficiently smooth (e.g., Hölder continuous). We are led to a slightly different factorization problem, in which pairs , instead of the partial indices appear. These pairs provide the relevant information about the dimension of the kernel and cokernel and thus answer the invertibility problem.     

Stochastic gain in population dynamics

We introduce an extension of the usual replicator dynamics to adaptive learning rates. We show that a population with a dynamic learning rate can gain an increased average payoff in transient phases and can also exploit external noise, leading the system away from the Nash equilibrium, in a resonancelike fashion. The payoff versus noise curve resembles the signal to noise ratio curve in stochastic resonance. Seen in this broad context, we introduce another mechanism that exploits fluctuations in order to improve properties of the system. Such a mechanism could be of particular interest in economic systems.     

Dynamical model for chemically driven running droplets

We propose coupled evolution equations for the thickness of a liquid film and the density of an adsorbate layer on a partially wetting solid substrate. Therein, running droplets are studied assuming a chemical reaction underneath the droplets that induces a wettability gradient on the substrate and provides the driving force for droplet motion. Two different regimes for moving droplets--reaction-limited and saturated regime--are described. They correspond to increasing and decreasing velocities with increasing reaction rates and droplet sizes, respectively. The existence of the two regimes offers a natural explanation of prior experimental observations.     

Hierarchical porous silica materials with a trimodal pore system using surfactant templates

Porous silica exhibiting a hierarchically ordered trimodal pore system with a well-defined reverse opal microstructure and bimodal mesoporosity in the walls has been prepared by using polystyrene latex spheres, a novel block copolymer and an ionic liquid surfactant as templates. The resulting materials exhibit hierarchical order at three length scales (small mesopores: 2-3 nm; large mesopores: 11-12 nm; macropores: 360 nm).     

Functional MRI using intravascular contrast agents: detrending of the relative cerebrovascular (rCBV) time course

In pharmacological fMRI experiments in animal models, blood pool contrast agents may be used to map cerebral blood volume change as a surrogate for neural activation. When the background signal drift due to contrast agent washout is non-negligible over the duration of the signal changes of interest, time-course detrending is essential for accurate interpretation of the experiment. Detrending approaches based on estimation of the background signal from a baseline period of the time course prior to pharmacological (or functional) challenge were evaluated with the aim of identifying a robust method of estimating the contrast agent washout contribution to the background signal drift. For fMRI studies in the rat, it was found that a constrained fit of a mono-exponential washout model was more accurate than a constant background approximation and unconstrained fits for experiments investigating the functional response to rapid pharmacological challenges such as cocaine and amphetamine. Moreover, the constrained fitting approach allows shorter baseline periods than unconstrained extrapolation, reducing the required duration of the experiment.     

The importance of cochlear processing for the formation of auditory brainstem and frequency following responses

A model for the generation of auditory brainstem responses (ABR) and frequency following responses (FFRs) is presented. The model is based on the concept introduced by Goldstein and Kiang [J. Acoust. Soc. Am. 30, 107-114 (1958)] that evoked potentials recorded at remote electrodes can theoretically be given by convolution of an elementary unit waveform (unitary response) with the instantaneous discharge rate function for the corresponding unit. In the present study, the nonlinear computational auditory-nerve model recently developed by Heinz et al. [ARLO 2(3), 91-96 (2001)] was used to calculate the instantaneous discharge rate ri(t) for fibers i in the frequency range from 0.1 and 10 kHz. The summed activity across frequency was convolved with a unitary response which is assumed to reflect contributions from different cell populations within the auditory brainstem, recorded at a given pair of electrodes on the scalp. Predicted potential patterns are compared with experimental data for a number of stimulus and level conditions. Clicks, chirps as defined in Dau et al. [J. Acoust. Soc. Am. 107, 1530-1540 (2000)], long-duration stimuli comprising the chirp, as well as tones and slowly varying tonal sweeps were considered. The results demonstrate the importance of considering the effects of the basilar-membrane traveling wave and auditory-nerve processing for the formation of ABR and FFR. Specifically, the results support the hypothesis that the FFR to low-frequency tones represents synchronized activity mainly stemming from mid- and high-frequency units at more basal sites, and not from units tuned to frequencies around the signal frequency.     

Asymptotics of Determinants of Bessel Operators

 For aL ^∞ (ℝ₊)∩L ¹ (ℝ₊) the truncated Bessel operator B _τ (a) is the integral operator acting on L ² [0,τ] with the kernel

Activation parameters for the reactive intermediates relevant to carbonylation catalysts based on cobalt carbonyls

Time-resolved spectroscopic techniques have been used to prepare and to interrogate transient species that are models for reactive intermediates in cobalt-catalyzed hydroformylation. Flash photolysis of acetylcobalt carbonyl complexes of the type RC(O)Co(CO)3(PR'3) (A; R = CH3, CD3, or C2H5; R' = Ph or nBu) leads to CO photodissociation to give the "unsaturated" intermediate [RC(O)Co(CO)2(PR'3)] (I), which decays by two competitive pathways, alkyl migration to the cobalt to give RCo(CO)3PR'3 (M) and reaction with CO to re-form A. With the perdeuterioacetyl complex (R = CD3, R' = Ph), rate constants both of CO trapping (kco) and of methyl migration (kM) were just slightly smaller than those of the perprotio analogue (kh/kd = 1.04 +/- 0.01 and 1.07 +/- 0.09, respectively). Thus, any stabilization of the "vacant" coordination site of I by agostic interactions with the acetyl methyl group appears to be kinetically insignificant, consistent with the previous conclusion (Inorg. Chem. 2000, 39, 3098-3106) that this site is stabilized by an eta 2-coordinated carbonyl. Changing the phosphine ligand has a greater influence on the kinetics of I. The species generated by the flash photolysis of the trialkyl phosphine complex CH3C(O)Co-(CO)3(P(nBu3)) exhibited a much larger kM than was the case for the PPh3 analogue, although there was little difference in the kco values. Similarly, kM proved to be sensitive to the nature of R as demonstrated by the slower alkyl migration (at 298 K) for the intermediate formed by CO photodissociation from the propionyl complex C2H5C(O)Co(CO)3PPh3 relative to the acetyl analogue. Nonetheless, all these intermediates displayed analogous time-resolved infrared spectra and general kinetics behavior in benzene solution (implying common mechanisms for decay), so it is concluded that all are present as the eta 2-chelated acyl structure under these conditions.