Outer ellipsoidal approximations of the reachable set at infinity for linear systems

Outer ellipsoidal approximations to the reachable set at infinity for a linear control system with bounded scalar controls are obtained using a new method based on quadratic Lyapunov functions. These outer approximations are compared with those given by an algorithm due to Sabin and Summers, and also with certain tangential outer approximations, obtained using a fixed-point iteration scheme.This research was supported by the Natural Sciences and Engineering Research Council of Canada. The authors gratefully acknowledge the assistance of Mr. Ryan Davies, recipient of an NSERC Undergraduate Research Award.     

Discrimination of interval size in short tone sequences

This study investigates the discrimination of small changes of interval size in short sequences of musical tones. Major, minor and neutral thirds were varied in increments of 15 cents. The nine subjects had varying degrees of amateur musical experience-their level of musical training was lower than that of professional musicians. In some experiments the stimuli were presented purely melodically and in others they were presented together with a sustained tone at a higher pitch. Some subjects were able to make use of the additional cues from beats in the latter case. Category widths for identification were measured at around 70 cents and just-noticeable differences in frequency were measured at around 10 cents. Little significant variation of inter-stimulus sensitivity index d' was observed across the stimulus sets, i.e., there was little evidence for "anchors" or "landmarks" within the range of tunings employed. However, for major thirds, discrimination of the 15 cent increment between 400 and 415 cents was reduced compared to discrimination of other 15 cent increments within the stimulus sets.     

Intelligibility of speech in noise at high presentation levels: effects of hearing loss and frequency region

These experiments examined how high presentation levels influence speech recognition for high- and low-frequency stimuli in noise. Normally hearing (NH) and hearing-impaired (HI) listeners were tested. In Experiment 1, high- and low-frequency bandwidths yielding 70%-correct word recognition in quiet were determined at levels associated with broadband speech at 75 dB SPL. In Experiment 2, broadband and band-limited sentences (based on passbands measured in Experiment 1) were presented at this level in speech-shaped noise filtered to the same frequency bandwidths as targets. Noise levels were adjusted to produce approximately 30%-correct word recognition. Frequency bandwidths and signal-to-noise ratios supporting criterion performance in Experiment 2 were tested at 75, 87.5, and 100 dB SPL in Experiment 3. Performance tended to decrease as levels increased. For NH listeners, this "rollover" effect was greater for high-frequency and broadband materials than for low-frequency stimuli. For HI listeners, the 75- to 87.5-dB increase improved signal audibility for high-frequency stimuli and rollover was not observed. However, the 87.5- to 100-dB increase produced qualitatively similar results for both groups: scores decreased most for high-frequency stimuli and least for low-frequency materials. Predictions of speech intelligibility by quantitative methods such as the Speech Intelligibility Index may be improved if rollover effects are modeled as frequency dependent.     

Accelerated imidization reactions using microwave radiation

Microwave radiation has been clearly shown to result in enhancement of the rate of reaction for an imidization reaction. Analysis of the kinetic parameters showed that the apparent activation energy for the reaction was reduced from 105 to 55 kJ/mol, under the conditions of this experiment. The mechanism which has been proposed to explain this enhancement is based on the concept of a nonuniform temperature on a molecular scale, rather than a true reduction in the activation energy. © 1992 John Wiley & Sons, Inc.     

Mass spectral fragmentation pattern of 5-methyl-4-[(phenylamino)methylene]-2,4-dihydro-3h-pyrazol-3-one and its 2-methyl and 2-phenyl derivatives

The mass spectral fragmentation patterns of 5-methyl-4-[(phenylamino)methylene]-2,4-dihydro-3H-pyrazol-3-one and its 2-methyl and 2-phenyl derivatives have been elucidated. The principal initial fragmentation route involves rupture of the exocyclic CH-NH bond. Minor routes involve loss of H, OH and C₆H₅ from the molecular ion and rupture of the pyrazolone ring.     

Compactness in Spaces of Vector Valued Continuous Functions and Asymptotic Almost Periodicity

We characterize the precompact sets in spaces of vector valued continuous functions and use the resulting criteria to investigate asymptotic behaviour of such functions defined on a halfline. This problem arose in the context of a qualitative study of solutions to the abstract Cauchy problem. We give particular consideration to the relationship between vector valued asymptotically almost periodic functions on a subinterval [α, ∞] of the real line and precompactness of the set of its translates. Our compactness criteria are also applied to a question concerning the approximation property for spaces of vector valued continuous functions with topologies induced by weighted analogues of the supremum norm. as well as to obtain nonlinear variants on factorization of compact operators through reflexive Banach spaces.     

Chemical constitution and activity of bipyridylium herbicides. Part IX. N-alkoxy quaternary salts of 4,4′bipyridyl

4,4′-Bipyridyl N-oxide and 4,4′-bipyridyl N,N'-dioxide react with alkating agents to afford N-alkoxy N'-alkyl and N,N'-dialkoxy diquaternary salts of 4,4′-bipyridyl respectively. The diquaternary salts were very much less active as herbicides than paraquat. Unlike paraquat they cannot be regarded as reversible one electron transfer systems.     

Semiconducting polymers based on charge-transfer complexes. II. Crystal structure of poly-N-4-[4-(methylthio)phenoxy]butyrylethylenimine

Of the two electron-donor-containing polymers whose synthesis was described in Part I of this series, one was crystalline. This polymer, which contains (methylthio)phenoxy electron-donating groups on the side chains of an N-acyl-substituted polyethylenimine, could be indexed in a triclinic unit cell of dimensions a = 4.35 Å, b = 24.0 Å, c = 12.7 Å, and α = β = γ = 90°. The polymer has the side chains alternating on each side of the polymer backbone. They extend to form at 24.0 Å repeat in that direction. The thickness of the ribbonlike molecule is 4.35 Å, while the repeat distance along the polymer backbone is 12.7 Å, which includes four monomer units.     

Approximation techniques in complex reaction kinetics

We examine the kinetic model D. The differential equations describing this reaction scheme are cast in a nondimensional form and analyzed in four basic approximation regimes: a ‘pseudo-first order’ approximation valid for small values of the ratio of the initial concentrations of the reactants; an asymptotic solution valid for large values of k₃; the standard steady state (Bodenstein) approximation; and an approximation to a second order system without intermediate. Interconnecting relationships between the various approximations derived are examined, and the approximations are compared to numerical solutions to the full equations. The results are assessed from the standpoint of the experimental kineticist, and it is suggested that the reaction studied, and consequently many other more complex reactions, may under certain circumstances be subject to non-unique interpretation.