Linear relations in the Calkin algebra for composition operators

We consider this and related questions: When is a finite linear combination of composition operators, acting on the Hardy space or the standard weighted Bergman spaces on the unit disk, a compact operator?

     

Annoyance due to railway vibration at different times of the day

The time of day when vibration occurs is considered as a factor influencing the human response to vibration. The aim of the present paper is to identify the times of day during which railway vibration causes the greatest annoyance, to measure the differences between annoyance responses for different time periods and to obtain estimates of the time of day penalties. This was achieved using data from case studies comprised of face-to-face interviews and internal vibration measurements (N=755). Results indicate that vibration annoyance differs with time of day and that separate time of day weights can be applied when considering exposure-response relationships from railway vibration in residential environments.     

Moment excitation and the measurement of moment mobilities

Frequency response functions (FRF), such as mobilities, are widely used in the analysis of vibration and structure-borne sound and it is important that this FRF data can be measured accurately for all important degrees of freedom. In some cases three translational and three rotational components of both excitation and response may be of importance; i.e. three forces and moments, and three velocities and angular velocities. Of these, the measurement of angular velocity due to moment excitation is one of the most challenging. This paper describes a known approach, sometimes referred to as the central difference method, which can be used for this purpose. The central difference method is thought to be one of the most practicable methods for measuring moment mobilities because it avoids the need for a moment exciter; instead finite differences are used to approximate the moment mobility which is a spatial derivative of the more easily measured velocity to force mobility ratio. There does however remain some doubt regarding the accuracy of the central difference method because of the finite difference approximation made and the method's possible susceptibility to random and bias errors. To better understand the finite difference error, an error analysis using a Taylor series expansion and simulated experiments for plate and beam structures are provided. It is then argued that random and bias errors associated with the measurement chain should now, with modern instrumentation, be less of a problem. An experimental validation of the method using two approaches is used to test this hypothesis. It is concluded that the central difference method provides a good balance between measurement effort and data quality making it widely applicable.     

Vinyl addition polymerization of norbornene with cationic (allyl)Ni catalysts: Mechanistic insights and characterization of first insertion products

Several cationic (allyl)Ni(II) complexes were synthesized and shown to be highly active for (2,3)‐vinyl addition polymerization of norbornene to yield polymers with low molecular weight distributions (MWDs) ranging from 1.4–1.9. In all cases slow initiation was followed by rapid propagation which prevents molecular weight control of the poly(norbornene). One of the intermediates in the polymerization process has been identified and characterized by NMR spectroscopy as the first insertion product resulting from the insertion of norbornene into the Ni? C allyl bond in cis‐exo fashion. This insertion product was synthesized independently and NMR studies showed that the first insertion of norbornene into the Ni? C allyl bond is a reversible process. © 2009 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 47: 2560–2573, 2009     

Indirect measurement of acoustic power into a small room at low frequencies

An essential step towards improving sound insulation is a reliable means of quantifying the performance. However, for various reasons sound insulation measurements at low frequencies are associated with relatively high uncertainty and wide variance values. The objective of this research is to develop a method of sound insulation measurement which complements the standard ISO 140 measurement methods by providing improved accuracy at low frequencies. In this paper part of the problem is considered, namely the measurement of power radiated into the receiver room. The ‘peak envelope method’ is based on mode theory and the measurement employs a pair of microphones in the receiver room and a calibrated volume velocity source. No reverberation time measurements are required. The theory is outlined and computer simulations and trial measurements are carried out in order to validate the theory. Good agreement in numerical and experimental validation is demonstrated. We conclude that the peak envelope method is suitable for the measurement of radiated sound power at modal frequencies where ISO 140 methods are poorly adapted. In order to obtain transmission loss, a measure of incident power in the source room will also be required, which will be the subject of future works.     

Composition operators within singly generated composition <Emphasis Type="Italic">C</Emphasis>*-algebras

Let ϕ be a linear-fractional self-map of the open unit disk D, not an automorphism, such that ϕ(ζ) = η for two distinct points ζ,η in the unit circle ∂D. We consider the problem of determining which composition operators, acting on the Hardy space H ², lie in C*(C _ϕ ,K), the unital C*-algebra generated by the composition operator C _ϕ and the ideal K of compact operators. This necessitates a companion study of the unital C*-algebra generated by the composition operators induced by all parabolic non-automorphisms with common fixed point on the unit circle.