Relative weak mixing is generic

A classical result of Halmos asserts that among measure preserving transformations the weak mixing property is generic. We extend Halmos' result to the collection of ergolic extensions of a fixed, but arbitrary,aperiodic transformation T_0. We then use a result of Ornstein and Weiss to extend this relative theorem to the general(countable) amenable group.     

On whistling of pipes with a corrugated segment: Experiment and theory

Corrugated pipes are commonly used because of their local rigidity combined with global flexibility. The flow through such a pipe can induce strong whistling tones, which is an environmental nuisance and can be a threat to the mechanical integrity of the system. This paper considers the use of a composite pipe: a shorter corrugated pipe segment embedded between smooth pipe segments. Such a pipe retains some flexibility, while the acoustical damping in the smooth pipe reduces whistling tones. Whistling is the result of coherent vortex shedding at the cavities in the wall. This vortex shedding is synchronized by longitudinal acoustic waves traveling along the pipe. The acoustic waves trigger the vortex shedding, which reinforces the acoustic field for a critical range of the Strouhal number values. A linear theory for plane wave propagation and the sound production is proposed, which allows a prediction of the Mach number at the threshold of whistling in such pipes. A semi-empirical approach is chosen to determine the sound source in this model. This source corresponds to a fluctuating force acting on the fluid as a consequence of the vortex shedding. The functional form of the Strouhal number dependency of the dimensionless sound source amplitude is based on numerical simulations. The magnitude of the source and the Strouhal number range in which it can drive whistling are determined by matching the model to results for a specific corrugated pipe segment length. This semi-empirical source model is then applied to composite pipes with different corrugated segment lengths. In addition, the effect of inlet acoustical convective losses due to flow separation is considered. The Mach number at the threshold of whistling is predicted within a factor 2.     

Intersection of Isomorphic Linear Codes

Given an (n, k) linear code over GF(q), the intersection of with a codeπ( ), whereπS_n, is an (n, k₁) code, where max{0, 2k−n}k₁k. The intersection problem is to determine which integers in this range are attainable for a given code . We show that, depending on the structure of the generator matrix of the code, some of the values in this range are attainable. As a consequence we give a complete solution to the intersection problem for most of the interesting linear codes, e.g. cyclic codes, Reed–Muller codes, and most MDS codes.     

N.m.r. spectra of cyclic amines. II—Factors influencing the chemical shifts of α-protons in aziridines

Proton magnetic resonance spectra of trans and cis-2,3-diphenylaziridine (1 and 2) and their N-ethyl derivatives 3 and 4 were measured in carbon tetrachloride, chloroform, and benzene-d₆ at low temperatures (1 and 3) and in dry conditions (1 and 2). On the basis of these results it was concluded that an N-ethyl group exerts a shielding influence on a cis ring proton and a deshielding influence on a trans ring proton. From results obtained by measuring the ¹H n.m.r. spectra of 1–4 in deuterochlorofom-trifluoroacetic acid it was derived that the lone pair of the aziridine nitrogen exerts a shielding influence on cis related ring hydrogens. In most N-alkylaziridines the effect of the N-alkyl group predominates.     

Application of the generalized internal reference method for the characterization of parameters causing drift in inductively-coupled plasma emission spectrometry

Drift in signals limits the performance of inductively-coupled plasma (i.c.p.) emission spectrometry. The generalized internal reference method was applied to deconvolute the drift of an i.c.p. system. The plasma parameters were correlated to the drift components and the error boundary for the method was found. In the system studied, it was found that fluctuations in the nebulizer uptake rate were responsible for short-term signal changes. Long-term signal drift was caused mainly by flow variations of both cooling gas and aerosol carrier gas. The incident power to the plasma was found to be stable compared to other sources of drift. The method was found to be adequate for evaluating the origins of i.c.p. drift.