Measuring the efficiency of trigonometric series estimates of a density

Some types of density estimators, particularly those based on trigonometric series, converge reasonably quickly to their limit except in the neighbourhood of one or two singularities. In this situation the mean integrated square error, the traditional measure of the efficiency of a density estimator, is an unsatisfactory measure. The notion of partial mean integrated square error is introduced and used to compare the performance of trigonometric series estimators. The results lead to consideration of some new estimators which have excellent properties from the points of view of both efficiency and ease of computation.     

Further results on integral generalized inverses of integral matrices

This paper further investigates integral generalized inverses of integral matrices.     

A general survey of the proton spin–lattice relaxation rates of steroids

The spin-lattice relaxation rates of the aromatic, alkene, hydroxyl, methine and methyl protons of 19 steroid derivatives have been measured using the null point method. A simple procedure is described whereby the R₁ values of molecules which have different motional tumbling rates can be directly inter-compared, and it is shown that such ‘normalized’ relaxation data can provide novel insight concerning both the geometry and the local molecular motion of these substances in solution.     

Grenzflächen Lösung/Luft. II. Adsorption von oberflächenaktiven Substanzen in verdünnten wäßrigen Lösungen. Anomale Schwingungsstrahl-Erscheinungen

Colloid and Polymer Science -     

Activity interference and noise annoyance

Debate continues over differences in the dose-response functions used to predict the annoyance at different sources of transportation noise. This debate reflects the lack of an accepted model of noise annoyance in residential communities. In this paper a model is proposed which is focussed on activity interference as a central component mediating the relationship between noise exposure and annoyance. This model represents a departure from earlier models in two important respects. First, single event noise levels (e.g., maximum levels, sound exposure level) constitute the noise exposure variables in place of long-term energy equivalent measures (e.g., 24-hour L_eq or L_dn). Second, the relationships within the model are expressed as probabilistic rather than deterministic equations. The model has been tested by using acoustical and social survey data collected at 57 sites in the Toronto region exposed to aircraft, road traffic or train noise. Logit analysis was used to estimate two sets of equations. The first predicts the probability of activity interference as a function of event noise level. Four types of interference are included: indoor speech, outdoor speech, difficulty getting to sleep and awakening. The second set predicts the probability of annoyance as a function of the combination of activity interferences. From the first set of equations, it was possible to estimate a function for indoor speech interference only. In this case, the maximum event level was the strongest predictor. The lack of significant results for the other types of interference is explained by the limitations of the data. The same function predicts indoor speech interference for all three sources—road, rail and aircraft noise. The results for the second set of equations show strong relationships between activity interference and the probability of annoyance. Again, the parameters of the logit equations are similar for the three sources. A trial application of the model predicts a higher probability of annoyance for aircraft than for road traffic situations with the same 24-hour L_eq. This result suggests that the model may account for previously reported source differences in annoyance.