Variations on a theorem of Davenport concerning abundant numbers

Let \sigma(n) = \sum_{d \mid n}d be the usual sum-of-divisors function. In 1933, Davenport showed that that n/\sigma(n) possesses a continuous distribution function. In other words, the limit D(u):= \lim_{x\to\infty} \frac{1}{x}\sum_{n \leq x,~n/\sigma(n) \leq u} 1 exists for all u \in [0,1] and varies continuously with u. We study the behavior of the sums \sum_{n \leq x,~n/\sigma(n) \leq u} f(n) for certain complex-valued multiplicative functions f. Our results cover many of the more frequently encountered functions, including \varphi(n), \tau(n), and \mu(n). They also apply to the representation function for sums of two squares, yielding the following analogue of Davenport's result: For all u \in [0,1], the limit $$\tilde{D}(u):= \lim_{R\to\infty} \frac{1}{\pi R}\#\{(x,y) \in \Z^2: 0<x^2+y^2 \leq R \text{ and } \frac{x^2+y^2}{\sigma(x^2+y^2)} \leq u\}$$ exists, and \tilde{D}(u) is both continuous and strictly increasing on [0,1]

Policing Public Houses in Victorian England

This article examines the policing of that most important site for leisure and pleasure among the Victorian working-classes – the pub. It begins with an examination of how changes in policing arrangements from the late-eighteenth century into Victoria’s reign both reflected growing societal anxiety over the conduct of drinking places and led to increased action against them. It provides analyses of the overall incidence of prosecution of publicans in the period up to the important licensing legislation of 1869 and 1872. It examines that legislation and its effects and then turns its attention to the offences of permitting drunkenness and serving a drunken person as particularly indicative of the broader question of the conduct of public houses and of customers’ behaviour within them, setting out trends in their prosecution. It then analyses what underlay the trends revealed, taking in the key variables of the law, the practicalities of its enforcement by the police, the attitudes of the magistracy and the actual conduct of individual publicans and drinkers, within the context of economic, social and cultural changes. By the late-nineteenth and early twentieth centuries, it is argued, pubs were more orderly places, but the achievement of that end was the product of a much more complex set of variables than simply policing arrangements

Engineering features of the San Fernando earthquake of February 9, 1971

Because of its consequences, the San Fernando earthquake was a major earthquake from the engineering point of view, even though it was only a moderate shock in seismological terms. As a result of the many effects of the earthquake, a large number of detailed studies and reports will be forthcoming from a wide variety of sources, and the papers collected in this volume are only preliminary studies of some of the more important and interesting engineering features of the earthquake. The papers were prepared by staff and students working in earthquake engineering within the Division of Engineering and Applied Science at the California Institute of Technology. The timely financial support of the Engineering Division of the National Science Foundation and the Earthquake Research Affiliates of the California Institute of Technology in conducting the research and preparing this report is gratefully acknowledged

On‐line student feedback: A pilot study

This paper reports on the outcomes of two experimental trials of the use of on‐line questionnaires to assess student satisfaction with courses at the London School of Economics and Political Science. In the first year, eighteen course modules were selected from three departments, surveying a total of 1,100 student places. Students on ten of the courses were invited to complete the ‘experimental’ on‐line survey and the remainder were invited to complete the paper‐based questionnaires which have been in use for several years. In the second year, the scale of the experiment was increased, to include forty‐six courses across seven departments. Response rates were compared and possible barriers to completion of the on‐line questionnaire were considered Whilst electronic monitoring indicated that 95 per cent (first trial) and 80 per cent (second trial) of those contacted for the on‐line survey opened the introductory email, only 23 per cent (first trial) and 27 per cent (second trial) completed the on‐line survey, compared with a 60 per cent response rate on the paper‐based survey. The on‐line response is also slightly lower than that achieved by postal surveys of LSE students (30–50 per cent response rates). Whilst some technical difficulties could have acted as a barrier, motivation appeared to be the main barrier. Initial results from the second trial, which included two reminder emails and some small incentives, show that it is possible to increase the response rate, but this may still be unacceptably low for staff whose promotion prospects may be affected by results. A third trial has been proposed, looking at ways in which the process as a whole could be amended, to overcome the problem of ‘survey fatigue’ that the current system faces

Too sick to drive : how motion sickness severity impacts human performance

There are multiple concerns surrounding the development and rollout of self-driving cars. One issue has largely gone unnoticed - the adverse effects of motion sickness as induced by self-driving cars. The literature suggests conditionally, highly and fully autonomous vehicles will increase the onset likelihood and severity of motion sickness. Previous research has shown motion sickness can have a significant negative impact on human performance. This paper uses a simulator study design with 51 participants to assess if the scale of motion sickness is a predictor of human performance degradation. This paper finds little proof that subjective motion sickness severity is an effective indicator of the scale of human performance degradation. The performance change of participants with lower subjective motion sickness is mostly statistically indistinguishable from those with higher subjective sickness. Conclusively, those with even acute motion sickness may be just as affected as those with higher sickness, considering human performance. Building on these results, it could indicate motion sickness should be a consideration for understanding user ability to regain control of a self-driving vehicle, even if not feeling subjectively unwell. Effectiveness of subjective scoring is discussed and future research is proposed to help ensure the successful rollout of self-driving vehicles

George W. Housner (1910–2008)

George W. Housner, Carl F Braun Professor of Engineering, emeritus, died after a short illness on 10 November 2008, just a few weeks before his 98th birthday. He was in the retirement home in Pasadena where he had lived for several years. For all of us who knew George, this marked the end of an era. Few people have guided and nurtured a field the way George led earthquake engineering over a period of several decades. He had a profound effect on many people and will long be remembered. His impact was so pervasive that he earned the title "Father of Earthquake Engineering." This article records some of my thoughts about this remarkable man

Memorial - Fritz Matthiesen (1926-1981)

R. B. "Fritz" Matthiesen died on 26 October 1981, at the age of 54, a victim of cancer, and his untimely death was a sad loss to his colleagues in earthquake engineering and seismology. We all miss his technical abilities, his sharp wit, and his irreverent ways of dealing with bureaucracy. Fritz had long been active in the affairs of the Seismological Society of America and was on the Board of Directors at the time of his death. His special technical interests were in the measurement and interpretation of strong ground motion and in the full-scale testing of structures such as buildings, dams, and nuclear reactors, and he was one of the world leaders in these fields. Until recently, he was Chief of the Seismic Engineering Branch of the U.S. Geological Survey, where he worked the past eight years of his career

Proceedings of the Fifth World Conference on Earthquake Engineering [Book Review]

The recently issued two-volume set of the Proceedings of the Fifth World Conference on Earthquake Engineering consists, essentially, of all the papers presented at the last world conference held in Rome in July of 1973. There are approximately 420 papers divided about equally between those 10 pages long and the shorter 4-page papers. The volumes include all the papers which were issued as preprints, a few submitted too late for preprinting, and some 30 discussions. Several of the discussions are categorized as free discussions, and are actually additional papers. Also included in the Proceedings is a list of the 850 participants from the 45 countries represented at the conference; an index of the papers, by session; an index of authors; and a brief section containing data about the International Association for Earthquake Engineering, the sponsoring organization. In the same section are the brief speeches given at the opening and closing ceremonies, administrative reports, and a few photographs. This general material comprises 168 pages, bringing the total for the volumes to nearly 3,200 pages. The massive volumes, 3½ in thick, are well-bound in maroon fabrikoid with gold lettering. The papers are reproduced photographically from originals supplied by the authors so there is considerable variation in typography. The quality of both the printing and the paper is very good, however, and the legibility of text, figures and photographs is at least equal to any of the Proceedings of previous world conferences

Millimeter-wave communication for a last-mile autonomous transport vehicle

Low-speed autonomous transport of passengers and goods is expected to have a strong, positive impact on the reliability and ease of travelling. Various advanced functions of the involved vehicles rely on the wireless exchange of information with other vehicles and the roadside infrastructure, thereby benefitting from the low latency and high throughput characteristics that 5G technology has to offer. This work presents an investigation of 5G millimeter-wave communication links for a low-speed autonomous vehicle, focusing on the effects of the antenna positions on both the received signal quality and the link performance. It is observed that the excess loss for communication with roadside infrastructure in front of the vehicle is nearly half-power beam width independent, and the increase of the root mean square delay spread plays a minor role in the resulting signal quality, as the absolute times are considerably shorter than the typical duration of 5G New Radio symbols. Near certain threshold levels, a reduction of the received power affects the link performance through an increased error vector magnitude of the received signal, and subsequent decrease of the achieved data throughput