bluuebunny/crossref_metadata_2025 huggingface dataset:
Functional normalizations for the branching process with infinite mean
Authors: Barbour Andrew D. , Schuh H.-J.
Published: July 2016

It is well known that, in a Bienaymé-Galton–Watson process (Zn
) with 1 < m = EZ
1 < ∞ and EZ
1 log Z
1 <∞, the sequence of random variables Znm –n
converges a.s. to a non–degenerate limit. When m =∞, an analogous result holds: for any 0< α < 1, it is possible to find functions U such that α n U (Zn
) converges a.s. to a non-degenerate limit. In this paper, some sufficient conditions, expressed in terms of the probability generating function of Z
1 and of its distribution function, are given under which a particular pair (α, U) is appropriate for (Zn
). The most stringent set of conditions reduces, when U (x)
x, to the requirements EZ
1 = 1/α, EZ
1 log Z
1 <∞.
Exponential growth of a branching process usually implies stable age distribution
Authors: Berndtsson Bo , Jagers Peter
Published: July 2016

Start a Bellman–Harris branching process from one or several ancestors, whose ages are identically distributed random variables. Assume that the life-length distribution decays more quickly than exponentially and that the distribution of ages at start does not give too much mass to high ages (in a sense to be made precise). Then, if the expected population size is an exponential function of time, the ages must follow the stable age distribution of the process.
First-passage percolation processes with finite height
Authors: Herrndorf Norbert
Published: July 2016

We consider first-passage percolation in an infinite horizontal strip of finite height. Using methods from the theory of Markov chains, we prove a central limit theorem for first-passage times, and compute the time constants for some special cases.
The risk-sensitive homing problem
Authors: Kuhn Jonathan
Published: July 2016

The ‘homing' optimal control problem, described in Whittle and Gait (1970), is given a risk-sensitive formulation. It is shown that the reduction of an optimally controlled homing problem to the treatment of an uncontrolled process, demonstrated by Whittle and Gait, can be achieved in the risk-sensitive case. Two scalar problems are analyzed in detail.
On the busy-period distributions of M/G/1/K queues by state-dependent arrivals and FCFS/LCFS-P service disciplines
Authors: Shanthikumar J. George , Sumita Ushio
Published: July 2016

The busy-period distributions of M/G/1/K queues with state-dependent arrival rates are considered. Two recursion formulas for the Laplace–Stieltjes transforms of the busy periods under the FCFS and preempt resume LCFS service disciplines are obtained. It is shown that the busy-period distributions for the two service disciplines are, in general, different, in contrast to the fact that they coincide for ordinary M/G/1 queues. For deterministic service times and arrival rates non-increasing in the number of customers in the system, stochastic ordering between these two busy periods is also established.
Perturbation theory and finite Markov chains
Authors: Schweitzer Paul J.
Published: July 2016

A perturbation formalism is presented which shows how the stationary distribution and fundamental matrix of a Markov chain containing a single irreducible set of states change as the transition probabilities vary. Expressions are given for the partial derivatives of the stationary distribution and fundamental matrix with respect to the transition probabilities. Semi-group properties of the generators of transformations from one Markov chain to another are investigated. It is shown that a perturbation formalism exists in the multiple subchain case if and only if the change in the transition probabilities does not alter the number of, or intermix the various subchains. The formalism is presented when this condition is satisfied.
On recurrence and transience of growth models
Authors: Kersting G.
Published: July 2016

Let Xn
be non-negative random variables, possessing the Markov property. We given criteria for deciding whether Pr(X
n
→∞) is positive or 0. It turns out that essentially this depends on the magnitude of E(Xn

+1 | Xn
= x) compared to that of E(X
2

n+1 | Xn
= x) for large x. The assumptions are chosen such that for example population-dependent branching processes can be treated by our results.
A search game with one object and two searchers
Authors: Nakai Teruhisa
Published: July 2016

We consider a non-zero-sum game in which two searchers (player I and II) compete with each other for quicker detection of an object hidden in one of n boxes. Let p (q) be the prior location distribution of the object for player I (II). Exponential detection functions are assumed for both players. Each player wishes to maximize the probability that he detects the object before the opponent detects it. In the general case, a Nash equilibrium point is obtained in the form of a solution of simultaneous differential equations. In the case of p = q, we obtain an explicit solution showing the surprising result that both players have the same equilibrium strategy even though the detection rates are different.
Oscillating random walk models for GI/G/1 vacation systems with Bernoulli schedules
Authors: Keilson J. , Servi L. D.
Published: July 2016

Processors handling multi-class traffic typically alternate between serving a particular class of traffic and performing other tasks, e.g., secondary service tasks or routine maintenance. The stochastic behavior of such systems is modeled by a newly introduced class of Bernoulli GI/G/1 vacation models. For this model, when a vacation is completed and customers are present, a customer is served. When a customer has just been served and other customers are present, the server accepts a customer with fixed probability p or commences a vacation of prespecified random duration with probability 1 – p. Whenever no customers are present, a vacation is taken. When p = 0 or p = 1 this schedule reduces to the previously introduced single service schedule and the exhaustive service schedule, respectively. An analysis of all three schedules on a state space incorporating server vacations is presented using simple methods in the complex plane. It is shown that the recent decomposition results for exhaustive service extend to the more general class of Bernoulli schedules.
Interval and band estimation for curves with jumps
Authors: Gijbels Irène , Hall Peter , Kneip Aloïs
Published: July 2016

Jump points in curves arise when the conditions under which data are generated change suddenly, for example because of an unplanned change in a treatment. This paper suggests bootstrap methods for quantifying the error in estimates of jump points, and for constructing confidence intervals for jump points and confidence bands for the curve. These problems have the unusual feature that the sampling error of the jump-point estimator often has a highly non-normal distribution, which depends intimately on the distribution of regression errors. The methods are illustrated by a simulation study as well as by an application to data on the annual flow volume of the Nile river.
Restricted quasi-score estimating functions for sample survey data
Authors: Lin Y.-X. , Steel D. , Chambers R. L
Published: July 2016

This paper applies the theory of the quasi-likelihood method to model-based inference for sample surveys. Currently, much of the theory related to sample surveys is based on the theory of maximum likelihood. The maximum likelihood approach is available only when the full probability structure of the survey data is known. However, this knowledge is rarely available in practice. Based on central limit theory, statisticians are often willing to accept the assumption that data have, say, a normal probability structure. However, such an assumption may not be reasonable in many situations in which sample surveys are used. We establish a framework for sample surveys which is less dependent on the exact underlying probability structure using the quasi-likelihood method.
Transforming a random variable to a prescribed distribution: an application to school-based assessment
Authors: Brown Timothy C.
Published: July 2016

When can one find a smooth transformation of a random variable so that the transformed random variable has a specified distribution? If the random variable is continuous, the solution is elementary; if it is discrete, it may be impossible. In this paper, a simple method is given of transforming a random variable in a smooth way to match a specified number of quantiles of an arbitrary distribution. The problem arose from a request for a simple way of transforming marks given in school assessment so that the distribution of transformed marks matches the distribution of external assessment.
The marriage of statistics and seismology
Authors: Vere-Jones David
Published: July 2016

Daryl Daley has kindly invited me to write some prefatory words, autobiographical in character, to the collection of articles which follows. I am very happy to do this, but first let me express my appreciation of the efforts which Daryl, Peter Thomson, and the contributors have put into the making of this volume. It is a wonderful tribute, which I greatly appreciate. May I also take the opportunity to acknowledge the help of all of those colleagues, whether or not they have contributed directly to this volume, whose support, professional advice, knowledge, competence and companionship have made my years as statistician and tyro seismologist extremely rewarding. To all such, a big thank you.
Integrated processes and the discrete cosine transform
Authors: Davies Robert B.
Published: July 2016

A time-series consisting of white noise plus Brownian motion sampled at equal intervals of time is exactly orthogonalized by a discrete cosine transform (DCT-II). This paper explores the properties of a version of spectral analysis based on the discrete cosine transform and its use in distinguishing between a stationary time-series and an integrated (unit root) time-series.
Limit theorems for random mating in infinite populations
Authors: Ellison B. E.
Published: July 2016

This paper is concerned with the distribution of “types” of individuals in an infinite population after indefinitely many nonoverlapping generations of random mating. The absence of selection and mutation is assumed. The probabilistic law which governs the production of an offspring may be asymmetrical with respect to the “sexes” of the two parents, but the law is assumed to apply independently of the “sex” of the offspring. The question of the existence of a limit distribution of types, the rate at which a limit distribution is approached, and properties of limit distributions are treated.
On the offspring number distribution in a genetic population
Authors: Feldman M. W.
Published: July 2016

We consider a dioecious diploid population ofNindividuals,N1males andN2=N–N1females. The alleles will be represented byaandA, and the population reproduces according to the Wright scheme, that is, by random mating with non-overlapping generations.
On the survival of a gene in a subdivided population
Authors: Pollak Edward
Published: July 2016

A classical type of problem in population genetics is that of calculating the probability that a line descended from a particular gene will become extinct. In one problem of this sort, dealt with by Fisher (1922) and Haldane (1927), it is assumed that the population being studied is very large and that initially the number of genes of a particular type, say typeA, is small. These authors obtained the solution by the use of the theory of branching processes.
An application of stationary point processes to queueing theory and textile research
Authors: Rao J. Sudarsana
Published: July 2016

Throughout this paper we shall be interested in a certain integer-valued process n(t) (t ≧ 0) which is encountered in queueing theory and textile research.
Characterization of distributions by the identical distribution of linear forms
Authors: Eaton Morris L.
Published: July 2016

Throughout this paper, we shall write ℒ(W) = ℒ(Z) to mean the random variables W and Z have the same distribution. The relation “ℒ(W) = ℒ(;Z)” reads “the law of W equals the law of Z”.
Exponential ergodicity in derived Markov chains
Authors: Teugels Jozef L.
Published: July 2016

A general proposition is proved stating that the exponential ergodicity of a stationary Markov chain is preserved for derived Markov chains as defined by Cohen [2], [3]. An application to a certain type of continuous time Markov chains is included.
The two-dimensional Poisson process and extremal processes
Authors: Pickands III James
Published: July 2016

In recent years many applications of probability theory have involved such concepts as records, inter-record times and extreme order statistics. The results have generally been proved by diverse methods. In the present work a unifying structure is presented, which makes possible the simplification and extension of some of these results. The approach taken is to place all relevant processes on the same sample space. The underlying sample space is a homogeneous two-dimensional Poisson process.
Normal approximations to discrete unimodal distributions
Authors: Quinn B. G. , MacGillivray H. L.
Published: July 2016

Sufficient conditions are presented for the limiting normality of sequences of discrete random variables possessing unimodal distributions. The conditions are applied to obtain normal approximations directly for the hypergeometric distribution and the stationary distribution of a special birth-death process.
On fractional linear bounds for probability generating functions
Authors: Lefevre Claude , Hallin Marc , Narayan Prakash
Published: July 2016

The best upper and lower bounds for any probability generating function with meanmand finite variance are derived within the family of fractional linear functions with meanm. These are often intractable and simpler bounds, more useful for practical purposes, are then constructed. Direct applications in branching and epidemic theories are briefly presented; a slight improvement of the bounds is obtained for infinitely divisible distributions.
Necessary and sufficient conditions for stability of a bin-packing system
Authors: Courcoubetis C. , Weber R. R.
Published: July 2016

Objects of various integer sizes,o1, · ··,on,are to be packed together into bins of sizeNas they arrive at a service facility. The number of objects of sizeoiwhich arrive by timetis, where the components ofare independent renewal processes, withAt/t → λast → ∞. The empty space in those bins which are neither empty nor full at timetis called thewasted spaceand the system is declaredstabilizableif for some finiteBthere exists a bin-packing algorithm whose use guarantees the expected wasted space is less thanBfor allt.We show that the system is stabilizable if the arrival processes are Poisson and λ lies in the interior of a certain convex polyhedral cone Λ. In this case there exists a bin-packing algorithm which stabilizes the system without needing to know λ. However, if λ lies on the boundary of Λ the wasted space grows asand if λ is exterior to Λ it grows asO(t); these conclusions hold even if objects may be repacked as often as desired.
Linear dynamic errors-in-variables models
Authors: Deistler M.
Published: July 2016

Linear dynamical systems where both inputs and outputs are contaminated by errors are considered. A characterization of the sets of all observationally equivalent transfer functions is given, the role of the causality assumption is investigated and conditions for identifiability in the case of Gaussian as well as non-Gaussian observations are derived.
Local Gaussian modelling of stochastic dynamical systems in the analysis of non-linear random vibrations
Authors: Ozaki Tohru
Published: July 2016

Stochastic dynamical system models for non-linear random vibrations are considered and their discrete-time version, non-linear time series models are introduced using the local Gaussian modelling method. Some computational problems and implications of the present method in non-linear time series analysis are discussed.
ANOVA models with random effects: an approach via symmetry
Authors: Speed T. P.
Published: July 2016

The standard ANOVA models with random effects for multi-indexed arrays of random variables with an arbitrary nesting structure on the indices are considered from the viewpoint of symmetry. It is found that the covariance matrix of such an array has sufficient symmetry to permit viewing the usual components of variance as a generalised spectrum and the linear models of random effects as a generalised spectral decomposition.
Optimal buffer allocation in a two-stage queueing system
Authors: Sparaggis Panayotis D. , Gong Wei-Bo
Published: July 2016

We study the buffer allocation problem in a two-stage cyclic queueing system. First, we show that transposing the number of buffers assigned to each queue does not affect the throughput. Second, we prove that the optimal buffer allocation scheme, in the sense of maximizing the system's throughput, is the one for which the absolute difference between the number of buffers, assigned to each queue, is minimized, i.e., it becomes either 0 or 1. This optimal allocation is insensitive to the general-type service-time distributions. These two distributions may be different and service times may even be correlated.
Heavy Tails of Discounted Aggregate Claims in the Continuous-Time Renewal Model
Authors: Tang Qihe
Published: July 2016

We study the tail behavior of discounted aggregate claims in a continuous-time renewal model. For the case of Pareto-type claims, we establish a tail asymptotic formula, which holds uniformly in time.
Asymptotic behaviour of continuous time, continuous state-space branching processes
Authors: Grey D. R.
Published: July 2016

Results on the behaviour of Markov branching processes as time goes to infinity, hitherto obtained for models which assume a discrete state-space or discrete time or both, are here generalised to a model with both state-space and time continuous. The results are similar but the methods not always so.
ZOONOTIC ENCOUNTERS AT THE SLAUGHTERHOUSE: PATHWAYS AND POSSIBILITIES FOR THE CONTROL OF CYSTIC ECHINOCOCCOSIS IN NORTHERN MOROCCO
Authors: Bardosh Kevin Louis , Berbri Ikhlass El , Ducrotoy Marie , Bouslikhane Mohammed , Ouafaa Fassi Fihri , Welburn Susan C.
Published: July 2016

This study traces the biosocial dynamics of Echinococcus granulosus – a zoonotic tapeworm spread between dogs, livestock and people – at slaughterhouses in Morocco. One of the most important parasitic zoonoses worldwide, this neglected cestode is responsible for a debilitating, potentially life-threatening, human disease and significant livestock production losses. Transmission can be interrupted, among other ways, by restricting dogs from eating cyst-infected livestock viscera. Recent epidemiological studies in Sidi Kacem province, northern Morocco, found that government-operated slaughterhouses were ‘hotspots’ for hydatid cysts in livestock and infection in dogs. An ethnographic approach was used to compliment these studies, exploring ‘how’ and ‘why’ cysts were being openly discarded. All seven visited slaughterhouses had low levels of hygiene, oversight and infrastructure. This was described locally as perpetuating a sense of ‘chaos’ that normalized (un)hygienic practices and justified the ignoring of state rules and regulations. However deference to ‘poor’ infrastructure, both physically and symbolically, served to under-emphasize local institutional logics, which were mediated by prevailing risk perceptions, economic practices and local socio-political norms. These included inter-departmental government relationships, the motivation of veterinary technicians, the political lobbying of butchers and market-based mitigation strategies. The study shows the importance of understanding E. granulosus from a biosocial perspective, and the need for more long-term, participatory and integrated ‘One Health’ approaches for neglected zoonotic diseases.
COMMUNITY CO-DESIGNED SCHISTOSOMIASIS CONTROL INTERVENTIONS FOR SCHOOL-AGED CHILDREN IN ZANZIBAR
Authors: Person B. , Knopp S. , Ali S. M. , A’kadir F. M. , Khamis A. N. , Ali J. N. , Lymo J. H. , Mohammed K. A. , Rollinson D.
Published: July 2016

Top-down biomedical interventions to control schistosomiasis in sub-Saharan Africa have had limited success, primarily because they fail to engage with the social, political, economic and ecological contexts in which they are delivered. Despite the call to foster community engagement and to adapt interventions to local circumstances, programmes have rarely embraced such an approach. This article outlines a community co-designed process, based upon Human-Centered Design, to demonstrate how this approach works in practice. It is based on initial work undertaken by social science researchers, public health practitioners and community members from the Zanzibar Islands, Tanzania, between November 2011 and December 2013. During the process, 32 community members participated in a qualitative and quantitative data-driven workshop where they interpreted data on local infections from S. haematobium and co-designed interventions with the assistance of a facilitator trained in the social sciences. These interventions included the implementation of novel school-based education and training, the identification of relevant safe play activities and events at local schools, the installation of community-designed urinals for boys and girls and the installation of community-designed laundry-washing platforms to reduce exposure to cercariae-contaminated fresh water. It is suggested that the a community co-designed process, drawing from Human-Centered Design principles and techniques, enables the development of more sustainable and effective interventions for the control of schistosomiasis.
Effects of multisensory integration processes on response inhibition in adolescent autism spectrum disorder
Authors: Chmielewski W. X. , Wolff N. , Mückschel M. , Roessner V. , Beste C.
Published: July 2016

Background

In everyday life it is often required to integrate multisensory input to successfully conduct response inhibition (RI) and thus major executive control processes. Both RI and multisensory processes have been suggested to be altered in autism spectrum disorder (ASD). It is, however, unclear which neurophysiological processes relate to changes in RI in ASD and in how far these processes are affected by possible multisensory integration deficits in ASD.

Method

Combining high-density EEG recordings with source localization analyses, we examined a group of adolescent ASD patients (n = 20) and healthy controls (n = 20) using a novel RI task.

Results

Compared to controls, RI processes are generally compromised in adolescent ASD. This aggravation of RI processes is modulated by the content of multisensory information. The neurophysiological data suggest that deficits in ASD emerge in attentional selection and resource allocation processes related to occipito-parietal and middle frontal regions. Most importantly, conflict monitoring subprocesses during RI were specifically modulated by content of multisensory information in the superior frontal gyrus.

Conclusions

RI processes are overstrained in adolescent ASD, especially when conflicting multisensory information has to be integrated to perform RI. It seems that the content of multisensory input is important to consider in ASD and its effects on cognitive control processes.
‘It makes you think anything is possible’: Representing diversity in music theory pedagogy
Authors: Davidson Robert , Lupton Mandy
Published: July 2016

This paper critiques a traditional approach to music theory pedagogy. It argues that music theory courses should draw on pedagogies that reflect the diversity and pluralism inherent in 21st century music making. It presents the findings of an action research project investigating the experiences of undergraduate students undertaking an innovative contemporary art music theory course. It describes the students’ struggle in coming to terms with a course that integrated composing, performing, listening and analysing coupled with what for many was their first exposure to the diversity of contemporary art music. The paper concludes with suggesting that the approach could be adopted more widely throughout music programs.
CONTACT, CONTEXT, AND COLLOCATION
Authors: Kennedy Terry Kristen M.
Published: July 2016

This study uses a mixed-effects model to examine the acquisition of targetlike patterns of phonological variation by 17 English-speaking learners of French during study abroad in France. Naturalistic speech data provide evidence for the incipient acquisition of a phonological variable showing sociostylistic variation in native speaker speech: the elision of /l/ in third-person subject clitic pronouns (il vient[il vjɛ̃] ∼ [i vjɛ̃] “he is coming”). Speech data are compared and correlated with the results of asocial network strength scaledesigned for the study abroad learning context. Results demonstrate that phonological variation patterns are acquired in a predictable order based on token type and collocation and that social networks with native speakers are statistically significant predictors of phonological variation patterns.
Kinetic Heating in Relation to Structural Integrity
Authors: James David
Published: July 2016

This short paper is confined to a discussion on one aspect of the Structural Design of Supersonic Transports. It is chosen because it covers the area in which the impact of supersonics is probably most critical from the structural point of view, i.e. kinetic heating.

It is of utmost importance that the significance of kinetic heating is not exaggerated. Adequate attention must be paid to assessing the degree to which past experience is relevant if excess weight is to be avoided.

It is in this direction that the discussion is aimed.

In view of the need to keep the paper short, attention is concentrated on the Mach 2 class of aeroplane constructed largely of aluminium alloy. Much of what is said will also have relevance to the Mach 3 class of aeroplane.
Large Rocket Engines for Space Vehicles and Missiles
Authors: Hoffman S. K.
Published: July 2016

The history of Rocketdyne's activity in the field of large liquid-propellant rocket engines is outlined in a chronological review of applicable United States ballistic and space projects. Within security limitations, major rocket engine component improvements and general fabrication techniques are discussed. The trends and new developments in liquid-propellant rocket engine designs are presented and a forecast of future engines is made.
Meteorological Measurements in the Upper Atmosphere
Authors: Robinson G. D.
Published: July 2016

It should not be necessary to explain the presence of a meteorologist at a symposium on any aspect of upper atmosphere research. Meteorologists understand their science to comprise the dynamics, thermodynamics and chemistry of atmospheres, wherever atmospheres occur. They are happy to have the facilities for observation and even experiment in the higher layers of the earth's atmosphere which rocket and satellite vehicles begin to provide, but can point to a considerable body of existing knowledge obtained by other means.
Nuclear Power in Flight
Authors: Baxter A. D.
Published: July 2016

The 1,190th lecture to be given before the Society—and the 44th Main Lecture to be held at a Branch centre—" Nuclear Power in Flight", by Professor A. D. Baxter, M.Eng., F.R.Ae.S., M.I.Mech.E., at that time Director and Chief Executive, Rockets and Nuclear Power, and now Executive Director (Engineering), The de Havilland Engine Co. Ltd., was given under the auspices of the Swindon Branch of the Society on 2nd February 1961. Mr. S. R. Hughes, A.F.R.Ae.S., A.F.I.A.S., Chairman of the Swindon Branch, opened the meeting by welcoming the President of the Society, Dr. E. S. Moult, C.B.E., B.Sc.Eng., F.R.Ae.S., M.I.Mech.E., and other distinguished guests attending this first Main Society Lecture to be given at Swindon. Dr. Moult, who presided for the rest of the meeting, expressed his great pleasure at being present on this occasion. Introducing the lecturer, the President said that Profesor Baxter, as he was still known, was educated at Liverpool University and from 1930-34 served an apprenticeship with the Daimler Company. During this time he took his pilot's “A” licence and was commissioned in the R.A.F.O. After a year as Research Engineer with the Institution of Automobile Engineers, he joined the Royal Aircraft Establishment in 1935 as a Technical Engineer working on gas turbine research and later, rocket propulsion. From 1947 to 1950 he was Superintendent, Rocket Propulsion Dept., R.A.E., and then joined the new College of Aeronautics as Professor of Aircraft Propulsion, becoming Deputy Principal of the College also, in 1954. In 1957 Professor Baxter left the College of Aeronautics to join The de Havilland Engine Co. Ltd. as Chief Executive, Rocket Engine Division.
A Subjective Experiment with Helicopter Noises
Authors: Robinson D. W. , Bowsher J. M.
Published: July 2016

Following upon an experiment on the subjective effects of jet engine noise we have recently undertaken a similar experiment, this time on the subjective aspects of helicopter noise. The purpose of the earlier experiment was to determine the reliability of various methods of rating based on spectrum analysis, so far as comparisons between jet- and piston-engined aircraft are concerned. The main objective of the present experiment was to find if these methods are applicable to the pulsating types of noise characteristic of helicopters.
Some Thrust Control Methods For Solid Propellant Rockets
Authors: Pearce K. W.
Published: July 2016

Solid propellant rockets are now being used in vehicles whose flight paths are mostly outside the atmosphere and need close control. Engines for such vehicles must not simply provide accelerating thrust but should also be capable of having the direction, magnitude and duration of this thrust altered at will. Some devices and methods for accomplishing such control have been described elsewhere, see Refs. 1, 2, 3 and 4. I shall attempt both to discuss these in more detail and to introduce others which I believe have not yet been mentioned.
Vibration of Centrally Stiffened Rectangular Plate
Authors: Kirk C. L.
Published: July 2016

Natural frequencies of free flexural vibration of rectangular plates may, in many cases, be considerably increased by attaching to the plate one or more elastic stiffening ribs parallel to one edge, or by casting or machining the plate and stiffeners integrally.

Hoppmann has determined by a semi-empirical method the natural frequencies of an integrally stiffened simply-supported square plate, using the concept of a homogeneous orthotropic plate of uniform thickness having elastic compliances which are equivalent to those of the stiffened plate. Filippov has obtained the exact solution for the fundamental frequency of a simply-supported square plate having a number of equally spaced stiffeners and has considered the effect of point loads applied to the stiffeners in a direction perpendicular to the plane of the plate.
A Review of Current Developments in Agricultural Aviation
Authors: Ripper W. E.
Published: July 2016

The increasing importance of agricultural aviation can best be judged by a table setting out the area treated in the U.S.A., U.S.S.R., U.K. and other countries, which was compiled from recent publications. Fig. 1 shows how important a sector of aviation agricultural aviation has become.

Like other aircraft operations, agricultural aviation is not particularly profitable. Therefore a certain amount of work has gone into economic studies and into development work on methods for improving the service rendered to agriculture in order to improve the economy of aircraft operation.
Flow Fields Connected by Moving Waves
Authors: Woods W. A.
Published: July 2016

The significance of joining flow regions with moving waves is discussed and a generalised treatment of simple, one dimensional, moving shock waves is presented analytically and in chart form. The problem is next considered with the shock wave replaced by different types of non-steep waves and their corresponding charts given.

Possible and impossible flow configurations are examined and the results presented in the form of a diagrammatic table. An alternative shock wave chart is described in an appendix and worked examples, showing the use of the charts, are presented.
Stress Distribution Around Edge Slits in a Plate Loaded in Tension —the Effect of Finite Width of Plate
Authors: Dixon J. R.
Published: July 2016

Two-dimensional photoelastic tests have been carried out on uni-axially loaded flat-plate specimens with two collinear edge slits, to investigate the effect of finite plate width on the elastic stress distribution. It was found that the effect of slitlength/ plate-width ratio on the elastic stress concentration at the end of the edge slit of lengthlwas virtually the same as that for a central slit of length2lin a plate of the same width, and could be adequately expressed by existing theories.
Rain Erosion Aspects of Aircraft and Guided Missiles
Authors: Fyall A. A. , King R. B. , Strain R. N. C.
Published: July 2016

“All-weather” operational requirements have added considerably to aircraft and missile design problems as the effects of various meteorological hazards, predominantly rain, are aggravated by high speed flight. The problem of rain erosion is reviewed with regard to the functional requirements of the components, the flight plan of the vehicle and the occurrence of rain over the geographical terrain of operation. The factors affecting rain erosion characteristics such as type of material, surface finish, shape of component, speed and rainfall intensity are discussed and empirical data derived. The influences on the problem of radar limitation in rain, the probability of rain occurrence and the effect of wind and wind-shear are mentioned. Details given of equipment for the simulation of rain erosion are concerned principally with the R.A.E. “whirling arm” and rocket runway high speed sled techniques. Correlation of test results from these facilities and flight tests are briefly discussed.

Degree of erosion of a material is defined in relation to the particular application of the material and details are given of the characteristics of numerous materials, both metals and non-metals. The utilisation of these materials for such applications as radomes, transparencies, high temperature materials, de-icing systems are briefly discussed together with methods of extending the rain erosion “life” of materials by design or by use of protective coatings.
Lessons Gained in Helicopter Air Traffic Control from Federal Aviation Agency Activities
Authors: Fitzek R. A.
Published: July 2016

I should like to express my gratitude to the Society, on behalf of the Federal Aviation Agency of the United States, for the opportunity of participating in this meeting.

Before speaking of the lessons gained in Helicopter Air Traffiic Control some background information is necessary on the types of helicopter operations which are being conducted in the United States.

As in many countries, helicopter operations are conducted by both the military services and civil operators. The military operations are primarily those of a tactical training nature and search and rescue work. Civil helicopter operations are conducted mainly for transport and utility purposes.

In addition to numerous civil air taxi operators providing transport by helicopter, we have three commercial scheduled helicopter airlines; New York Airways, Chicago Airways, and Los Angeles Airways. These three helicopter airlines serve the aerodromes and residential communities in the metropolitan areas of the cities from which they derive their names. Utility helicopter flying includes such services as forest fire fighting, insecticide spraying of farm crops, power line inspection, and construction work, just to name a few.
On the Equivalence of the Galerkin and Rayleigh-Ritz Methods
Authors: Singer Josef
Published: July 2016

The Galerkin method for the approximate solution of elasticity problems (see e.g.Ref. 1) is usually presented as an alternative to the Rayleigh-Ritz method. The main distinction between the two methods is stated to be that the former begins with an equation of equilibrium, whereas the latter begins with a total potential energy expression. The two methods are not always equivalent, and the conditions for equivalence are given in Duncan's lucid presentation of the method (Refs. 2 and 3, which unfortunately have been out of print for some time). These conditions, however, are generally omitted from discussions of the Galerkin method, and it is the purpose of this note to re-emphasise them in a slightly different form.
Crime in Aircraft
Authors: Wilberforce Richard
Published: July 2016

The Inaugural Lecture of the Air Law Group of the Society “Crime in Aircraft” by the Hon. Mr. Justice Wilberforce was given in the Lecture Theatre, 4 Hamilton Place, London W.l. on 31st October 1962. Mr. L. A. Wingfield, M.C., D.F.C., A.R.Ae.S., Solicitor to the Society, presided. Introducing the lecturer Mr. Wingfield said that the Hon. Mr. Justice Wilberforce was a Judge of the Supreme Court (Chancery Division). He had also been the leader for the United Kingdom at no less than four diplomatic Conferences on Air Law—Geneva in 1948, Rome in 1952, The Hague in 1955 and Guadalajara in 1961—he had also been the Chief United Kingdom member of the Legal Committee of I.C.A.O.; to find a more distinguished contribution to air law than Sir Richard's would be difficult.

The Society's Air Law Group arose indirectly from a lecture to the Society in January 1961 by Mr. H. Caplan on “The Law versus Science in Aeronautics”. The Group was formed in September of that year, and since its inception Sir Richard had acted as Chairman. One of the first tasks tackled by the Group had been the study of the draft convention adopted by I.C.A.O. at Munich in September 1959 on offences occurring on board aircraft. At the request of the Ministry of Aviation the Steering Committee of the Group, voicing an independent view, reported on the draft convention.

Not only was this the Group's inaugural lecture, it was also the first occasion in the Society's 96 years that it had been addressed by one of Her Majesty's Judges.

Before beginning his lecture the Hon. Mr. Justice Wilberforce congratulated the Society on its initiative in forming the Air Law Group and paid tribute to the Secretary of the Society, Dr. A. M. Ballantyne, T.D., B.Sc, F.R.Ae.S., F.A.I.A.A., Hon.F.C.A.S.I., for the work he had done and the assistance he had given in organising the Group.

The following report is taken from the tape recording of the lecture.
The Development of the “Radio Altimeter–Trailing Static” Method of Measuring Aircraft Static Pressure Errors
Authors: McDaniel John D.
Published: July 2016

During the flight development of a high altitude bomber some difficulty was encountered in the measurement of static pressure error, due, in the main, to the relatively high ceiling and Mach number limits of the aircraft.

There was found to be a need for a method that was self-contained within the test aircraft, allowing a complete flexibility of test conditions. This report describes the method evolved which requires the use of ai radio altimeter and a low speed trailing static head.
Agricultural Aviation in the U.S.S.R.
Authors: Smirnov E. A.
Published: July 2016

The 21st lecture to be given before the Agricultural Aviation Group of the Society, “Agricultural Aviation in the U.S.S.R.” by Mr. E. A. Smirnov of Aeroflot, was given in the Lecture Theatre on 17th October 1962. Air Commodore A. H. Wheeler, C.B.E., M.A., F.R.Ae.S., Chairman of the Agricultural Aviation Group Committee, presided.

Introducing the lecturer, Air Commodore Wheeler said how grateful the Group was to Mr. Smirnov for agreeing to talk on this subject which was of great interest to the members of the Group. Mr. Smirnov served as a pilot in the Second World War and afterwards went to the Construction and Technology Institute in Moscow and became a scientific engineer at the Engineering and Scientific Institute of Aeroflot. He was Station Manager at London Airport for two years, later becoming General Manager of Aeroflot in the United Kingdom. Mr. Smirnov was a Companion member of the Society.
Stresses in a Plate Pierced by two Unequal Circular Holes
Authors: Davies G. A. O. , Hoddinott J. R.
Published: July 2016

The problem of two identical circular holes in an infinite sheet has been solved by Ling using bipolar co-ordinates and taking advantage of the double symmetry.

The case of any two unequal holes is of interest in that one common situation is that of a small circular hole close to a relatively larger one. In this case it is tempting merely to use the classical single hole solution, first for the larger hole and then for the small hole situated in the “uniform” stress field produced by the larger one. The accuracy of this simple method of superposition is examined.

The notation of Muskhelishvili is followed where the problem consists of finding two functions of the complex variable z=x+iy which are analytic in the region and satisfy the boundary conditions on both holes and at infinity.
On the Buckling of Thin Walled Tubes Under Axial Impact
Authors: Redwood R. C.
Published: July 2016

In some recent impact tests in which thin walled square tubes were loaded axially to produce large scale buckling of the walls, a difference occurred between the behaviour at high speeds and that at low speeds. The tubes, standing on an anvil, were struck by a falling steel tup which was guided to strike the tubes approximately axially. At the higher speeds damage was confined to the impact end of the tube, with a short wavelength buckle adjacent to the end and longer waves farther from the end. At lower speeds damage occurred at either end, or, jn many cases, in the central region of the tube. The wavelengths in these low speed tests were longer than those occurring at high speeds. These two types of behaviour are illustrated on Fig. 1.
The Choice of a Hodograph Boundary for Contracting Ducts
Authors: Gibbincs J. C.
Published: July 2016

A recent paper on the potential incompressible flow through two-dimensional contracting ducts raises some interesting points that are relevant to the hodograph technique for solving this problem.

In this paper, Lau obtains a contraction shape by placing a source in a uniform flow that is contained in a doubly infinite strip. The resulting flow pattern is sketched in Fig. 1. The flow is from a region of unit velocity to one of velocity R, where R is the contraction ratio. A streamline, intermediate in position between ψ = 0 and ψ=1.0, is adopted as the contraction profile.
Sir Frederick Handley Page: The Man and his Work
Authors: Lachmann G. V.
Published: July 2016

I feel greatly honoured having been invited to deliver the Second Handley Page Memorial Lecture and, indeed, grateful for the opportunity to pay tribute to a great Englishman and aeronautical pioneer, who for 40 years was my personal friend and, for over 30, my Chief. As no other man, he has decisively influenced the course of my life.
The Development of Legislation for Hovercraft
Authors: Barrowclouch A. R.
Published: July 2016

I proprose to consider some of the problems which arise in fitting the hovercraft into our legal system and to suggest in a tentative way, not so much the solution to these problems, but rather the lines on which I feel that solutions should be approached. It is unnecessary to emphasise that the views I express are entirely my own; for whose else could they be?

Now it will be noticed that the title of this lecture, “The Development of Legislation for Hovercraft”, assumes that legislation will be necessary to deal with hovercraft; but a moment’s thought, or a single example, will show how well justified the assumption is.
Legal Liabilities Arising out of Crop Spraying Operations
Authors: Brooks J. L.
Published: July 2016

This subject is one that seems to have received more consideration in agricultural, legal and insurance circles in the U.S.A., Australia and New Zealand than in England which is, perhaps, understandable in view of the differences in terrain, crops and aircraft operating facilities between the various countries.

There are a number of American legal reports touching upon crop spraying liability and several Australian and New Zealand cases, but few English cases. Certainly there have been a number of claims in this country for damage to persons and property arising from crop spraying operations, but it is seldom that these claims proceed to trial and perhaps the reasons for this will become apparent as the various aspects of liability are considered.
Some Considerations Affecting the Design and Operation of Supersonic Civil Transports
Authors: Courtney A. L.
Published: July 2016

From some points of view this is a difficult time to be giving a general talk on supersonic civil transports. The pioneering period is over, and the really interesting lectures when bright new ideas and shapes were discussed have mostly all been given. The design of the Anglo-French “Concord” is now pretty well settled and a fair amount of information about it has been made public. The information which has not been made public is withheld for obvious reasons of commercial security, and I am therefore caught between not giving too much away on the present Concord and repeating a lot which has already been said.
The Development of French Helicopters
Authors: Morain Paul H. L.
Published: July 2016

Five years have now elapsed since the last report on helicopter development in France was given by Francois Legrand, then Chief of the Rotary Wing Section at the “Service Téchnique de l'AéYonautique”. At that time, Sud-Aviation had been in existence for two years and the production of helicopters was at an early stage, with almost only French operators. In 1963, Mr. Legrand became Sud-Aviation helicopter chief designer; since 1959, the position of France in the helicopter production world has asserted itself considerably.
Some Factors Affecting Fares
Authors: Courtney A. L.
Published: July 2016

As one of the first speakers at this Symposium, with no particular axe to grind and no panacea to offer, I think my most useful contribution will be to provide some sort of backcloth for later contributors. I therefore propose to discuss the relative effects of some of the factors affecting the design efficiency and operating costs of short-range aircraft so as to try to arrive at some impression of what are the more important things to concentrate on. This has been done before at various times, but I think it is worth doing again as a starting point for this discussion. The views expressed are my own and not necessarily those of RAE or MoA.

I shall be talking mainly in terms of generalised long-term effects, and the factors and exchange rates quoted will be the overall effects on an aircraft still in the design stage, assuming that it is re-optimised if necessary as each factor is varied. Without implying any preference one way or the other, I will assume a conventional wing-plus-body design with jet or fan engines; other contributors will be dealing with the possibilities of all-wing layouts and with the question of propellers versus jets for short ranges. I assume that we are thinking in terms of stage lengths of the order of 250-500 miles, and the costs and exchange rates will be quoted for this sort of range; so far as relative sensitivities are concerned the precise value is not very important once one is in this bracket (as compared with 1000-1500 miles, for instance).