bluuebunny/crossref_metadata_2025 huggingface dataset:
Selective interaction of a Poisson and renewal process: first-order stationary point results
Authors: Lawrance A. J.
Published: July 2016

The simple stationarity of a previously derived equilibrium process of responses in a renewal inhibited stationary point process is established by deriving the joint distribution of the number of responses in contiguous intervals in the process. For a renewal inhibited Poisson process the variancetime function of the process is obtained; the distribution of an arbitrary between-response interval and the synchronous counting distribution are also derived following analytic justification of the required results. These results strengthen earlier results in the theory of stationary point processes. Three other point processes arising from the interaction are briefly discussed.
One-to-one functions on the positive integers
Authors: Ailam Gedalia , Tata Mahabanoo N.
Published: July 2016

Let {an
} be an increasing sequence of positive integers and let be the family of all functions from the positive integers into the positive integers, which satisfy

Assume that are random functions with probabilities

and for all n > 1

and 0 elsewhere, i.e., all permissible values of f, given the past, are equally likely.
Finite queues in parallel under a generalized channel selection rule
Authors: Hall William K. , Disney Ralph L.
Published: July 2016

Consider a queueing system of the following type: random arrivals enter the system, where they are assigned to one of r service channels. Each arrival is then serviced and discharged from the system. The classical results for this class of problems are based upon systems where customers join a single queue and then are randomly assigned to an available server from this queue. (See, for instance, Takács (1962).)
Traffic light queues as a generalization to queueing theory
Authors: Mine Hisashi , Ohno Katsuhisa
Published: July 2016

Fixed-cycle traffic light queues have been investigated by probabilistic methods by many authors. Beckmann, McGuire and Winsten (1956) considered a discrete time queueing model with binomial arrivals and regular departure headways and derived a relation between the stationary mean delay per vehicle and the stationary mean queue-length at the beginning of a red period of the traffic light. Haight (1959) and Buckley and Wheeler (1964) considered models with Poisson arrivals and regular departure headways and investigated certain properties of the queue-length. Newell (1960) dealt with the model proposed by the first authors and obtained the probability generating function of the stationary queue-length distribution. Darroch (1964) discussed a more general discrete time model with stationary, independent arrivals and regular departure headways and derived a necessary and sufficient condition for the stationary queue-length distribution to exist and obtained its probability generating function. The above two authors, Little (1961), Miller (1963), Newell (1965), McNeil (1968), Siskind (1970) and others gave approximate expressions for the stationary mean delay per vehicle for fixed-cycle traffic light queues of various types. All of the authors mentioned above dealt with the queue-length.
On the relation between customer and time averages in queues
Authors: Brumelle Shelby L.
Published: July 2016

Little [8] gave conditions sufficient to obtain the formula L = λW, where L is the time average queue size, W is the expected wait in queue, and λ is the arrival rate of customers. This formula is applicable to a very general class of queuing models and is one of the most useful results in queuing theory.
Optimal search for a randomly moving object in a special case
Authors: Hellman Olavi
Published: July 2016

Search for an object whose motion is a symmetrical two-dimensional diffusion process is considered in the case where a given amount of search of constant density is distributed, during a given interval of time, over a fixed circular area. An expression for the probability of detection of the object during this interval of time is derived in the special case where the location of the object at time zero is given. The application of this expression would involve numerical work.
A note on the characterization of a U-shaped probability density function
Authors: Ghosh P. , Shanbhag D. N.
Published: July 2016

In this note a characterization for a U-shaped probability density function is given using a well-known result for unimodal distributions due to Khinchine. As a corollary of this result, a characteristic property based on moments is found.
More bounds on the expectation of a convex function of a random variable
Authors: A. Ben-Tal , Hochman E.
Published: July 2016

Jensen gave a lower bound to Eρ(T), where ρ is a convex function of the random vector T. Madansky has obtained an upper bound via the theory of moment spaces of multivariate distributions. In particular, Madansky's upper bound is given explicitly when the components of T are independent random variables. For this case, lower and upper bounds are obtained in the paper, which uses additional information on T rather than its mean (mainly its expected absolute deviation about the mean) and hence gets closer to Eρ(T).

The importance of having improved bounds is illustrated through a nonlinear programming problem with stochastic objective function, known as the “wait and see” problem.
Strategy stability in complex randomly mating diploid populations
Authors: Hines W. G. S.
Published: July 2016

A class of Lyapunov functions is used to demonstrate that strategy stability occurs in complex randomly mating diploid populations. Strategies close to the evolutionarily stable strategy tend to fare better than more remote strategies. If convergence in mean strategy to an evolutionarily stable strategy is not possible, evolution will continue until all strategies in use lie on a unique face of the convex hull of available strategies.

The results obtained are also relevant to the haploid parthenogenetic case.
A connection between the limit and the maximum random variable of a branching process in varying environments
Authors: Klebaner F. C. , Schuh H.-J.
Published: July 2016

We show for a certain class of Galton–Watson branching processes in varying environments (Zn
)
n
that moments of the maximum random variable sup
n

Zn/Cn
exist if and only if the same moments of lim
nZn/Cn
exist, where Cn
is a sequence of suitable constants.
The transposition replacement policy with a partial memory
Authors: Nelson Peter R.
Published: July 2016

Consider as a model for any serial list a bookshelf with books B
1, ···, Bn. At each unit of time book is demanded with probability pi
and is replaced one position to the left of where it was removed (or in the same position if it is already at the left-hand end). If this transposition is made only when Bi
has been demanded k times in a row, we show that the average position of the next book demanded is a monotone decreasing function of k.
A renewal look at switching rules in the MIL-STD-105D sampling system
Authors: Yang Grace L.
Published: July 2016

A sampling system, MIL-STD-105D, used in quality control consists of three sampling plans with different acceptance probabilities used in turn for lot inspection. The decision to switch plan is based on the history of the lot acceptance records and a set of stopping rules. We derive the performance measure, average outgoing quality (AOQ), of this sampling system from a renewal process in which AOQ is expressed in terms of the moments of the stopping times. The renewal approach is simpler than that of the Markov chain generally used in computing AOQ for an infinite sequence of lots; it also provides a formula for AOQ for a finite sequence of lots.
On a decomposition result for a class of vacation queueing systems
Authors: Loris-Teghem Jacqueline
Published: July 2016

We consider a single-server infinite-capacity queueing sysem with Poisson arrivals of customer groups of random size and a general service time distribution, the server of which applies a general exhaustive service vacation policy. We are concerned with the steady-state distribution of the actual waiting time of a customer arriving while the server is active.
Interconnected population processes
Authors: Renshaw E.
Published: July 2016

This paper investigates the effect of migration between two colonies each of which undergoes a simple birth and death process. Expressions are obtained for the first two moments and approximate solutions are developed for the probability generating function of the colony sizes.
A heavy traffic result for the finite dam
Authors: Blomqvist Nils
Published: July 2016

The steady state content Z of a finite dam in discrete time is investigated for small absolute values of the expected net input and correspondingly large values of the dam capacity. It is shown that under general conditions Z has, asymptotically, a truncated exponential distribution, a result that supplements previous knowledge in queueing theory.
On a generalization of gamma processes
Authors: Çinlar Erhan
Published: July 2016

We introduce a class of increasing processes with independent increments that reduce to gamma processes under the further condition of stationarity. Each such process can be reduced to a simple gamma process by a stochastic integral transformation. Applications to deformation laws of materials such as concrete are mentioned.
Extinction of non-homogeneous Galton-Watson processes
Authors: Jirina Miloslav
Published: July 2016

In the paper the problem of the extinction of non-homogeneous Galton-Watson processes with one type of particle is studied. It is proved that the process becomes extinct if the expectations of the process do not converge to a limit (finite or infinite). If the expectations have a finite limit, then simple necessary and sufficient conditions for the extinction are proved. The general case remains open; however two more sufficient conditions which are also necessary under some restrictions are given.
An immigration super-critical branching diffusion process
Authors: Radcliffe J.
Published: July 2016

This paper is an extension of Davis (1965) by allowing immigration. Mean square convergence is proved for a random variable in a branching diffusion process allowing immigration.
On branching processes allowing immigration
Authors: Yang Y. S.
Published: July 2016

Continuous time one-type branching processes allowing immigration are considered. The invariant measure, which is shown to be unique, is exhibited. From this, a condition for positive recurrence similar to that of Heathcote's in the discrete time case is obtained. For the critical discrete time case, Seneta's sufficient condition for positive recurrence is improved to give a necessary and sufficient condition.
An extension of Erlang's formulas which distinguishes individual servers
Authors: Chaiken Jan M. , Ignall Edward
Published: July 2016

For a particular kind of finite-server loss system in which the number and identity of servers depends on the type of the arriving call and on the state of the system, the limits of the state probabilities (as t → ∞) are found for an arbitrary service-time distribution.
On record values and record times
Authors: Shorrock R. W.
Published: July 2016

A correspondence between record values and independent increment point processes is established. The asymptotic behaviour of record value sequences is studied, and results on the asymptotic behaviour of record times (for continuous F) are obtained as special cases. The joint law of the kth record value and the kth record time is also derived.
Clone-selection and optimal rates of mutation
Authors: Eshel Ilan
Published: July 2016

The paper employs methods of multitype branching processes to evaluate the probability of survival of mutable clones under environmental conditions which are unfavorable to the original parent of the clone. When other factors are taken to be constant, the long-term survival probability of a clone is implicitly demonstrated as a function of the intrinsic rate of mutation carried by this clone. The existence of a mutation rate which maximizes clone survival probability is shown and the effects of environmental deterioration on this optimal rate are studied. Finally, rigorous quantitative results are obtained for the classical situation of a Poisson distribution of offspring numbers. These results are then applied to the biological problem of indirect selection (Eshel (1972)).
An M/G/1 model with finite waiting room in which a customer remains during part of service
Authors: Rosenlund Stig I.
Published: July 2016

An M/G/1 service system with finite waiting room is studied. A customer is served by one server in phases, during some of which a place in the waiting room is occupied. The busy period length distribution is obtained from a system of integral equations leading to a linear system in Laplace-Stieltjes transforms. An asymptotic expression, for large intensity of arrival, for the expectation of this length is given. An efficiency measure giving the long run customer loss ratio is obtained. The model is shown to apply to an inventory and a container traffic problem.
A Poisson limit theorem for incomplete symmetric statistics
Authors: Berman M. , Eagleson G. K.
Published: July 2016

Silverman and Brown (1978) have derived Poisson limit theorems for certain sequences of symmetric statistics, based on a sample of independent identically distributed random variables. In this paper an incomplete version of these statistics is considered and a Poisson limit result shown to hold. The powers of some tests based on the incomplete statistic are investigated and the main results of the paper are used to simplify the derivations of the asymptotic distributions of some statistics previously published in the literature.
On the best-choice problem when the number of observations is random
Authors: Petruccelli Joseph D.
Published: July 2016

We consider the problem of maximizing the probability of choosing the largest from a sequence of N observations when N is a bounded random variable. The present paper gives a necessary and sufficient condition, based on the distribution of N, for the optimal stopping rule to have a particularly simple form: what Rasmussen and Robbins (1975) call an s(r) rule. A second result indicates that optimal stopping rules for this problem can, with one restriction, take virtually any form.
Proportional intensities and strong ergodicity for Markov processes
Authors: Scott Mark , Isaacson Dean L.
Published: July 2016

By assuming the proportionality of the intensity functions at each time point for a continuous-time non-homogeneous Markov process, strong ergodicity for the process is determined through strong ergodicity of a related discrete-time Markov process. For processes having proportional intensities, strong ergodicity implies having the limiting matrix L satisfy L · P(s, t) = L, where P(s, t) is the matrix of transition functions.
Continuity and convergence of the percolation function in continuum percolation
Authors: Sarkar Anish
Published: July 2016

We consider a percolation model on the d-dimensional Euclidean space which consists of spheres centred at the points of a Poisson point process of intensity ?. The radii of the spheres are random and are chosen independently and identically according to a distribution of a positive random variable. We show that the percolation function is continuous everywhere except perhaps at the critical point. Further, we show that the percolation functions converge to the appropriate percolation function except at the critical point when the radius random variables are uniformly bounded and converge weakly to another bounded random variable.
On crossing times for multidimensional walks with skip-free components
Authors: Borovkov K. A.
Published: July 2016

The paper deals with processes in (or ), one of whose components is skip-free. We obtain identities for distributions of hitting times for the components of the process generalizing the well-known one for the one-dimensional case. These relations reflect the fact that in this case spatial and time coordinates play, in some sense, symmetric roles. They turn out to be useful for solving several problems. For example, they allow us to find the distribution of the number of jumps of the process, which fall in a fixed set before the skip-free component of the process hits a fixed level. Examples are given showing how our results can be applied to models in branching processes, queueing, and risk theory.
A solvable model for a finite-capacity queueing system
Authors: Giorno V. , Negri C. , Nobile A. G.
Published: July 2016

Single–server–single-queue–FIFO-discipline queueing systems are considered in which at most a finite number of customers N can be present in the system. Service and arrival rates are taken to be dependent upon that state of the system. Interarrival intervals, service intervals, waiting times and busy periods are studied, and the results obtained are used to investigate the features of a special queueing model characterized by parameters (λ (Ν –n), μn). This model retains the qualitative features of the C-model proposed by Conolly [2] and Chan and Conolly [1]. However, quite unlike the latter, it also leads to closed-form expressions for the transient probabilities, the interarrival and service probability density functions and their moments, as well as the effective interarrival and service densities and their moments. Finally, some computational results are given to compare the model discussed in this paper with the C-model.
A sharp upper probability bound for the occurrence of at least m out of n events
Authors: Platz Ole
Published: July 2016

Consider a fixed set of n events. Let S
1 denote the sum of the probabilities of occurrence of each event and S
2 the sum of the probabilities of occurrence of each of the pairs of events. Using a dual linear programming method a sharp upper bound is derived for the probability of occurrence of at least m out of the n events when S
1 and S
2 are given. The bound improves one of the inequalities obtained by Sathe et al. (1980).
A note on survival models under a Markov process
Authors: Griffith William S. , Srinivasan C.
Published: July 2016

A number of extensions of the class preservation results in the Esary, Marshall and Proschan shock model have been investigated by various authors in recent years, most recently by Ghosh and Ebrahimi. In this note, generalizations are obtained using different methods for the IFR and NBUE cases when the shocking process is a regular continuous-time Markov process with stationary transition probabilites.
Boundary coiflets for wavelet shrinkage in function estimation
Authors: Johnstone Iain M. , Silverman Bernard W.
Published: July 2016

There are standard modifications of certain compactly supported wavelets that yield orthonormal bases on a bounded interval. We extend one such construction to those wavelets, such as ‘coiflets', that may have fewer vanishing moments than had to be assumed previously. Our motivation lies in function estimation in statistics. We use these boundary-modified coiflets to show that the discrete wavelet transform of finite data from sampled regression models asymptotically provides a close approximation to the wavelet transform of the continuous Gaussian white noise model. In particular, estimation errors in the discrete setting of computational practice need not be essentially larger than those expected in the continuous setting of statistical theory.
Estimation for discretely observed diffusions using transform functions
Authors: Kelly Leah , Platen Eckhard , Sørensen Michael
Published: July 2016

This paper introduces a new estimation technique for discretely observed diffusion processes. Transform functions are applied to transform the data to obtain good and easily calculated estimators of both the drift and diffusion coefficients. Consistency and asymptotic normality of the resulting estimators is investigated. Power transforms are used to estimate the parameters of affine diffusions, for which explicit estimators are obtained.
Extremal problems for regenerative phenomena
Authors: Kingman J. F. C.
Published: July 2016

This paper explores the possibility of a calculus of variations powerful enough to prove inequalities for the p-functions of regenerative phenomena such as that conjectured by Davidson and proved by Dai. It is shown that this is unlikely to be achieved by compactifying the space of standard p-functions, and a more promising approach is that of working in a compact subspace. The analysis leads to a class of candidate p-functions which contains all the maxima of general functionals.
Representations of continuous-time ARMA processes
Authors: Brockwell Peter J.
Published: July 2016

Using the kernel representation of a continuous-time Lévy-driven ARMA (autoregressive moving average) process, we extend the class of nonnegative Lévy-driven Ornstein–Uhlenbeck processes employed by Barndorff-Nielsen and Shephard (2001) to allow for nonmonotone autocovariance functions. We also consider a class of fractionally integrated Lévy-driven continuous-time ARMA processes obtained by a simple modification of the kernel of the continuous-time ARMA process. Asymptotic properties of the kernel and of the autocovariance function are derived.
Point process convergence of stochastic volatility processes with application to sample autocorrelation
Authors: Davis Richard A. , Mikosch Thomas
Published: July 2016

The paper considers one of the standard processes for modeling returns in finance, the stochastic volatility process with regularly varying innovations. The aim of the paper is to show how point process techniques can be used to derive the asymptotic behavior of the sample autocorrelation function of this process with heavy-tailed marginal distributions. Unlike other non-linear models used in finance, such as GARCH and bilinear models, sample autocorrelations of a stochastic volatility process have attractive asymptotic properties. Specifically, in the infinite variance case, the sample autocorrelation function converges to zero in probability at a rate that is faster the heavier the tails of the marginal distribution. This behavior is analogous to the asymptotic behavior of the sample autocorrelations of independent identically distributed random variables.
A stochastic population process and its application to bubble chamber measurements
Authors: Brockwell P. J. , Moyal J. E.
Published: July 2016

A particle travels along the half-line [0,∞) in such a way that it has probability λδu + o(δu) of generating an event in any small element (u,u + δu) of its track. The particle is observed only in the line segment 0 ≦ u ≦ x and successive events occur at X
1, X
2, …, X
n (0 ≦ X
1 ≦ X
2 ≦ … ≦ X
n ≦ x) where X
1, …,Xn
are random variables and the number n of events in [0, x] is also random. The distances

constitute a finite univariate population process as defined by Moyal [1], the individuals being the distances Yi
with state space [0, x].
Asymptotic absorption probabilities for a Poisson process
Authors: Gallot S.
Published: July 2016

An expression is found (Theorem 1) for the probability that a sample function of a Poisson process never exceeds some given function and some examples are given.
A bound for the maximum of a number of random variables
Authors: Gallot S.
Published: July 2016

In this note, we refine an upper bound, established by P. Whittle, for the probability that the maximum of a number of random variables x
1, …, xn
is less than a given value C when

and

are given probabilities in terms of which the bound will be expressed.
On survival probabilities and extinction times for some branching processes
Authors: Pollak Edward
Published: July 2016

We consider branching processes for which the first three moments of the distribution of offspring exist. Let f(t) andz be, respectively, the generating function of the distribution of offspring and the smallest positive root of the equation f(t) = t. Then if M = f'(z) and fn
(t) is equal to the generating function of the distribution of nth generation descendants of a single individual, it is known that, quite generally, (z – fn
(0)) / Mn
tends toward a constant as n increases. A method is derived for obtaining upper and lower bounds for this constant, which gives an exact solution when there is a geometric distribution of offspring and good bounds when there are Poisson or negative binomial offspring distributions. With some further calculations, one can also obtain finite upper and lower bounds for the mean time to extinction of a line descended from an individual, given there is extinction. These bound apply even ifzis less than 1. Numerical values are given for the Poisson and negative binomial cases.
Distribution of the branching-process population among generations
Authors: Samuels M. L.
Published: July 2016

In a standard age-dependent branching process, let Rn
(t) denote the proportion of the population belonging to the nth generation at time t. It is shown that in the supercritical case the distribution {Rn
(t); n = 0, 1, …} has asymptotically, for large t, a (non-random) normal form, and that the mean ΣnRn
(t) is asymptotically linear in t. Further, it is found that, for large n, Rn
(t) has the shape of a normal density function (of t).

Two other random functions are also considered: (a) the proportion of the nth generation which is alive at time t, and (b) the proportion of the nth generation which has been born by time t. These functions are also found to have asymptotically a normal form, but with parameters different from those relevant for {Rn
(t)}.

For the critical and subcritical processes, analogous results hold with the random variables replaced by their expectations.
On the busy periods for the M/G/1 queue with finite and with infinite waiting room
Authors: Cohen J. W.
Published: July 2016

The Laplace-Stieltjes transform of the distribution of the busy period for the M/G/1 system with infinite waiting room can be obtained by using an argument from branching theory. In the present paper it is shown that by applying this argument it is rather easy to derive the expression for the joint distribution of the busy period and the maximum number of customers present simultaneously during this busy period for the M/G/1 system with infinite waiting room as well as the expression for the distribution of the busy period for the M/G/1 system with finite waiting room.
Random environment branching processes with equal environmental extinction probabilities
Authors: Raffety Donald C.
Published: July 2016

R-positivity theory for Markov chains is used to obtain results for random environment branching processes whose environment random variables are independent and identically distributed and whose environmental extinction probabilities are equal. For certain processes whose eventual extinction is almost sure, it is shown that the distribution of population size conditioned by non-extinction at time n tends to a left eigenvector of the transition matrix. Limiting values of other conditional probabilities are given in terms of this left eigenvector and it is shown that the probability of non-extinction at time n approaches zero geometrically as n approaches ∞. Analogous results are obtained for processes whose extinction is not almost sure.
NEGLECTED TROPICAL DISEASES IN BIOSOCIAL PERSPECTIVE
Authors: Parker Melissa , Polman Katja , Allen Tim
Published: July 2016

The term ‘neglected tropical diseases’ (NTDs) points to the need for a biosocial perspective. Although ‘diseases’ are widely understood as biological phenomena, ‘neglect’ is inherently social. Social priorities, social relations and social behaviour profoundly influence the design, implementation and evaluation of control programmes. Yet, these dimensions of neglect are, themselves, neglected. Instead, emphasis is being placed on preventive chemotherapy – a technical, context-free approach which relies almost entirely on the mass distribution of drugs, at regular intervals, to populations living in endemic areas. This article reflects on the processes which have enabled an NTD ‘brand’ identity to emerge, and it comments on a disquieting disengagement with some of the more critical insights about the consequences of mass drug administration. Building on the work of biosocial scholars studying other aspects of health and disease, a more adequate, evidence-based approach is delineated. Developing such an approach is an iterative process, requiring on-going engagement with both biological and social insights as they emerge. Considerable theoretical, methodological and political challenges lie ahead, but it is essential they are overcome, if the sustainable control of NTDs is to become a reality.
Neronianis Temporibus:The So-CalledArae Incendii Neronianiand the Fire of A.D. 64 in Rome's Monumental Landscape
Authors: Closs Virginia
Published: July 2016

This essay examines the evidence for the Domitianic ‘Arae Incendii Neroniani’, a presumed set of monumental altars dedicated to Vulcan in fulfilment of a vow dating back to the Neronian Fire ofa.d. 64. A close reading of the text of the dedicatory inscription creates a framework for exploring the larger historical and cultural context of these monuments, which offer a significant illustration of Flavian rhetoric concerning Rome's post-Neronian transformation. Reaffirming Julio-Claudian notions of civic identity, collective memory, and the ruler's privileged relationship with the gods, the Arae also constitute a conspicuous form of posthumous reproach to Nero.
The Application of the Schlieren-Interferometer to the Study of Supersonic Flow Around Unyawed Axi-Symmetric Bodies
Authors: Waterhouse J. F. , Spencer H. B.
Published: July 2016

This note describes our recent attempts to apply the schlieren-interferometer to the study of supersonic flow around axi-symmetric bodies at zero incidence, and in particular shows how the density field distribution for a cone has been derived.

Various optical techniques, e.g. shadowgraph, schlieren and interferometric, have been used in the study of gas flows where density changes are significant. In some instances, however, a qualitative investigation is insufficient and although it is possible to obtain quantitative data from most optical methods, the interferometer has proved, so far, to be the most valuable in this respect.
The Generation of Sound by Aerodynamic Means
Authors: Curle N.
Published: July 2016

A summary is given of some of the more important experimental results relating to the noise radiated from a cold subsonic turbulent jet. These are then related to the predictions of Lighthill's general theory of aerodynamic noise.
Integrated Flight Systems for Multi-Engined
Transport Rotorcraft
Authors: Sullivan N. , Simpson J. A.
Published: July 2016

Scheduled Transport flying has developed continuously and more or less logically over a period of more than thirty years to its present state of regularity. During this time various equipments have been introduced, to help the pilots in their task of flying from A and finding and landing at B in all weathers; and further equipments have been introduced to relieve the pilots of the considerable strain of simultaneously flying the aircraft and using these primary aids.

While many of these equipments have been brought to such a stage of usefulness and reliability as to be regarded as essential to flight safety, they have not encroached on the fundamental safety concept of:

Two pilots.

Adequate “engine out” performance.

Infallible airframe and flying controls.

Fuel reserve for diversion.
The Economics of Telecommunication Satellite Systems
Authors: Stratford Alan H.
Published: July 2016

I am taking as a starting point the basic assumption that the most immediate and feasible use for an earth satellite from an economic and commercial point of view is as a link in the existing world telecommunication system. This is a small part of the field of U.S. space programmes, but is the first application of satellite systems to be commercially viable. It is now uppermost in our minds and the tests to be made during this summer give immediate reality to the project.
Trends in unsteady aerodynamics
Authors: Jones W. P.
Published: July 2016

The Sixth Lanchester Memorial Lecture, “Trends in Unsteady Aerodynamics,” was given by Dr. W. P. Jones, M.A., D.Sc., F.R.Ae.S., F.A.I.A.A., of the National Physical Laboratory, on 22nd November 1962. Professor A. R. Collar, M.A., D.Sc, F.R.Ae.S., F.A.I.A.A., F.C.A.S.I., President-Elect, took the Chair for the President who was visiting the overseas Divisions.

Before the lecture, Professor Collar introduced Dr. William Greulick, Scientific Attaché U.S. Embassy, who presented the John Scott Award to Mr. J. W. Sparke, R.A.E., for his invention of the Visual Glide Path Indicator, in use at most major airports of the world and adopted as the U.S. Standard. Dr. Greulick gave a short history of the Award, which was founded by John Scott, a chemist from Edinburgh, in 1816 and given to the City of Philadelphia. Its premiums were for distribution among “ingenious men and women who made useful inventions” and the award was of a truly international character. It was now of the value of $1,000, with a copper medal and a scroll.

Professor Collar, introducing the Lecturer, said that Lanchester had been a great scientist, a musician, a poet and an engineer of distinction in a great number of fields. It was to him a pleasure and a privilege to preside on this occasion, especially as he himself had delivered the second Lanchester Lecture. He was delighted that Professor Schlichting and Professor Young, two other Lecturers in the series, were present. Dr. von Kantian and Monsieur Legendre, the two other Lanchester lecturers, regretted that they could not be present.

The Sixth Lecturer, Dr. W. P. Jones, was Superintendent of the Aerodynamics Division of the National Physical Laboratory. He had been educated at St. David's College, Lampeter, and at The Quee's College, Oxford. He had joined the N.P.L. staff in 1935, where Professor Collar was himself working at the time, and had been at Teddington since then, except for a year (1960-61) when he was the Jerome C. Hunsaker Visiting Professor at Massachusetts Institute of Technology. Dr. Jones had written a large number of scientific papers on aerodynamic problems related to flutter and aeroelasticity and was the Editor of the AGARD “Manual on Aeroelasticity,” a volume of great substance and interest.
The Aeronautical Industry in the Europe of Tomorrow
Authors: Bloch René
Published: July 2016

The Sixteenth Louis Bleriot Lecture, “The Aeronautical Industry in the Europe of Tomorrow,” was given in London in the Society's Lecture Theatre by Captain R. M. Bloch, F.N., F.R.Ae.S., A.F.A.I.A.A. Mr. B. S. Shenstone, M.A.Sc, F.R.Ae.S., F.A.I.A.A., F.C.A.S.I., President of the Society, was in the chair.

Introducing the Lecturer, the President reminded the audience that the Bleriot Lectures were given alternately in Paris and London. This year was London's turn and their lecturer was a Frenchman, Captain Rene Bloch. Captain Bloch had many duties: he was Assistant Director of Aeronautics for International Affairs in the French Ministry of Defence, he was the French Representative of the NATO Maritime Patrol Aircraft Steering Committee and Permanent Chairman of the Technical Sub-Committee. He was also French Co-Chairman of the Anglo-French Naval Aviation Committee. Captain Bloch had a number of degrees, including the diploma of the Ecole Polytechnique and he was an M.A. of Harvard. He was a Chevalier de la Legion d'Honneur, a Combatant Volontaire de la Resistance and he held the Medaille de la France Libre and the Medialle de l'Aeronautique. He was a member of A.F.I.T.A.E., an Associate Fellow of the American Institute of Aeronautics and Astronautics, a member of the Institute of Radio Engineers, New York and he had recently been elected a Fellow of the Royal Aeronautical Society. They would appreciate that Captain Bloch's background and experience was certainly wide enough for him to speak with authority on his subject—“The Aeronautical Industry in the Europe of Tomorrow.”
Aquaplaning on Runways
Authors: Gray W. E.
Published: July 2016

In the past few years pilots landing in very heavy rain, or just after it, have found their wheel-brakes ineffective due to the layer of water, and this has been called aquaplaning; the word is preferable to “hydroplaning” which already has a well-established meaning in a deep-water context. The nature of this phenomenon has been speculated upon by NASA since 1959 and by Mr. Gadd of the NPL in 1961 (see R.Ae.S. Journal, March 1963). The latter gives the impression that in Britain we are still speculating, but in fact we know quite a lot about it now; much has been described in an RAE Technical Note last November and this was added to at a Take-off and Landing Symposium at Farnborough in December 1962. These sources are being drawn upon here.
The Compressible Discharge Coefficient of a Borda Pipe and other Nozzles
Authors: Frost T. H.
Published: July 2016

Bragg, in ref. 1, gives a theoretical treatment for the variation of the discharge coefficient in compressible flow of any shaped nozzle with applied pressure ratio given one set of values. This shows that the discharge coefficient of any nozzle with a value less than unity at a pressure ratio approaching unity, rises continuously as the pressure ratio increases and reaches the maximum at a pressure ratio of infinity (zero back pressure). This is based on the assumption that the flow conditions at the Vena contracta are uniform and at unity Mach number once the applied pressure ratio is equal to/ or above the critical (sonic) value.
Some Reflections on Parachute Design, 1797-1837
Authors: Jackson S. B.
Published: July 2016

The casual reader might think that there is a mistake in the title of this paper, but the first authenticated descent by parachute was made in 1797 by Andre Jacques Garnerin in Paris. Subsequently, M. Garnerin also made the first parachute descent in England, in 1802, and some thirty-five years later Mr. Robert Cocking, then sixty-one years of age, made a descent in a parachute of a very different design. This descent resulted in his losing his life.

In the interim period between the two descents in England, considerable speculation arose about the designs. The authorities in “Aerostation” of the day put forward some remarkable hypotheses about the problems involved and it might perhaps be of interest to the many people who are now familiar with parachutes to read about them. It is no accident, of course, that the parachute first made a positive appearance at this time. Man had just learnt to free himself from the earth by means of hot air and gas balloons and thus the need for a means of escape was born.
Circular Plates with Bending Moments Applied at Several Points Along the Boundary
Authors: Gajendar N.
Published: July 2016

Nadai and Bassali have discussed problems concerning plates supported at several points. Timoshenko and Woinowsky-Krieger have studied circular plates supported at several points along the boundary. In the present note the author has obtained an analytical solution for the problem of circular plates with bending moments applied at several points along the boundary. Some particular cases are also considered.
Propelling Nozzle Research
Authors: Lewis W. G. E.
Published: July 2016

The current interest in supersonic transport aircraft makes it appropriate to consider the problems of propulsion nozzle systems for high speed flight. The discussion will be confined mainly to this field of activity.

In the absence of external drag and weight factors, the ideal configuration to maintain optimum thrust at all flight speeds would employ a mechanically variable area ratio nozzle. By such means the jet flow could be fully and properly expanded at all times.

A practical design to accommodate such variations is inherently complex, and so an alternative solution using aerodynamic techniques has been sought. It is necessary to remember that the success of whatever method is eventually chosen must rest on its ability to combine a high performance at cruise with very small loss during other critical phases of the flight plan.

This paper describes some of the results of a nozzle research programme aimed primarily at solving the above problem, with an attempt to explain the philosophy behind the aerodynamic techniques tried. Some discussion is given of the experimental difficulties in establishing a sufficiently accurate standard of measurement for design point performance. In a few chosen configurations experimental results have been extensively backed by theoretical studies.

The need to demonstrate off-design behaviour in the presence of an external flow field is stressed, with special reference to the misleading results often obtained from static tests.

Finally, some attention is given to the question of base bleed, with its repercussions on the installation of the propulsion nozzle in an aircraft.
Difficulties and Advantages of Supersonic Civil Transport—A Discussion
Authors: Shenstone B. S.
Published: July 2016

THE SST project is the largest, most expensive and most dubious project ever undertaken in the development of civil aircraft. It is dubious because of the concern about the side effects of supersonic flying on a regular basis, the main one being the sonic boom. Apparently the more one learns about the sonic boom, the more intractable it appears.

The project is unique in that in Europe it was instigated by, and financed by, the Governments for airlines and not by airlines. A similar, although not exactly the same, pattern is followed in the USA.

Another main characteristic of the SST is that no airline has ever asked for it, but the project existing has tempted a few airlines to put in tentative orders, which has encouraged other airlines out of fear to put in other orders.

The general run of technical unknowns is pretty well-known, one of them being how to get rid of the heat caused by the friction of the air at the high speeds involved. However, probably the greatest doubt lies in the improbability that the SST will be able to be profitable in operation. I agree that it is possible to make any given number of calculations on this matter, all with reasonable degrees of honesty, and half of them will show that airlines will make money and the other half will show the opposite. This is merely a measure of our lack of knowledge of these aircraft.
The Interaction of Demand and Supply
Authors: Williams A. T. , Longton P. A.
Published: July 2016

In the Introduction to the second paper in this series (September 1965 IOURNAL), a simple flow diagram illustrates the relationship between demand and supply for aircraft and air transport which is shown in Fig. 1.

Manufacturers supply airlines with aircraft from which a fleet is built. The airlines are thus faced with problems of capital investment and procurement programmes, which were discussed under the heading of fixed costs in the second paper.

The discussion of problems of fleet effectiveness and optimal utilisation begun in the second paper, and elaborated in the third (October 1965 JOURNAL), is continued in Section A of the present one.

Attention is then switched in Section B to the demand for air transport. On the basis of demand for transport of passengers and freight, airlines must determine routes, allocate frequencies to these routes, and prepare time-tables.

The paper concludes the discussion of Operational Research applied to airlines by summarising the models used in the series in the light of the aims specified in the first paper (August .1965 JOURNAL).
Private Enterprise in British Air Transport
Authors: Laker F. A.
Published: July 2016

The twenty-first British Commonwealth Lecture, “Private Enterprise in British Air Transport”, was given before the Society by F. A. Laker, ARAeS, on 14th October 1965 in the Lecture Theatre, 4 Hamilton Place, London W.1. The Chair was taken by the President, Sir George Gardner, KBE, CB, HonDSc, BSc, HonFRAeS. Introducing the Lecturer, Sir George said that after a brief start in automobile engineering, Mr. Laker had switched in 1938 to aircraft—with Short Brothers. He thought that Mr. Laker really came into prominence in 1947 when he formed Aviation Traders Ltd, and not long afterwards Air Charter Ltd, which later merged with the Airwork Group. Mr. Laker had kept on expanding his interests and formed British United Airways of which, as they knew, he was Managing Director. Mr. Laker was a qualified pilot, as well as an engineer and flew his own Cessna aircraft round the various bases of his organisation. He was also President of the Society of Licensed Aircraft Engineers and Technologists.
Recent Data on the Collapse of Spherical Caps under External Pressure
Authors: Klein Bertram
Published: July 2016

Recently additional tests have been performed to measure the external pressure necessary to collapse spherical caps. Bellinfante used plastic domes that were machined readily and accurately to final size. The Douglas test data shown in Fig. 1 are considered to be excellent. (2b is the base of the dome).

Thurston used aluminium caps that were chemically etched to final size. However, he intentionally put small dents at the apex. These initial distortions cause wide scatter in the test data as shown in Figs. 2(a) and 2(b). Examination of the recorded waviness reported -by Thurston indicates that the more perfect shells reached higher loads than the others. Note, for example, specimens 1, 6, 11, 16, 28, and 38. Also, usually the more wavy specimens exhibited the lower buckling loads. See specimens 4, 7, 9, 12, 17, 22, 27. Since Thurston's specimens were chemically etched to very thin gauges, the thickness variation could be significant. He does not report actual thickness variation in the shell, but states it could be about 15 per cent at worst.
A Suggestion for Compressible Flow Graphs for use in Subsonic Flow
Authors: Bradbury L. J. S.
Published: July 2016

The present re-look at compressible flow graphs arose during extensive testing of jet blowing models in low speed tunnels. In these tests, it is often necessary to calculate such quantities as jet thrusts, mass flow rates and velocities assuming isentropic expansion to the tunnel static pressure from the measured values of the stagnation pressure and temperature. These jet flows are usually compressible but subsonic and, in order to make these calculations, use has to be made either of Bernoulli's compressible flow equation or, alternatively, the extensive compressible flow graphs that are now available.
Solid Propellant Rocket Motors
Authors: Maxwell W. R. , Young G. H. S.
Published: July 2016

A solid propellant rocket motor consists essentially of a propellant charge in a container fitted with an expansion nozzle and igniter. Since, before a rocket motor can be designed, it is necessary to have some knowledge of the properties of the propellant to be used, a description will first be given of the propellants which are currently available.
A Chest Injury in an Isolated Geo-politically Sensitive Area: Questions in Management
Authors: Rahdon Richard A. , Bridgewater Franklin H.G. , Harris Mark A.
Published: July 2016

The reported case of a stab wound to the chest occurred in an isolated area with no specialized surgical care available. The need for transport and specifically by air, introduced particular questions in management. On a humanitarian basis and in line with its mandate, the Peace Monitoring Group, a United Nations endorsed entity in Bougainville, Papua New Guinea, provided transport to a facility with an appropriate standard of care. The questions of need for patient evacuation and chest drainage, with the timing of this maneuver are considered.