bluuebunny/crossref_metadata_2025 huggingface dataset:
The Use of High Strength Aluminium Alloys
Authors: James D.
Published: July 2016

The object of this paper is to present some of the user experience with the high strength aluminium alloys. The somewhat tarnished reputation of the Aluminium-Zinc-Magnesium alloys is undoubtedly due to their premature introduction; the very substantial weight savings offered by the relatively high static strength values proving too strong an attraction at the end of the war-time era dominated by short term considerations.

It will be appreciated that there is a wide range of alloys in this family. Table I lists the composition ranges of typical French, American and British specifications together with a proprietary alloy, of German origin, which is of particular interest. Manufacturers have their own favoured compositions within the permitted ranges. Fig. 1 shows diagrammatically the wide variation in percentage of the principal alloying elements zinc, magnesium and copper.
On the Effective “Length” of Two-Dimensional Contracting Ducts
Authors: Gibbings J. C.
Published: July 2016

The note by W. T. F. Lau upon the effective “length” of two-dimensional contracting ducts has raised further points of interest.

Lau's paper presents three different criteria which can control a contraction length. Of these three, the second and third, that respectively are based upon the approach of the centre-line velocity to its asymptotic value and upon the approach of the flow to uniformity, were compared in ref. 1. The first criterion that is based upon the approach of the boundary slope to zero is not in general identical with the second.
Technical Workings and Future Trends within IATA
Authors: Gilmore J. L.
Published: July 2016

Every Time I speak of “IATA” or use the term, I speak of it and its activity as a corporate body of member airlines. It is the member airlines of IATA who make and agree policies and accordingly it should be understood that it is never a separate entity.

IATA acts under direction, it is neither cartel nor employers’ association, nor is it charlatan in character. It has been maligned, misunderstood, misinterpreted, and yet there is little evidence that it has deviated from its aims and objectives—in one sentence—to ensure that all air traffic moves with the greatest possible safety, speed and efficiency and with the utmost economy for both airline and public.
The Royal Aero Club of the United Kingdom
Authors: Blake J. H.
Published: July 2016

While not of the same venerable age as the Royal Aeronautical Society, the Royal Aero Club can lay claim to a respectable antiquity having celebrated its golden jubilee on 24th September 1961. Registered on 29th October 1901, the Aero Club antedated a potential rival by two days. As it was by a very short time the earliest, so for many years it continued the only, authority on the practice of the art of flying, and still reigns supreme in many aspects of sporting and private aviation.

While many of the detailed aspects of the work grew inevitably, over the years, into separate sports with their own organisations, affiliated to the parent Club, the basic responsibilities of looking after the interests and promoting the well-being of private flying in this country have never left us.
Cylindrical Shell Flutter—Theory and Experiment
Authors: Johns D. J.
Published: July 2016

Despite the fact that there have been few reported instances of the flutter of circular, cylindrical, iso-tropic shells, there still remains a challenge to the analyst to derive a theory which will correlate with the available experimental data.
The State of Affairs in the Army
Authors: McCullagh F. M.
Published: July 2016

The Purpose of Army light aircraft, fixed-wing and helicopter, is to help ground units to carry out their normal tactical task more effectively. Therefore the main roles are:

Reconnaissance.

Fire support.

Exercise of command.

Tactical movement.

Logistic support.

For special-to-arm tasks, light helicopters are integrated into certain major units of the Royal Armoured Corps, Royal Artillery, Royal Engineers, Royal Signals and Infantry. The aircraft must be capable of living in the field and be easy to maintain. Aircraft strengths in these units vary from six in an air squadron of the Royal Armoured Corps, to three in an air platoon in an infantry battalion.
Acting upon User Experience—Civil and Military Systems Compared
Authors: Lockwood-Goose B.
Published: July 2016

To Enable a Design Authority to act upon User Experience, full and accurate information is required about the defect as soon as possible after it has occurred.

A skin crack in an aircraft structure, the loss of a turbine blade in a jet engine or excessively high brush wear in a generator, are all defects. The reasons for them being defects can be quite different in each case. One can therefore readily see that to solve these defects the designer needs to know not only everything about the failure, but also the environment (in the broadest possible sense) that led to the failure
Some Thoughts on Contracting for Reliability
Authors: Smedley A. W.
Published: July 2016

I Would like to emphasise at the outset that the title of this short paper is “Some thoughts on contracting for reliability”, and that what I say does not necessarily represent the official policy of my Company, if indeed a company can have any very firm official policy on a subject which is amenable to so many and varied methods of treatment. For this same reason I am not attempting to recommend any particular treatment of the problem, but rather to talk around some aspects of the matter, and to try to consider how some equitable incentive method of contracting to produce a defined standard of reliability might be applied.
On the Selection of a Root of a Quadratic Equation Applied to a Problem in Gas Dynamics
Authors: Woods W. A. , Daneshyar H.
Published: July 2016

An account of the solution of a quadratic equation associated with a gas dynamic problem is given. Numerical examination of the equation Indicated that a conditional statement was required In a computer programme to determine the sign to be used in front of a square root. The necessity for this conditional statement was examined by studying a general quadratic equation. The study has also led to the formulation of a rule on the selection of a “desired root” of a quadratic equation.
Air Transport Auxiliary: Its Place in Aviation History
Authors: Wills P. A.
Published: July 2016

Air Transport Auxiliary (ATA) came into existence soon after the outbreak of war in September 1939. Its flag was finally hauled down on 30th November 1945. In these six years it grew from an idea in the mind of Gerard d'Erlanger to an organisation employing at its peak in 1944, 550 male pilots, 108 women pilots, 109 flight engineers and a ground staff of about 2800, a total of around 3500 people.

Experience leads me to the conclusion that the coefficient of relative man-power (and hence economic) efficiency of a specialised civilian as opposed to a necessarily unspecialised Service organisation is between 3 and 5, hence that ATA released for more direct operational war services between 9000 and 15000 men and women.
Helicopter Noise
Authors: Davidson I. M. , Harcest T. J.
Published: July 2016

Nowhere in the literature of helicopter noise can one find a general understanding; only isolated, inconsistent, and often inadequately documented facts. These could, of course, be reviewed but hardly with profit; it is easier to ask critical questions of nature than of previous investigators.

For fundamental reasons the helicopter in its present state of development is not in fact matched to the bulk, low-cost transport of passengers. But for equally good reasons the phenomena of aerodynamically generated noise now bid fair to banish from inhabited localities all other forms of vertical take-off and landing aircraft so that, if a city-centre to city-centre aircraft transport system is ever to be practicable, it will most probably be based on some metamorphosis of the helicopter.
Buckling of Orthotropic Circular Plates
Authors: Pandalai K. A. V. , Patel Sharad A.
Published: July 2016

This Note is concerned with the axisymmetric buckling of orthotropic circular plates. A circular plate fabricated with radial and/or circumferential reinforcements may be idealised as an orthotropic plate of uniform thickness h having different material properties in the radial and circumferential directions.
A Study of the Flow Field Associated with a Steadily-Rolling Slender Delta Wing
Authors: Harvey J. K.
Published: July 2016

In this paper an experiment is described in which a detailed study was made of the flow field associated with a slender sharp-edged delta wing which was rolling steadily at zero angle of attack to an air stream. The investigation was made by performing two pressure surveys: first , one of the static pressure acting on the wing’s surface and second by measuring the total-head distribution in the neighbourhood of the wing. From the former the local rolling-moment coefficients, Clp, are evaluated and these are compared with the predictions for attached flow, thus assessing the contributions to the forces acting on the wing which arise as a consequence of the leading-edge separations. The second set of surveys is used to construct a picture of the flow-field details and this is compared with that known to occur on a similar wing when it is set at an angle of attack to the airstream. One interesting finding is that the secondary separation which appears to cause the discrepancy between the theoretical predictions and the measurements made on slender wings at incidence, is absent in this configuration and thus it is concluded that these data could be used for a more meaningful test of the theory.
Subsonic Adiabatic Flow in a Duct of Constant Cross-Sectional Area
Authors: Ward Smith A. J.
Published: July 2016

Starting from the momentum integral equation an analysis is made of fully-developed flow in a straight pipe. This analysis shows the assumptions implicit in the one-dimensional theory of adiabatic constant-area flow with friction. For conditions of practical interest the approximations associated with the use of the one-dimensional flow theory are shown to be small.

Flow with a developing velocity profile and flow in a bend are then analysed. Introducing approximations revealed in the analysis of fully-developed flow, a simple relation is obtained between the variation of mean flow properties along the duct under incompressible and compressible flow conditions. This relation may be written in the same form as the corresponding relation derived using the one-dimensional flow theory. In a similar manner to one-dimensional flow theory, the relation is readily extended to apply over a series of components of constant cross-sectional area.

The results of the analysis are also presented in terms of static and total pressure loss coefficients. This form of presentation demonstrates that there are appreciable effects of Mach number, on the pressure loss coefficients, where they are often assumed to be small.

The analysis does not enable the variation of the mean flow properties to be calculated ab initio. Its application is to be found in problems where a knowledge of the performance of a component, or series of components, is required under compressible flow conditions, the performance under incompressible flow conditions already being available from theoretical or experimental data.

A comparison of predicted and experimental data for flow in bends and flow in combinations of duct components shows good agreement over much of the subsonic speed regime.
The Behaviour and Effects of Laminar Separation Bubbles on Aerofoils in Incompressible Flow
Authors: Ward Julian W.
Published: July 2016

A survey of information on laminar separation bubbles and their effect on the stalling characteristics of aerofoils is presented. It is shown that there are two principal kinds of bubbles and that their existence can be predicted. It is believed that their behaviour may be related to the kind of boundary layer transition process present.

It is intended that a second part of this paper will describe the characteristics of aerofoils at Reynolds numbers typical of model aircraft and show how the observed phenomena are related to the behaviour of laminar separation bubbles.
Computer Applications in the Development of Efficient Aircraft Structures
Authors: Taig I. C.
Published: July 2016

The emergence of electronic computers has brought about a revolution in the analysis of aircraft structures in the past decade which is now generally accepted throughout the Industry. But the major impact of computers on design has, in my opinion, not yet been realised and I hope, in this short paper, to show how powerful a tool they can become in the hands of imaginative design engineers. The direct benefits to the designer lie in the ability of the computers to perform large amounts of routine arithmetic in a short space of time. This capability enables us to obtain an insight into structural behaviour and to consider the influence of the aircraft environment and design alternatives from the earliest stages of design. By the development of general purpose computer programmes for handling routine calculations the structural designer can be freed from much of the laborious calculation associated with complex structures and he is able to devote more time to creative work. An even more important indirect benefit is the basic re-thinking of design processes which is necessary in order to reduce them to routine arithmetic. We begin to realise that many aspects of efficient design such as continuity, cost and weight can be introduced as quantitative parameters instead of relying on intuitive compromise.
Light and Executive Aircraft and Their Future Prospects in the United Kingdom
Authors: Robertson F. H.
Published: July 2016

The 55th Main Lecture to be given at a Branch centre, “Light and Executive Aircraft and Their Future Prospects in the United Kingdom,” by F. H. Robertson, A.F.R.Ae.S., Chief of Preliminary Design, Short Bros, and Harland Ltd., was held under the auspices of the Christchurch Branch on 12th December 1962. Mr. E. W. J. Gray, F.R.Ae.S., President of the Christchurch Branch, opened the proceedings by welcoming the President and Secretary of the Society and visitors from the Society's branches at Luton, Bristol and Cheltenham as well as visitors from Shoreham. Mr. Gray then asked the President, Mr. B. S. Shenstone, M.A.Sc, F.R.Ae.S., F.A.I.A.A., F.C.A.S.I., to preside for the rest of the meeting.

Introducing the lecturer, the President said that Mr. Robertson had spent five years with Vickers-Armstrongs Ltd., three in the works and two in the D.O., and then joined Hawker Aircraft in 1934 as a junior draughtsman; in 1936 he had gone to Aeronca Aircraft Ltd. for a year and in 1937 had joined Miles Aircraft Ltd. as senior draughtsman, becoming Chief of Experimental Design. From 1946-1952 he had been with Saunders-Roe Ltd., where he became Chief Project Engineer, and in 1952 had joined Short Bros, and Harland Ltd. After several years as Chief Project Designer, he became the Company's Chief Designer, Light Aircraft in 1959. He was now Chief of Preliminary Design. He was sure that Mr. Robertson was known to many of them, either personally or from things he had written, and they would know that he rarely said anything with which they could all agree. He thought that what Mr. Robertson would say in his lecture would be of the same order.
The Pilot's Point of View
Authors: Miles E. C.
Published: July 2016

In 1962 the passenger fatal accident rate was less than one passenger fatality per 100 million passenger miles. This is a figure which can be used to demonstrate the safety of flying relative to other forms of transport.

I am not going to discuss the merits of the criterion of “passenger miles.” Whatever one says about it the rate achieved last year does demonstrate a notable improvement on the pioneer days of aviation when the airline passenger achieved a reputation of daring by accepting the risks then present.
Instrument Aids for Take-off
Authors: Fearnside K.
Published: July 2016

The take-off manoeuvre is described in outline and the safety requirements applicable to this phase of flight are briefly reviewed.

A more detailed inspection of the take-off manoeuvre reveals some of the difficulties which confront the pilot and indicates the type of additional information with which he should be provided.

Means of providing such information and the problem of measuring the necessary quantities are discussed and this leads to a description of the range of equipment currently being developed and under consideration by Smiths Aviation Division.

This includes: —

(i) A ground run indicator

(ii) A ground run predictor

(iii) A pitch rate indicator

(iv) A take-off director.

Finally, some thoughts are presented on the subject of instrument displays and the problem of incorporating the required additional information into existing flight systems.
Runway Slipperiness and Slush
Authors: Horne Walter B. , Leland Trafford J. W.
Published: July 2016

A review is made of recent research in the United States relating to runway slipperiness and to slush-drag or fluid-drag effects on aircraft ground performance. The formation of fluid spray and its drag effects on aircraft are traced from spray origin at the intersection of the tyre and runway to impingement on the aircraft over the complete aircraft ground-velocity range. Six manifestations of tyre hydroplaning are presented and discussed: fluid-drag peak, tyre spin-down, loss of aircraft directional stability, loss of aircraft braking traction, suppression of bow wave, and progressive detachment of the tyre footprint from the fluid-covered runway surface as ground speed is increased. A convenient formula for estimating tyre-hydroplaning speed is indicated to be

where Vp=hydroplaning speed, knots

p=tyre-inflation pressure, lb/sq in.

Comparison with available experimental data is shown. The effects of fluid viscosity and density on runway slipperiness are discussed. The effects of some runway-surface textures, tyre-tread patterns, and aircraft landing-gear wheel arrangements on slipperiness are described. The paper also includes indications of areas of interest that need further study.
Rotorcraft Work at the Aeroplane and Armament Experimental Establishment
Authors: Poole J.
Published: July 2016

The A. & A.E.E. has been associated with rotorcraft in this country almost from their earliest days. For example, the records show that a C30A Autogiro was evaluated at Martlesham Heath in 1935. After the outbreak of war responsibility for development work in the rotary wing field was assumed by the Airborne Forces Establishment (later the Airborne Forces Experimental Establishment) and the accounts of such developments as the Rotachute and the airborne jeep have since become well known. In 1945 the A.F.E.E. was declared to be the official testing establishment for prototype helicopters and this responsibility has remained until the present time. The A.F.E.E. was merged in 1951 with the A. & A.E.E., becoming the Airborne and Helicopter Division of the latter Establishment.
Approximate Trajectories for Maximum Range
Authors: Raybould Brian
Published: July 2016

On reading the paper by D. J. Bell in the February edition of the Journal, I noticed that there was no mention of an adaptation of the energy height approach to solutions of maximum range trajectories. I was surprised to find no documentation concerned with this approach and would like to indicate this technique which I have used several times.
A New Formula for Pressure Versus Flow Deflection at Hypersonic Speeds
Authors: Opatowski T.
Published: July 2016

Analytical studies involving the pressure on inclined surfaces in hypersonic flow are made difficult by the lack of an explicit and simple relationship connecting the pressure p with the flow deflection angle 8. The various existing relationships are either too complicated or valid only over a very limited range.
Growth of The Royal Aeronautical Society
Authors: Wingfield L. A.
Published: July 2016

On A recent visit to New Zealand in September 1965, I enjoyed the privilege of attending, as Solicitor to the Society, a meeting of the New Zealand Division Council. Any visitor from the Society to Commonwealth countries is welcomed warmly, and must bring a message from the Old Country. Feeling so remote, they are hungry for any news of any sort. For lack of better material I based my talk to them on my personal association with the Society over the past 45 years.

Such a period of years covers much of the Society's struggle for recognition and retention of its position as the leading technical and scientific Aeronautical body. In this I have been privileged to help.
Some British Contributions to Aerodynamics
Authors: Stephens A. V.
Published: July 2016

A Comprehensive review of British contributions to aerodynamics would fill many volumes and take years to compile. For while some aspects of the science are embarrassingly well documented—every library possesses the monumental reports of the Aeronautical Research Council from 1909 onwards and the no less compendious Journals of the Society—other aspects are hardly illuminated at all.

Progress in aerodynamics has flowed in three main streams springing from the work of, first the research establishments and universities, second design offices and flight sections of the aircraft industry and third, the flying schools of the RAF.
Early Days. Memories of People and Places
Authors: Fage A.
Published: July 2016

Some of my recollections relate to the Aerodynamics Division at the NPL and the ARC, so to refresh my memory of their origin I have referred to the First Report of the Advisory Committee for Aeronautics—later renamed Aeronautical Research Committee—for the year 1909–10. It states there that this Committee was appointed on 30th April 1909, that it was to deal with the scientific study of the problems of flight with a view to their practical solution, and that the NPL was to organise, at Teddington, a special department to research and experiment on problems submitted to it; and further, that the Committee had put themselves in communication with the Aeronautical Society, the Royal Aero Club and the Aerial League with a view to rendering such assistance as might be possible in their work, that arrangements had been made at the Imperial College of Science and Technology for lectures in aeronautics for advanced students, and that two research scholarships in aeronautics had been founded.
Flying-Boats
Authors: Knowler Henry
Published: July 2016

This Account of Flying-Boats will deal mainly with British craft, and must necessarily have a personal approach from one who has been involved in flyingboat development over nearly the whole of its life history.

The prehistoric giant amphibians suffered eclipse through changing environment; similarly changed conditions in Aviation caused the still-evolving flying-boat to come to the end of its economic life. Probably concrete runways were the basic reason for the disappearance of flying-boats for both civil and military use, since landplanes were then no longer restricted either in size of efficiency or aerodrome conditions.
The Pioneers, God Bless 'Em
Authors: Russell G. C. D.
Published: July 2016

It is a remarkable calibre of man who is attracted to aviation. Those enthusiasts who formed Britain's Aeronautical Society 100 years ago were optimistic visionaries. For they had to wait 37 years before man's first controlled powered flight. Very few of the members then, in 1903, are alive today. And this is also true of those other optimists who, inspired by the Wrights’ great achievement, have led the world during the past 63 years into the astronautic age.
Reminiscences of 50 Years of Aviation
Authors: Walker C. C.
Published: July 2016

My Boyhood in the 1880's covered a period when there was not much general interest in the possibility of mechanical flight. It was looked upon as a rather fanciful idea best left to Jules Verne. There was, however, plenty of evidence that the obstacles to achieving it were not fundamental but mainly quantitative. Cayley, Stringfellow and Henson had produced results which need not have discouraged other seekers of progress. Hargreaves was producing elastic-driven models and one could buy Chinese elastic-driven toy helicopters which flew well for under 1s.
Test Flying During the Century
Authors: Penrose Harald
Published: July 2016

Those who have taken an untried aeroplane into the air for its first flight will know there is a quality about that moment which goes far beyond the coldly scientific assessment of which it is part. Here is a new creation which feels as though imbued with life, and one becomes its very heart and brain. It is a joint endeavour and a double proving—an embarkation into a beckoning unknown, however familiar the sky has become through previous flights in other aircraft.
Ejection Seats
Authors: Martin James
Published: July 2016

The invitation to write, a short article on Martin-Baker ejection seats for this Centenary Souvenir issue was a real problem. Due to space limitation it will only be possible to write a sketchy outline of the vast amount of effort which has gone into 21 years of research and development in connection with this work, and so it will not be possible on this occasion to write a detailed technical paper. I think it would be more interesting to recall some of the outstanding achievements of a pioneering nature.
Kalman-Bucy Filtering for Linear Systems Driven by the Cox Process with Shot Noise Intensity and Its Application to the Pricing of Reinsurance Contracts
Authors: Dassios Angelos , Jang Ji-Wook
Published: July 2016

In practical situations, we observe the number of claims to an insurance portfolio but not the claim intensity. It is therefore of interest to try to solve the ‘filtering problem’; that is, to obtain the best estimate of the claim intensity on the basis of reported claims. In order to use the Kalman-Bucy filter, based on the Cox process incorporating a shot noise process as claim intensity, we need to approximate it by a Gaussian process. We demonstrate that, if the primary-event arrival rate of the shot noise process is reasonably large, we can then approximate the intensity, claim arrival, and aggregate loss processes by a three-dimensional Gaussian process. We establish weak-convergence results. We then use the Kalman-Bucy filter and we obtain the price of reinsurance contracts involving high-frequency events.
On Ultimate Ruin in a Delayed-Claims Risk Model
Authors: Yuen Kam C. , Guo Junyi , Ng Kai W.
Published: July 2016

In this paper, we consider a risk model in which each main claim induces a delayed claim called a by-claim. The time of delay for the occurrence of a by-claim is assumed to be exponentially distributed. From martingale theory, an expression for the ultimate ruin probability can be derived using the Lundberg exponent of the associated nondelayed risk model. It can be shown that the Lundberg exponent of the proposed risk model is the same as that of the nondelayed one. Brownian motion approximations for ruin probabilities are also discussed.
On the Extinction of a Class of Population-Size-Dependent Bisexual Branching Processes
Authors: Xing Yongsheng , Wang Yongjin
Published: July 2016

In this paper, we study a class of bisexual Galton-Watson branching processes in which the law of offspring distribution is dependent on the population size. Under a suitable condition on the offspring distribution, we prove that the limit of mean growth-rate per mating unit exists. Based on this limit, we give a criterion to identify whether the process admits ultimate extinction with probability one.
On the Effect of Finite Buffer Truncation in a Two-Node Jackson Network
Authors: Sakuma Yutaka , Miyazawa Masakiyo
Published: July 2016

We consider a two-node Jackson network in which the buffer of node 1 is truncated. Our interest is in the limit of the tail decay rate of the queue-length distribution of node 2 when the buffer size of node 1 goes to infinity, provided that the stability condition of the unlimited network is satisfied. We show that there can be three different cases for the limit. This generalizes some recent results obtained for the tandem Jackson network. Special cases and some numerical examples are also presented.
Doob: A Half-Century on
Authors: Bingham N. H.
Published: July 2016

Probability theory, and its dynamic aspect stochastic process theory, is both a venerable subject, in that its roots go back to the mid-seventeenth century, and a young one, in that its modern formulation happened comparatively recently - well within living memory. The year 2003 marked the seventieth anniversary of Kolmogorov's Grundbegriffe der Wahrscheinlichkeitsrechnung, usually regarded as having inaugurated modern (measure-theoretic) probability theory. It also marked the fiftieth anniversary of Doob's Stochastic Processes. The profound and continuing influence of this classic work prompts the present piece.
Ageing Properties and Series System
Authors: Bon Jean-Louis , Illayk Abbas
Published: July 2016

The comparison of lifetimes has been treated extensively during the last decade. A wide variety of mathematical objects have been defined, which, in reliability theory, are used to quantify ageing properties. In this work, using the equilibrium variable, we give a new viewpoint on ageing properties. Moreover, we give new bounds on the moments of series systems.
Nonzero-sum games for continuous-time Markov chains with unbounded discounted payoffs
Authors: Guo Xianping , Hernández-Lerma Onésimo
Published: July 2016

In this paper, we study two-person nonzero-sum games for continuous-time Markov chains with discounted payoff criteria and Borel action spaces. The transition rates are possibly unbounded, and the payoff functions might have neither upper nor lower bounds. We give conditions that ensure the existence of Nash equilibria in stationary strategies. For the zero-sum case, we prove the existence of the value of the game, and also provide arecursiveway to compute it, or at least to approximate it. Our results are applied to a controlled queueing system. We also show that if the transition rates areuniformly bounded, then a continuous-time game is equivalent, in a suitable sense, to a discrete-time Markov game.
Portfolio optimization with unobservable Markov-modulated drift process
Authors: Rieder Ulrich , Bäuerle Nicole
Published: July 2016

We study portfolio optimization problems in which the drift rate of the stock is Markov modulated and the driving factors cannot be observed by the investor. Using results from filter theory, we reduce this problem to one with complete observation. In the cases of logarithmic and power utility, we solve the problem explicitly with the help of stochastic control methods. It turns out that the value function is a classical solution of the corresponding Hamilton-Jacobi-Bellman equation. As a special case, we investigate the so-called Bayesian case, i.e. where the drift rate is unknown but does not change over time. In this case, we prove a number of interesting properties of the optimal portfolio strategy. In particular, using the likelihood-ratio ordering, we can compare the optimal investment in the case of observable drift rate to that in the case of unobservable drift rate. Thus, we also obtain the sign of the drift risk.
Rarity and exponentiality: an extension of Keilson's theorem, with applications
Authors: Grübel Rudolf , Reich Marcus
Published: July 2016

We generalize a theorem due to Keilson on the approximate exponentiality of waiting times for rare events in regenerative processes. We use the result to investigate the limit distribution for a family of first entrance times in a sequence of Ehrenfest urn models. As a second application, we consider approximate pattern matching, a problem arising in molecular biology and other areas.
Asymptotic behaviour of critical controlled branching processes with random control functions
Authors: González M. , Molina M. , del Puerto I.
Published: July 2016

In this paper, we investigate the asymptotic behaviour of controlled branching processes with random control functions. In a critical case, we establish sufficient conditions for both their almost-sure extinction and for their nonextinction with a positive probability. For some suitably chosen norming constants, we also determine different kinds of limiting behaviour for this class of processes.
Processor-sharing and random-service queues with semi-Markovian arrivals
Authors: Wu De-An , Takagi Hideaki
Published: July 2016

We consider single-server queues with exponentially distributed service times, in which the arrival process is governed by a semi-Markov process (SMP). Two service disciplines, processor sharing (PS) and random service (RS), are investigated. We note that the sojourn time distribution of a type-lcustomer who, upon his arrival, meetskcustomers already present in the SMP/M/1/PS queue is identical to the waiting time distribution of a type-lcustomer who, upon his arrival, meetsk+1 customers already present in the SMP/M/1/RS queue. Two sets of system equations, one for the joint transform of the sojourn time and queue size distributions in the SMP/M/1/PS queue, and the other for the joint transform of the waiting time and queue size distributions in the SMP/M/1/RS queue, are derived. Using these equations, the mean sojourn time in the SMP/M/1/PS queue and the mean waiting time in the SMP/M/1/RS queue are obtained. We also consider a special case of the SMP in which the interarrival time distribution is determined only by the type of the customer who has most recently arrived. Numerical examples are also presented.
Efficient algorithms for transient analysis of stochastic fluid flow models
Authors: Ahn Soohan , Ramaswami V.
Published: July 2016

We derive several algorithms for the busy period distribution of the canonical Markovian fluid flow model. One of them is similar to the Latouche-Ramaswami algorithm for quasi-birth-death models and is shown to be quadratically convergent. These algorithms significantly increase the efficiency of the matrix-geometric procedures developed earlier by the authors for the transient and steady-state analyses of fluid flow models.
On increasing-failure-rate random variables
Authors: Ross Sheldon M. , Shanthikumar J. George , Zhu Zegang
Published: July 2016

We provide sufficient conditions for the following types of random variable to have the increasing-failure-rate (IFR) property: sums of a random number of random variables; the time at which a Markov chain crosses a random threshold; the time until a random number of events have occurred in an inhomogeneous Poisson process; and the number of events of a renewal process, and of a general counting process, that have occurred by a randomly distributed time.
Optimal doubling strategy against a suboptimal opponent
Authors: Katsikopoulos Konstantinos V. , Şimşek Özgür
Published: July 2016

For two-person zero-sum games, where the probability of each player winning is a continuous function of time and is known to both players, the mutually optimal strategy for proposing and accepting a doubling of the game value is known. We present an algorithm for deriving the optimal doubling strategy of a player who is aware of the suboptimal strategy followed by the opponent. We also present numerical results about the magnitude of the benefits; the results support the claim that repeated application of the algorithm by both players leads to the mutually optimal strategy.
Nonstationarity and randomization in the Reed-Frost epidemic model
Authors: Lefèvre Claude , Picard Philippe
Published: July 2016

The purpose of this paper is to determine the exact distribution of the final size of an epidemic for a wide class of models of susceptible–infective–removed type. First, a nonstationary version of the classical Reed–Frost model is constructed that allows us to incorporate, in particular, random levels of resistance to infection in the susceptibles. Then, a randomized version of this nonstationary model is considered in order to take into account random levels of infectiousness in the infectives. It is shown that, in both cases, the distribution of the final number of infected individuals can be obtained in terms of Abel–Gontcharoff polynomials. The new methodology followed also provides a unified approach to a number of recent works in the literature.
Large-time asymptotics for the density of a branching Wiener process
Authors: Révész Pál , Rosen Jay , Shi Zhan
Published: July 2016

Given an ℝ
d
-valued supercritical branching Wiener process, let ψ(A, T) be the number of particles in A ⊂ ℝ
d
at time T (T = 0, 1, 2, …). We provide a complete asymptotic expansion of ψ(A, T) as T → ∞, generalizing the work of X. Chen.
Alternating branching processes
Authors: Mayster Penka
Published: July 2016

We introduce the idea of controlling branching processes by means of another branching process, using the fractional thinning operator of Steutel and van Harn. This idea is then adapted to the model of alternating branching, where two Markov branching processes act alternately at random observation and treatment times. We study the extinction probability and limit theorems for reproduction by n cycles, as n → ∞.
Range of Asymptotic Behaviour of the Optimality Probability of the Expert and Majority Rules
Authors: Berend Daniel , Sapir Luba
Published: July 2016

We study the uncertain dichotomous choice model. In this model, a group of expert decision makers is required to select one of two alternatives. The applications of this model are relevant to a wide variety of areas. A decision rule translates the individual opinions of the members into a group decision, and is optimal if it maximizes the probability of the group making a correct choice. In this paper, we assume the correctness probabilities of the experts to be independent random variables selected from some given distribution. Moreover, the ranking of the members in the group is (at least partly) known. Thus, one can follow rules based on this ranking. The extremes are the expert rule and the majority rule. The probabilities of the two extreme rules being optimal were compared in a series of early papers, for a variety of distributions. In most cases, the asymptotic behaviours of the probabilities of the two extreme rules followed the same patterns. Do these patterns hold in general? If not, what are the ranges of possible asymptotic behaviours of the probabilities of the two extreme rules being optimal? In this paper, we provide satisfactory answers to these questions.
A Note on the Extremal Index for Space-Time Processes
Authors: Turkman K. F.
Published: July 2016

Let {X(
s
, t),
s
= (s
1, s
2) ∈ ℝ2, t ∈ ℝ} be a stationary random field defined over a discrete lattice. In this paper, we consider a set of domain of attraction criteria giving the notion of extremal index for random fields. Together with the extremal-types theorem given by Leadbetter and Rootzen (1997), this will give a characterization of the limiting distribution of the maximum of such random fields.
First Passage Problems for Asymmetric Wiener Processes
Authors: Lefebvre Mario
Published: July 2016

The problem of computing the moment generating function of the first passage time T to a > 0 or −b < 0 for a one-dimensional Wiener process {X(t), t ≥ 0} is generalized by assuming that the infinitesimal parameters of the process may depend on the sign of X(t). The probability that the process is absorbed at a is also computed explicitly, as is the expected value of T.
User-Optimal State-Dependent Routeing in Parallel Tandem Queues with Loss
Authors: Spicer Scott , Ziedins Ilze
Published: July 2016

We consider a system of parallel, finite tandem queues with loss. Each tandem queue consists of two single-server queues in series, with capacities C
1 and C
2 and exponential service times with rates μ1 and μ2 for the first and second queues, respectively. Customers that arrive at a queue that is full are lost. Customers arriving at the system can choose which tandem queue to enter. We show that, for customers choosing a queue to maximise the probability of their reaching the destination (or minimise their individual loss probability), it will sometimes be optimal to choose queues with more customers already present and/or with greater residual service requirements (where preceding customers are further from their final destination).
Availability of periodically inspected systems with Markovian wear and shocks
Authors: Kharoufeh Jeffrey P. , Finkelstein Daniel E. , Mixon Dustin G.
Published: July 2016

We analyze a periodically inspected system with hidden failures in which the rate of wear is modulated by a continuous-time Markov chain and additional damage is induced by a Poisson shock process. We explicitly derive the system's lifetime distribution and mean time to failure, as well as the limiting average availability. The main results are illustrated in two numerical examples.
Average optimality for Markov decision processes in borel spaces: a new condition and approach
Authors: Guo Xianping , Zhu Quanxin
Published: July 2016

In this paper we study discrete-time Markov decision processes with Borel state and action spaces. The criterion is to minimize average expected costs, and the costs may have neither upper nor lower bounds. We first provide two average optimality inequalities of opposing directions and give conditions for the existence of solutions to them. Then, using the two inequalities, we ensure the existence of an average optimal (deterministic) stationary policy under additional continuity-compactness assumptions. Our conditions are slightly weaker than those in the previous literature. Also, some new sufficient conditions for the existence of an average optimal stationary policy are imposed on the primitive data of the model. Moreover, our approach is slightly different from the well-known ‘optimality inequality approach’ widely used in Markov decision processes. Finally, we illustrate our results in two examples.
Boundedly rational quasi-Bayesian learning in coordination games with imperfect monitoring
Authors: Chen Hsiao-Chi , Chow Yunshyong , Hsieh June
Published: July 2016

In this paper we study players' long-run behaviors in evolutionary coordination games with imperfect monitoring. In each time period, signals corresponding to players' underlying actions, instead of the actions themselves, are observed. A boundedly rational quasi-Bayesian learning process is proposed to extract information from the realized signals. We find that players' long-run behaviors depend not only on the correlations between actions and signals, but on the initial probabilities of risk-dominant and non-risk-dominant equilibria being chosen. The conditions under which risk-dominant equilibrium, non-risk-dominant equilibrium, and the coexistence of both equilibria emerges in the long run are shown. In some situations, the number of limiting distributions grows unboundedly as the population size grows to infinity.
Hazard rate ordering of order statistics and systems
Authors: Navarro Jorge , Shaked Moshe
Published: July 2016

LetX= (X1,X2, …,Xn) be an exchangeable random vector, and writeX(1:i)= min{X1,X2, …,Xi}, 1 ≤i≤n. In this paper we obtain conditions under whichX(1:i)decreases iniin the hazard rate order. A result involving more general (that is, not necessarily exchangeable) random vectors is also derived. These results are applied to obtain the limiting behaviour of the hazard rate function of the lifetimes of various coherent systems in reliability theory. The notions of the Samaniego signatures and the minimal signatures of such systems are extensively used in the paper. An interesting relationship between these two signatures is obtained. The results are illustrated in a series of examples.
On the time behaviour of Okazaki fragments
Authors: Bartoszek Krzysztof , Bartoszek Wojciech
Published: July 2016

We find explicit analytical formulae for the time dependence of the probability of the number of Okazaki fragments produced during the process of DNA replication. This extends a result of Cowan on the asymptotic probability distribution of these fragments.
On the infinite-horizon probability of (non)ruin for integer-valued claims
Authors: Ignatov Zvetan G. , Kaishev Vladimir K.
Published: July 2016

We consider a compound Poisson process whose jumps are modelled as a sequence of positive, integer-valued, dependent random variables, W
1,W
2,…, viewed as insurance claim amounts. The number of points up to time t of the stationary Poisson process which models the claim arrivals is assumed to be independent of W
1,W
2,…. The premium income to the insurance company is represented by a nondecreasing, nonnegative, real-valued function h(t) on [0,∞) such that lim
t→∞
h(t) = ∞. The function h(t) is interpreted as an upper boundary. The probability that the trajectory of such a compound Poisson process will not cross the upper boundary in infinite time is known as the infinite-horizon nonruin probability. Our main result in this paper is an explicit expression for the probability of infinite-horizon nonruin, assuming that certain conditions on the premium-income function, h(t), and the joint distribution of the claim amount random variables, W
1,W
2,…, hold. We have also considered the classical ruin probability model, in which W
1,W
2,… are assumed to be independent, identically distributed random variables and we let h(t)=u + ct. For this model we give a formula for the nonruin probability which is a special case of our main result. This formula is shown to coincide with the infinite-horizon nonruin probability formulae of Picard and Lefèvre (2001), Gerber (1988), (1989), and Shiu (1987), (1989).
On extreme ruinous behaviour of Lévy insurance risk processes
Authors: Klüppelberg C. , Kyprianou A. E.
Published: July 2016

In this short note we show how new fluctuation identities and their associated asymptotics, given in Vigon (2002), Klüppelberg et al. (2004) and Doney and Kyprianou (2006), provide the basis for establishing, in an elementary way, asymptotic overshoot and undershoot distribitions for a general class of Lévy insurance risk processes. The results bring the earlier conclusions of Asmussen and Klüppelberg (1996) for the Cramér-Lundberg process into greater generality.
On stochastic recursive equations of sum and max type
Authors: Rüschendorf Ludger
Published: July 2016

In this paper we consider stochastic recursive equations of sum type,, and of max type,, whereAi,bi, andbare random, (Xi) are independent, identically distributed copies ofX, anddenotes equality in distribution. Equations of these types typically characterize limits in the probabilistic analysis of algorithms, in combinatorial optimization problems, and in many other problems having a recursive structure. We develop some new contraction properties of minimalLs-metrics which allow us to establish general existence and uniqueness results for solutions without imposing any moment conditions. As an application we obtain a one-to-one relationship between the set of solutions to the homogeneous equation and the set of solutions to the inhomogeneous equation, for sum- and max-type equations. We also give a stochastic interpretation of a recent transfer principle of Rösler from nonnegative solutions of sum type to those of max type, by means of random scaled Weibull distributions.
Stochastic orders and majorization of mean order statistics
Authors: de la Cal Jesús , Cárcamo Javier
Published: July 2016

We characterize the (continuous) majorization of integrable functions introduced by Hardy, Littlewood, and Pólya in terms of the (discrete) majorization of finite-dimensional vectors, introduced by the same authors. The most interesting version of this result is the characterization of the (increasing) convex order for integrable random variables in terms of majorization of vectors of expected order statistics. Such a result includes, as particular cases, previous results by Barlow and Proschan and by Alzaid and Proschan, and, in a sense, completes the picture of known results on order statistics. Applications to other stochastic orders are also briefly considered.