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Our earlier paper ‘The money supply, economic management and the gilt-edged market’ (J.I.A.96, 1) introduced the money supply as being ‘of importance to investment, in general because of possible changes in the economic management in the United Kingdom, and in particular because of the possible implications for the gilt-edged market’. To a large extent these changes have come about; the Authorities are now placing greater emphasis than in 1969 on controlling the money supply and support for the gilt-edged market was withdrawn when the Bank of England published Competition and Credit Control in May 1971.2. The present paper is more fundamental for investment. The introduction to the earlier paper referred to our main research project into the uses of the financial statistics which were first published in 1962 as a result of the Radcliffe Committee Report. Changes in the management of the economy and the gilt-edged market were side issues, however important; the present paper describes some of the interim conclusions of the main project which is still continuing.

Investment conditions have changed widely and rapidly in the post-war era; and since the publication of Mr Lewis G. Whyte's textbook, Principles of Finance and Investment, there has been a spate of papers on investment theory, each of them either covering a small part of the subject or setting forth a particular view.The aims of this paper are:I. To suggest a balanced and consistent approach to investment principles as they affect funds of actuarial interest.II. To discuss the application of these principles to particular types of funds.III. To discuss the characteristics of the securities that are available in present-day conditions to implement investment policy.These aims may sound comprehensive, but within the limitations of a paper it is only possible to touch on them briefly.

In these four pages, this paper can be neither a complete introduction nor a complete survey of the role of computer graphics in simulation. However, these examples drawn from the experience of the Naval Post graduate School computer laboratory will illustrate a wide class of applications which may suggest uses in other fields. The interested reader should refer to the January 1971 issue of SIMULATION (which was devoted entirely to computer graphics applications in simulation) and to the supplementary reading list at the end of this paper.

This paper is primarily concerned with investment by life offices and pension funds in British Government stocks with lives of more than 5 years, although there are important implications for all classes of investors. Investing in British Government stocks over the post-war period has become a highly technical process. The advent of the electronic computer has opened up an entirely new field of statistical data thus making some of the old methods obsolete. The paper illustrates some of the new techniques developed by the author and his colleagues. Other actuaries have also been developing new approaches and it is hoped that they will contribute to a lively and constructive discussion.

Although this paper deals with the application of mathematical formulae to mortality data, it is not concerned with ‘graduation’ if that word is held to imply the fitting of a particular curve to a particular experience with the object of satisfying statistical tests. Nor is the paper concerned with the development of any philosophical theory of mortality. The experiments which it describes were undertaken in the hope of finding a standard type of curve which would give a good over-all representation of adult mortality in general. If such a curve could be found, an examination of the variations in its parameters might contribute something to an understanding, not of the nature of mortality itself, but of the differences—more particularly the secular differences—between one mortality experience and another.

The question of the effect of duplicate policies on the variance of the number of deaths in a mortality experience based on policies (not lives) has been discussed in two recent papers (Seal [1947] and Beard and Perks [1949]). The second of these papers shows that this variance depends on the sampling process envisaged and gives formulae for the variance under four such processes. It is the purpose of this paper to consider some practical aspects of the treatment of duplicates in a mortality experience.

Little space in the Journal has been devoted in the past specifically to graduation tests, and nowhere have the tests generally applied been concisely set out and fully discussed. The only papers during the last forty years on the subject have been by Seal and Daw; both these papers were submitted and discussed during the war years, with the result that many actuaries were unable to be present and state their views; indeed, many of us did not even know of them until the numbers of the Journal in question were published, and an opportunity to study them did not arise until after the war.

Handwriting Recognition Technology has been improving much under the purview of pattern recognition and image processing since a few decades. This paper focuses on the comprehensive survey on on-line handwriting recognition system along with the real application by taking Nepali natural handwriting (a real example of one of the cursive handwritings). The survey mainly includes pre-processing, feature vector and similarity measures in between the non-linear 2D sequences of coordinates, and their effective applications. A very highlighting topic "Dynamic Time Warping Algorithm'' (DTW) is introduced, which has been popular in determining the distance between two non-linear sequences ranging from handwriting to speech recognition. Besides these contemporary research issues/areas, stroke number and order free Nepalese natural handwritten recognition system is presented in the second step. Writing one's own style brings unevenness in writing units, which is the most difficult part to classify. Writing units reveal number, shape, size, order of stroke, and speed in writing. Variation in the number of strokes, their order, shapes and sizes, tilting angles and similarities among characters from one another are the important factors, which are to be considered in classification for Nepali. This paper utilizes structural properties of those alphanumeric characters, which have variable writing units. It uses a string of pen tip's positions and tangent angles of every consecutive point as a feature vector sequence of a stroke. We constructed a prototype recognizer that uses the DTW algorithm to align handwritten strokes with stored strokes' templates and determine their similarity. Separate system is trained for original and preprocessed writing samples and achieved recognition rates of 85.87% and 88.59% respectively. This introduces novel real time handwriting recognition on Nepalese alphanumeric characters, which are independent of number of strokes, as well as their order. Key Words: Handwriting Recognition System; Pre-processing; Feature Vector; Dynamic Time Warping; Agglomerating Hierarchical Clustering; Nepali. DOI: 10.3126/kuset.v5i1.2845 Kathmandu University Journal of Science, Engineering and Technology Vol.5, No.1, January 2009, pp 31-55

An important part of the work of an actuary consists in making and testing graduations of mortality statistics. Much space has been devoted in the Journal to methods of graduation, but for many years, apart from the recent paper by H. L. Seal (J.I.A. Vol. lxxi, p. 5), little attention seems to have been paid to the testing of graduations. Although statistical methods are usually employed in making the tests, consideration has not often been given to ascertaining whether mortality statistics fulfil the conditions necessary for the tests to be strictly applicable. It is the purpose of this paper to set out some investigations into this question. Such matters may be thought to be of only theoretical interest, since, in practice, the tests work satisfactorily as a general rule; but actuaries should not employ their tools in a mechanical fashion without realizing fully their limitations and implications, and the question therefore takes on a practical as well as a theoretical aspect. It is hoped that this paper will show how far the tests of a graduation are satisfactory in theory and practice and indicate where modifications are required.

This paper stems from a suggestion that it would be worth while to bring to the notice of the profession the progress which has been made and the statistical problems that have arisen in the study of epidemiology in its wider sense, viz. the study, not merely of the spread of communicable disease as was formerly implied by this term, but of the natural history of disease; its prevalence, causation, symptomology and prognosis. It would, however, require a series of papers to cover so wide a field and would demand medical as well as statistical competence. It therefore seemed advisable to use the more restrictive title chosen in order to emphasize the fact that, in the main, consideration is devoted to statistical rather than to clinical aspects.

The purpose of this paper is to provide an opportunity for discussion within our profession of ‘the use of an actuarial approach and actuarial evidence’ in the assessment of damages arising out of personal injury and fatal accident litigation. The need for such a paper was intimated in the pages of our Journal by William Phillips in his Review of Principles of the Law of Damages by Professor Harry Street. Since the publication of what Phillips described as ‘from the actuarial point of view…the most important legal textbook which has been published in the last 50 years’ the employment of actuaries in this field has been widely discussed within the legal profession. The most important recent development has been the inclusion of personal injury litigation as Item VI of the first programme of the Law Commission set up by the Law Commission Act, 1965. The words quoted in the first sentence above are taken from the list of ‘Questions for Examination’ under (b) of Item VI, ‘Assessment of Damages’. The current examination being conducted by the Law Commission makes this a particularly appropriate time for a sessional meeting on this subject. The writer has had the advantage of a sight of a preliminary Working Paper prepared by the Law Commission and will be quoting certain extracts from that paper below. It must however be stressed that the Working Paper is a preliminary one which attempts to do no more than canvass views: it in no way sets out the conclusions of the Law Commission on the matters discussed.

Mr Elphinstone, in his recent paper to the Faculty of Actuaries, has reawakened interest in the method of graduation devised by Sir Edmund T. Whittaker some 32 years ago. Except for Professor A. C. Aitken who, in a paper( in the Proceedings of the Royal Society of Edinburgh and a note in the Transactions of the Faculty of Actuaries, gave a brilliant alternative solution of the equations on which Whittaker's method depends, English and Scottish writers have paid little attention to the method. Robert Henderson's paper published in 1924 stimulated American actuaries, and their investigations have continued up to the present time. The book by Kingsland Camp (reviewed J.I.A. lxxvii, 327) gives numerous practical developments of Robert Henderson's work. Students should not overlook a most valuable paper by Charles A. Spoerl which deals comprehensively with almost every aspect of the subject.

The development of sickness insurance of the type dealt with in this paper has been a long process, commencing in a tentative fashion, probably a century ago, in Europe. In 1900, E. Hamza, at that time actuary of a Russian insurance company, contributed to the Third International Congress a paper of interesting historical significance which is clearly based on long experience in Germany. In his paper he developed an approach fundamentally different from the traditional British approach. British methods—which can be described with complete adequacy at this stage as a continuation of Friendly Society actuarial technique—have stood the test of time for at least 150 years and it is the purpose of this paper to analyse the two lines of development; to pose the question of their efficacy in the future; and to outline alternative methods depending on modern mathematical techniques.

GASP IV is a FORTRAN-based simulation language which provides the framework for modeling systems involving both continuous and discrete phenomena. A general ization of the definition of "event" allows for time to be advanced in a next-event fashion while permit ting a step-wise evaluation of system state variables described by difference or differential equations. Subprograms are included in GASP IV to handle the details of state and event control (including state- variable integration when necessary), information storage and retrieval, collection and analysis of data on system performance, and generation of reports and plots. In this paper, the GASP IV philosophy and modeling approach are described. Descriptions of the subpro grams included in GASP IV and the required user- written subprograms are given. The types of applica tions that have utilized GASP IV are listed. A com panion paper (beginning on p. 71) presents a detailed example of the use of GASP IV for simulating a continuous reaction process involving discrete startups and shutdowns.

This paper is mainly concerned with the division of a trust fund between the beneficiaries, when an actuary is asked for a solution which, in his opinion, is fair to all parties concerned. It may be that the beneficiaries are all sui juris and form a closed class, in which case they approach the actuary as umpire, and adopt a passive role, at least until they have considered the implications of his recommendations. Alternatively, the actuary's report may be required to assist the Court to approve a scheme involving beneficiaries, e.g. infants, whom it is the Court's object to protect. In that case the actuary's role—as discussed later in the paper—is rather different, but it may still be necessary for him to state what in his judgment would be an impartial solution.

In this paper, the effect of the method of control on the transfer function of two-phase servomotors is investigated. The methods of control considered are the amplitude, time-phase, frequency, voltage-frequency, pulse-width and space-phase control. Torque equations are derived for different methods. The motor gain and time-constant are determined from the torque-speed and speed-signal characteristics. The servomotor torque, speed, time-constant and gain — and their dependence on the signal magnitude — are compared for the different methods of control. It is shown that for the same value of the signal, the motor time-constant may vary between 2·2 msec and 45 msec and the gain may be increased six times if the method of control is changed.

SummaryThis paper investigates the recalculation from its base date of theFinancial TimesIndex of Industrial Ordinary Shares (hereafter called theFTIndex) using the ordinary arithmetic mean of the values of its constituents, rather than the geometric mean that is actually used in its calculation. The value of this arithmetic version of theFTIndex represents that of a portfolio invested equally in each of the original constituents at the base date. The behaviour of the recalculated index may therefore be described in portfolio terms.The arithmeticized index has been calculated at each end-year since the base date of theFTIndex (1 July 1935). By the end of 1970 its value was 38% higher than that of the (geometric)FTIndex. The percentage by which the new index exceeded the original was found to have increased approximately linearly with time; a least-squares linear fit over the whole period indicated that the percentage excess of the arithmetic version over the original index had increased on average by 0·8% a year. A separate fit for the period from end-1960 onwards shows that this rate had increased to 2·7% per year, and even over the period since 1950, it has been 1·1% per year. Use of these relationships gives a rough adjustment of theFTIndex for portfolio comparison purposes.We also calculated a series of arithmetic indices with base dates at the end of each year since the original base date of theFTIndex. In the majority of calendar years since its foundation, theFTIndex has not fallen far behind the corresponding arithmetic version over the twelve month period. However, over periods of more than a year, the geometric and arithmetic indices can show dramatically different results, particularly if the percentage change in the index value is considered. It is clear that longer-term changes in the value of theFTIndex cannot be interpreted as the changes that would have occurred in the value of a portfolio equally invested in the thirty constituent shares at the beginning of the period.None of these findings affects the usefulness of theFTIndex for its original purpose, as a sensitive daily indicator of changes in the industrial ordinary share market. It is purely its long-run use as a portfolio standard that is misleading. For this purpose the more recently instituted arithmetic indices are likely to be useful in the future. Meanwhile, our arithmeticizedFTIndex values may be useful to correct the downward drift imposed on theFTIndex by its geometric construction.

This paper is concerned with attempts that have been made to incorporate measures of risk in the selection of financial investments. The methodology that is developed here has been primarily aimed at the evaluation of capital investment projects, but the concepts and ideas are also relevant in the financial investment field. Implicit in all this discussion is the fact that when information is obtained in order to calculate an internal rate of return or a net present value, the figures put into the calculation are estimates rather than precise and exact quantities. In some instances the estimates may be felt to be very good, whilst in other cases it may be felt that there is a wide range of possible deviations. Hence the evaluation of any project or projects should, correctly, be described not by a single criterion but by a range of possible values, some of which are judged to be more likely than others. Having said this, there now comes the need to decide upon the method by which choice is to be exercised. Should it be by the choice of the highest average value of the criterion, or by choosing some more conservative rule?

While attention in the iron and steel industry has been focused on the study and analysis of the flow of materials through the main productive units (blast furnaces, steel works, and rolling mills), the analysis of this flow through the nonproductive units (the mixer and soaking pits) is generally over looked. These two units would create serious bottle necks in production if their capacities were not properly determined before being installed. This paper considers the soaking-pit/rolling-mill complex as a queueing system in which the soaking pits are viewed as units circulating a cyclic queue, and the rolling mill as the service station. A simulation model representing the pit-mill system is developed: (1) To predict the improvement in the capacity of the system through adding more pits (2) To predict the effect of breakdowns and mainte nance or the shutdown of a pit. Several criteria, including their economic aspects, are used to measure the performance of the system. The optimal capacity of the system is determined such that an economic balance between the cost of service and the cost of waiting for that service is achieved.

In the course of preparing a paper dealing with statistics relating to fire insurance (Beard, 1957) the need arose to find numerical values of the confluent hypergeometric function for parameter values well outside any tabulated range, and this note is concerned with various approximations investigated in the course of these experiments.

This paper presents a generalization of the parameter plane method in that it considers the case when the characteristic equation coefficients are nonlinear functions of the system adjustable parameters. The generalized method is then applied to the system analysis in which the coefficients are linear functions of two parameters and their product. As a simple and rapid procedure for factoring polynomials in the parameter plane, the method is used in the design of linear continuous multivariable control systems. A non-linear system with two nonlinearities is also considered whereby the stability and existence of limit cycles are investigated.

Due to rise in the price of fossil fuels and technical advances in the area of renewable energy, integrated systems became more popular now a day. However uncertain nature of wind, solar irradiation due to weather and climate change, integration of renewable power generation system complicates the ELD formulation. The paper presents optimum scheduling of integrated solarwind- thermal system using backtracking search algorithm (BSA). BSA is a novel population based stochastic search optimization technique, having simple structure and only one control parameter as population size. BSA has two new types of operator’s as crossover and mutation for exploration and exploitation of search space of problem desired to be optimized and also satisfies all associated constraints of the objective function.Keywords: BSA, Photovoltaic cell, Valve point loading effect, Probability density function.

Tuberculosis at the present time still causes over 20,000 deaths a year in England and Wales and is one of the major medical problems of the day. The mortality of the disease has been considered several. times recently in papers or discussions of the Institute (Pedoe, 1947; Elderton, 1947; Conybeare, 1948), and always it is the mortality by calendar years that has been mentioned or implied. It is the purpose of this note to draw attention to the somewhat different picture obtained when generation mortality rates for tuberculosis are examined.

There have been many sales of insurance companies in recent years, but there is nothing in the literature of the Institute which deals with valuation for this purpose. It is hoped that this paper and the discussion on it will fill this gap.

Iterative techniques for function optimization have been considered extensivezy for use in all-digital computation. Relatively little has been done to take advantage of the much higher integration speed of hybrid computation systems. This paper demonstrates application of one simple procedure in a hybrid envi ronment and compares the results to those obtained by an efficient digital procedure. Even though a much more efficient procedure was used on the digital, time-saving factors between 8 and 2 were obtained via the simpler hybrid implementation. Since the dollar cost of the hybrid is much less than that of the digital, the hybrid has a large advantage per solution.

The first part of this paper concerns the influence of nitration; the proposed 64 per cent NO3H/36 per cent AcOH mixture is considered to be the best, particularly with native cellulose of high degree of polymerization ( DP w = 4700 ); nitration to 13·9–14 per cent N is regularly found for a time of contact of 1·5 hr at 2° with the nitration mixture. The weight average mol. wt., the degree of substitution and the polydispersity obtained by GPC in THF have been determined. In the second part of this work, the enzymic degradation by a cellulasic extract of Basidiomycete is followed during 0–48 hr periods on different types of celluloses. After nitration, the residual cellulose is characterized by its mol. wt. and polydispersity. The rate of enzymic modification is discussed and related to the structure of the substrates.

The right way to negotiate with Europe is the way in which, at its best, the Common Market has handled its own problems. One should start from the view that there is a collective European interest to be served, as there always is. One should then make sure that the separate national interests are reconciled with the interests of Europe. Only a man who thinks in European terms can make this adjustment of national and European interests successfully.The Times—29 July 1970.This paper must be forward-looking. To dwell on the past, and even the present, would fill many pages to little purpose. The author is convinced after reviewing many files of documents that the European Common Market would not have gone forward if its founders had allowed themselves to be sidetracked by narrow interests. This perhaps sounds ominous to experts in particular fields, such as actuaries, for it is not always a happy position when political motives may overrule, or cut short, technical considerations. But the concept of the Common Market is a political one and this is becoming more apparent as the years roll on. The collective European interest will prevail but that does not mean that British philosophy and practice cannot make a distinguished contribution to European thought in the field of insurance, particularly life assurance. In practical terms, it is clearly not possible to argue for the adoption of British practice in its entirety. But I do believe that unless the profession takes every opportunity to argue the merits of our own ways of providing life assurance in the private sector, we may well live to regret the omission.

Although pensions have been discussed at the Institute on many occasions in recent years, the papers submitted have generally been limited to some particular aspect of the subject, such as the preservation of pension rights, the position of pension funds in the national economy, or the influence of State pensions, whereas the subject of the valuation process has been to some extent neglected.

Summary In a recent paper [7] the authors studied the optimal control policy of the following queueing system. Customers arrive at a service station according to a time homogeneous Poisson process with a known arrival intensity, λ. The service time at the station is a random variable having a negative exponential distribution with intensity μ, which is under control and can be varied over a certain range, according to the management policy.

No mortality curve appears yet to have been devised which both fits the national statistics at all ages, and also has a simple philosophical explanation. The object of this paper may be stated as being the building up of a new mortality curve from its component parts, as many as possible of these parts having a philosophical background, and the whole being applicable to the national data.

The present paper considers the VLF radiation characteristics from a thin dipole antenna in a warm magnetoplasma. Formal solutions are derived for the portions of the dipole radiation resistance due to the thermal modes (Rt) and the whistler mode (Rw). In this derivation the ions are assumed to be cold, and the effects of finite electron temperatures are included by means of a scalar pressure term. Two particular orientations of the dipole are considered (parallel and perpendicular to the static magnetic field line). A detailed analysis is made for frequencies in the range between the electron gyrofrequency (fHe) and the lower-hybrid-resonance frequency (fLHR). Several numerical plots of Rt ∥, and Rw∥, are presented for typical VLF magnetospheric plasma parameters. They show that for frequencies ( f) not close to fLHR, Rt∥, is generally < 2 x 10-1 Rw∥, whereas as f → fLHR, R t , ≃ 10-1 Rw and R t∥ ≃ Rw∥. Using these numerical values of Rt∥, and Rw∥,, the dipole whistler mode radiation efficiences ηw have been estimated for a number of specific cases. In most cases ηw ≳ 70 %, but falls as low as ∼ 38 % at f ≃ f≳ LHR.

This paper describes a new solid-state, monolithic inte grated analog multiplier, based on the controlled-trans conductance principle that is designed for high speed, high accuracy, and excellent linearity. A novel differ ential amplifier circuit permits cancellation of undesired nonlinearities, and carefully matched device geometries account for the good accuracy of the new multiplier. With an inherent voltage gain of A v = 1/10, the multi plier will provide a ± 10 V output at ± 10 mA with linearity approaching 0.1 % at 100 Hz. The multiplier package may be used in conjunction with an external operational amplifier and external resistors, and offers the advantages of monolithic construction (low cost, ex cellent temperature tracking) with the precision of ad justable-parameter, discrete construction.

In earlier work we have reported on CELIA, a program for simulating the behavior of linear iterative arrays of cells. The action of a cell is influenced by both its neighbors. Our main application area was biology, where the program can be used to test hypotheses about the developmental rules for organisms. More recently we have been applying our program to test proposed solutions to some fairly complicated biozogically-based problems. We have investigated whether one can achieve regulative global polarity in organisms without polarity in individual cells, by solving the French flag problem of Wolpert, using only symmetric elements. In our attempted simulation of pigmentation patterns on the shells of sea-snails, we have found it necessary to find a solution to a generalized version of the firing squad synchronization problem, in which the firing squad is growing while it is trying to synchronize itself. We found that our original program CELIA was some what awkward for simulating such complicated situa tions. A new program has been devised in which the state of the individual ceZZs is described by a set of attributes and each attribute itself may be a list structure. The present paper reports on these changes and ex plains how they turn out to be useful in the appli cations mentioned above.

This paper deals with a design of optimal parameters of PI regulator in voltage control loop. The design aims to minimize voltampere (VA) loading of synchronous reference frame (SRF) based multi converter-DVR in parallel feeder distribution systems. To improve the power quality by using power conditioner with multi converters in each feeder distribution system under different load considerations, a dynamic model of synchronous-reference- frame (SRF) has been adopted. It is desirable to have optimization of PI components and generate the reference compensate voltages for series active filters (SAF) of MC-DVR. Therefore, series active filters help to inject optimal voltages at optimal angle in such a way that a minimum VA loading of MCDVR is possible. The optimal value PI components and optimal series injected angle of series active power filters are computed using particle swarm optimization (PSO) technique and the results are verified with genetic algorithm (GA). The simulation results show that the proposed PSO technique causes minimum error and minimum VA loading angle by optimally choosing parameters of PI and minimum VA angle as compared to GA technique.Keywords: Active power filter (APF), synchronous reference frame (SRF), Genetic algorithm (GA), Particle Swarm Optimization (PSO) and multi converter dynamic voltage restorer (MC-DVR).

Helical channels are widely applied in different application areas. In a converging diverging nozzle, helical channels are mainly used for cooling of its wall. The characteristics of fluid flow and heat transfer inside helical duct for a converging diverging nozzle is not commonly dealt in present literatures. In this paper CFD simulations are carried out for a helical rectangular duct of a converging diverging nozzle. In the present study the nozzle is oriented horizontally as a counter flow heat exchanger and analysis is done on ten helical ducts by changing the flow rates of four different fluids like water, ethanol, kerosene and Nano fluid. The fluid flow and heat transfer characteristics for the above fluids are studied along with the correlations for the prediction of Nusselt number for each fluid.Keywords: fluid flow, heat transfer, helical duct, Nusselt number, Dean number

The present paper is in two main parts: (1) a general discussion of the population factors which have led to a focusing of attention upon ageing with some reference to recent advances in gerontology and (2) a consideration of the actuarial implications of current gerontological research.

Most of the activity of actuaries with computers to date has been concerned with putting actuarial work on to computers, or—at one stage further back—putting life office data on to a computer data-processing system. This paper attempts to contemplate the next stage, the effect of computer knowledge and familiarity on the profession and its techniques.

The two-fold purpose of this paper is:(i) To hypothesize the existence of a Basic Curve of Deaths, a curve to which it is suggested all curves of deaths are, as it were, striving to attain—the ‘idea’ of a curve of deaths, almost in a Platonic sense, a curve applicable not only to humanity, but equally to all forms of life.(ii) To seek a representation of that curve by a function containing as few parameters as possible, on the principle that while there are other functions which fit the observations more exactly, we here prefer a simple function which fits them well enough.

refer as B2. Three interrelated topics connected with these proposed models will be discussed: (1) useful ways of visualizing B, and B as sales processes, both independently and in contrast to each other; (2) the derivation of the expectation and variance of B, and B in order to provide a kit of useful tools; (3) applications of these models in a marketing context and suggestions on extending their usefulness beyond merely a means for visualizing a sales process in the abstract. * The author is an associate professor, School of Business Administration, State University of New York at Buffalo (formerly University of Buffalo). An earlier version of this paper was presented on April 1, 1964, at the meetings of the 1963-1964 Mathematical Models Seminar of the University of Chicago, sponsored by the Ford Foundation. I am indebted to Professor Alex Orden, the seminar leader, for his encouragement, and to the Ford Foundation for partial support. ' Other recent efforts in economics and marketing stress disaggregation. Analytical Markov chain models in marketing emphasize an approach whose basic interacting units are individual households [2, 7, 8 and 12]. A recent practically minded macrosimulation by the Simulmatics Corporation [11] provides another example of disaggregation. A few thousand hypothetical individuals representing media choice "types" and classified by various demographic and economic variables constitute a small "experimental" universe. A stochastic selection of media for the various categories is first determined for each individual and only then aggregated. Another wellknown effort in the same direction has been made in Wisconsin under Guy Orcutt's leadership[9]. Population and labor force processes were simulated. The basic micro-units, the individuals, interacted directly. The aggregates were cumulations of individual responses. 2 To get a more general result we can allow both positive and negative value for P and limit the absolute value of P to a value smaller than one. Positive serial correlation, however, is typical of sales and, hence, P is assumed positive. 3 It appears that B, lies conceptually between a sum of N random independent variables where N is a constant [3] and a product of two independent random variables [1, 5, 6, 10, 13].

The model considered in this paper describes a queueing system in which the station is dismantled at the end of a busy period and re-established on arrival of a new customer, in such a way that the closing-down process consists of N 1 phases of random duration and that a customer 𝒞 n who arrives while the station is being closed down must wait a random time idn (i = 1, ···, N 1) if the ith phase is going on at the arrival instant. (For each fixed index i, the random variables idn are identically distributed.) A customer 𝒞 n arriving when the closing-down of the station is already accomplished has to wait a random time (N 1 + 1) dn corresponding to the set up time of the station. Besides, a customer 𝒞 n who arrives when the station is busy has to wait an additional random time 0 dn. We thus have (N 1 + 2) types of “delay” (additional waiting time). Similarly, we consider (N 2 + 2) types of service time and (N 3 + 2) probabilities of joining the queue. This may be formulated as a model with (N + 2) types of triplets (delay, service time, probability of joining the queue). We consider the general case where the random variables defining the model all have an arbitrary distribution. The process {wn }, where wn denotes the waiting time of customer 𝒞 n if he joins the queue at all, is not necessarily Markovian, so that we first study (by algebraic considerations) the transient behaviour of a Markovian process {vn } related to {wn }, and then derive the distribution of the variables wn.

Previous investigationA previous investigation into the mortality of diabetics was made by A. J. Steeds following the analysis of data based upon a large London clinic. The present paper is based on data derived more recently from the experience of the patients attending a large Birmingham clinic.Diabetes mellitus2. Diabetes mellitus is a very ancient disease which may be described as a disturbance of the normal insulin mechanism of the body. The pancreas is a gland which secretes insulin for the purpose of converting sugar and starches into the energy forms required by the body (the metabolism of carbohydrates) and disturbance in this metabolism is accompanied by an abnormality in the breakdown of fats. Apart from physical damage to the pancreas the causes of diabetes are various and obscure (although they are thought to include heredity, overweight and, in females, a high level of childbearing). It is generally accepted that diabetes in young lives is a more severe form associated with insulin deficiency, whereas in older lives the disease is of a milder type, but there are many exceptions to this broad division.

This paper presents an analytical procedure for sensitivity analysis of nonlinear control systems, which is based upon the Krylov-Bogoliubov asymptotical methods and the algebraic concept of the parameter plane analysis of nonlinear systems. In the sensitivity analysis, the effects on self-excited nonlinear oscillations of small amplitude perturbations are considered. The proposed analysis is useful to obtain information about the relative stability of sustained oscillations. The change in the amplitude and frequency of stable sustained oscillations due to small variations in system parameters can be evaluated by this method. The proposed analysis procedure is suitable for simulation on digital computers.

In a paper read before the Institute in January 1936, E. W. Phillips discussed developments in computing machines and made the following prediction : If it [the light-ray machine] is provided with all the necessary material on the morning of 1st January, the whole of the valuation will be completed within 15 minutes or so. Indeed when the actuary arrives there will still be time to complete the valuation over again on eight or nine other bases before he goes out to lunch, and yet have ready the figures necessary for the Annual General Meeting in the afternoon.

It is apparent that much of the congestion in road traffic is due to interference between vehicles at intersections, and this has led to the appearance of several mathematical discussions of the problems of delay at intersections of various types (Cohen and Stam (1963), Cohen and de Lange (1965), Hawkes (1965), (1966), Tanner (1962), Weiss and Maradudin (1962)). Comparatively little work has appeared on the problem of delay caused by vehicles turning right* across an opposing stream of vehicles, although Hawkes (1966) and Newell (1959) discuss this problem explicitly, and the models considered by all of these authors may be regarded as having some application to the right-turning problem. The characteristic feature of the problem considered here is that it concerns two traffic streams, neither of which has overriding priority, but either of which may control the intersection at any time: thus in both streams there are vehicles which turn right and these may be released either by a suitable gap in the opposing stream or by the arrival of an opposing right-turning vehicle. Of the authors mentioned above Hawkes (1963), Newell (1959), and Tanner (1953) considered in their models two streams neither of which had complete priority over the other, but in their cases the mechanism by which control of the junction passed from one stream to the other differed from that considered here. The model used in this paper is a simplified version of the model of Cohen and Stam (1963), adapted to the right-turning situation.

This paper presents the development of an algorithm for control of the sampling interval in discrete systems. The proposed strategy is based on the use of a sensitivity function which reflects the influence of discrete changes in hold circuit output on system response. The actual algorithm is hybrid, including both continuous computation and logical decisions. The method is illustrated by examples with a linear and a nonlinear sampled-data control system. The adaptive systems, where the sampling interval is variable, are shown to lead to significant reductions in the total number of samples required in an interval, as compared to equivalent systems with a fixed sampling rate.

A significant factor which affects the accurate prediction of the discharge coefficients of square edged orifice plates is the precise shape of the edge. A rounding of only 0·002 of the orifice diameter can increase the coefficient by 1% so that a reliable method of assessing the edge sharpness is of considerable benefit to the instrument engineer. In the work described in this paper, a systematic intercomparison of three methods of measuring orifice edge sharpness has been undertaken. The methods tested involved casting, lead foil impression and optical techniques, and their relative reliability and effectiveness has been assessed. While the results obtained from the casting and lead foil methods showed good agreement, the foils did not follow the edge profiles as closely as the castings. The casting procedure can also be used to determine the shapes of re-entrant profiles which will not be detected using lead foil impressions. However, the casting method required more skill and considerably more time to complete measurements than the impression method. The optical method proved to be the least reliable, since measurements depended on subjective judgment. Nevertheless, this measuring procedure could be completed more quickly than the others, and these tests indicated that it may be used to examine large diameter plates for burrs or excessive rounding.

This paper extends the usefulness of an earlier report by evaluating an approximation for the transient response. The approximation examined is that of equivalent oil column stiffness; this has been used in the past, without evaluation, for displacement but is extended here to cover pressure transients. The comparisons between approximate and correct displacement responses indicate that the former is of sufficient accuracy for most practical purposes. In the two very different cases investigated, the approximation gives conservative estimates of the pressure peak.

International audience; This paper presents a method for animating human characters, especially dedicated to walk planning problems. The method is integrated in a randomized motion planning scheme, including a steering method dedicated to human walk. This steering method integrates a character motion controller assuming realistic animations. The navigation of the character through a virtual environment is modeled as a composition of Bézier curves. The controller is based on motion capture data editing techniques. This approach satisfies some essential computer graphics criteria: a realistic result, a low response time, a collision-free motion in possibly constrained 3D environments. The approach has been implemented and successfully demonstrated on several examples.

Hybrid Monte Carlo techniques for the solution of linear boundary-value problems have previously been developed. This paper is not primarily concerned with implementing these techniques., but extends the class of problems that can be solved by them and improves the method first described by Little, which in its original form is shown to be valid only in a special case and not generally applicable to linear boundary-value problems.

The paper first offers a parallel between two approaches to conceptual clustering, namely formal concept analysis (augmented with the introduction of new operators) and bipartite graph analysis. It is shown that a formal concept (as defined in formal concept analysis) corresponds to the idea of a maximal bi-clique, while sub-contexts, which correspond to independent "conceptual worlds" that can be characterized by means of the new operators introduced, are disconnected sub-graphs in a bipartite graph. The parallel between formal concept analysis and bipartite graph analysis is further exploited by considering "approximation" methods on both sides. It leads to suggest new ideas for providing simplified views of datasets, taking also inspiration from the search for approximate itemsets in data mining (with relaxed requirements), and the detection of communities in hierarchical small worlds. © 2013 Copyright the authors.