Choosing the Operational Research Programme for B.I.S.R.A

This paper examines some important problems in the evaluation and selection of research projects, with particular reference to operational research projects in a central industry research organization. A method for project evaluation is suggested which provides data suitable for use in a powerful and flexible formal procedure for project selection. In evaluating a project, the assessment of resource requirements is based on a probabilistic network plan of the project, and the estimates of benefits are derived from the marginal effects on the industry of performing or not performing the project, using discounted cash flow techniques. The procedure for project selection chooses not only the projects to be undertaken, but also the team sizes that should be used. A wide variety of constraints can be imposed on the system to reflect different aspects of management policy or other special factors. The procedures described have been implemented, and have proved well worth while.     

Analysis of pseudo-periodic chronological series with irregularly time-spaced data in view to their prediction. II. Fourier analysis

The problem originates from the necessity to predict luminosities of large-amplitude variable stars that are to be observed by the astronomical satellite HIPPARCOS. The data have a specific character: they are unequally time-spaced and can be missing during a long time in comparison to the pseudo-period. So the classical method of time-series analysis must be adapted and new methods are to be searched. In this paper we present a numerical solution derived from a Fourier analysis.     

Analysis of pseudo-periodic chronological series with irregularly time-spaced data in view to their prediction. I. Proposed problem

The problem originates from the necessity to predict luminosities of large-amplitude variable stars that are to be observed by the astronomical satellite HIPPARCOS. The data have a specific character: they are unequally time-spaced and can be missing during a long time in comparison to the pseudo-period. So the classical method of time-series analysis must be adapted and new methods are to be searched. In the following papers we present two solutions: a numerical one derived from a Fourier analysis and a symbolic one.     

The averaging method for asymptotic evolutions. II. Quantum open systems

The method of averaging is applied to study the reduced evolution of a quantum open system. Successive approximate evolutions are derived, and they are shown to be asymptotic to the exact evolution of the open system, under conditions which are satisfied in the case of a system coupled to a quasi-free reservoir, whose correlation functions are exponentially descreasing in time.     

Editorial: Math. Log. Quart. 1/2007

Dear Readers, A happy and successful 2007 to all of you. I wish to draw your attention again to an enlargement of the Editorial Board of our journal. We are pleased to welcome three new members: Ramon Jansana (Barcelona), Klaus Meer (Odense), and Andrzej Roslanowski (Omaha). I would like to thank the outgoing member, Peter Koepke (Bonn), for the work he has done in supporting MLQ. Also, it is more than justified that the name of our Editorial Assistant, who always faithfully compiles the final layout, can now be seen at the cover. All readers are once more encouraged to contact the Editorial Office or a member of the Editorial Board with any suggestions concerning the contents or the editorial work of our journal. In particular, proposals for issues devoted to special subjects or conferences are highly welcome. In 2007 there will be two such issues: one will be dedicated to “Trends in Constructive Mathematics” and a further one will deal with “Computability and Complexity in Analysis”. It should finally be mentioned that our publishing house is celebrating its 200th anniversary in 2007. During its whole history, Wiley has grown and evolved and has always been successful in serving the needs of its customers. So we can be sure to have a good background for the further development of our journal. (© 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

O.R. Education — A Survey of Young O.R. Workers

This paper presents the results of a survey into O.R. education that was conducted with the help of those attending the Young O.R. Conference (YOR II) held at Nottingham University in March 1982. The results of a workshop debate held at the conference into the direction of O.R. education are also discussed.The conclusions drawn are that O.R. education in this country appears to be quite successful but that it is failing to deal satisfactorily with a number of issues. These issues relate to keeping up-to-date with changes in computer technology and their impact upon O.R. workers; the teaching of methodology to deal with ill-defined problems; preparation for the political and working environment of organizations; and the fostering of desirable personal characteristics.     

A Hierarchy of Models for Planning in a Division of I.C.I.

In any large diverse company, organizational divisions are necessary to enable management to manage efficiently. The use of models in planning enables activities to be cohesively planned, but divisions must still be drawn. This paper describes the system of models developed for planning in one division of I.C.I. It sets out a philosophy of approach to modelling, covering many individual case studies which have forced the problem of divisions to be tackled. The solutions chosen appear to work well in one management environment.     

O.R. and Public Expenditure Planning and Control

The problems of public expenditure planning and control to which O.R. can make a contribution are identified. Suggestions are made for research by those in O.R. both within government and in universities. Recent work in the Treasury on financial models and information systems are discussed in terms of how such work might be applied elsewhere and extended to include measures of achievement. The topics covered include planning for uncertainty and theory development by O.R. in models of inflation and social justice.     

A knowledge-based approach to scheduling in an F.M.S.

This paper reports the development of a computer-based system for production scheduling in a dedicated FMS. The system is based on the state-operator framework commonly used in artificial intelligence. Such a system consists of three components: (i) a knowledge base of states, which describes both the current task domain situation and the goal to be achieved; (ii) a set of operators that are used to manipulate the knowledge base; and (iii) a control strategy to decide which operators to apply next and to resolve conflicts. Some of the interesting features of the scheduling system include: (i) the ability to detect resource conflicts; (ii) the ability to determine alternate routes for a given part in the event of a resource conflict; and (iii) the ability to amend plans if an alternate route is found. These features allow the system to take advantage of the flexible routing for parts that an FMS allows. The system has been implemented using the XLISP programming language. Implementation considerations are discussed. A small but comprehensive example is presented. Further research directions are suggested.     

Bilinear Control and Application to Flexible a.c. Transmission Systems

The purpose of this paper is an integrated overview of bilinear systems (BLS) research which has evolved over the past few decades, and a new result on control of flexible a.c. transmission systems (FACTS) is presented. BLS may be derived in many cases from principles of physics, chemistry, biology, socioeconomics, and engineering. In other cases, BLS are more accurate approximations to nonlinear systems than are traditional linear systems, as shown for example by the added bilinear terms (in state and control) for the Taylor series.While an appropriately designed linear control system may be optimum relative to some quadratic performance index without added constraints, bilinear or parametric control can be designed to improve more global performance and indeed to increase the region of attainable states. Such controllability and stabilization of BLS and of a series line-capacitor controlled FACTS is presented.     

2.3. Methodology of OR

We present and analyze a generalization of the standard decision analysis model of sequential decisionmaking under risk. The decision tree is assumed given and all probabilities are assumed to be known precisely. Utility values are assumed to be affine in an imprecisely known parameter. The affine form is sufficiently general to allow importance weights or the utility values themselves to be represented by the imprecise parameter. Parameter imprecision is described by set inclusion. A relation on all available alternatives is assumed given for each decision node. The intent of each (not necessarily complete) relation is to model the decisionmaker's directly expressed preferences among the available alternatives at the associated decision node. A numerical procedure is developed to determine the set of all strategies that may be optimal and the corresponding set of all possible parameter values. An example illustrates the procedure.     

Developments in operational research: R.W. Eglese and G.K. Rand (eds.) Pergamon, Oxford, 1984, vii + 110 pages, $20.00

A practical method of calculating the distribution of the number of customers in the single server queueing system with inhomogeneous arrival rate and discrete service time distribution is proposed. The system is formulated as an inhomogeneous Markov chain in discrete time, leading to recurrence relations for the state probabilities. The recurrence relations are then solved numerically. Various measures of performance, such as mean and variance of the number of customers in the system and virtual waiting time can be obtained from these results. Examples are presented to demonstrate the scope of the method, including time-dependent behaviour of homogeneous queues; cyclic behaviour of queues with cyclic arrival rates; and a previously published study of an airport runway in which the author had to resort to crude interpolation to obtain results. The method can be further extended to provide a reasonably accurate approximation for some systems with continuous distributions of service times.     

A critical appraisal of some cosmic ray data for the I.G.Y.

Cosmic ray recordings made with comparable instruments at stations where one would expect similar responses to primary variations of intensity have been examined. Discrepancies of the order of a few per cent. are sometimes observed. The discrepancies are often too large to be explained either on the basis of statistical errors or through the application of improper meteorological corrections. The order of magnitude of the discrepancies in intensity averaged on a bi-hourly, 6-hourly and 24-hourly basis is evaluated. The validity of drawing conclusions of physical significance from the I.G.Y. data under various conditions is discussed. The importance of applying appropriate statistical tests to available data is emphasised.     

Scientific heritage of L.P. Shilnikov

This is the first part of a review of the scientific works of L.P. Shilnikov. We group his papers according to 7 major research topics: bifurcations of homoclinic loops; the loop of a saddle-focus and spiral chaos; Poincare homoclinics to periodic orbits and invariant tori, homoclinic in noautonous and infinite-dimensional systems; Homoclinic tangency; Saddlenode bifurcation — quasiperiodicity-to-chaos transition, blue-sky catastrophe; Lorenz attractor; Hamiltonian dynamics. The first two topics are covered in this part. The review will be continued in the further issues of the journal.     

Transverse cracks in cross-ply laminates. 1. Stress analysis

During service loading of cross-ply laminates, transverse cracks occur in plies. The cracks parallel to the fiber direction are extended over the full thickness of transverse plies and often cross the entire test specimen width. It is widely recognized that the changes of laminate thermomechanical constants, caused by the transverse cracking of composite laminates, can be significant. Theoretical stress analysis in the cross-ply laminates in the vicinity of cracks is performed using numerical (FE) and analytical methods. The effect of transverse cracks on the degradation of elastic properties will be discussed in Part 2 [1]. Approximate analytical micromechanical models based on shear lag predictions, variational analysis, and numerical 2D finite element calculations were verified in their predictive abilities. The three variational models used are based on the principle of minimum complementary energy and have different degrees of accuracy with respect to the stress assumptions used (Hashin's, 2D 0° and 2D 0°/90° models). Using FEM, the plane stress and strain state were analyzed. The effect of material properties and layer thickness on the stress distribution in a 90° layer was evaluated by varying the crack spacing. The crack opening displacement (COD), normalized with respect to the far field strain, is proposed as a measure of reduction of the mechanical properties. Since the CODs are rather insensitive to the crack spacing (crack density) in a wide region, they will be used in modeling the stiffness reduction in these laminates [1].Translated from Mekhanika Kompozitnykh Materialov, Vol. 33, No. 6, pp. 796–820, November–December, 1997.     

Algebraic classification of physical structures with zero. II. Topological aspects

Some topological analogs are obtained of the author’s previous results on the classification of physical structures. A topological-algebraic axiomatics is considered enabling us to replace the algebraic axiom corresponding to the main equation of a physical structure by a more natural axiom. A physical structure of rank different from (2, 2) is shown to be a pair of vector spaces with a nondegenerate bilinear form over a topological skew field. The obtained results are applied to the classification of physical structures of rank different from (2, 2). The structures of rank (2, 2) are also considered. To describe them, a topological group structure corresponding to the biform action is introduced on the set of measurements.     

Moving boundary i.b.v.p.s for Schrödinger equations: Solution bounds and related results

The paper is concerned with i.b.v.p.s for Schrödinger equations, linear and nonlinear, in a straight line region with prescribed, moving boundaries, upon which (time-dependent) Dirichlet conditions are specified. Bounds, in terms of data, are obtained for the L₂ norm of the spatial derivative of the solutions, or for a measure related thereto: in the context of expanding boundaries, pointwise bounds for the solution may be inferred both in the linear case and in some nonlinear cases (e.g. the defocusing case). Asymptotic properties of the bounds for the aforementioned norm are discussed in the linear case. The methodology of the paper is based on a particular compact formula for the aforementioned norm of an arbitrary, complex-valued function whose values are assigned, as functions of time, on the assigned, moving boundaries of a straight line region. The application of the methodology to i.b.v.p.s for other p.d.e.s is discussed briefly.     

Nonlinear Approximation with Dictionaries. II. Inverse Estimates

In this paper, which is the sequel to [16], we study inverse estimates of the Bernstein type for nonlinear approximation with structured redundant dictionaries in a Banach space. The main results are for blockwise incoherent dictionaries in Hilbert spaces, which generalize the notion of joint block-diagonal mutually incoherent bases introduced by Donoho and Huo. The Bernstein inequality obtained for such dictionaries is proved to be sharp, but it has an exponent that does not match that of the corresponding Jackson inequality.     

In memore of E.M. Landis

The purpose of this paper is to establish local theory for retarded functional differential equations with infinite delay, Some new conditions are proposed, and new results are obtained which is more general than the previous one. Our phase space is pseudo-metric space. We do not need x₊ to be continuous in t on phase space. Our theorems are especially effective for Volterra integro-differential equations