An achromatic collimator for a multi-window flight simulator

Some flight simulators, known as multi-window simulators, are required to produce a wide field of view obtained by viewing a number of TV monitors through separate collimators. The extra requirement for shadowgraph projection of additional cueing information such as the sky and the horizon on to a dome above the pilot's head means that it is impossible to use the conventional concave mirror collimator. An alternative system is the Pancake Window but this gives insufficient light output.This paper describes the design of a three-element, all-plastic, one aspheric surface, achromatic, collimating lens which overcomes these problems. It is based on work carried out for the Royal Aircraft Establishment.     

Defining the size and location of the slit in rainbow holography

A simple method is described for defining the size and location of the slit in a rainbow holography optical system in order to guarantee the optimal observation conditions of the reconstructed image. A brief explanation of the basic principles of rainbow holography is given and the projection of viewing slits and pseudoscopic, or orthoscopic, images is considered. An application of the method for afocal systems used in rainbow holography is presented.     

Scaling spectra and return times of dynamical systems

The grand canonical version of the spectrum of singularities formalism is presented, relying naturally upon certain Markov transition graphs. The structure of a graph is simply determined by the close return times of the dynamical system described. Thus, an intimate connection exists between the shape of the singularity curve and a small but interesting set of dynamical properties.     

Bifurcation and disaggregation in urban/regional spatial modelling: A technical note

Using the Lowry-Garin model as an example, we illustrate the complexity of bifurcation and aggregation issues in urban/regional spatial systems. As a first step, a disaggregate version of the Lowry-Garin model is formulated. Then the general conditions for bifurcation are identified in terms of disaggregate labor-force participation rate, population-serving ratio and accessibility indices. Physical interpretation of these conditions is also given.     

Possibilistic linear regression analysis for fuzzy data

Fuzzy data given by expert knowledge can be regarded as a possibility distribution by which possibilistic linear systems are defined. Recently, it has become important to deal with fuzzy data in connection with expert knowledge. Three formulations of possibilistic linear regression analysis are proposed here to deal with fuzzy data. Since our formulations can be reduced to linear programming problems, the merit of our formulations is to be able to obtain easily fuzzy parameters in possibilistic linear models and to add other constraint conditions which might be obtained from expert knowledge of fuzzy parameters. This approach can be regarded as a fuzzy interval analysis in a fuzzy environment.     

Deterministic one-dimensional cellular automata

A formal treatment of some of the properties of deterministic, rule 150, elementary one-dimensional cellular automata (CA) with null boundary conditions is presented. The general form of the characteristic polynomial of the CA global rule transition matrix is obtained. Mathematical relationships between the CA register lengths and the order of the corresponding group or semigroup structures are derived.     

Numerical Energy Conservation for Multi-Frequency Oscillatory Differential Equations

The long-time near-conservation of the total and oscillatory energies of numerical integrators for Hamiltonian systems with highly oscillatory solutions is studied in this paper. The numerical methods considered are symmetric trigonometric integrators and the St?rmer–Verlet method. Previously obtained results for systems with a single high frequency are extended to the multi-frequency case, and new insight into the long-time behaviour of numerical solutions is gained for resonant frequencies. The results are obtained using modulated multi-frequency Fourier expansions and the Hamiltonian-like structure of the modulation system. A brief discussion of conservation properties in the continuous problem is also included. AMS subject classification (2000) 65L05, 65P10     

一种可用于生产效率评价的灰靶评估算法

本文在分析和比较了DEA和灰靶评估两种方法之后，给出一种可用于生产效率评价的灰靶评估算法。该算法由于运用了DEA方法中的“生产效率”概念，弥补了灰靶评估算法不能对不同的被评价单元进行效率评价的不足，从而拓宽了灰靶评估算法的应用背景。文章最后给出实例分析。     

Corrigendum to “Discrepancy principle for the dynamical systems method” [Communications in Nonlinear Science and Numerical Simulation 10 (2005) 95–101]

Consider an operator equation B(u) − f = 0 in a real Hilbert space. Let us call this equation ill-posed if the operator B′(u) is not boundedly invertible, and well-posed otherwise. The dynamical systems method (DSM) for solving this equation consists of a construction of a Cauchy problem, which has the following properties: (1) it has a global solution for an arbitrary initial data, (2) this solution tends to a limit as time tends to infinity, (3) the limit is the minimal-norm solution to the equation B(u) = f. A global convergence theorem is proved for DSM for equation B(u) − f = 0 with monotone operators B.