Multidimensional scaling: An analysis of 1980–1990 computers

Computer performance is an important issue for engineering and economic aspects of computer usage, planning, design and research. The Co-plot methodology graphically relates attributes, observations and interrelations between attributes, thus enabling the simultaneous study of all the observations and variables of a given data set. An analysis of performance attributes of computers from the 1980's (1981–1991) was carried out according to the Co-plot methodology. The analysis shows that during this decade, computer performance became more dependent on IO rate, cache size and multiprocessing, and less dependent on memory-size and IO addressing capabilities. At the same time, the high correlation between CPU speed and performance was maintained.     

Aircraft wake vortices – prediction and mitigation

The current abstract presents selected topics investigated within the wake-vortex research program of DLR. Two approaches are addressed that both aim at increasing airport capacity without compromising safety. One approach is to directly alleviate wake vortex strength and stability by constructive measures at the aircraft wings. The other approach utilizes the dominant influence of meteorological parameters like turbulence, wind shear, and temperature stratification on wake vortex fate. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

OR analysis of sporting rules – A survey

This paper surveys the academic OR/analytics literature describing research into the laws and rules of sports and sporting competitions. The literature is divided into post hoc analyses and proposals for future changes, and is also divided into laws/rules of sports themselves and rules/organisation of tournaments or competitions.     

Dynamic flow modelling in precipitator vessels – A study of turbulence modelling approaches

Precipitation is a fundamental unit process within the Bayer circuit for the production of smelter-grade alumina, with the predominant technology used in this unit process being the mechanically-agitated draft-tube precipitator. Previous physical modelling studies have identified dynamic behaviour in these vessels which could potentially impact fluid residence time and the ability to obtain adequate solids suspension. In the current study the commercial CFD code ANSYS CFX14 is used to simulate the dynamic, single phase flow behaviour in a laboratory-scale replica of a full-scale precipitator. Simulations are conducted to investigate the impact of mesh refinement and turbulence model selection, with two-equation, Reynolds Stress and the Scale Adaptive Simulation (SST–SAS) models being investigated. The impact of the different modelling choices on the accuracy of the simulations is assessed through comparison of the CFD results with high-quality Laser Doppler Velocimetry (LDV) data obtained in a laboratory-scale vessel.     

Multidimensional thermoelasticity for nonsimple materials – well-posedness and long-time behavior

An initial-boundary value problem for the multidimensional type III thermoelaticity for a nonsimple material with a center of symmetry is considered. In the linear case, the well-posedness with and without a (second-order in space) Kelvin–Voigt and/or frictional damping in the elastic part as well as the lack of exponential stability in the elastically undamped case are proved. Further, a frictional damping for the elastic component is shown to lead to exponential stability. A Cattaneo-type hyperbolic relaxation for the thermal part is introduced and the well-posedness and uniform stability under a nonlinear frictional damping are obtained using a compactness-uniqueness-type argument. Additionally, a connection between exponential stability and exact observability of unitary strongly continuous groups is established.     

Numerical analysis of quenching – Heat conduction in metallic materials

Metallic materials present a complex behavior during heat treatment processes. In a certain temperature range, change of temperature induces a phase transformation of metallic structure, which alters physical properties of the material. Indeed, measurements of specific heat and conductivity show strong temperature-dependence during processes such as quenching of steel. Several mathematical models, as solid mixtures and thermal–mechanical coupling, for problems of heat conduction in metallic materials, have been proposed. In this work, we take a simpler approach without thermal–mechanical coupling of deformation, by considering the nonlinear temperature-dependence of thermal parameters as the sole effect due to those complex behaviors. The above discussion of phase transformation of metallic materials serves only as a motivation for the strong temperature-dependence as material properties. In general, thermal properties of materials do depend on the temperature, and the present formulation of heat conduction problem may be served as a mathematical model when the temperature-dependence of material parameters becomes important. For this mathematical model we present the error estimate using the finite element method for the continuous-time case.     

Integral analysis method – IAM

This paper presents the theoretical foundations of the new integral analysis method (IAM), and its application to a facility location problem. This methodology integrates the cardinal and ordinal criteria of combinatorial stochastic optimization problems in four stages: definition of the problem, cardinal analysis, ordinal analysis and integration analysis. The method uses the concepts of stochastic multicriteria acceptability analysis (SMAA), Monte Carlo simulation, optimization techniques and elements of probability. The proposed method (IAM) was used to determine optimal locations for the retail stores of a Colombian coffee marketing company.     

Anti-optimization technique – a generalization of interval analysis for nonprobabilistic treatment of uncertainty

Anti-optimization technique, on the one hand, represents an alternative and complement to traditional probabilistic methods, and on the other hand, it is a generalization of the mathematical theory of interval analysis. In this study, in terms of interval analysis or interval mathematics, the arithmetic operations and the partial order relation of anti-optimization technique can be defined, and the convex model variables and the convex model extension function of convex models can also be introduced. The comparison of the Lagrange multiplier method with the convex model extension method for evaluating the region of static displacements of structures with uncertain-but-bounded parameters shows that the width of the upper and lower bounds on the static displacement yielded by the Lagrange multiplier method of convex models is tighter than those produced by the convex model extension.     

A Hierarchy of Multidimensional Hénon-Heiles Systems

Abstract A hierarchy of multidimensional Hénon-Heiles (M-H-H) systems are constructed via the x- and t _n -higher-order-constrained flows of KdV hierarchy. The Lax representation for the M-H-H hierarchy is determined from the adjoint representation of the auxiliary linear problem for the KdV hierarchy. By using the Lax representation the classical Poisson structure and r-matrix for the hierarchy are found and the Jacobi inversion problem for the hierarchy is constructed. Supported by National Research Project “Nonlinear Sciences”     

Multidimensional extension of the Morse–Hedlund theorem

A celebrated result of Morse and Hedlund, stated in 1938, asserts that a sequence x$x$ over a finite alphabet is ultimately periodic if and only if, for some n$n$, the number of different factors of length n$n$ appearing in x$x$ is less than n+1$n+1$. Attempts to extend this fundamental result, for example, to higher dimensions, have been considered during the last fifteen years. Let d≥2$d\ge 2$. A legitimate extension to a multidimensional setting of the notion of periodicity is to consider sets of Z^d${\mathbb{Z}}^d$ definable by a first order formula in the Presburger arithmetic 〈Z;<,+〉$〈\mathbb{Z};<,+〉$. With this latter notion and using a powerful criterion due to Muchnik, we exhibit a complete extension of the Morse–Hedlund theorem to an arbitrary dimension d$d$ and characterize sets of Z^d${\mathbb{Z}}^d$ definable in 〈Z;<,+〉$〈\mathbb{Z};<,+〉$ in terms of some functions counting recurrent blocks, that is, blocks occurring infinitely often.     

Multidimensional analogues of the geometrics⇌t duality

Customarily, the s⇌t duality property for scattering amplitudes, e.g., for the Veneziano amplitude, is naturally related to two-dimensional geometry. Saito and the author previously proposed a simple geometric construction of such amplitudes. Here, we construct analogues of one such amplitude related to multidimensional Euclidean spaces; the three-dimensional case is discussed in detail. The result is a variant of the Regge calculus closely related to integrable models. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 124, No. 1, pp. 169–176, July, 2000.     

Application of homotopy analysis method for fractional Swift Hohenberg equation – Revisited

In this article, the homotopy analysis method is used to obtain the approximate analytical solutions of the non-linear Swift Hohenberg equation with fractional time derivative. The fractional derivative is described in Caputo sense. Numerical results reveal that the method is easy to implement, reliable and accurate when applied to time fractional nonlinear partial differential equations. Effects of parameters of physical importance on the probability density function and the convergence of the approximate series solution using residual error formula with the proper choices of auxiliary parameter for various fractional Brownian motions and standard motion are depicted through graphs and tables for different particular cases.     

A Multidimensional Generalization of Shukla's 8ψ8 Summation

Abstract. We give an r -dimensional generalization of H. S. Shukla's very-well-poised ₈ ψ ₈ summation formula. We work in the setting of multiple basic hypergeometric series very-well-poised over the root system A _r-1 or, equivalently, the unitary group U(r) . Our proof, which is already new in the one-dimensional case, utilizes an A _r-1 nonterminating very-well-poised ₆ φ ₅ summation by S. C. Milne, a partial fraction decomposition, and analytic continuation.     

On problems of the laminar–turbulent transition

The initial stage of the laminar–turbulent transition is reconstructed. Its mechanism is based on spinodal decomposition (diffusion separation).     

Determination of the relaxation and retardation spectra – a view from the up-to-date signal processing perspective

The problem of determination of relaxation and retardation spectra (RRS) is considered from the viewpoint of up-to-date signal processing. It is shown that the recovery of RRS represents the Mellin deconvolution problem, which transforms into the Fourier deconvolution problem for data on a logarithmic time or frequency scale, where it can also be treated as the inverse filtering problem. On this basis, discrete deconvolution (inverse) filters operating with geometrically sampled data are proposed to use as RRS estimators. Appropriate frequency responses and algorithms are derived for estimating RRS from eight different material functions. The noise amplification coefficient is suggested to use as a measure for quantifying the degree of ill-posedness and illconditioness of the RRS recovery problem and algorithms. A methodology is developed for designing RRS estimators with a desired noise amplification, producing maximum accurate spectra for available limited input data. Practical algorithms for determining RRS are proposed, and their performance is studied. The algorithms suggested are compared with the so-called moving-average formulae. It is demonstrated that the minimum frequency range for recovering the point estimate of a relaxation spectrum depends on the allowable noise amplification (the degree of ill-conditioness) and is in no way limited by 1.36 decades, as it is stated by the sampling localization theorem.     

Simplex—Karyon Algorithm of Multidimensional Continued Fraction Expansion

A simplex–karyon algorithm for expanding real numbers α = (α₁,..., α _d ) in multidimensional continued fractions is considered. The algorithm is based on a (d + 1)-dimensional superspace S with embedded hyperplanes: a karyon hyperplane K and a Farey hyperplane F. The approximation of numbers α by continued fractions is performed on the hyperplane F, and the degree of approximation is controlled on the hyperplane K. A local ?(r)-strategy for constructing convergents is chosen, with a free objective function ?(r) on the hyperplane K.