Asymptotic stabilization of the position of a rigid body with fixed point without velocity measurements

The problem of stabilization of a rigid body with a fixed point in reference to its velocity and position is considered. It is assumed that the rigid body is controlled by three external torques. The proposed controlling torques need neither the measurements of the velocity nor the information about the inertial parameters. Such a control may be realized by the on-line solution of the auxiliary differential equations.The stability of the closed loop nonlinear system is established by means of the Lyapunov function and Barbashin's theorem. The proposed control may be applied to stabilize the satellites controlled by the reactive jets.     

Exact and general FT1 penultimate distributions of extreme wind speeds drawn from tail-equivalent Weibull parents

We present a contribution to the current debate on methodologies for assessing extreme wind speeds. We review long-established extreme theory in the light of recent developments and show that it is unnecessary, indeed inappropriate, to resort to asymptotic models. We develop Cramér's method for the general penultimate distribution of extremes for the case of Weibull parents into a new model for extreme wind speeds that avoids the issues of asymptotic convergence and the associated errors. We demonstrate that the 30-year record of hourly mean wind speed at Boscombe Down, UK, has right-tail equivalence to the Weibull distribution and use this record to demonstrate the new model.     

Singular stress fields in interfacial notches of hybrid metal matrix composites

This paper presents results from a study on the singular stress fields in metal matrix composites in which dual matrices exist. The adjoining metallic matrices flanking the interface can deform plastically with powerlaw strain hardening. These matrices may have both different hardening exponents and different yield strengths. An asymptotic analysis coupled with numerical eigen-analysis solved the spatial structure of the singular stress field at radial- and angular-dependent parts: . The dependence of the strength of the singular stresses on the matrix properties is discussed. The effects of local geometry on the nature of singular stresses are addressed. Highlights for interfacial notches are reported here. The drivers for this study are interfacial notches and free-edges in hybrid metal matrix composites (Fig. 1). However, the results can also be applied to other advanced structures which are composed of two or more distinct components or phases such as bone-implant interfaces and surface mounts in electronic packages     

A numerical study on low and higher-order potential based BEM for 2D inviscid flows

A formal error analysis of the order of approximation of a potential based boundary element method (BEM) for two-dimensional flows is performed in order to derive consistent approximations for the potential integrals. Two higher-order approaches satisfying consistency requirements to attain second and third order convergence in the potential are selected for numerical implementation. From the formal local expansions of the potential integrals the influence coefficients are derived and evaluated analytically. In order to assess the methods accuracy, the low and higher-order methods are applied to two-dimensional steady flows around analytical foils. A numerical error analysis is done and a comparison between their theoretical and numerical asymptotic order of accuracy performed. The first author acknowledges the financial support granted by Fundação para a Ciência e a Tecnologia, Ph.D. grant PRAXISXXI/BD/2226/99. This work was done under the project PRAXIS/2/2.1/MAR/1723/95.     

Approximate Bayesian methods

Summary This paper develops asymptotic expansions for the ratios of integrals that occur in Bayesian analysis: for example, the posterior mean. The first term omitted isO(n ⁻²) and it is shown how the termO(n ⁻¹) can be of importance.     

Further results on the effect of intraclass correlation among training samples in discriminant analysis

The effect of intraclass correlation among training samples on the misclasification probabilities of Bayes' procedure has been recently studied by Basu and Odell.⁽¹³⁾ This paper investigates the effect further by expressing the misclassification probabilities in the form of asymptotic expansions. It is subsequently shown that contrary to previous conclusions the misclassification probabilities do change in the presence of simple equicorrelation among the training samples.     

Generation of waves by a moving oscillatory source in magnetohydrodynamics

The two-dimensional linear gravity waves created by a moving oscillatory source in an incompressible, inviscid, electrically conducting fluid of infinite depth where a constant magnetic field acts outside the air-water interface are considered. To determine the unsteady asymptotic waves, Bleistien's method had been applied to the Fourier transform solution. Several physically interesting results about the four waves generated, together with their fronts, are found and also the effect of magnetic force on the gravity waves has been studied.     

CONSISTENT ESTIMATION OF THE FOURTH-ORDER CUMULANT SPECTRAL DENSITY

Abstract. In this paper we consider the estimation of the fourth-order cumulant spectral density. Indeed this is the first case where the cumulant depends on lower-order product moments for a mean-zero stationary process. The proposed estimator of the fourth-order cumulant spectral density is constructed by replacing product moments with appropriately weighted estimates of product moments according to the definition of the fourth-order cumulant spectral density. Asymptotic unbiasedness and consistency are shown to hold for these estimators under stationarity and absolute summability of cumulants up to various orders with no restrictions on the frequencies. An expression for the asymptotic variance is also obtained.     

Throughput bounds for closed queueing networks

Analytical lower and upper bounds for the throughput of closed queueing networks with single and delay (infinite) servers are studied in this paper. The numerical evaluation of these bounds requires a small number of significant operations which is independent of the population N. This is in contrast to the exact computation of the throughput which requires at least O(N) operations as N tends to infinity. The bounds are given by simple closed-form analytical expressions and may be more suitable for various performance studies than the algorithmical form of the exact solution.In this paper, the previously known balanced-job bounds are generalized to networks containing delay servers (terminals) and a hierarchy of bounds is obtained for single and multiple class networks. For the single class network, further new bounds are derived: lower and upper bounds that require the evaluation of one square root and an upper bound that requires a constant number of exponentiations. This upper bound does not employ the balancing of server loadings and is especially useful for asymptotic analysis in the case of a large number of customers N.     

Convergence to equilibria in recurrence equations

In this paper, we deal with linear and nonlinear perturbations of first-order recurrence systems with constant coefficients having infinitely many equilibria. We give sufficient conditions for the asymptotic constancy of the solutions of the perturbed equation. As a consequence of our main theorem, we obtain sufficient conditions for systems of higher-order difference equations to have asymptotic equilibrium.