We suggest an advanced algorithm for semi-analytical calculation of orbital perturbations of Earth artificial satellites caused by the gravity attraction of the “3rd-bodies” (the Moon, the Sun, major planets). A new accurate analytical series for the relevant perturbation function is developed. It is obtained through a careful spectral analysis of the long-term DE406 planetary/lunar ephemerides and valid over 2000 years, 1000-3000. The series is used in the author’s semi-analytical model of satellite motion. The results of the motion prediction of several Earth satellites obtained by means of the semi-analytical model and a numerical integration method are compared.

A common tool in the practice of Markov chain Monte Carlo (MCMC) is to use approximating transition kernels to speed up computation when the desired kernel is slow to evaluate or is intractable. A limited set of quantitative tools exists to assess the relative accuracy and efficiency of such approximations. We derive a set of tools for such analysis based on the Hilbert space generated by the stationary distribution we intend to sample, $L_2(\pi)$. Our results apply to approximations of reversible chains which are geometrically ergodic, as is typically the case for applications to MCMC. The focus of our work is on determining whether the approximating kernel will preserve the geometric ergodicity of the exact chain, and whether the approximating stationary distribution will be close to the original stationary distribution. For reversible chains, our results extend the results of Johndrow et al. (2015) from the uniformly ergodic case to the geometrically ergodic case, under some additional regularity conditions. We then apply our results to a number of approximate MCMC algorithms.

In this paper, we study uniform perturbations of von Neumann subalgebras of a von Neumann algebra. Let $M$ and $N$ be von Neumann subalgebras of a von Neumann algebra with finite probabilistic index in the sense of Pimsner and Popa. If $M$ and $N$ are sufficiently close, then $M$ and $N$ are unitarily equivalent. The implementing unitary can be chosen as being close to the identity.

Titan longitudinal librations are dependent on the satellite internal structure and the elastic behavior of the surface. The elastic deformation of the surface is related to the perturbing potential through the Love theory. In a previous paper, we described the deformation as a response to the tidal potential exerted by Saturn at orbital frequency. Here we improve the tidal deformation reponse by including the effect of the libration angle and the orbital perturbations. We then provide the libration amplitudes associated with the rotational model of a tidally deformed three-layer Titan evolving on a non-Keplerian orbit.

In this paper we consider near inclusions $A\,{{\subseteq }_{\gamma }}\,B$ of ${{\text{C}}^{*}}$-algebras. We show that if $B$ is a separable type $\text{I}$${{\text{C}}^{*}}$-algebra and $A$ satisfies Kadison's similarity problem, then $A$ is also type $\text{I}$. We then use this to obtain an embedding of $A$ into $B$.

Secondary flows consisting of two pairs of vortices arise when two fluid streams meet at a confluence, such as in the airways of the human lung during expiration or at the vertebrobasilar junction in the circulatory system, where the left and right vertebral arteries converge. In this paper the decay of these secondary flows is studied by considering a four-vortex perturbation from Poiseuille flow in a straight, three-dimensional pipe. A polynomial eigenvalue problem is formulated and the exact solution for the zero Reynolds number R is derived analytically. This solution is then extended by perturbation analysis to produce an approximation to the eigenvalues for R ≪ 1. The problem is also solved numerically for 0 ≤ R ≤ 2,000 by a spectral method, and the stability of the computed eigenvalues is analysed using pseudospectra. For all Reynolds numbers, the decay rate of the swirling perturbation is found to be governed by complex eigenvalues, with the secondary flows decaying more slowly as R increases. A comparison with results from an existing computational study of merging flows shows that the two models give rise to similar secondary flow decay rates.

The paper deals with periodic systems of ordinary differential equations (ODEs). A new approach to the investigation of variations of multipliers under perturbations is suggested. It enables us to establish explicit conditions for the stability and instability of perturbed systems.

We explain an array of basic functional analysis puzzles on the way to general spectral flow formulae and indicate a direction of future topological research for dealing with these puzzles.

Fish communities of a fourth order stream impounded by a weir were studied in Southern Nigeria. Fifty-eight species were recorded of which 90% occurred upstream while reservoir and downstream accounted for 48% and 43% respectively. The distribution of some fish families indicated the effects of habitat alterations caused by reservoir and downstream conditions. The fauna upstream was different from that of reservoir and downstream. Relative abundance of non-cichlids common to reservoir and downstream showed 42% similarity. The longitudinal distribution of three non-cichlid populations was different in reservoir and downstream. Non-cichlid species richness was almost similar in reservoir and downstream, but its general diversity and evenness were higher in reservoir than its downstream. Fish community changes in this stream are discussed.

L'objectif de ce travail est de déterminer une forme de profil de vitesse à l'entrée d'un tube circulaire, ainsi que la forme géométrique de la paroi de la conduite correspondant, permettant de maximiser le transfert de chaleur à l'intérieur de la conduite. On considère la convection mixte, bidimensionnelle, laminaire pour un fluide newtonien, en géométrie axisymetrique. Le profil de vitesse axiale à l'entrée du tube optimum, est obtenu numériquement, en résolvant le système d'équations aux dérivées partielles en coordonnées cylindriques, par une méthode aux différences finies. Pratiquement ce profil est obtenu en modifiant sur une longueur donnée, la forme de la paroi de la conduite créée par des perturbations particulières du profil amont, ce qui permet de générer le profil choisi.

Additive perturbation results for the generalized Drazin inverse of Banach space operators are presented. Precisely, if Ad denotes the generalized Drazin inverse of a bounded linear operator A on an arbitrary complex Banach space, then in some special cases (A + B)d is computed in terms of Ad and Bd. Thus, recent results of Hartwig, Wang and Wei (Linear Algebra Appl. 322 (2001), 207–217) are extended to infinite dimensional settings with simplified proofs.

Let P be the transition matrix of a positive recurrent Markov chain on the integers, with invariant distribution π. If (n)P denotes the n x n ‘northwest truncation’ of P, it is known that approximations to π(j)/π(0) can be constructed from (n)P, but these are known to converge to the probability distribution itself in special cases only. We show that such convergence always occurs for three further general classes of chains, geometrically ergodic chains, stochastically monotone chains, and those dominated by stochastically monotone chains. We show that all ‘finite’ perturbations of stochastically monotone chains can be considered to be dominated by such chains, and thus the results hold for a much wider class than is first apparent. In the cases of uniformly ergodic chains, and chains dominated by irreducible stochastically monotone chains, we find practical bounds on the accuracy of the approximations.

We study the effect of perturbations in the data of a discrete-time Markov reward process on the finite-horizon total expected reward, the infinite-horizon expected discounted and average reward and the total expected reward up to a first-passage time. Bounds for the absolute errors of these reward functions are obtained. The results are illustrated for a finite as well as infinite queueing systems (M/M/1/S and ). Extensions to Markov decision processes and other settings are discussed.

In many Markov chain models, the immediate characteristic of importance is the positive recurrence of the chain. In this note we investigate whether positivity, and also recurrence, are robust properties of Markov chains when the transition laws are perturbed. The chains we consider are on a fairly general state space : when specialised to a countable space, our results are essentially that, if the transition matrices of two irreducible chains coincide on all but a finite number of columns, then positivity of one implies positivity of both; whilst if they coincide on all but a finite number of rows and columns, recurrence of one implies recurrence of both. Examples are given to show that these results (and their general analogues) cannot in general be strengthened.