Renewal theorem for a class of stationary sequences

Summary A renewal theorem is obtained for stationary sequences of the form _n=(...,X _n-1,X _n,X _n+1...), whereX _n, , are i.i.d. r.v.s. valued in a Polish space. This class of processes is sufficiently broad to encompass functionals of recurrent Markov chains, functionals of stationary Gaussian processes, and functionals of one-dimensional Gibbs states. The theorem is proved by a new coupling construction.Research supported by the National Science Foundation     

How large can a hereditarily separable or hereditarily Lindelöf space be?

The main result of this paper is that ifV satisfies GCH andω ₁<λ<μ are arbitrary regular cardinals, then in some cardinal preserving forcing extensionW ofV we have λ^<λ=λ=2 ^N 0,μ=2 ^λ and there are a hereditarily separableX ?2 ^λ with |X|= \(2^{\aleph _0 } \) =μ and a hereditarily LindelöfY ?2 ^μ withw(Y)= \(2^{2^\aleph 0} \) =μ. So far similar results have only been obtained under the assumption of CH.     

Observables on hypergraphs

Observables on hypergraphs are described by event-valued measures. We first distinguish between finitely additive observables and countably additive ones. We then study the spectrum, compatibility, and functions of observables. Next a relationship between observables and certain functionals on the set of measures M(H) of a hypergraph H is established. We characterize hypergraphs for which every linear functional on M(H) is determined by an observable. We define the concept of an effect and show that observables are related to effect-valued measures. Finally, we define operational transformations from M(H) to itself and show that they can be described as a certain combination of effects.On leave from University of Berne, Institute of Mathematical Statistics, Sidlerstrasse 5, CH-3012 Berne, Switzerland.     

An explicit formula for the discussion of stability in autonomous Hamiltonian systems

The well known theorem of Arnold and Moser gives (in most cases) an answer to the question of the stability of the equilibria of autonomous Hamiltonian systems which can be reduced to two degrees of freedom. To apply their theorem, the Hamiltonian has to be transformed into its Birkhoff normal form of order two. In this paper this transformation is reduced to the multiplication of polynomials, which can easily be performed algebraically on a computer. The conical precessions of a dynamically symmetric satellite in a circular orbit serve as an example.

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Zusammenfassung Der bekannte Satz von Arnold und Moser liefert (auer in wenigen Ausnahmefällen) eine Antwort auf die Frage nach der Stabilität von Gleichgewichtslagen autonomer Hamiltonscher Systeme, die sich auf zwei Freiheitsgrade reduzieren lassen. Damit dieser Satz angewendet werden kann, mu die Hamiltonfunktion auf ihre Birkhoff-Normalform der Ordnung zwei transformiert werden. Diese Transformation wird hier auf Multiplikationen von Polynomen reduziert, die einfach, in symbolischer Weise, auf dem Computer ausgeführt werden können. Als Beispiel dienen die konischen Präzessionen eines dynamisch symmetrischen Satelliten auf einer Kreisbahn.

     

Complete integrability of the supersymmetric model (cos φ)2

Complete integrability of the supersymmetric, two-dimensional sine-Gordon model of field theory within the framework of the Hamiltonian interpretation of the method of the inverse problem is proved. The classical r-matrix of the model is computed, and its equivalence to the r-matrix the Grassmann Thirring model is established. Variables of creation-annihilation type are constructed, and the spectrum of elementary excitations of the system is obtained.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 120, pp. 122–135, 1982.     

A two-stage nonlinear cochlear model possesses automatic gain control

A model of the cochlea is explored using as stimuli two simultaneously presented sinusoids of equal amplitude. The model consists of two stages: a linear bandpass filter, followed by a reservoir-type representation of the hair-cell/nerve-fiber complex. Fast Fourier transforms of the model's output were computed. While the amplitudes of the individual response components were strongly nonlinear functions of intensity, the ratio of the magnitudes of the response components at the frequencies of the two stimulating sinusoids was found to be nearly equal, over a wide intensity range, to the ratio of the amplitudes which those stimulating sinusoids possessed at the output of the filter. Thus the reservoir stage exerts "automatic gain control".     

Gallium arsenide avalanche-type S-diode based on a n+-π-ν-n structure

The results are presented of an investigation of the electrical characteristics of avalanche S-diodes based on a new type of structure (⁺---n), which is obtained by diffusing iron in GaAs with n = 1.10¹⁷ cm^–3. The diodes have regions of S-type negative differential resistance (NDR), for both bias polarities and have a number of other features by comparison with diodes based on the --n structures with fused contacts. We discuss the mechanism for the formation of the NDR region of the voltage-current characteristics of the diode.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 4, pp. 54–58, April, 1986.     

Separation and determination of volatile compounds in synthetic wine samples by gas chromatography using UV-visible molecular absorption spectrometry as detector

This paper shows the separation and determination of eight compounds containing the OH group (ethanol, pentanol, 3-methyl-1-butanol, hexanol, phenol, benzyl-alcohol, phenylethanol and geraniol) in synthetic wine by gas chromatography using UV-Vis molecular absorption spectrometry as detection system. All the parameters affecting the separation and determination were optimised using some methods of experiment design. The analytical characteristics of each compound were calculated and detection limits ranging from 2.3 to 74 mg l(-1) have been obtained.