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.     

Polyene chains in molecular electronics

Current ideas of soliton switching as a possible route towards molecular electronics are reviewed. The relation between photoinduced dipole moments in dye molecules and soliton motion is pointed out. Derivates of -carotene are presented as candidates for components of molecular electronic devices.Dedicated to K. Dransfeld on the occasion of his 60th birthday     

On the diffusion field in the neighborhood of two identical spheres

Summary Under steady state conditions the reduction in the diffusive flux into a sphere due the presence of a neighboring, identical sphere is calculated. Taking the flux into a sphere as 1 when the particles are at infinite separation, the flux decreases to a minimum value of 0.693 when the spheres are touching.

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Zusammenfassung Unter stationären Bedingungen wird die Abnahme des Diffusionsflusses in eine Kugel, bedingt durch eine benachbarte identische Kugel, berechnet.Wird der Diffusionsfluß in eine Kugel gleich 1 gesetzt, wenn die Partikel unendlich weit voneinander entfernt sind, so nimmt der Diffusionsfluß auf einen Minimalwert von 0,693 ab, wenn sich die Kugeln berühren.

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With 2 figures     

Synthesis in the 2-mercaptobenzothiazole series

The reduction of some dihydrothiazolobenzothiazolium salts with sodium borohydride may take place in two directions: with the formation of thiazolidino[2, 3-b]benzathiazolines and with the cleavage of the C-S bond to give N-(-mercaptoethyl)benzothiazolines. The behavior of thiazolidino[2, 3-b]benzothiazoline under the conditions of acid and alkaline hydrolysis has been studied.For communication VI, see [1].     

2.6 Foods

Abstracts2 Particular products and fields of application

2.6 Foods