Charged particle evaporation from compound nuclei formed by bombardment of58Ni with 70 MeV16O ions II

The experimental data have been compared with the result of extensive compound nucleus calculations based on the statistical theory. The shapes and the absolute cross sections for the high energy parts of the proton- and -spectra are reproduced with a level density parametera 0·11 A MeV^–1 and a moment of inertiaJ1·3J _rig. The same parameters fairly well reproduce the angular distributions corresponding to the high energy parts of the spectra whereas deviations between theory and experiment are observed for the lower energies where particles emitted by higher order processes contribute. The observed total cross section for emission of an -particle is 500 mb or 1·7 times calculated value. For protons the corresponding numbers are 2313 mb and 3·0. The increase in cross section is ascribed to the process in which several particles are evaporated. Various methods are discussed for determination of the average orbital angular momentum of the emitted particle or the average spin of the daughter nucleus.On leave fromFaculty of Matematics and Physics, Charles University, Prague, Czechoslovakia.     

Risikominimierung bei der Portfolioplanung unter besonderer Berücksichtigung singulärer Kovarianzmatrizen

Zusammenfassung Bisher waren die Untersuchungen über Erwartungswert-Streuungs-effiziente Wertpapiermischungen auf den Fall nichtsingulärer Kovarianzmatrizen beschränkt. Der Fall singulärer Kovarianzmatrizen war bisher nicht konstruktiv behandelt worden. Es wird in dem vorstehenden Papier in einem allgemeinen Ansatz, der auch den Fall singulärer Kovarianzmatrizen zuläßt, die allgemeine Gültigkeit des Separationstheorems und des Zwei-Fonds-Theorems nachgewiesen.

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Summary Previous studies of mean-variance-efficient portfolios got constructive results in the case of non-singular covariance matrices only, singular covariance matrices were not treated in a constructional way. The present paper proves the Separation Theorem and the Two-Fonds-Theorem within a general framework including the case of singular covariance matrices.

     

On the interactive solution to a multicriteria scheduling problem

Summary A mixed integer multiple criteria model is formulated for scheduling problems. Its solution is obtained by an interactive method based on the Tchebycheff-approximation. For solving greater problems some modifications are discussed at the end of the paper, which are essentially based on the notion of heuristic efficiency.

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Zusammenfassung Da bei Ablaufplanungsproblemen häufig mehrere Zielsetzungen zu beachten sind, wird im folgenden Beitrag hierzu ein gemischt-ganzzahliges multikriterielles Entscheidungsmodell formuliert. Seine Lösung erfolgt mit Hilfe eines interaktiven Verfahrens. Zur numerischen Lösung größerer Problemstellungen sind einzelne Verfahrensmodifikationen erforderlich, die im wesentlichen auf dem im letzten Abschnitt eingeführten Begriff der heuristischen Effizienz aufbauen.

     

Principles of alignment of multibeam lasers for thermonuclear purposes

The concrete object of the investigation is the alignment of the high-power 12-channel Del'fin neodymium-glass laser facility. The objects of the alignment are the optical channel of the laser installation, the system for pointing and focusing the laser radiation on the target, the system for positioning the target in the focal volume, and the system for monitoring the optical quality of the elements of the laser installation and laser beams and also the conditions of the target irradiation in the vacuum chamber. The list of requirements that must be satisfied by the alignment beams, the possible sources of alignment beams, the makeup of the apparatus, and the methods of aligning the laser facility are considered. The principles and the actual systems of automatic alignment of the optical elements are described, as are the operating models of the automatized units. The problem of simulating the working laser beams by the alignment beams and the possibility of automatizing the control of the spatial and angular characteristics of the laser radiation are discussed. The system for controlling the alignment processes by means of a laser is considered, as is also a scheme for incorporating the automatized alignment subsystem in the overall system for the automation of the Del'fln facility.Translated from Trudy Ordena Lenina Fizicheskogo Instituta im. P. N. Lebedeva, Vol. 103, pp. 52–83, 1978.     

Decomposition of weakly aging distributions

A class of weakly aging distribution functions is introduced and a number of properties of this class are derived. It is proved in particular that a random variable , having a weakly aging distribution function, can be written as a sum of two independent random variables, one of which has exponential distribution with a parameter equal to the modulus of the singular point of Me^–s nearest the coordinate origin.Translated from Matematicheskie Zametki, Vol. 22, No. 4, pp. 571–574, October, 1977.     

A linear multistep numerical integration scheme for solving systems of ordinary differential equations with oscillatory solutions

In ^[1], a set of convergent and stable two-point formulae for obtaining the numerical solution of ordinary differential equations having oscillatory solutions was formulated. The derivation of these formulae was based on a non-polynomial interpolant which required the prior analytic evaluation of the higher order derivatives of the system before proceeding to the solution. In this paper, we present a linear multistep scheme of order four which circumvents this (often tedious) initial preparation. The necessary starting values for the integration scheme are generated by an adaptation of the variable order Gragg-Bulirsch-Stoer algorithm as formulated in ^[2].     

A new ℋ -space formalism

The equations governing geometrical objects in ? space are written in terms of operators adapted to families of left shear-freeσ ⁰= 0) cross sections of complexified null infinity (C I ⁺). The concept of ?-conformai weight (HCW) is introduced, and a derivative operatorI _a ^′ , which is closely connected with the covariant derivative but which (unlike the covariant derivative) maps objects having well-defined HCW to other such objects, is defined. A function ?, derived from the Gaussian curvature of left shear-free slicings ofC I ⁺ and having a well-defined HCW, is shown to contain all the curvature information for ? space.     

Nuclear structure effect in internal conversion of the 166 kev hinderedM1 transition in139La

The internal conversion coefficients were calculated for the 165.853 keV 5/2⁺7/2⁺ hindered transition in ₅₇ ¹³⁹ La using the new computer program NICC for conversion coefficients of all atomic shells. The algorithm employed in this code is described. The analysis of precise experimental data yielded the nuclear penetration parameter=4.2±0.8. This value was found to be in accord with theoretical estimates and to correspond to the Nilsson deformation parameter=–0.056±0004 of the¹³⁹La nucleus. Using the Nilsson wave functions for above the mixing ratio ² = N(E2)/N(M1) was determined to be less than 8.10^–5, which supports the assumption of a pureM1 multipolarity of this transition.Presented at the 26th All-Union Conference on Nuclear Spectroscopy and Nuclear Structure (February 1976, Baku, USSR).We are obliged to Dr. B. N.Subba Rao for the communication of his value for the investigated transition.     

A measurement of the lifetimes of Ξ0 and Λ hyperons

The mean lifetimes of the Λ and Ξ⁰ hyperons have been measured in a short neutral beam at the CERN Proton Synchrotron. Λ and Ξ⁰ decays have been identified by measuring their decay products in a magnetic spectrometer and in a lead glass hodoscope. The experimental results, based on 53 000 Λ decays and 6300 Ξ⁰ decays are

From the result for τ_Ξ⁰ together with existing data on τ_Ξ^? we obtain a violation of the $\text{ΔI =}\text{1}\text{2}$ rule in non-leptonic Ξ decays.