X-ray,Hα, and radio observations of the two-ribbon flare of 16 May, 1981

The paper is a contribution to the study of two-ribbon flares. A variety of observational material, i.e. Hα pictures, radio spectrum in the frequency band of 150–1000 MHz, radio map at 6 cm, fluxes at other frequencies, magnetograms and X-ray flux in a broad energy interval, enabled us to study the development of the 16 May, 1981 flare. The onset of the flare could be described by the model of Van Tend and Kuperus. A diminishing of the magnetic shear during the activation of the filament was observed. From radio and X-ray data it was found that pulsed acceleration took place in the region under the rising filament, the electrons propagating in a limited region both upwards to greater heights and downwards into the footpoints. Internal oscillations of the filament were observed. A manifestation of the primary process of interplanetary shock-wave generation was found. The 6 cm radio sources could be localized in the footpoints of magnetic loops.     

Optimal sequencing for a multipurpose water supply system

The optimal sequencing of a multipurpose water supply system in the Hajduhátság region of Hungary is determined by dynamic programming. The goal function minimizes the present value of capital costs, operation costs, and economic losses due to water shortages. Future water requirements are considered to be random variables because of natural and forecasting uncertainties. The nonlinear optimization problem at each stage is equivalent to a readily solved game theoretical problem, the solution of which is straightforward. Sensitivity analysis performed with respect to economic losses, water requirements and discount rate, showed that optimal development and sequencing depend largely on the economic losses and the discount rate.     

Light curves of the eclipsing systems of RS CVn-type

This work presents the light curves for rotating spotted stars generated by a computational code developed by us. This code is based in a model of the system and its analytical solution. The work also present an analysis of the photometric curve variations with the changes in the model's parameters.As a first result we have simulated a temporal evolution of the light curve when the photospheric spot varies its size and position and we reproduced some observational light curves of the II Peg star.Work supported by Dirección de Investigación, Universidad de La Serena, Chile.     

Correlation of hard X-ray and type III bursts in solar flares

The observed correlations between X-ray and type III radio emissions from solar bursts are described by means of a bivariate distribution function. Procedures for determining the form of this distribution are described using a sample of data analyzed by Kane (1981). With the help of this distribution a model is constructed to explain the correlation between the X-ray spectral index and the ratio of X-ray to radio intensities. Implications of the model are discussed.     

Heat balance for the high-temperature component of a solar flare

Shortly after the occurrence of the impulsive spikes of the two-ribbon flare of May 21, 1980, a temperature analysis of the X-ray emitting flare plasma showed the presence of a low-temperature component [n = 15 × 10¹⁰ cm^#X2212;3; T = 20 × 10⁶ K] and a high-temperature component [n = 2 × 10¹⁰ cm^#X2212;3; T = 40 × 10⁶ K]. The mean free path of an electron in the hot component is comparable to the size of the source (≈ 10⁴ km). Heat losses from the hot source can therefore not be described with classical formulae. Theoretical arguments show that most likely the electron to ion temperature ratio T _e/T_i in the hot plasma is close to unity. This implies the presence of a hot ion component (T _i ≈ 40 × 10⁶ K) as well. Under these conditions (T _e ≈ T _i) heat flux limitation by electrostatic turbulence is ineffective. However, reduction of the heat flux is still possible due to the breakdown of classical theory. It is demonstrated that only non-classical current dissipation processes can sustain a hot source against cooling by a saturated heat flux. Investigation of the collisionality as a function of position along a magnetic loop shows that the breakdown of classical theory should be expected to occur first near the base of the loop. We conclude that the newly discovered hot source is important for the energy budget of the flare, even if the heat losses are considerably reduced. It is estimated that for the May 21, 1980 flare a total of about 10³¹ ergs were necessary to maintain the hot source against heat losses over the time period that it was observed (≈ 10 min).     

Radiative transfer for polarized light: Equivalence between Stokes parameters and coherency matrix formalisms

Two formal solutions of the radiative transfer equation for polarized light have been proposed. One uses the Stokes parameters to describe the polarization, while the other uses the coherency matrix. It is shown in the present work that they are equivalent. Both can be used to compute response and contribution functions for the Stokes parameters and both require the solution of systems of differential equations with similar numbers of independent variables. New equations to solve the radiative transfer problem using the Stokes parameters formalism are presented. In addition, a computer code which synthesizes the Stokes profiles by means of these equations is described.The National Center for Atmospheric Research is sponsored by the National Science Foundation.     

Note on Lagrange's inversion formula

An inductive algorithm is proposed to solve Lagrange's implicit equation when its right hand member is a power series in the small parameter.     

A generalization of Szebehely's equation for three dimensions

Szebehely's equation for the potential generating a prescribed family of orbits in two dimensions is generalized for three-dimensional orbits. A simultaneous system of first-order linear partial differential equations is derived for the determination of the potential in the three-dimensional case. Solutions of this system are found in several cases including Kepler's problem too.Paper presented at the 1981 Oberwolfach Conference on Mathematical Methods in Celestial Mechanics.This paper is dedicated to Professor Victor Szebehely on the occasion of his 60th birthday.