Numerical evaluation of the dilogarithm of complex argument

A numerical algorithm to evaluate the dilogarithmic function of a complex argument is proposed. The use of the dilogarithm in celestial mechanics appears in the exact Delaunay normalization of some functions involving the equation of the centre.     

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.     

Experimental investigation of the critical ionization velocity in gas mixtures

The critical ionization velocity which is of cosmogonic and astrophysical interest has hitherto mainly been investigated for pure gases. Since in space we always have gas mixtures, it is of interest also to study gas mixtures. The present report, which is a summary of a more detailed report (Axnäs, 1976), summarizes the results of systematic experiments on the critical ionization velocity as a function of the mixing ratio for binary gas mixtures of H₂, He, N₂, O₂, Ne and Ar. The apparatus used is a coaxial plasma gun with an azimuthal magnetic field. The discharge parameters are chosen so that the plasma is weakly ionized. In some of the mixtures it is found that one of the components tends to dominate in the sense that only a small amount (regarding volume) of that component is needed for the discharge to adopt a limiting velocity close to that for the pure component. Thus in a mixture between a heavy and a light component having nearly equal ionization potentials, the heavy component dominates. Also, if there is a considerable difference in ionization potential between the components, the component with the lowest ionization potential tends to dominate.Paper dedicated to Professor Hannes Alfvén on the occasion of his 70th birthday, 30 May, 1978.     

Structure of the 5-minute solar oscillations 1976–1980

The discrete structure in the 5 min velocity oscillations of the solar surface has been confirmed by a re-analysis of data obtained between 1976 and 1979, and in addition a preliminary analysis of 1980 data show excellent consistency of the determined frequencies over the five year period. It is further shown that atmospheric transparency, as measured by the power in the solar intensity fluctuations, shows no correlation with the measured amplitude of the velocity fluctuations, over 2 orders of magnitude.Proceedings of the 14th ESLAB Symposium on Physics of Solar Variations, 16–19 September 1980, Scheveningen, The Netherlands.     

Mean surface brightness as a criterion for or against the expansion of the Universe

Using the well-known relation for the mean surface brightness, the author gives the concept of the decision regarding the expansion of the Universe. The most serious obstacle on this way was the low precision of parameter measurements which one could achieve in the past. This paper brings the first step for eventual judgement if the Universe expand or not because the accuracy of measurements has advanced. In this sence, we need some more determinations with present accuracy to give the decisive result because the mean surface brightness must faint by 1.46 mag per square arc sec for red shift of 0.4, and this is sufficient to measure and statistically elaborate it.     

Image recovering from the modulated CCD imagers

The CCD imagers have a spatial resolution comparable to the size of a constituent photosensitive cell. The modulation by means of a rotating Ronchi grating helps to exceed this limit. While the grating rotates in front of the CCD imager the counts of each cell are modulated thus producing a time-varying modulation pattern. The small systematic variations of the form of the pattern encode the fragment of the image pertaining to the cell. The images can be recovered from the modulation patterns by means of the least-squares as well as maximum entropy reconstruction technique. Both methods are able to decode the modulation patterns having high signal-to-noise ratio, however, maximum entropy reconstruction seems to be more robust. A gain in spatial resolution may be of the order of magnitude under favourable circumstances.     

SPLITTING OF CALIBRATION DATA BY CLUSTER ANALYSIS

from eorresponding valuesof x.The most eommon aPProaeh to this Problem 15 linear regression(or ealibration),but1 inear methods are usually best suited for quite limited regions alld are not generallyaPPlieable.If a linear fit 15 not satisfactory,alternative aPProaehes are non一linear regression,non一Parametrie regression,transformations and sPlitting of the data into subgrouPs     

High-pressure phase transitions — examples of classical predictability

We present 19 examples of materials whose high pressure phase transition points can be determined within a particular classical theory of dense matter. Theoretical predictions are compared with experimental results, and some possible causes of discrepancies are discussed.     

Is special relativity a key to the ‘enigma’ of non-locality phenomenon,in the end?

An idea is put forward that the events considered in the non-locality phenomenon are co-local and simultaneous in the reference frame of information moving with the velocity of light. Then, the special relativity can explain many aspects of the issue. Furthermore, the impact of the idea is discussed in relation to problems of the Mach principle and those of the Planck era connected to the closeness or openess of our Universe.     

Inverse problem in hydrogeology

The state of the groundwater inverse problem is synthesized. Emphasis is placed on aquifer characterization, where modelers have to deal with conceptual model uncertainty (notably spatial and temporal variability), scale dependence, many types of unknown parameters (transmissivity, recharge, boundary conditions, etc.), nonlinearity, and often low sensitivity of state variables (typically heads and concentrations) to aquifer properties. Because of these difficulties, calibration cannot be separated from the modeling process, as it is sometimes done in other fields. Instead, it should be viewed as one step in the process of understanding aquifer behavior. In fact, it is shown that actual parameter estimation methods do not differ from each other in the essence, though they may differ in the computational details. It is argued that there is ample room for improvement in groundwater inversion: development of user-friendly codes, accommodation of variability through geostatistics, incorporation of geological information and different types of data (temperature, occurrence and concentration of isotopes, age, etc.), proper accounting of uncertainty, etc. Despite this, even with existing codes, automatic calibration facilitates enormously the task of modeling. Therefore, it is contended that its use should become standard practice.

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Resumen Se sintetiza el estado del problema inverso en aguas subterráneas. El énfasis se ubica en la caracterización de acuíferos, donde los modeladores tienen que enfrentar la incertidumbre del modelo conceptual (principalmente variabilidad temporal y espacial), dependencia de escala, muchos tipos de parámetros desconocidos (transmisividad, recarga, condiciones limitantes, etc), no linealidad, y frecuentemente baja sensibilidad de variables de estado (típicamente presiones y concentraciones) a las propiedades del acuífero. Debido a estas dificultades, no puede separarse la calibración de los procesos de modelado, como frecuentemente se hace en otros campos. En su lugar, debe de visualizarse como un paso en el proceso de entendimiento del comportamiento del acuífero. En realidad, se muestra que los métodos reales de estimación de parámetros no difieren uno del otro en lo esencial, aunque sí pueden diferir en los detalles computacionales. Se discute que existe amplio espacio para la mejora del problema inverso en aguas subterráneas: desarrollo de códigos amigables al usuario, acomodamiento de variabilidad a través de geoestadística, incorporación de información geológica y diferentes tipos de datos (temperatura, presencia y concentración de isótopos, edad, etc), explicación apropiada de incertidumbre, etc. A pesar de esto, aún con los códigos existentes, la calibración automática facilita enormemente la tarea de modelado. Por lo tanto, se sostiene que su uso debería de convertirse en práctica standard.

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Résumé Létat du problème inverse des eaux souterraines est synthétisé. Laccent est placé sur la caractérisation de laquifère, où les modélisateurs doivent jouer avec lincertitude des modèles conceptuels (notamment la variabilité spatiale et temporelle), les facteurs déchelle, plusieurs inconnues sur différents paramètres (transmissivité, recharge, conditions aux limites, etc.), la non linéarité, et souvent la sensibilité de plusieurs variables détat (charges hydrauliques, concentrations) des propriétés de laquifère. A cause de ces difficultés, le calibrage ne peut être séparé du processus de modélisation, comme cest le cas dans dautres cas de figure. Par ailleurs, il peut être vu comme une des étapes dans le processus de détermination du comportement de laquifère. Il est montré que les méthodes dévaluation des paramètres actuels ne diffèrent pas si ce nest dans les détails des calculs informatiques. Il est montré quil existe une large panoplie de techniques d ‹inversion : codes de calcul utilisables par tout-un-chacun, accommodation de la variabilité via la géostatistique, incorporation dinformations géologiques et de différents types de données (température, occurrence, concentration en isotopes, âge, etc.), détermination de lincertitude. Vu ces développements, la calibration automatique facilite énormément la modélisation. Par ailleurs, il est souhaitable que son utilisation devienne une pratique standardisée.