The formulas are derived for calculation of the third-order aberration coefficients for a thick spherical lens in air with a given value of its focal length and for an object at infinity. Equations were described for the re-calculation of aberration coefficients for different values of focal length and also entrance pupil and object positions. and V článku jsou odvozeny vztahy pro výpočet aberačních koeficientů třetího řádu pro tlustou čočku ve vzduchu a pro danou ohniskovou vzdálenost a pro předmět v nekonečnu. Dále jsou uvedeny rovnice pro přepočet aberačních koeficientů pro libovolnou hodnotu ohniskové vzdálenost, polohu vstupní pupily a polohu předmětu.
This paper aims to provide a comprehensive survey of phrasal and clausal comparative constructions in the N. W. Caucasian language Abkhaz (in relation to data from the standard, Abzhywa dialect). Following the lead of Knecht (1976), the following three terms will be used throughout this article: (a) Remainder = in the phrasal comparative, a single NP (preceded by “than” in English); in the clausal comparative, the remains of the clause; (b) Trigger = the quantified constituent in the controlling clause; (c) Target = the compared constituent in the comparative clause obligatorily deleted by Comparative Deletion.
In der vorliegenden Arbeit werden die allgemeinen Beziehungen abgeleitet, durch die die Abnahme der Sonnenflecken vom Mittelpunkt zum Rand der Sonnenscheibe mit Rücksicht auf die Verteilung der Sonnenflecken in heliographischen Breiten bestimmt wird, wobei drei verschiedene Methoden der Darstellung dieser Abnahme verwendet werden. Durch eine annähernde Berechnung wird gezeigt, dass alle drei Methoden praktische einen übereinstimmenden Verlauf der Abnahme ergeben, und dass die verschiedene Sonnenfleckenzahl in verschiedenen heliographischen Breiten praktisch keinen Enfluss auf den Verlauf der Abnahme der Sonnenflecken gegen den Sonnenrand ausübt. Die von Fr. Reggenhausen bestimmte Abnahme der Sonnenflecken gegen den Sonnenrand unterscheidet sich aus unbekannten Gründen wesentlich von den übrigen Bestimmungen und von unseren eigenen Resultaten.
The abundance of the objects with splitted nuclei among the candidates - the members of tight systems can be explained by the existence of bright HII regions in their central parts and also by the existence of dust lanes in their nuclear regions. 270 objects out of our lists are listed in IRAS catalogue.
We propose results about sign-constancy of Green's functions to impulsive nonlocal boundary value problems in a form of theorems about differential inequalities. One of the ideas of our approach is to construct Green's functions of boundary value problems for simple auxiliary differential equations with impulses. Careful analysis of these Green's functions allows us to get conclusions about the sign-constancy of Green's functions to given functional differential boundary value problems, using the technique of theorems about differential and integral inequalities and estimates of spectral radii of the corresponding compact operators in the space of essential bounded functions.
We offer the quantitative estimation of stability of risk-sensitive cost optimization in the problem of optimal stopping of Markov chain on a Borel space X. It is supposed that the transition probability p(⋅|x), x∈X is approximated by the transition probability p˜(⋅|x), x∈X, and that the stopping rule f˜∗ , which is optimal for the process with the transition probability p˜ is applied to the process with the transition probability p. We give an upper bound (expressed in term of the total variation distance: supx∈X∥p(⋅|x)−p˜(⋅|x)∥) for an additional cost paid for using the rule f˜∗ instead of the (unknown) stopping rule f∗ optimal for p.