A new method of positional reduction of all-sky photographs taking into account the difference of zenith and the centre of projection is presented. The importance of the exact knowledge of the exposure. time for the evaluation of meteor photographs is demonstrated.
Photographic Zenith Tube Zeiss (PZT) has been regularly used at Ondřejov Astronomical Observatory to determine latitude variations and clock corrections within the frame of Earth rotations service
since 1973. About 45 thousand star transits near the zenith of the observatory were observed and used to improve positions and proper motions of the stars three times, during the history of the observations. To derive the first two catalogues, PZT78 and PZT83 (based on the observations in 1973-1978 and 1973-1983 respectively), PZT observations were combined with star positions in AGK2 and AGK3 catalogues in order to obtain proper motions with higher precision. The most recent catalogue, PZT86, is based solely on PZT observations in the period 1973-1986. The algorithms used to derive all these catalogues as well as their precision and accuracy are discussed in the paper, and their comparison with AGK2/AGK3 given.
Již podruhé se v bubenečské vile Lanně sešli odborníci zabývající se historickými astronomickými deskami. První setkání se konalo před dvěma lety, kdy se diskutovaly problémy desek sužovaných degradací emulze vlivem dlouhého a často nešetrného skladování - letošní akce se zúčastnilo 44 odborníků z 20 zemí od Mexika až po Čínu. and Petr Skala.
We complement the recently introduced classes of lower and upper semilinear copulas by two new classes, called vertical and horizontal semilinear copulas, and characterize the corresponding class of diagonals. The new copulas are in essence asymmetric, with maximum asymmetry given by 1/16. The only symmetric members turn out to be also lower and upper semilinear copulas, namely convex sums of Π and M.
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In this paper we prove two results. The first is an extension of the result of G. D. Jones [4]: (A) Every nontrivial solution for \[ \left\rbrace \begin{array}{ll}(-1)^n u^{(2n)} + f(t,u) = 0,\hspace{5.0pt}\text{in} \hspace{5.0pt}(\alpha , \infty ), u^{(i)}(\xi ) = 0, \quad i = 0,1,\dots , n-1, \hspace{5.0pt} \text{and} \hspace{5.0pt}\xi \in (\alpha , \infty ), \end{array}\right.\] must be unbounded, provided $f(t,z)z\ge 0$, in $E \times \mathbb R$ and for every bounded subset $I$, $f(t,z)$ is bounded in $E \times I$. (B) Every bounded solution for $(-1)^n u^{(2n)} + f(t,u) = 0$, in $\mathbb R$, must be constant, provided $f(t,z)z\ge 0$ in $\mathbb R \times \mathbb R$ and for every bounded subset $I$, $f(t,z)$ is bounded in $\mathbb R \times I$.
The nonlinear difference equation (E) xn+1 − xn = anϕn(xσ(n) ) + bn, where (an), (bn) are real sequences, ϕn : −→ , (σ(n)) is a sequence of integers and lim n−→∞ σ(n) = ∞, is investigated. Sufficient conditions for the existence of solutions of this equation asymptotically equivalent to the solutions of the equation yn+1 − yn = bn are given. Sufficient conditions under which for every real constant there exists a solution of equation (E) convergent to this constant are also obtained.
Asymptotic behavior of solutions of an area-preserving crystalline curvature flow equation is investigated. In this equation, the area enclosed by the solution polygon is preserved, while its total interfacial crystalline energy keeps on decreasing. In the case where the initial polygon is essentially admissible and convex, if the maximal existence time is finite, then vanishing edges are essentially admissible edges. This is a contrast to the case where the initial polygon is admissible and convex: a solution polygon converges to the boundary of the Wulff shape without vanishing edges as time tends to infinity.
The BIPF algorithm is a Markovian algorithm with the purpose of simulating certain probability distributions supported by contingency tables belonging to hierarchical log-linear models. The updating steps of the algorithm depend only on the required expected marginal tables over the maximal terms of the hierarchical model. Usually these tables are marginals of a positive joint table, in which case it is well known that the algorithm is a blocking Gibbs Sampler. But the algorithm makes sense even when these marginals do not come from a joint table. In this case the target distribution of the algorithm is necessarily improper. In this paper we investigate the simplest non trivial case, i. e. the 2×2×2 hierarchical interaction. Our result is that the algorithm is asymptotically attracted by a limit cycle in law.