HIPPARCOS satellite should be launched in 1989. It will measure positions, proper motions, and parallaxes of about 110 000 selected stars brighter than 13, with a precision of 2 milliseconds of arc. Accurate positions (up to 1.5 arc second at the date of observation) and magnitudes (up to O. Smag) have to be known in advance. The star selection has to be optimized with respect to both scientific priorities defined by the ESA Selection Committee, and to technical constraints for satellite operation. The Input Catalogue under construction contains stars selected among the 700 000 ones proposed in 1902 ty the worldwide astronomical community. The Input Catalogue consortium is in charge of making the identifications, providing the necessary data with the required accuracy, and making the selection. A first provisional version has been established in February 1987 and its content is described :
- "survey" of bright stars, about complete up to a limiting magnitude function of both galactic latitude and spectral type, about 55000 stars.
- Painter stars from proposed programmes : nearby stars ; stars with high proper motion ; variable stars, in particular Cepheids and RR Lyrae for distance scale calibration ; open cluster stars ; stars for galactic structure studies > stars in the Magellanic Clouds / stars for reference frame ; stars for linking to the extragalactic system ; minor planets.
A rough estimate of the star distribution versus spectral types and distance is presented. The fulfilment of important astrometric or astrophysical programmes is evaluated.
We set up axioms characterizing logical connective implication in a logic derived by an ortholattice. It is a natural generalization of an orthoimplication algebra given by J. C. Abbott for a logic derived by an orthomodular lattice.
Let G be a finite group and H a subgroup. Denote by D(G;H) (or D(G)) the crossed product of C(G) and \mathbb{C}H (or \mathbb{C}G) with respect to the adjoint action of the latter on the former. Consider the algebra \left \langle D(G), e\right \rangle generated by D(G) and e, where we regard E as an idempotent operator e on D(G) for a certain conditional expectation E of D(G) onto D(G; H). Let us call \left \langle D(G), e\right \rangle the basic construction from the conditional expectation E: D(G) → D(G; H). The paper constructs a crossed product algebra C(G/H ×G) \rtimes \mathbb{C}G, and proves that there is an algebra isomorphism between \left \langle D(G), e\right \rangle and C(G/H×G) \rtimes \mathbb{C} G., Qiaoling Xin, Lining Jiang, Zhenhua Ma., and Obsahuje seznam literatury
The basis number of a graph $G$ was defined by Schmeichel to be the least integer $h$ such that $G$ has an $h$-fold basis for its cycle space. He proved that for $m,n\ge 5$, the basis number $b(K_{m,n})$ of the complete bipartite graph $K_{m,n}$ is equal to 4 except for $K_{6,10}$, $K_{5,n}$ and $K_{6,n}$ with $n=5,6,7,8$. We determine the basis number of some particular non-planar graphs such as $K_{5,n}$ and $K_{6,n}$, $n=5,6,7,8$, and $r$-cages for $r=5,6,7,8$, and the Robertson graph.