PEAK COVARIANCE STABILITY OF A RANDOM RICCATI EQUATION ARISING FROM KALMAN FILTERING WITH OBSERVATION LOSSES

We consider the stability of a random Riccati equation with a Markovian binary jump coefficient. More specifically, we are concerned with the boundedness of the solution of a random Riccati difference equation arising from Kalman filtering with measurement losses. A sufficient condition for the peak covariance stability is obtained which has a simpler form and is shown to be less conservative in some cases than a very recent result in existing literature. Furthermore, we show that a known sufficient condition is also necessary when the observability index equals one.     

Der Einfluß der Temperatur auf die Giftwirkung des DDT bei Honigbienen (Apis mellifica L.)

Summary The action of DDT on honey-bees depends to a high extent on the temperature (see graph). At 36°C (breeding temperature) DDT has a far weaker insecticidal action than at 20°C (laboratory temperature). This shows that the insecticidal properties of DDT diminish with the raise of temperature.This resistance to DDT at higher temperature is most propitious for bee-keeping and also explains the fact why in agricultural practice there has been no corroborated case of poisoning of bees, though in laboratory tests DDT avered itself to be toxic to bees.     

CONSTRUCTIVE KISSING NUMBERS IN HIGH-DIMENSIONAL SPACES

In the present paper, we focus on constructive spherical codes. By employing algebraic geometry codes, we give an explicit construction of spherical code sequences. By making use of the idea involved in the proof of the Gilbert-Varshamov bound in coding theory, we construct a spherical code sequence in exponential time which meets the best-known asymptotic bound by Shamsiev and Wyner.