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.     

Un curare d'une Erythrine africaine

Summary An alcaloid C₁₆H₁₉NO₃ has been isolated fromErythrina tholloniana; the iodohydrate of this erythroidine has a melting point of 225°C and 239°C for its chlorhydrate. It has a powerful curare-like action on the frog or on its isolated sciatic-sartorius preparation; at a concentration of less than 1/1,000,000, a complete neuromuscular block is produced: the electrical stimulation of the motor nerve does not produce any contraction, but the muscle reacts by an end-plate potential having the same characteristics (shape, duration, possibility of summation) as the electrical waves produced in the same preparation curarized by ordinary curare or by quaternary ammonium derivatives. Decurarization by veratrine 1/200,000 is accompanied by the same electrical reactions as those which have been described in preparations treated by curare.On mammals, the alcaloid has little curariform activity; on the isolated phrenic-diaphragm preparation of the rat, incomplete block was produced at a concentration of 1/5000.     

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.