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.     

Solid-state Synthesis of Carbon-nanostructures

1 Results In addition to single wall and multiwall carbon nanotubes[1], several structures,which are more or less related to fullerenes,including carbon nanohorns[2a], carbon nanospheres[2b] and onion like carbon structures[2c] have been reported.A new simple straight forward method to access some of these structures is the solid-state pyrolysis of different organometallic complexes in a sealed vessel,which led so far to carbon nanotubes[3a,b], carbon nanocables[3c] and onions[3d].     

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.