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.     

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.     

Philosophy of chemistry and the image of science

The philosophical analysis of chemistry has advanced at such a pace during the last dozen years that the existence of philosophy of chemistry as an autonomous discipline cannot be doubted any more. The present paper will attempt to analyse the experience of philosophy of chemistry at the, so to say, meta-level. Philosophers of chemistry have especially stressed that all sciences need not be similar to physics. They have tried to argue for chemistry as its own type of science and for a pluralistic understanding of science in general. However, when stressing the specific character of chemistry, philosophers do not always analyse the question ‘What is science?’ theoretically. It is obvious that a ‘monistic’ understanding of science should not be based simply on physics as the epitome of science, regarding it as a historical accident that physics has obtained this status. The author’s point is that the philosophical and methodological image of science should not be chosen arbitrarily; instead, it should be theoretically elaborated as an idealization (theoretical model) substantiated on the historical practice of science. It is argued that although physics has, in a sense, justifiably obtained the status of a paradigm of science, chemistry, which is not simply a physical science, but a discipline with a dual character, is also relevant for elaborating a theoretical model of science. The theoretical model of science is a good tool for examining various issues in philosophy of chemistry as well as in philosophy of science or science studies generally.