The paper is devoted to the thermal explosion problem in the case of autocatalytic reaction given both heat transfer and diffusion. By means of the method of integral manifolds there are investigated critical regimes and are found critical values of parameter for plane-parallel and for cylindrical reactors. This work was written while V.A. Sobolev was a visitor at both the Boole Centre for Rese...

In this work a sufficient condition is shown to obtain transitivity in families of piecewise increassing maps with an inevitable discontinuity x=0. Specifically, it that the characteristics large class transformations real line x=0 be transitive (exhibits dense orbit), they are following: f has no fixed points, vertical asymptote at and preimage zero different from empty. particular, famous Boo...

The computational method of parametric probability analysis is introduced. It is demonstrated how to embed logical formulas from the propositional calculus into parametric probability networks, thereby enabling sound reasoning about the probabilities of logical propositions. An alternative direct probability encoding scheme is presented, which allows statements of implication and quantification...