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In this book set theory INC# based on intuitionistic logic with restricted modus ponens rule is proposed. It proved that intuitionistic logic with restricted modus ponens rule can to safe Cantor naive set theory from a triviality Considering only pure sets, the naive set comprehension principle says, for anycondition, that there is a set containing all and only the sets satisfying this condition. Infirst-order logic, this can be formulated as the following schematic principle, where may be any formula in whichy does not occur freely: yxx y . 1.1 Russell's paradox shows that the instance...

The book presents, a new large deviations principles (SLDP) of non-Freidlin-Wentzell type, corresponding to the solutions Colombeau-Itos SDE. Using SLDP we present a new approach to construct the Bellman function V(t,x) and optimal control u(t,x) directly,i.e.,without any reference to the Bellman equation, by way of using strong large deviations principle for the solutions Colombeau-Itos SDE. As important application such SLDP, the generic imperfect dynamic models of air-to-surface missiles are given in addition to the related simple guidance law. A four, examples have been illustrated...