A general kinetic method, based upon population balances of generating functions, is applied to the prediction of the microstructure and molecular size of non‐linear terpolymers obtained through the coordination polymerization of two monovinyl monomers and a non‐conjugated diene. A rather complex kinetic scheme involving crosslinking and long‐chain branching is considered. It is shown that even in these conditions it is possible to carry out the prediction of molecular size and mass distributions, sequence size distributions, and z‐average mean‐square radius of gyration of the polymers. The influence of some kinetic parameters on the properties of the products is studied, considering a homogeneous operation in a semi‐batch reactor. The used simulation method is able to predict these properties before and after gelation whenever it occurs.
The dynamical algebras of the trigonometric and hyperbolic symmetric Pöschl-Teller Hamiltonian hierarchies are obtained. A kind of discrete-differential realizations of these algebras are found which are isomorphic to so(3, 2) Lie algebras. In order to get them, first the relation between ladder and factor operators is investigated. In particular, the action of the ladder operators on normalized eigenfunctions is found explicitly. Then, the whole dynamical algebras are generated in a straightforward way. 相似文献
The Dubins–Savage inequality is generalized by using the pth (1<p≤2) conditional moment of the martingale differences. This inequality is further extended under suitable conditions when p>2. Another martingale inequality due to Freedman is also generalized when 0<p≤2. Implications of these inequalities for strong convergence are discussed. Some general exponential inequalities are also
given for martingales (supermartingales) under suitable conditions.
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