Enlargement of the Wiener filtration by an absolutely continuous random variable via Malliavin’s calculus

Summary. The analytic treatment of problems related to the asymptotic behaviour of random dynamical systems generated by stochastic differential equations suffers from the presence of non-adapted random invariant measures. Semimartingale theory becomes accessible if the underlying Wiener filtration is enlarged by the information carried by the orthogonal projectors on the Oseledets spaces of the (linearized) system. We study the corresponding problem of preservation of the semimartingale property and the validity of a priori inequalities between the norms of stochastic integrals in the enlarged filtration and norms of their quadratic variations in case the random element F enlarging the filtration is real valued and possesses an absolutely continuous law. Applying the tools of Malliavin’s calculus, we give smoothness conditions on F under which the semimartingale property is preserved and a priori martingale inequalities are valid. Received: 12 April 1995 / In revised form: 7 March 1996     

A new family of proximity graphs: Class cover catch digraphs

Motivated by issues in machine learning and statistical pattern classification, we investigate a class cover problem (CCP) with an associated family of directed graphs—class cover catch digraphs (CCCDs). CCCDs are a special case of catch digraphs. Solving the underlying CCP is equivalent to finding a smallest cardinality dominating set for the associated CCCD, which in turn provides regularization for statistical pattern classification. Some relevant properties of CCCDs are studied and a characterization of a family of CCCDs is given.     

Dicyclopentadienyl complexes of titanium,niobium, and tungsten in the controlled synthesis of poly(methyl methacrylate)

Organometallic compounds Cp₂TiCl₂, (EtC₅H₄)₂NbCl₂, and (PrⁱC₅H₄)₂WCl₂ were assessed as additives that control polymer chain growth in the polymerization of methyl methacrylate. In the presence of compounds mentioned in amounts comparable with that of the initiator, a uniform process with no gel-effect occured and respective linear increase in the molecular weight of the polymer up to high degrees of the monomer conversion was observed.     

产品定级中挑选专家的数学模型

在工农业产品评定级别中，专家组的水平是至关重要的。文中给出一个挑选专家组成员的数学模型，可以检验专家对参评产品的决策水平，为评价所评结论的可信度提供参考依据。     

Group classification of unsteady boundary layer equations of a class of non-Newtonian fluids

Two dimensional unsteady boundary layer equations of a general model of non-Newtonian fluids were investigated in this study. In this model, the shear stress is taken as an arbitrary function of the velocity gradient. Group classification of the equations with respect to shear stress is done using two different approaches: (1) classical theory (2) equivalence transformations. Both approaches yield identical results. It is found that the principle Lie Algebra extends only for cases of Newtonian and Power-Law flows.     

Letter: Note on Invariants of the Weyl Tensor

Algebraically special gravitational fields are described using algebraic and differential invariants of the Weyl tensor. A type III invariant is also given and calculated for Robinson-Trautman spaces.     

Quantitative theory of living free‐radical polymerization. III. Calculation of copolymerization products' spinodal

The problem of finding conditions of the loss of thermodynamic stability by the reaction system was solved on the basis of the developed theory of living free‐radical copolymerization. The spinodal's calculations were carried out for a significant number of systems differing in the values of kinetic, stoichiometric, and thermodynamic parameters. Analysis of the results of such calculations revealed some regularities in the spinodal curves' behavior and permitted us to classify their possible topological types. © 2003 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 41: 892–902, 2003     

Visions: The coming revolutions in particle physics

We study the branching ratio, CP-violating asymmetry, forward-backward asymmetry and the CP-violating asymmetry in the forward-backward asymmetry for the exclusive decay B → Kτ⁺τ⁻ in the two Higgs doublet model with tree level flavor changing neutral currents (model III). We analyse the dependencies of these quantities on the neutral Higgs boson contributions and the CP parameter sinθ in the model III. We observe that to determine the neutral Higgs boson effects, the measurements of the forward-backward asymmetry and the CP-violating asymmetry in the forward-backward asymmetry for the decay B → Kτ⁺τ⁻ are promising.