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Abstract We compute the group of K 1 -zero-cycles on the second generalized involution variety for an algebra of degree 4 with symplectic involution. This description is given in terms of the group of multipliers of similitudes associated to the algebra with involution. Our method utilizes the framework of Chernousov and Merkurjev for computing K 1 -zero-cycles in terms of R -equivalence classes of prescribed algebraic groups. This gives a computation of K 1 -zero-cycles for some homogeneous varieties of type C 2. [ABSTRACT FROM AUTHOR]

AbstractIn this paper we present Thom?s transversality theorem in o-minimal structures (a generalization of semialgebraic and subanalytic geometry). There are no restrictions on?the differentiability class and the dimensions of manifolds involved in comparison withthe general case. [ABSTRACT FROM AUTHOR]

A concept of higher order complexity is proposed in this letter. If a randomness-finding complexity [Rapp & Schmah, 2000] is taken as the complexity measure, the first-order complexity is suggested to be a measure of randomness of the original time series, while the second-order complexity is a measure of its degree of nonstationarity. A different order is associated with each different aspect of complexity. Using logistic mapping repeatedly, some quasi-stationary time series were constructed, the nonstationarity degree of which could be expected theoretically. The estimation of the second-order complexity of these time series shows that the second-order complexities do reflect the degree of nonstationarity and thus can be considered as its indicator. It is also shown that the second-order complexities of the EEG signals from subjects doing mental arithmetic are significantly higher than those from subjects in deep sleep or resting with eyes closed. [ABSTRACT FROM AUTHOR]

We study the subgroup B0(G) of H²(G, &doubleQ;/&doubleZ;) consisting of all elements which have trivial restrictions to every Abelian subgroup of G. The group B0(G) serves as the simplest nontrivial obstruction to stable rationality of algebraic varieties V/G where V is a faithful complex linear representation of the group G. We prove that B0(G) is trivial for finite simple groups of Lie type Aℓ. [ABSTRACT FROM AUTHOR]