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tical and that an individual agent can hardly influence the outcome of the game. Moreover, each individual strategy is influenced by some averages of functions of the states of the other agents. In the limit when. n. →+∞, a given agent feels the presence of the others through the statistical distribution of the states.
name a few. In particular, Courant presented a unified approach to this question by introducing the notion of Dirac structures [6], by which one could obtain a Poisson bracket on admissible functions on a submanifold Q. In some cases, one can indeed obtain a Poisson structure on all functions on Q.ThenQbecomes a Poisson manifold itself.
76 S.D. Bajpai and M.S. Arora 1. INTRODUCTION . Gauss’ hypergeometric polynomials xn 2Fl (’"~) ~ !; c ; ; - x lead to the generalization of the classical polynomials associated with the names of Jacobi, Gegenbauer, Legendre and Chebyshev.Therefore, they appear to represent a very important class of polynomials. In view of this, it seems worthwhile to investigate the matter of their ...
28 REMARKS. (1) Z does not depend on the choice of the Spin‘-structure on M since F± are determined up to a twist with a complex line bundle. (2) Z has a distinguished antiholomorphic involution -c such that has no real points and the twistor lines are invariant under r. (3) The twistor fibres have the normal bundle NF/Z ~ OF(1)~2. (ii) A unique holomorphic line bundle L on Z which is ...
108 Comets, Brendel and Mentré In the following, we will denote with a bold font the vector of individual observations for subject i. The second level of variability characterises variations between the different individuals.
311 precisely, we assume A > 0 and also D ~ 0.Let ~,1 and h2 be the solutions of À 2 + Bh + (AC DE) = 0, then the characteristic strip satisfies the following equations: or Let us denote too = dz - p dx - q dy, cvi = Ddp + C dx + À1 dy and W2 = Ddq + h2 dx + A dy. Take an exterior product of cvl and cv2, and substitute into their product the contact relations of second order = 0,
We go on to establish in this setting and for this class the full range of conclusions which sometimes goes by the name of the signature package. In particular, we prove a new and purely topological theorem, asserting the stratified homotopy invariance of the higher signatures of X , defined through the homology L -class of X , whenever the ...
p-ADIC BOUNDARVALUEY S 53 hyperplanes. The action of the group G := GLd+i{K) on Pd preserves the missing hyperplanes, and therefore gives an action of G on X and a continuous action of G on the infinite dimensional locally convex K-vector space 0(X) of rigid functions on X. The (p-adic) holomorphic discrete series representations are modelled on this
to name but a few examples. In each of these equations, the letter ζ stands for a space or time/space white noise who is so irregular that we do not expect any solution u of the equation to be regular enough for the nonlinear terms, or the product u ζ, in the equations to make sense on the sole basis of the regularizing properties of the heat semigroup.
221 mapping defined by 30 = 0 and 3p -- 1 for all p ~ 0 is a quan- tifier ; this quantifier will be called simple.(The reason for the terms "discrete", borrowed from topology, and "simple", borrowed from algebra, will become apparent later; cf. sections 3 and 5, respectively. ) (iii) Suppose that A is the class of all subsets of some set and that G is a group of one-to-one transformations of