Let k be an algebraically closed field of characteristic not equal to 2 or 3, let G be an almost simple algebraic group of type F4, G2 or D4 and let θ be an automorphism of G of finite order, coprime to the characteristic. In this paper we consider the θ-group (in the sense of Vinberg) associated to these choices; we classify the positive rank automorphisms and give their Kac diagrams and we de...

In the present paper we prove a form of Arnold diffusion. The main result says that for a ”generic” perturbation of a nearly integrable system of arbitrary degrees of freedom n > 2 H0(p) + εH1(θ, p, t), θ ∈ T, p ∈ B, t ∈ T = R/T, with strictly convex H0 there exists an orbit (θǫ, pe)(t) exhibiting Arnold diffusion in the sens that sup t>0 ‖p(t)− p(0)‖ > l(H1) > 0 where l(H1) is a positive const...

Suppose that at any stage of a statistical experiment a control variable X that affects the distribution of the observed data Y at this stage can be used. The distribution of Y depends on some unknown parameter θ, and we consider the problem of testing multiple hypotheses H1 : θ = θ1, H2 : θ = θ2, . . . , Hk : θ = θk allowing the data to be controlled by X, in the following sequential context. ...

For simplicity, we adopt the following rules: n denotes an element of N, X, X1 denote sets, r, p denote real numbers, s, x0, x1, x2 denote real numbers, S, T denote real normed spaces, f , f1, f2 denote partial functions from R to the carrier of S, s1 denotes a sequence of real numbers, and Y denotes a subset of R. The following propositions are true: (1) Let s2 be a sequence of real numbers an...

Let Θ be a smooth compact oriented manifold without boundary, imbedded in a euclidean space E, and let γ be a smooth map of Θ into a Riemannian manifold Λ. An unknown state θ ∈ Θ is observed via X = θ + ǫξ where ǫ > 0 is a small parameter and ξ is a white Gaussian noise. For a given smooth prior λ on Θ and smooth estimators g(X) of the map γ we derive a second-order asymptotic expansion for the...

We present a formula expressing Earle’s twisted 1-cocycle on the mapping class group of a closed oriented surface of genus ≥ 2 relative to a fixed base point, with coefficients in the first homology group of the surface. For this purpose we compare it with Morita’s twisted 1-cocycle which is combinatorial. The key is the computation of these cocycles on a particular element of the mapping class...

The general form of non-entangling unitary maps for measurement schemes is determined. It is shown that any POVM admits a non-entangling measurement. We prove the following. Proposition 1 Let H1,H2 be complex separable Hilbert spaces, φ0 a unit vector in H2. Assume U : H1 ⊗ H2 → H1 ⊗ H2 is a unitary map such that for all φ ∈ H1, U(φ ⊗ φ0) = φ′ ⊗ φ′ for some unit vectors φ′ ∈ H1, φ′ ∈ H2. Then U...

let a be a banach algebra. a is called ideally amenable if for every closed ideal i of a, the first cohomology group of a with coefficients in i* is trivial. we investigate the closed ideals i for which h1 (a,i* )={0}, whenever a is weakly amenable or a biflat banach algebra. also we give some hereditary properties of ideal amenability.

with D as the time-invariant demand, f (θ, a) the time-invariant number of firms with (θ, a), and ag, au the time-invariant exit ages for good and unsure firms. It suggests that PtAt must also be time-invariant. We let PtAt = PA. Proof. f (0) represents the time-invariant entry size at the steady state. Let V (θ, a) be the time-invariant expected value of staying of a firm with belief θ and age...

3.5 Consistency of approximate M-estimators of ψ type. As in Sec. 3.3, let (X, A, P) be a probability space and Θ a locally compact separable metric space. Let ψ(θ, x) be a function of x in X and θ ∈ Θ with values in a Euclidean space R m. Let X 1 , X 2 ,. .. be independent with values in X and distribution P. A sequence of estimators T n := T n (X 1 ,. .. , X n) with values in Θ will be called...