For a class of quasiperiodically forced time-discrete dynamical systems of two variables (θ, x) ∈ T1 × R+ with nonpositive Lyapunov exponents we prove the existence of an attractor Γ with the following properties: 1. Γ is the closure of the graph of a function x = φ(θ). It attracts Lebesgue-a.e. starting point in T1 × R+. The set {θ : φ(θ) 6= 0} is meager but has full 1-dimensional Lebesgue mea...

and Applied Analysis 3 Let T be a positive number. In the following we take ΩT 0, T × 0, 1 . Let vl and vr be in C0 0, T , R and m0 ∈ L∞ 0, 1 , ρ0 ∈ W1,∞ 0, 1 . We set Γl {t ∈ 0, T | vl t > 0}, Γr {t ∈ 0, T | vr t < 0}. 1.3 In the following, we will always suppose that the sets Pl {t ∈ 0, T | vl t 0}, Pr {t ∈ 0, T | vr t 0} 1.4 have a finite number of connected components. Finally, let ml, ρl ∈...

This supplement contains the proofs of Theorem 2, Propositions 2 and 3, Lemma 1 and Eq.(14). 7 Proof of Theorem 2 Rather than prove Theorem 2 directly it is convenient to first prove an analogue of the Theorem in the context of multivariate Normal random vectors. This is done in section 7.1. The proof of Theorem 2 is then given in section 7.2 7.1 Confidence Bound For Multivariate Normal Vectors...

We build a variational theory of geodesics of the Tanaka-Webster connection ∇ on a strictly pseudoconvex CR manifold M . Given a contact form θ on M such that (M, θ) has nonpositive pseudohermitian sectional curvature (kθ(σ) ≤ 0) we show that (M, θ) has no horizontally conjugate points. Moreover, if (M, θ) is a Sasakian manifold such that kθ(σ) ≥ k0 > 0 then we show that the distance between an...

Motivated by a question of Vincent Lafforgue, we study the Banach spaces X satisfying the following property: there is a function ε → ∆ X (ε) tending to zero with ε > 0 such that every operator T : L 2 → L 2 with T ≤ ε that is simultaneously contractive (i.e. of norm ≤ 1) on L 1 and on L ∞ must be of norm ≤ ∆ X (ε) on L 2 (X). We show that ∆ X (ε) ∈ O(ε α) for some α > 0 iff X is isomorphic to ...

We give an instance when the extender algebra can preserve stationary subsets of ω1. In particular, we show that for any model operator satisfying certain conditions (satisfied by the currently known minimal inner models for large cardinal statements), any Ω-consistent statement about a rank initial segment of the universe can be forced over canonical model containing H(ω2) while preserving sta...

Braunstein and Caves showed how quantum information can be used to define a metric for quantum states, relying on attainability of a quantum information bound. We show that the bound is not generally attainable, but that a two-stage procedure of repeated measurements achieves the bound in the limit. We connect to the question of 'non-locality without entanglement': can a joint measurement on n ...

Motivated by a question of Vincent Lafforgue, we study the Banach spaces X satisfying the following property: there is a function ε → ∆ X (ε) tending to zero with ε > 0 such that every operator T : L 2 → L 2 with T ≤ ε that is simultaneously contractive (i.e. of norm ≤ 1) on L 1 and on L ∞ must be of norm ≤ ∆ X (ε) on L 2 (X). We show that ∆ X (ε) ∈ O(ε α) for some α > 0 iff X is isomorphic to ...

Claim A.2. Fix any σ ∈ Ω(R̂). Also, assume that, for each i, outcome ã ∈ A used in the construction of S above satisfies condition (7) in LS. Then, for any t and θ(t), if g = ĝ then m θ(t),θt i = (·, 0) and m θ(t),θt j = (·, 0) for any θ. Proof. Suppose not; then, for some t, θ(t) and θ, g = ĝ and the continuation regime next period at h(θ(t), θ) is either D or S for some i. By similar reasoning...

Some considerable damage to steel structures during the Hyogo-ken Nanbu Earthquake occurred. Among them, many exposed-type column bases failed in several consistent patterns, such as brittle base plate fracture, excessive bolt elongation, unexpected early bolt failure, and inferior construction work, etc. The lessons from these phenomena led to the need for improved understanding of column base...