We give a criterion for q-valent analytic functions in the unit disk to belong to Q K , a Möbius-invariant space of functions analytic in the unit disk in the plane for a nonde-creasing function K : [0, ∞) → [0, ∞), and we show by an example that our condition is sharp. As corollaries, classical results on univalent functions, the Bloch space, BMOA, and Q p spaces are obtained. 1. Introduction....

Part 3. Geometric Construction of Loop Eisenstein Series 31 11. Bloch’s Map 31 12. Adeleic Loop groups and G-bundles on a Punctured Surface 33 13. Affine flag varieties and extensions of G-bundles 38 14. Relative Chern classes and Central extensions 41 15. Loop Eisenstein Series and Geometric Generating Functions 47 16. Ribbons and a Formal Analogue 48 17. Example: Loop Eisenstein Series on P1. 53

In this paper we prove an identity between the elliptic regulators of some 2-isogenous elliptic curves. This allow us to prove a new exotic relation for the elliptic curve 20A of Cremona’s tables. Also we prove the (conjectured) exotic relation for the curve 20B given by Bloch and Grayson in [3].

The functionality of current neuroimaging using the MRI machine needs to be improved to diagnose more complex problems. A new mathematical concept based on the solutions of the Bloch NMR for MRI applications was adopted to resolve functionality problemsby the inclusion of molecular interactions. The signal loss factor 'E' caused by fluctuating velocity due to compartmental boundaries in the mac...

The quantization of the electronic two site system interacting with a vibration is considered by using as the integrable reference system the decoupled oscillators resulting from the adiabatic approximation. A specific Bloch projection method is applied which demonstrates how besides some regular regions in the fine structure of the spectrum and the associated eigenvectors irregularities appear...

Let φ be a holomorphic self-map of a bounded homogeneous domain D in C. In this work, we show that the composition operator Cφ : f 7→ f ◦ φ is bounded on the Bloch space B of the domain and provide estimates on its operator norm. We also give a sufficient condition for φ to induce an isometry on B. This condition allows us to construct non-trivial examples of isometric composition operators in ...

This paper characterizes the boundedness and compactness of the generalized composition operator (C φf)(z) = ∫ z 0 f ′(φ(ξ))g(ξ)dξ from Bloch type spaces to QK type spaces.

We study a coalition formation game with externalities where each agent’s payoff depends on the entire partition (see, e.g., Bloch (1996)). As in Bloch (1996) and Ray and Vohra (1999), we assume that coalitions form sequentially and once a coalition forms, it cannot dissolve nor can its members forge new coalitions with the rest of the agents. However, instead of an exogenously given protocol, ...

We construct an example of a torus T over a field K for which the Galois symbol K(K;T, T )/nK(K;T, T ) → H(K,T [n] ⊗ T [n]) is not injective for some n. Here K(K;T, T ) is the Milnor K-group attached to T introduced by Somekawa. We show also that the motiveM(T×T ) gives a counterexample to another generalization of the Milnor-BlochKato conjecture (proposed by Beilinson).