A Bloch ion has periodic symmetry and is distributed in space in a lattice array form. Its spatial density distribution is neutralized within each unit cell by a metal's electrons. The wave function repeats coherently modulo a Bravais lattice vector. Paired Bloch deuterons partitioned over a sufficiently large number of unit cells become superposed and coherently mixed by coordinate exchange. A...

Given an orientable complete hyperbolic 3-manifold of finite volume M we construct a canonical class α(M) in H3(B(SL2(C), T)) with B(SL2(C), T) the SL2(C)-orbit space of the classifying space for a certain family of isotropy subgroups. We prove that α(M) coincides with the Bloch invariant β(M) of M defined by Neumann and Yang in [13], giving with this a simpler proof that the Bloch invariant is...

ND band state D+ ions are treated as a sum over pairs. The wave functions of a D+ pair is assumed to be a product of a Bloch function in lattice space times a Bloch function in separation space. Overlap allows a strong force fusion reaction to 4He++. A coupling between the nuclear change and the ion charge distribution in the lattice is described. The change in ion charge distribution scatters ...

An analytic function φ mapping the unit disk into itself is said to belong to the hyperbolic little Bloch class if the ratio (1−|z|2)|φ′(z)|/(1−|φ(z)|2) converges to 0 as |z| → 1, while φ is in the little Bloch space if just the numerator of this expression converges to zero. Several constructions of inner functions in the little Bloch space have recently appeared. In this paper we construct a ...

We introduce a class of Möbius invariant spaces of analytic functions in the unit disk, characterize these spaces in terms of Carleson type measures, and obtain a necessary and sufficient condition for a lacunary series to be in such a space. Special cases of this class include the Bloch space, the diagonal Besov spaces, BMOA, and the so-called Qp spaces that have attracted much attention lately.

Let φ and ψ be analytic self-maps of the open unit disk D . Using pseudo-hyperbolic distance ρ(φ ,ψ) , we characterize the boundedness and compactness of the differences of generalized composition operators (C φ −Ch ψ ) f (z) = ∫ z 0 [ f ′(φ(ξ ))g(ξ )− f ′(ψ(ξ ))h(ξ )]dξ , z ∈ D between two Bloch-type spaces on D . The results generalize the corresponding results on the single generalized compo...