Imbed a n w 1 sphere in an n sphere, and the complement is divided into two components. I t seems that the closure of each of the resulting components should be a topological w-cell. This statement isn't true. The classical counterexample (in dimension 3) is the Alexander Horned Sphere. I t was conjectured, however, that if one restricts one's attention to some class of well-behaved imbeddings,...

Assuming the Bloch-Kato Conjecture, we determine precise conditions under which Hilbert 90 is valid for Milnor k-theory and Galois cohomology. In particular, Hilbert 90 holds for degree n when the cohomological dimension of the Galois group of the maximal p-extension of F is at most n.

A quantum breather on a translationally invariant one-dimensional anharmonic lattice is an extended Bloch state with two or more particles in a strongly correlated state. We discuss several effects that break the lattice symmetry and lead to spatial localization of the breather.

The sequential coalition formation model of Bloch (1996) to solve cooperative games with externalities exhibits some anomalies when related to classical concepts. We elaborate on these problems, define a modification of Bloch’s model and show that its order-independent equilibria coincide with the (pessimistic) recursive core (Kóczy, 2007). Subject classification: C71, C72

On integrable discretization of the inhomogeneous Ablowitz-Ladik model. Abstract An integrable discretization of the inhomogeneous Ablowitz-Ladik model with a linear force is introduced. Conditions on parameters of the discretization which are necessary for reproducing Bloch oscillations are obtained. In particular, it is shown that the step of the discretization must be comensurable with the p...

We give some sufficient and necessary conditions for an analytic function f on the unit ball B with Hadamard gaps, that is, for f (z)=∑k=1Pnk (z) (the homogeneous polynomial expansion of f ) satisfying nk+1/nk ≥ λ > 1 for all k ∈N, to belong to the space p(B)= { f |sup0<r<1(1− r2)‖R fr‖p <∞, f ∈H(B)}, p = 1,2,∞ as well as to the corresponding little space. A remark on analytic functions with Ha...

The space and time fractional Bloch-Torrey equation (ST-FBTE) has been used to study anomalous diffusion in the human brain. Numerical methods for solving ST-FBTE in three-dimensions are computationally demanding. In this paper, we propose a computationally effective fractional alternating direction method (FADM) to overcome this problem. We consider ST-FBTE on a finite domain where the time an...

We determine all Riemannian manifolds for which the tangent sphere bundles, equipped with the Sasaki metric, are local or global Riemannian product manifolds.