We investigate the analytic structure of solutions of non-relativistic Schrödinger equations describing Coulombic manyparticle systems. We prove the following: Let ψ(x) with x = (x1, . . . , xN ) ∈ R denote an N -electron wavefunction of such a system with one nucleus fixed at the origin. Then in a neighbourhood of a coalescence point, for which x1 = 0 and the other electron coordinates do not ...

For each group G having an infinite normal subgroup with the relative property (T) (e.g. G = H ×K, with H infinite with property (T) and K arbitrary) and each countable abelian group Λ we construct free ergodic measure-preserving actions σΛ of G on the probability space such that the 1’st cohomology group of σΛ, H (σΛ, G), is equal to Char(G) × Λ. We deduce that G has uncountably many non stabl...

For each group G having an infinite normal subgroup with the relative property (T) (for instance groups of the form G = H ×K, where H is infinite with property (T) and K is arbitrary) and each countable abelian group Λ we construct free ergodic measure-preserving actions σΛ of G on the probability space such that the 1’st cohomology group of σΛ, H (σΛ, G), is equal to Char(G)×Λ. We deduce that ...

For each group G having an infinite normal subgroup with the relative property (T) (for instance groups of the form G = H ×K, where H is infinite with property (T) and K is arbitrary) and each countable abelian group Λ we construct free ergodic measure-preserving actions σΛ on the probability space such that the 1’st cohomology group of σΛ, H (σΛ), is equal to Char(G)×Λ. We deduce that G has un...

Many types of learning require the mapping of information across situations. The proposed organizational framework extends the cognitive study of mappings across problems to include mappings across representations, solutions, and sociocultural contexts. I apply one-to-one, one-to-many, and partial mappings to analyze representative cases that include ones studied within alternative frameworks t...

In this paper, we present an effective method to characterize completely when a disconnected fractal square has only finitely many connected components. Our is establish some graph structures on squares reveal the evolution of connectedness during their geometric iterated construction. We also prove that every contains either or uncountably A few examples, including construction with exactly $m...

We study the matching conditions of intersecting brane worlds in Lovelock gravity in arbitrary dimension. We show that intersecting various codimension 1 and/or codimension 2 branes one can find solutions that represent energymomentum densities localized in the intersection, providing thus the first examples of infinitesimally thin higher codimension braneworlds that are free of singularities a...

We study the probability theory of countable dense random subsets of (uncountably infinite) Polish spaces. It is shown that if such a set is stationary with respect to a transitive (locally compact) group of symmetries then any event which concerns the random set itself (rather than accidental details of its construction) must have probability zero or one. Indeed the result requires only quasi-...

We examined 5d thick brane worlds constructed by a real scalar field. The solutions are obtained in terms of a simple form of smooth warp factor. For the case of dS brane, we found a disease of the solutions. For example, it is impossible to construct thick-brane worlds with our simple smoothing. This result is independent of supersymmetry or other symmetries. [email protected] yahiro@s...

In this paper, we study several analytic and graph-theoretic properties of asymptotic expanders. We show that expanders can be characterised in terms their uniform Roe algebra. Moreover, use to provide uncountably many new counterexamples the coarse Baum–Connes conjecture. Finally, vertex-transitive are actually particular, gives a C⁎-algebraic characterisation for graphs. achieve these results...