Decay and regularity for the schrödinger equation

Consider the Schrödinger equation {fx25-1}. The following estimates are proved: (A) IfV≡0 then for any 0≤α<1/2, {fx25-2}, and for α=1/2,s>1/2, {fx25-3} (B) If |V(x)|≤C(1+|x|²)^?1?δ, δ>0, then (if 0 is neither an eigenvalue nor a resonance of ?Δ+V), {fx25-4}.     

Decay and growth for a nonlinear parabolic difference equation

We prove a difference equation analogue of the decay-of-mass result for the nonlinear parabolic equation when and a new growth result when 0$">.

     

An axiomatization of the consistent non-transferable utility value

The Maschler–Owen consistent value for non-transferable utility games is axiomatized, by means of a marginality axiom.Previous versions: October 2003 (Center for the Study of Rationality DP-337), December 2004. Research partially supported by a grant of the Israel Academy of Sciences and Humanities. The author thanks Andreu Mas-Colell, Bezalel Peleg, Peter Sudhölter, the referees, and the editor for their comments and suggestions.     

On Carvalho's -theoretic formulation of the cobordism invariance of the index

We give an analytic proof of the fact that the index of an elliptic operator on the boundary of a compact manifold vanishes when the principal symbol comes from the restriction of a -theory class from the interior. The proof uses non-commutative residues inside the calculus of cusp pseudodifferential operators of Melrose.

     

On General Solutions for Field Equations in Einstein and?Higher Dimension Gravity

We prove that the Einstein equations can be solved in a very general form for arbitrary spacetime dimensions and various types of vacuum and non-vacuum cases following a geometric method of anholonomic frame deformations for constructing exact solutions in gravity. The main idea of this method is to introduce on (pseudo) Riemannian manifolds an alternative (to the Levi-Civita connection) metric compatible linear connection which is also completely defined by the same metric structure. Such a canonically distinguished connection is with nontrivial torsion which is induced by some nonholonomy frame coefficients and generic off-diagonal terms of metrics. It is possible to define certain classes of adapted frames of reference when the Einstein equations for such an alternative connection transform into a system of partial differential equations which can be integrated in very general forms. Imposing nonholonomic constraints on generalized metrics and connections and adapted frames (selecting Levi-Civita configurations), we generate exact solutions in Einstein gravity and extra dimension generalizations.