New Classes of Off-Diagonal Cosmological Solutions in Einstein Gravity

In this work, we apply the anholonomic deformation method for constructing new classes of anisotropic cosmological solutions in Einstein gravity and/or generalizations with nonholonomic variables. There are analyzed four types of, in general, inhomogeneous metrics, defined with respect to anholonomic frames and their main geometric properties. Such spacetimes contain as particular cases certain conformal and/or frame transforms of the well known Friedman-Robertson-Walker, Bianchi, Kasner and Gödel universes and define a great variety of cosmological models with generic off-diagonal metrics, local anisotropy and inhomogeneity. It is shown that certain nonholonomic gravitational configurations may mimic de Sitter like inflation scenarios and different anisotropic modifications without satisfying any classical false-vacuum equation of state. Finally, we speculate on perspectives when such off-diagonal solutions can be related to dark energy and dark matter problems in modern cosmology.     

Broadening the reactivity spectrum of a phthalocyanine catalyst while suppressing its nucleophilic, electrophilic and radical degradation pathways

A robust molecule that resists degradation via nucleophilic, electrophilic and radical attacks is described. Coordinated O(2) is reduced catalytically, producing efficiently thyil radicals in spite of the extreme electronic deficiency of the catalyst.     

Probing the Pore Size of Porous Ceramics with Controlled Amount of Magnetic Impurities via Diffusion Effects on the CPMG Technique

In our work, we will explore the possibility of implementing the well-known Carr–Purcell–Meiboom–Gill pulse sequence to determine the pore size of porous ceramics with magnetic impurities. The proposed approach exploits the diffusion dependence of the spin-echo signal in the presence of internal gradients occurring as a result of susceptibility contrast between the porous matrix and the confined liquid. For calibrating the technique, a comparison of the pore size data with those extracted from the so-called DDIF technique (DDIF, decay due to diffusion in the internal fields) is performed. This approach can be applied for nondestructive in situ characterization of soils, concrete, biological tissues or other structures with micrometer pore size.     

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.