Applications of Resonance Theory Without Analyticity Assumption

Uniqueness of static black holes without analyticity

We show that the hypothesis of analyticity in the uniqueness theory of vacuum, or electrovacuum, static black holes is not needed. More generally, we show that prehorizons covering a closed set cannot occur in well-behaved domains of outer communications. PACS numbers: 04.70.Bw, 04.50.Cd, 04.50.Gh

Hawking’s Local Rigidity Theorem without Analyticity

We prove the existence of a Hawking Killing vector-field in a full neighborhood of a local, regular, bifurcate, non-expanding horizon embedded in a smooth vacuum Einstein manifold. The result extends a previous result of Friedrich, Rácz and Wald, see [7, Proposition B.1], which was limited to the domain of dependence of the bifurcate horizon. So far, the existence of a Killing vector-field in a...

Natural resonance theory: III. Chemical applications

We describe quantitative numerical applications of the natural Ž . resonance theory NRT to a variety of chemical bonding types, in order to demonstrate the generality and practicality of the method for a wide range of . chemical systems. Illustrative applications are presented for 1 benzene and . . polycyclic aromatics; 2 CO , formate, and related acyclic species; 3 ionic and 2 . . polar compou...

Adaptive Resonance Theory Applications for Business Forecasting

Existence of Collateral Equilibrium without Survival Assumption

This paper shows the existence of a collateral equilibrium without assuming any hypotheses on the strict positivity, be they individual initial endowments, including the ex post initial endowments, or aggregated initial endowments. Because of dropping the strict positivity of social initial endowment we fail to get an equilibrium. Instead, we get a quasi-equilibrium. Then, appealing to the conc...