On the Stability of Certain Spin Models in 2+1 Dimensions

In this paper we prove large-data local stability theorems for several spin-field models in two dimensions, both in the focusing case (spherical target) and the defocusing case (hyperbolic target).     

Categorification and Group Extensions

We review several known categorification procedures, and introduce a functorial categorification of group extensions (Section 4.1) with applications to non-Abelian group cohomology (Section 4.2). The obstruction to the existence of group extensions (Section 4.2.4, Equation (9)) is interpreted as a coboundary condition (Proposition 4.5).     

Robust D-wave pairing correlations in a hole-doped spin-fermion model

Pairing correlations are studied numerically in a hole-doped spin-fermion model. Simulations performed on up to 12 x 12 clusters provide indications of D-wave superconductivity away from half-filling comparable to those of the 2D t-J model. The pairing correlations are the strongest in the direction perpendicular to the dynamic stripes that appear in the ground state at some densities. An optimal doping, where correlations are maximized, was observed at approximately 25% doping with an estimated T(c) approximately 100-200 K, in qualitative agreement with high-T(c) cuprates' phenomenology, while pairing correlations are suppressed by static stripe inhomogeneities.     

Redheffer's theorem revisited

Based on the Ben Artzi-Gohberg result concerning the equivalence between the invertibility of theL ²-operator and the exponential dichotomic evolution defined byA(t), the time-varying counterpart of the Redheffer theorem is considered under relaxed conditions.     

Interaction of propylene with a promoted Bi?Mo catalyst as determined from conductivity data

A new cell is described which allows simultaneous measurement of the electrical and catalytic properties of a promoted Bi–Mo catalyst. The electrical resistance data show that the interaction of propylene with the catalyst starts at 310 °C.

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, Bi–Mo. , 310°C.

     

The formation of flouride complexes of titanium(IV)

The complex formation equilibria between titanium(IV) and fluoride ions have been studied at 25°C in 3 M(Na)Cl ionic medium by measuring, with an ion selective electrode for F^?, the free HF concentration in acid Ti(IV) solutions. The [H⁺] was kept within 0.25 and I M where the predominant form of uncomplexed metal is the dihydroxotitanium(IV) ion, Ti(OH)²⁺₂. The potentiometric data have been explained by assuming Ti(OH)₂F⁺, TiF₄ and HTiF^?₆, with equilibrium constants given in Table 3. Within the accuracy of the present e.m.f. study, ±0.2 mV, no evidence for intermediate complexes bearing 2, 3 and 5 F^? was found.From a special series of measurements, carried out by replacing a large part of the Cl^? with ClO^?₄, it is concluded that no appreciable amount of Ti(IV)Cl complexes is formed at the 3 M level employed as ionic medium.     

Coiling, entrainment, and hydrodynamic coupling of decelerated fluid jets

From algal suspensions to magma upwellings, one finds jets which exhibit complex symmetry-breaking instabilities as they are decelerated by their surroundings. We consider here a model system--a saline jet descending through a salinity gradient--which produces dynamics unlike those of standard momentum jets or plumes. The jet coils like a corkscrew within a conduit of viscously entrained fluid, whose upward recirculation braids the jet, and nearly confines transverse mixing to the narrow conduit. We show that the underlying jet structure and certain scaling relations follow from similarity solutions to the fluid equations and the physics of Kelvin-Helmholtz instabilities.