Isometric immersions into a homogeneous Lorentzian Heisenberg group and rigidity

In this paper we prove an existence result for local and global isometric immersions of semi-Riemannian surfaces into the three dimensional Heisenberg group endowed with a homogeneous left-invariant Lorentzian metric. As a corollary, we prove a rigidity result for such immersions.

Short-time behaviour of demand and price viewed through an exactly solvable model for heterogeneous interacting market agents

We introduce a stochastic heterogeneous interacting-agent model for the short-time non-equilibrium evolution of excess demand and price in a stylized asset market. We consider a combination of social interaction within peer groups and individually heterogeneous fundamentalist trading decisions which take into account the market price and the perceived fundamental value of the asset. The resulting excess demand is coupled to the market price. Rigorous analysis reveals that this feedback may lead to price oscillations, a single bounce, or monotonic price behaviour. The model is a rare example of an analytically tractable interacting-agent model which allows LIS to deduce in detail the origin of these different collective patterns. For a natural choice of initial distribution, the results are independent of the graph structure that models the peer network of agents whose decisions influence each other. (C) 2009 Elsevier B.V. All rights reserved.

Rigidity theorems for complete spacelike hypersurfaces with constant scalar curvature in De Sitter space

In this paper we give a partially affirmative answer to the following question posed by Haizhong Li: is a complete spacelike hypersurface in De Sitter space S(1)(n+1)(c), n >= 3, with constant normalized scalar curvature R satisfying n-2/nc <= R <= c totally umbilical? (C) 2008 Elsevier B.V. All rights reserved.

Photoswitches and Luminescent Rigidity Sensors Based on fac-[Re(CO)(3)(Me(4)phen)(L)](+)

The fac-[Re(CO)(3)(Me(4)phen)(trans-L)](+) complexes, Me(4)phen = 3,4,7,8-tetramethyl-1,10-phenanthroline and L = 4-styrylpyridine, stpy, or 1,2-bis(4-pyridyl)ethylene, bpe, were synthesized and characterized by their spectroscopic, photochemical, and photophysical properties. The complexes exhibit trans-to-cis isomerization upon 313, 334, 365, and 404 nm irradiation, and the true quantum yields can be efficiently determined by absorption changes combined with (1)H NMR data. For fac-[Re(CO)(3)(Me(4)phen)(trans-bpe)](+) similar quantum yields were determined at all wavelengths investigated. However, a lower value (phi(true) = 0.35) was determined for fac-[Re(CO)(3)(Me(4)phen)(trans-stpy)](+) at 404 nm irradiation, which indicates different pathways for the photoisomerization process. The photoproducts, fac-[Re(CO)(3)(Me(4)phen)(cis-L)](+), exhibit luminescence at room temperature with two maxima ascribed to the (3)IL(Me4phen) and (3)MLCT(Re -> Me4phen) excited states. The luminescence properties were investigated in different media, and the behavior in glassy EPA at 77 K showed that the contribution of each emissive state is dependent on the excitation wavelength. The photochemical and photophysical behavior of the complexes were rationalized in terms of the energy gap of excited states and can be exploited in photoswitchable luminescent rigidity sensors.