Noise Corrections to Stochastic Trace Formulas

We review studies of an evolution operator for a discrete Langevin equation with a strongly hyperbolic classical dynamics and a Gaussian noise. The leading eigenvalue of yields a physically measurable property of the dynamical system, the escape rate from the repeller. The spectrum of the evolution operator in the weak noise limit can be computed in several ways. A method using a local matrix representation of the operator allows to push the corrections to the escape rate up to order eight in the noise expansion parameter. These corrections then appear to form a divergent series. Actually, via a cumulant expansion, they relate to analogous divergent series for other quantities, the traces of the evolution operators ⁿ. Using an integral representation of the evolution operator , we then investigate the high order corrections to the latter traces. Their asymptotic behavior is found to be controlled by sub-dominant saddle points previously neglected in the perturbative expansion, and to be ultimately described by a kind of trace formula.     

Variational problems on multiply connected thin strips III: Integration of the Ginzburg-Landau equations over graphs

We analyze the one-dimensional Ginzburg-Landau functional of superconductivity on a planar graph. In the Euler-Lagrange equations, the equation for the phase can be integrated, provided that the order parameter does not vanish at the vertices; in this case, the minimization of the Ginzburg-Landau functional is equivalent to the minimization of another functional, whose unknowns are a real-valued function on the graph and a finite set of integers.

     

Minimum-Phase Second-Order Systems and the Spectrum of the Semigroup Generator

Controller design is much easier for minimum-phase systems than for non-minimum phase systems. We show that a wide class of second-order in.nite-dimensional systems with velocity measurements are minimum-phase. The system does not need to be exponentially stable. We show that in general the spectrum can be quite arbitrary in the closed left half plane. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

23种挥发性有机化合物在3种吸附剂上漏出容量的测定评价

采用吸附热解吸－气相色谱－质谱法对23种挥发性有机化合物Chromosorb 106、Tenax TA、Tenax TG等3种吸附剂上漏出容量进行了测定。根据实验结果确定了不同的化合物应选择不同的吸附剂及相应的采样体积。结果表明,Chromosorb 106可较好地吸附低沸点的挥发性有机化合物,Tenax TA、Tenax TG均可用于沸点较高的挥发笥有机化合物吸附,这对测定大气中的有机化合物含量采样有一定的参考价值。     

Derailed Ohira-Bestmann Reaction of γ,δ-Unsaturated Aldehydes for the Stereoselective Synthesis of Cyclopenta[c]pyrazoles

The synthesis of cyclopenta[c]pyrazoles from γ,δ-unsaturated aldehydes by a domino sequence involving one-carbon homologation and intramolecular azomethine imine 1,3-dipolar cycloaddition is disclosed. The fused pyrazoles bearing aromatic and aliphatic substituents are obtained in good yields and excellent diastereomeric purity. Additionally, the synthetic utility of the pyrazole products generated by this method has been highlighted in a series of functionalization reactions. The method presented opens strategic opportunities for the synthesis of pyrazole-containing biologically active compounds.