Enantiodivergent synthetic entry to the quinolizidine alkaloid lasubine II

Intramolecular cycloaddition of the syn- and the anti-nitrone 9 and 13 leads stereoselectively to the azabicyclic compounds 10 and 14 which may provide access to both enantiomers of the quinolizidine alkaloid lasubine II.     

Insertion of arynes into thioureas: a new amidine synthesis

Arynes, generated from trimethylsilyl phenyltriflate precursors, have been found to react with thioureas via a formal π-insertion into the C═S bond. The reaction contrasts with that of ureas, which proceeds via benzyne σ-insertion into the C-N bond, and represents a new, operationally simple route to functionalized amidines.     

Exit time and invariant measure asymptotics for small noise constrained diffusions

Constrained diffusions, with diffusion matrix scaled by small ?>0, in a convex polyhedral cone G⊂R^k, are considered. Under suitable stability assumptions small noise asymptotic properties of invariant measures and exit times from domains are studied. Let B⊂G be a bounded domain. Under conditions, an “exponential leveling” property that says that, as ?→0, the moments of functionals of exit location from B, corresponding to distinct initial conditions, coalesce asymptotically at an exponential rate, is established. It is shown that, with appropriate conditions, difference of moments of a typical exit time functional with a sub-logarithmic growth, for distinct initial conditions in suitable compact subsets of B, is asymptotically bounded. Furthermore, as initial conditions approach 0 at a rate ?² these moments are shown to asymptotically coalesce at an exponential rate.     

Competition between hydrogen bonding and dispersion interactions in the indole···pyridine dimer and (indole)2···pyridine trimer studied in a supersonic jet

Structures of the indole···pyridine dimer and (indole)2···pyridine trimer have been investigated in a supersonic jet using resonant two-photon ionization (R2PI) and IR-UV double resonance spectroscopic techniques combined with quantum chemistry calculations. R2PI spectra of the dimer and the trimer recorded by electronic excitation of the indole moiety show that the red-shift in the band origin of the dimer with respect to the 0(0)(0) band of the monomer is larger compared to that of the trimer. The presence of only one conformer in the case of both the dimer and the trimer has been confirmed from IR-UV hole-burning spectroscopy. The structures of the dimer and the trimer have been determined from resonant ion dip infrared (RIDIR) spectra combined with ab initio as well as DFT/M05-2X and DFT/M06-2X calculations. It has been found that the dimer, observed in the experiment, has a V-shaped geometry stabilized by N–H···N and C–H···N hydrogen bonding interactions, as well as C–H···π and π···π dispersion interactions. The geometry of the trimer has been found to be a cyclic one stabilized by N–H···N, N–H···π, C–H···π, and C–H···N interactions. The most important finding of this current study is the observation of the mixed dimer and trimer, which are stabilized by hydrogen bonding as well as dispersion interactions.     

Bogomolov restriction theorem for Higgs bundles

Let (E,θ) be a stable Higgs bundle of rank r on a smooth complex projective surface X equipped with a polarization H. Let C⊂X be a smooth complete curve with [C]=n⋅H. If where , then we prove that the restriction of (E,θ) to C is a stable Higgs bundle. This is a Higgs bundle analog of Bogomolov's restriction theorem for stable vector bundles.     

Soliton interaction control through dispersion and nonlinear effects for the fifth-order nonlinear Schrödinger equation

Nonlinear Dynamics - Optical fiber communication has developed rapidly because of the needs of the information age. Here, the variable coefficients fifth-order nonlinear Schrödinger equation...     

Wobbling phenomena with logarithmic law nonlinear Schrödinger equations for incoherent spatial Gaussons

We apply the equivalence particle principle to several nonlinear Schrödinger equations (NLSEs) that model the propagation of a spatial beam with logarithmic law nonlinearity. Using this principle, expressions for acceleration, spatial frequency, spatial period and other variables for a spatial soliton can be derived from the solution of the homogenous NLSE with logarithmic law nonlinearity. These results agree well with numerical simulations of the perturbed NLSE. We show that if the expression of the acceleration is bounded this means the spatial soliton propagates with a swing effect.