Synthesis of Spirocyclic and Fused Isoxazoline Building Blocks

A highly efficient multigram synthesis of spirocyclic and fused isoxazoline building blocks is described. Isoxazoline-3-carboxylates were synthesized via a regioselective 1,3-dipolar cycloaddition reaction of 2-chloro-2-(hydroxyimino)acetate and carbo- or heterocyclic alkenes bearing endo- or exocyclic C=C double bonds, resulting in fused or spirocyclic isoxazolines, respectively. The preparation of up to 300 g of these compounds was achieved in a single run. The ester group of isoxazolines was then subjected to common synthetic transformations for the synthesis of corresponding building blocks, including alcohols, chlorides, azides, amines, aldehydes, carboxylic acids, amino acids and their derivatives, difluoromethyl-substituted compounds, and bicyclic γ-lactones. Additionally, a direct cycloaddition-based approach to the synthesis of aminoalkyl- and chloromethyl-substituted isoxazolines was proposed to improve their preparation. The described isoxazoline building blocks are expected to be valuable tools for drug discovery.     

A genetic algorithm based determination of the ground and excited (1Lb) state structure and the orientation of the transition dipole moment of benzimidazole

The structure of benzimidazole has been determined in the electronic ground and excited states using rotationally resolved electronic spectroscopy. The rovibronic spectra of four isotopomers and subsequently the structure of benzimidazole have been automatically assigned and fitted using a genetic algorithm based fitting strategy. The lifetimes of the deuterated isotopomers have been shown to depend on the position of deuteration. The angle of the transition dipole moment with the inertial a-axis could be determined to be -30 degrees. Structures and transition dipole moment orientation have been calculated at various levels of theory and were compared to the experimental results.     

The initial boundary value problem for the nonlinear parabolic equation in unbounded domain

In this paper we consider the mixed problem for the equation u _tt  + A ₁ u + A ₂(u _t ) + g(u _t ) = f(x, t) in unbounded domain, where A ₁ is a linear elliptic operator of the fourth order and A ₂ is a nonlinear elliptic operator of the second order. Under natural assumptions on the equation coefficients and f we proof existence of a solution. This result contains, as a special case, some of known before theorems of existence. Essentially, in difference up to previous results we prove theorems of existence without the additional assumption on behavior of solution at infinity.      

A PDE approach to large deviations in Hilbert spaces

We introduce a PDE approach to the large deviation principle for Hilbert space valued diffusions. It can be applied to a large class of solutions of abstract stochastic evolution equations with small noise intensities and is adaptable to some special equations, for instance to the 2D stochastic Navier–Stokes equations. Our approach uses a lot of ideas from (and in significant part follows) the program recently developed by Feng and Kurtz [J. Feng, T. Kurtz, Large Deviations for Stochastic Processes, in: Mathematical Surveys and Monographs, vol. 131, American Mathematical Society, Providence, RI, 2006]. Moreover we present easy proofs of exponential moment estimates for solutions of stochastic PDE.