A one pot, metathesis-hydrogenation sequence for the selective formation of carbon-carbon bonds

A combination of homogeneous hydrogenation and metathesis reactions allows highly efficient, stepwise chemo- and stereoselective formation of three separate 2,7-diaminosuberic acid derivatives in a single pot without isolation of intermediates.     

Nanoscale Borromean links for real

Borohydride reduction of a Borromean Ring (BR) complex containing six zinc(II) ions and 12 imine bonds has resulted in its demetallation, producing a neutral BR compound and also its free macrocycle, following cleavage of at least one of the imine bonds in the ethanolic reaction mixture.     

Finite speed of propagation and local boundary conditions for wave equations with point interactions

We show that the boundary conditions entering in the definition of the self-adjoint operator describing the Laplacian plus a finite number of point interactions are local if and only if the corresponding wave equation has finite speed of propagation.

     

The feasibility pump

In this paper we consider the NP-hard problem of finding a feasible solution (if any exists) for a generic MIP problem of the form min{c^Tx:Ax≥b,x_j integer ∀j ∈ }. Trivially, a feasible solution can be defined as a point x* ∈ P:={x:Ax≥b} that is equal to its rounding , where the rounded point is defined by := x*_j if j ∈ and := x*_j otherwise, and [·] represents scalar rounding to the nearest integer. Replacing “equal” with “as close as possible” relative to a suitable distance function Δ(x*, ), suggests the following Feasibility Pump (FP) heuristic for finding a feasible solution of a given MIP.We start from any x* ∈ P, and define its rounding . At each FP iteration we look for a point x* ∈ P that is as close as possible to the current by solving the problem min {Δ(x, ): x ∈ P}. Assuming Δ(x, ) is chosen appropriately, this is an easily solvable LP problem. If Δ(x*, )=0, then x* is a feasible MIP solution and we are done. Otherwise, we replace by the rounding of x*, and repeat.We report computational results on a set of 83 difficult 0-1 MIPs, using the commercial software ILOG-Cplex 8.1 as a benchmark. The outcome is that FP, in spite of its simple foundation, proves competitive with ILOG-Cplex both in terms of speed and quality of the first solution delivered. Interestingly, ILOG-Cplex could not find any feasible solution at the root node for 19 problems in our test-bed, whereas FP was unsuccessful in just 3 cases.     

Exact Inference for Random Dirichlet Means

Two characterisations of a random mean from a Dirichlet process, as a limit of finite sums of a simple symmetric form and as a solution of a certain stochastic equation, are developed and investigated. These are used to reach results on and new insights into the distributions of such random means. In particular, identities involving functional transforms and recursive moment formulae are established. Furthermore, characterisations for several choices of the Dirichlet process parameter (leading to symmetric, unimodal, stable, and finite mixture distributions) are provided. Our methods lead to exact simulation recipes for prior and posterior random means, an approximation algorithm for the exact densities of these means, and limiting normality theorems for posterior distributions. The theory also extends to mixtures of Dirichlet processes and to the case of several random means simultaneously.     

A Green's Function Approach to the Shift of Spectral Lines in Dense Plasmas

Variations of the spectral lines in high dense ion plasmas with temperature and pressure may be characterized by the broadening as well as by the shift of spectral lines. For dense hydrogen- and alkali-plasmas (free carrier density larger than 10¹⁶/cm³) one of the possible mechanisms responsible for line profiles is considered to be the Coulomb interaction with free charged carriers. Using thermodynamic Green's functions, a systematic approach to the theory of spectral lines starting from the complex dielectric function is outlined. The line shift is derived from a perturbative treatment of the two-particle Green's function in the surrounding plasma. The shift of several lines proportional to the carrier density is evaluated as a function of the temperature and compared with experimental results.