Distance-preserving approximations of polygonal paths

Given a polygonal path P with vertices $p_1,p_2,\dots ,p_n\in {\mathbb{R}}^d$ and a real number $t⩾1$, a path $Q=(p_{i_1},p_{i_2},\dots ,p_{i_k})$ is a t-distance-preserving approximation of P if $1=i_1<i_2<\cdots <i_k=n$ and each straight-line edge $(p_{i_j},p_{i_{j+1}})$ of Q approximates the distance between $p_{i_j}$ and $p_{i_{j+1}}$ along the path P within a factor of t. We present exact and approximation algorithms that compute such a path Q that minimizes k (when given t) or t (when given k). We also present some experimental results.     

Stereoselective preparation of (RP)-8-hetaryladenosine-3',5'-cyclic phosphorothioic acids

Cyclic adenosine monophosphate (cAMP) has been converted into its 8-bromo derivative and 2'O-TBDMS protected before activation of the phosphoric acid moiety with a reagent generated in situ from oxalyl chloride and DMF. Further reactions with primary amines furnished corresponding phosphoramidates with high stereoselectivity at the phosphorus atom. Cross-coupling reactions with the 8-bromopurine yielded 8-hetaryl derivatives. X-Ray analyses showed the amidates to possess the (S(P))-configuration. Carbon disulfide effected thiylation under strongly basic conditions stereospecifically provided the (R(P))-phosphorothioic acids.     

Ar+ and Xe+ velocities near the presheath-sheath boundary in an Ar/Xe discharge

The velocities of Ar+ and Xe+ ions near the presheath-sheath boundary in an Ar/Xe discharge are studied by particle-in-cell Monte Carlo simulation. For a pure argon discharge the argon ion has almost the same velocity profile as it does in the mixture of argon and xenon. Similarly, for a xenon discharge the xenon ion has almost the same velocity profile as it does in the mixture of argon and xenon. The ion speed at the sheath-presheath boundary is the same for an ion in a pure argon or xenon discharge and for the same ion in a mixture of argon and xenon. We conclude that, in our simulation, each ion reaches its own Bohm speed at the presheath-sheath interface.     

Excitation of radial collective modes in a quantum dot: Beyond linear response

The recent results on the linear breathing mode of the excitation spectrum of a quantum dot obtained by McDonald et. al [Phys. Rev. Lett. 111 , 256801 (2013)] are extended to the nonlinear regime. To accomplish this and analyze the results the response of five different models of two interacting electrons in a quantum dot to an external short lived radial excitation that is strong enough to excite the system well beyond the linear response regime is compared. The models considered describe the Coulomb interaction between the electrons in different ways ranging from mean‐field approaches to configuration interaction (CI) models, where the two‐electron Hamiltonian is diagonalized in a large truncated Fock space. The radially symmetric excitation is selected in order to severely put to test the different approaches to describe the interaction and correlations of an electron system in a nonequilibrium state. As can be expected for the case of only two electrons none of the mean‐field models can in full details reproduce the results obtained by the CI model. Nonetheless, some linear and nonlinear characteristics are reproduced reasonably well. All the models show activation of an increasing number of collective modes as the strength of the excitation is increased. By varying slightly the confinement potential of the dot it was observed how sensitive the properties of the excitation spectrum are to the Coulomb interaction and its correlation effects. In order to approach closer the question of nonlinearity one of the mean‐field models has been solved directly in a nonlinear fashion without resorting to iterations.     

Maximum-norm estimates for resolvents of elliptic finite element operators

Let be a convex domain with smooth boundary in . It has been shown recently that the semigroup generated by the discrete Laplacian for quasi-uniform families of piecewise linear finite element spaces on is analytic with respect to the maximum-norm, uniformly in the mesh-width. This implies a resolvent estimate of standard form in the maximum-norm outside some sector in the right halfplane, and conversely. Here we show directly that such a resolvent estimate holds outside any sector around the positive real axis, with arbitrarily small angle. This is useful in the study of fully discrete approximations based on -stable rational functions, with small.

     

Synthesis of juniperonic acid

Synthesis of juniperonic acid [(all-Z)-5,11,14,17-eicosatetraenoic acid], has been achieved in eight steps and in 19% overall yield starting from eicosapentaenoic acid.     

A simple and efficient kinetic spanner

We present a new and simple (1+ε)-spanner of size O(n/ε²) for a set of n points in the plane, which can be maintained efficiently as the points move. Assuming the trajectories of the points can be described by polynomials whose degrees are at most s, the number of topological changes to the spanner is O((n/ε²)λ_s+2(n)), and at each event the spanner can be updated in O(1) time.     

An Improved Synthesis of 2-Chlorinated Imidazo[1,2-α]-pyridines and the Application of this Procedure for the Synthesis of Several New Polychlorinated Imidazo[1,2-α]Pyridnes.

Polychlorinated imidazo[1,2-α]pyridines were synthesized as analogs of certain chlorinated benzimidazoles. The imidazo[1,2-α]pyridines were obtained by a condensation of ethyl bromoacetate and chlorinated 2-aminopyridines. These condensation products were treated with an ion exchange resin to effect an exchange of hydrobromide salts with hydrochloride salts. These compounds were subsequently treated with POCl₃ to convert the imidazo[1,2-α]pyridin-2-ones into 2-chloroimidazo[1,2-a]pyridines.