Reaktionen mit phosphororganischen Verbindungen, 49. Synthese und 1H-NMR-Spektren von (3-Acylbicyclo[2.2.1]hept-5-en-2-yl)phosphonsäureestern

Reactions with Organophosphorus Compounds, 49. Synthesis and ¹H NMR Spectra of (3-Acylbicyclo[2.2.1]hept-5-en-2-yl)phosphonates Reaction of the (E)-(β-acylvinyl)phosphonates 1 with cyclopentadiene yields the isomeric norbornylphosphonates 2 (endo-acyl, exo-P) and 3 (exo-acyl, endo-P) in a 7:3 ratio. With 1,3-cyclohexadiene the corresponding bicyclooctenyl derivatives 7 and 8 are obtained from 1a . The (Z)-phosphinylacrylate 4 gives with cyclopentadiene the isomers 5 (exo-CO₂Me, exo-P) and 6 (endo-CO₂Me, endo-P) in nearly equal amounts. The configuration of the cycloadducts has been proved by ¹H NMR spectroscopy.     

Role of pyridine in the catalytic activation of sodium hypochlorite in the presence of manganese porphyrin

Steric and electronic influences of various substituted pyridines support the hypothesis of the coordination of pyridine in the manganese porphyrin-catalysed epoxidation of olefins with sodium hypochlorite solution.     

Revisiting differential calculus in the light of an uncanny function

A metric jet can be linear without being the metric jet of a continuous linear map. We begin with giving such an amazing example and then we get interested in tangentiable maps whose tangent jet at a point is precisely a linear metric jet. For such maps, a local inversion theorem is still true.     

Uniform estimates for order statistics and Orlicz functions

We establish uniform estimates for order statistics: Given a sequence of independent identically distributed random variables ξ ₁, … , ξ _n and a vector of scalars x = (x ₁, … , x _n ), and 1 ≤ k ≤ n, we provide estimates for \mathbb E   k-min_{1 ￡ i ￡ n} |x_ix_i|{\mathbb E \, \, k-{\rm min}_{1\leq i\leq n} |x_{i}\xi _{i}|} and \mathbb E k-max_{1 ￡ i ￡ n}|x_ix_i|{\mathbb E\,k-{\rm max}_{1\leq i\leq n}|x_{i}\xi_{i}|} in terms of the values k and the Orlicz norm ||y_x||_M{\|y_x\|_M} of the vector y _x  = (1/x ₁, … , 1/x _n ). Here M(t) is the appropriate Orlicz function associated with the distribution function of the random variable |ξ ₁|, G(t) = \mathbb P ({ |x₁| ￡ t}){G(t) =\mathbb P \left(\left\{ |\xi_1| \leq t\right\}\right)}. For example, if ξ ₁ is the standard N(0, 1) Gaussian random variable, then G(t) = ?{\tfrac2p}ò₀^t e^-\fracs22ds {G(t)= \sqrt{\tfrac{2}{\pi}}\int_{0}^t e^{-\frac{s^{2}}{2}}ds }  and M(s)=?{\tfrac2p}ò₀^se^-\frac12t2dt{M(s)=\sqrt{\tfrac{2}{\pi}}\int_{0}^{s}e^{-\frac{1}{2t^{2}}}dt}. We would like to emphasize that our estimates do not depend on the length n of the sequence.     

Synthèse partielle et propriétés oncostatiques des pseudo-tubulosines,analogues de l'émétine et de la tubulosine

Partial Synthesis and Oncostatic Properties of Pseudotubulosines, Analogues of Emetine and Tubulosine Pseudotubulosines, structural analogues of emetine and tubulosine, have been synthesized by either Pictet-Spengler or Bischler-Napieralski condensation from dihydrocorynantheal or corynantheidal. Spectral data, cytotoxic and oncostatic properties of these new alkaloids are described.     

Homogenization of First Order Equations with (u/ε)-Periodic Hamiltonians Part II: Application to Dislocations Dynamics

This paper is concerned with a result of homogenization of a non-local first order Hamilton–Jacobi equation describing the dislocations dynamics. Our model for the interaction between dislocations involves both an integro-differential operator and a (local) Hamiltonian depending periodicly on u/ε. The first two authors studied in a previous work homogenization problems involving such local Hamiltonians. Two main ideas of this previous work are used: on the one hand, we prove an ergodicity property of this equation by constructing approximate correctors which are necessarily non periodic in space in general; on the other hand, the proof of the convergence of the solution uses here a twisted perturbed test function for a higher dimensional problem. The limit equation is a nonlinear diffusion equation involving a first order Lévy operator; the nonlinearity keeps memory of the short range interaction, while the Lévy operator keeps memory of long ones. The homogenized equation is a kind of effective plastic law for densities of dislocations moving in a single slip plane.     

Surface bodies and p-affine surface area

The surface body is a generalization of the floating body. Its relation to p-affine surface area is studied.     

Image Space Analysis for Constrained Inverse Vector Variational Inequalities via Multiobjective Optimization

In this paper, we employ the image space analysis to study constrained inverse vector variational inequalities. First, sufficient and necessary optimality conditions for constrained inverse vector variational inequalities are established by using multiobjective optimization. A continuous nonlinear function is also introduced based on the oriented distance function and projection operator. This function is proven to be a weak separation function and a regular weak separation function under different parameter sets. Then, two alternative theorems are established, which lead directly to sufficient and necessary optimality conditions of the inverse vector variational inequalities. This provides a partial answer to an open question posed in Chen et al. (J Optim Theory Appl 166:460–479, 2015).     

Subpicosecond pulse generation from a 1.56 μm mode-locked VECSEL

Near-transform-limited subpicosecond pulses at 1.56 μm were generated from an optically pumped InP-based vertical-external-cavity surface-emitting laser (VECSEL) passively mode-locked at 2 GHz repetition rate with a fast InGaAsNSb/GaAs semiconductor saturable absorber mirror (SESAM). The SESAM microcavity resonance was adjusted via a selective etching of phase layers specifically designed to control the magnitude of both the modulation depth and the intracavity group delay dispersion of the SESAM. Using the same VECSEL chip, we observed that the mode-locked pulse duration could be reduced from several picoseconds to less than 1 ps with a detuned resonant SESAM.