An optimal Poincaré inequality in for convex domains

For convex domains with diameter we prove

for any with zero mean value on . We also show that the constant in this inequality is optimal.

     

A general non-convex large deviation result with applications to stochastic equations

We prove an abstract large deviation result for a sequence of random elements of a vector space satisfying an “abstract exponential martingale condition”. The framework naturally generates non-convex rate functions. We apply the result to solutions of It? stochastic equations in R ^d driven by Brownian motion and a Poisson random measure. Received: 23 June 1999 / Revised version: 17 February 2000 / Published online: 22 November 2000     

Bishop–Phelps–Bollobás property for certain spaces of operators

We characterize the Banach spaces Y   for which certain subspaces of operators from _L1(μ)$L_1(\mu )$ into Y have the Bishop–Phelps–Bollobás property in terms of a geometric property of Y, namely AHSP. This characterization applies to the spaces of compact and weakly compact operators. New examples of Banach spaces Y with AHSP are provided. We also obtain that certain ideals of Asplund operators satisfy the Bishop–Phelps–Bollobás property.     

Interpenetrating polymer networks templated on bicontinuous microemulsions containing silicone oil, methacrylic acid, and hydroxyethyl methacrylate

Polydimethylsiloxane-poly(methacrylic acid—hydroxyethyl methacrylate) interpenetrating polymer networks (PDMS-P(MAA–HEMA) IPN) were formulated and polymerized simultaneously from bicontinuous microemulsion templates. Microemulsions containing reactive silicone oils and MAA/HEMA in aqueous solution were stabilized with silicone surfactants, and were then reacted at 50 °C for 3 h under an N₂ atmosphere. The formation of bicontinuous morphology was confirmed by laser scanning confocal microscopy, reversible swelling behavior, differential scanning calorimetry, texture analysis, and permeability to vitamin B₁₂ in aqueous solution. Incorporating polymerizable surfactants into the microemulsion aided in stabilizing the initial microemulsion structure during polymerization, yielding a more uniform IPN morphology with domain sizes of <200 nm at equilibrium swelling. The process developed here demonstrates a simple, single-step polymerization approach to forming IPNs from low viscosity microemulsion templates, and could potentially be extended to a variety of hydrophilic and hydrophobic monomers.     

Characterization of the train-average time-frequency parameters inherent in the low-power picosecond optical pulses generated by the actively mode-locked semiconductor laser with an external single-mode fiber cavity

The specific approach to characterizing the train-average parameters of low-power picosecond optical pulses with the frequency chirp, arranged in high-repetition-frequency trains, in both time and frequency domains is elaborated for the important case when the semiconductor laser is matched by an external single-mode fiber cavity and operates in the active mode-locking regime. This approach involves the joint Wigner time-frequency distributions, which can be created for those pulses due to exploitation of a novel interferometric technique. Practically, the InGaAsP/InP-heterolaser generating at the wavelength 1320 nm was used during the experiments carried out and an opportunity of reconstructing the corresponding joint Wigner time-frequency distributions was successfully demonstrated.     

Near-barrier fusion of the ⁸B + ⁵⁸Ni proton-halo system

Fusion cross sections were measured for the exotic proton-halo nucleus ?B incident on a ??Ni target at several energies near the Coulomb barrier. This is the first experiment to report on the fusion of a proton-halo nucleus. The resulting excitation function shows a striking enhancement with respect to expectations for normal projectiles. Evidence is presented that the sum of the fusion and breakup yields saturates the total reaction cross section.     

Synthesis of Novel Photochromic 6‐Benzyloxo‐spirobenzopyran Compounds

The synthesis of four novel derivatives of 1′,3′,3′‐trimethylspiro‐[2H‐1]‐benzopyran‐6‐benzyloxo‐2,2′‐indoline is reported. The synthetic approach to these compounds involves the preparation of the key compound, 3‐formyl‐4‐hydroxybenzophenone, by means of the Reimer–Tiemann reaction. The photochromic compounds were isolated and characterized by ¹H and ¹³C NMR as well as FT‐IR and UV‐VIS spectrometry. Comparative studies performed in these compounds showed a higher molar extinction coefficient and red shift of maximum absorption wavelength when the benzyloxo group is introduced in the spirobenzopyran molecule.