First total synthesis of natural 6-epiplakortolide e

[reaction: see text] Natural 6-epiplakortolide E was first synthesized from readily available 1-bromo-10-phenyldecane in 10 steps by using singlet oxygen-mediated Diels-Alder reaction to form cyclic peroxide followed by a directed iodolactonization to give the peroxylactone core.     

Total synthesis of the mycolactones

[structure: see text] The first total synthesis of the mycolactones is reported. This work unambiguously confirms our earlier relative and absolute stereochemical assignment of the mycolactones.     

Simulation of 3-D radiation beam patterns propagated through a planar interface from ultrasonic phased array transducers

Phased array transducers are quite often mounted on solid wedges with specific angles in many practical ultrasonic inspections of thin plates <10 mm in their thickness or welded joints with convex crowns. For the reliable application of phased array techniques with testing set-up, it is essential to have thorough understanding on the characteristics of radiation beam pattern produced in the interrogated medium. To address such a need, this paper proposes a systematic way to calculate full 3-D radiation beam patterns produced in the interrogated solid medium by phased array transducers mounted on a solid wedge. In order to investigate the characteristics of radiation beam patterns in steel, simulation is carried out for 7.5 MHz array transducers mounted on an acrylic wedge with the angle of 15.45 degrees with various of steering angles and/or focal planes.     

Mid-infrared pulses generated from the mixing output of an amplified, dual-wavelength Ti:sapphire system

We demonstrate the generation of femtosecond mid-infrared pulses by direct difference-frequency mixing in a AgGaS(2) crystal of two intense pulses from a dual-wavelength oscillator that have been simultaneously amplified in a single regenerative amplifier. A pulse energy of as much as 1.6 muJ was achieved at wavelengths of 9-11 mum.     

Spatial vector solitons consisting of counterpropagating fields

We present the experimental observation of a spatial vector soliton formed by counterpropagation of coherent optical fields. This is to our knowledge the first observation of a vector soliton in which the induced waveguide (potential) is periodic in the propagation direction. This vector soliton induces a waveguide and a thick grating within the waveguide, which can be used as a tunable optical waveguide filter.     

Interception of Deaminatively Generated Benzyl Carbenium Ions by Acetone

Essentially free benzyl carbenium ions were generated via protonation of phenyldiazomethane with benzoic acid in acetone. Interestingly, no proton transfer occurred below -20 degrees C. After protonation and dediazoniation of the diazoalkane at -20 degrees C, the solvent was found to intercept the deaminatively generated carbocations to yield initially the corresponding O-benzyl oxonium ion and benzyl benzoate. The onium ion, however, was labile under the reaction conditions, and decomposed into a cascade of products whose concentrations as a function of time were used to trace the reaction pathway. Thus, the O-benzyl oxonium ion reacted with benzoate ion to yield (2-benzyloxy)isopropyl benzoate; subsequent decomposition of this O-benzyl-O-benzoyl ketal produced 2,2-dibenzyloxypropane (a dibenzyl ketal), 2-benzyloxypropene, and benzyl alcohol. In a related study, benzyl cations were generated via thermolyses of N-benzyl-N-nitroso-O-benzoyl hydroxylamine at 0 and -70 degrees C. The product distributions were found to be temperature-dependent and different from that in the PhCHN(2) + PhCO(2)H case.     

Long, narrow all-light atom guide

A 1-mm-diameter all-light atom guide capable of transporting ultracold atoms tens of centimeters with high efficiency is described. We made the atom tunnel, a dark hollow beam that is blue detuned from resonance, by passing a few tens of milliwatts of energy from a TEM(00) diode laser beam through an optical sequence composed of three axicons and a simple lens. We demonstrate transport of 10(8)Cs atoms approximately 20 cm with minimal heating. We show that it is possible for one to control the direction and speed of the atoms in the tunnel by varying the detuning of the tunnel beam.     

A Counterexample in the Central Limit Theorem

We construct a c₀-valued random variable X such that (S_n/n)_nNhas a convergent subsequence, but X does not satisfy the centrallimit theorem. 1991 Mathematics Subject Classification 60B12.