Numerical reconstruction of an infrared wavefront utilizing an optical phase modulation device

We utilize nitroanisole, that absorbs infrared (IR) radiation as heat, as an optical modulation device based on a thermal process. The nitroanisole exhibits a thermal lens effect, i.e. a temperature dependent refractive index. Hence, the nitroanisole can induce phase modulation to visible light, in direct response to intensity of the incident IR radiation. The proposed method can be used to obtain the phase modulation distribution that corresponds to the IR intensity distribution, i.e. the IR hologram itself, on the nitroanisole by examining the phase map of visible light that is modulated upon passing through the nitroanisole. The IR wavefront can be reconstructed by calculating extracted IR holograms through the Fresnel transform. It is verified that both the amplitude and the phase of the IR wavefront can be reconstructed accurately by proposed method.     

Efficient [3,3]-sigmatropic rearrangement accelerated by a trifluoroacetyl group: synthesis of benzofurans under mild conditions

The [3,3]-sigmatropic rearrangement took place smoothly during the course of trifluoroacetylation of O-phenyloxime at below room temperature to give the dihydrobenzofuran or benzofuran as a result of concomitant cyclization.     

Regioselectivity in palladium-indium iodide-mediated allylation reaction of glyoxylic oxime ether and N-sulfonylimine

Allylation reaction of electron-deficient imines with allylic alcohol derivatives in the presence of a catalytic amount of palladium(0) complex and indium(I) iodide was studied. The reversibility of allylation was observed in the reaction of glyoxylic oxime ether having camphorsultam. As the important effect of water on regioselectivity, the gamma-adducts were kinetically formed from monosubstituted allylic reagents in the presence of water. The selective formation of thermodynamically stable alpha-adducts was observed in anhydrous THF. In contrast, the allylation of N-sulfonylimine gave the gamma-adducts with high regioselectivities even under anhydrous reaction conditions.     

Asymmetric synthesis of alpha-amino acids: indium-mediated reactions of glyoxylic oxime ether in aqueous media

The indium-mediated allylation and alkylation reactions of the Oppolzer camphorsultam derivative of glyoxylic oxime ether proceeded with excellent diastereoselectivity in aqueous media, providing a variety of enantiomerically pure alpha-amino acids.     

Stannyl radical addition-cyclization of oxime ethers connected with olefins

Stannyl radical addition-cyclization of oxime ethers connected with olefin moieties was studied. The radical reactions proceeded effectively by the use of triethylborane as a radical initiator to provide the functionalized pyrrolidines via a carbon-carbon bond-forming process.     

1,4-Dehydrogenation with a Two-Coordinate Cyclic (Alkyl)(amino)silylene

Cyclic (alkyl)(amino)silylene (CAASi) 1 has been found to successfully dehydrogenate 1,4-dihydroaromatic compounds containing various substituents to afford the corresponding aromatic compounds. The observed high substrate generality proves 1 to be a potential 1,4-dehydrogenation reagent for organic compounds. For the reaction with 9,10-dimethyl-9,10-dihydroanthracene, silylene 1 activated not only benzylic C−H bonds but also aromatic C−H bonds to yield a silaacenaphthene derivative, which is an unprecedented reaction of silylenes. The results of the experimental and computational study of the reaction of CAASi 1 with 9,10-dihydroanthracene and 1,4-cyclohexadiene are consistent with the notion that 1,4-dehydrogenation with CAASi 1 proceeds mainly through a stepwise hydrogen-abstraction mechanism.     

Detection of high-energy gamma rays from winter thunderclouds

A report is made on a comprehensive observation of a burstlike gamma-ray emission from thunderclouds on the Sea of Japan, during strong thunderstorms on 6 January 2007. The detected emission, lasting for approximately 40 sec, preceded cloud-to-ground lightning discharges. The burst spectrum, extending to 10 MeV, can be interpreted as consisting of bremsstrahlung photons originating from relativistic electrons. This ground-based observation provides the first clear evidence that strong electric fields in thunderclouds can continuously accelerate electrons beyond 10 MeV prior to lightning discharges.     

Highly effective synthetic methods for substituted 2-arylbenzofurans using [3,3]-sigmatropic rearrangement: short syntheses of stemofuran a and eupomatenoid 6

A new and efficient synthesis of 2-arylbenzofurans has been achieved via a route involving acylation and subsequent [3,3]-sigmatropic rearrangement of oxime ethers. Its synthetic utility is demonstrated by a short synthesis of stemofuran A and eupomatenoid 6 in which no procedure for protection of the phenolic hydroxyl groups is needed. [reaction--see text]     

Palladium-indium iodide-mediated allylation and propargylation of glyoxylic oxime ether and hydrazone: the role of water in directing the diastereoselective allylation

Allylation and propargylation of glyoxylic oxime ether in the presence of a catalytic amount of palladium(0) complex and indium(I) iodide were studied. Excellent diastereoselectivities in allylation were achieved in the presence of water, although low diastereoselectivities were observed in the absence of water. Propargylation of glyoxylic oxime ether proceeded with good diastereoselectivities in the presence of LiBr or LiCl.     

A converse of Loewner–Heinz inequality and applications to operator means

Let f(t)$f(t)$ be an operator monotone function. Then A?B$A?B$ implies f(A)?f(B)$f(A)?f(B)$, but the converse implication is not true. Let A?B$A?B$ be the geometric mean of A,B?0$A,B?0$. If A?B$A?B$, then B⁻¹?A?I$B^{-1}?A?I$; the converse implication is not true either. We will show that if f(λB+I)⁻¹?f(λA+I)?I$f{(\lambda B+I)}^{-1}?f(\lambda A+I)?I$ for all sufficiently small λ>0$\lambda >0$, then f(λA+I)?f(λB+I)$f(\lambda A+I)?f(\lambda B+I)$ and A?B$A?B$. Moreover, we extend it to multi-variable matrices means.