Quantum-Like Representation Algorithm for Trichotomous Observables

We study the problem of representing statistical data (of any origin) by a complex probability amplitude. This paper is devoted to representation of data collected from measurements of two trichotomous observables. The complexity of the problem eventually increases compared to the case of dichotomous observables. We see that only special statistical data (satisfying a number of nonlinear constraints) have the quantum-like representation.     

α-Geodesical Skew Divergence

The asymmetric skew divergence smooths one of the distributions by mixing it, to a degree determined by the parameter λ, with the other distribution. Such divergence is an approximation of the KL divergence that does not require the target distribution to be absolutely continuous with respect to the source distribution. In this paper, an information geometric generalization of the skew divergence called the α-geodesical skew divergence is proposed, and its properties are studied.     

Proton transfer in water–hydroxyl mixed overlayers on Pt(1 1 1): Combined approach of laser desorption and spatially-resolved X-ray photoelectron spectroscopy

Proton transfer in water–hydroxyl mixed overlayers on a Pt(1 1 1) surface was studied by a combination of laser induced thermal desorption (LITD) method and spatially-resolved X-ray photoelectron spectroscopy (micro-XPS). The modulated pattern OH + H₂O/H₂O/OH + H₂O was initially prepared by the LITD method; vacant area with a 400 μm width was first formed in the mixed OH + H₂O overlayer by irradiation of focused laser pulses, and followed by refilling the vacant area with pure H₂O. Spatial distribution changes of OH and H₂O were measured as a function of time with the micro-XPS technique, which indicated that H₂O molecules in the central region flow into the OH + H₂O region. From quantitative analyses using a diffusion equation, we found that the proton transfer in the mixed overlayer consists of at least two pathways: direct proton transfer from H₂O to OH in the nearest site and the proton transfer to the next-nearest site via H₃O⁺ formation. The time scale of first and second path was estimated to be 5.2 ± 0.9 ns and 48 ± 12 ns at 140 K, respectively. In the presence of water capping layer, however, the rate of proton transfer is reduced by an order of magnitude, which would be explained by peripatetic behavior of proton into H₂O capping layer.     

Preparation,structure, and unique thermal [2+2], [4+2], and [3+2] cycloaddition reactions of 4-vinylideneoxazolidin-2-one

The terminal allene C(alpha)=C(beta) bonds of 4vinylidene-2-oxazolidinone (2) readily undergo [2+2] cycloaddition with a wide variety of terminal alkynes, alkenes, and 1,3-dienes irrespective of their electronic nature under strictly thermal activation conditions (70-100 degrees C) and provide 3substituted (Z)-methylenecyclobutenes 6, 3substituted methylenecyclobutanes 7 and 8, and 3vinylmethylenecyclobutanes 9, respectively, in good to excellent yields. Alkenes react with 2 with complete retention of configuration. The [2+2] cycloaddition is concluded to proceed via a concerted [(pi(2s)+pi(2s))(allene) + pi(2s)] Hückel transition state on the basis of experimental evidences and quantum mechanical methods. Some highly polarized enones and nitrile oxide, on the other hand, react with 2 selectively at the internal C(4)=C(alpha) double bonds and give spiro compounds 10 and 11, respectively. The bent allene bonds (173-176 degrees) and the unique reactivity associated with 2 are attributed to a low-lying LUMO (C(alpha)=C(beta)) that is substantiated by a through-space sigma*(N-SO(2))-pi*(C(alpha)=C(beta)) orbital interaction.     

Ultrabroadband (>2000 cm-1) multiplex coherent anti-Stokes Raman scattering spectroscopy using a subnanosecond supercontinuum light source

We have developed ultrabroadband (>2000 cm(-1)) multiplex coherent anti-Stokes Raman scattering (CARS) spectroscopy using a subnanosecond (sub-ns) microchip laser source. A photonic crystal fiber specifically designed for sub-ns supercontinuum (SC) generation has been used for obtaining ultrabroadband Stokes radiation, which enables us to achieve simultaneous vibrational excitation in the range from 800 to 3000 cm(-1). We have successfully obtained multiplex CARS spectra for several molecular liquids. Since the CARS system using the sub-ns SC is simple and compact, it can be easily applied to ultrabroadband multiplex CARS microspectroscopy.     

Palladium-catalyzed 1,3-diol fragmentation: synthesis of omega-dienyl aldehydes

2-(1'-Hydroxy-2'-propenyl)cycloalkan-1-ols undergo dehydrative C1-C2 bond cleavage and provide omega-dienyl aldehydes under the catalysis of Pd(0) and 9-phenyl-9-BBN.     

Nickel‐Catalyzed Homoallylation of Aldehydes and Ketones with 1,3‐Dienes and Complementary Promotion by Diethylzinc or Triethylborane

Regio‐ and stereoselective homoallylation of saturated aldehydes and ketones to give bishomoallyl alcohols 1,3‐anti‐ 1 is achieved with [Ni(acac)₂] (cat.) and Et₂Zn [Eq. (a)]. This new catalyst system thus complements the previously reported combination of [Ni(acac)₂] with Et₃B, which offers advantages in the homoallylation of unsaturated and aromatic aldehydes. acac=acetylacetonato.