Aqueous Heterogeneity at the Air/Water Interface Revealed by 2D‐HD‐SFG Spectroscopy

Water molecules interact strongly with each other through hydrogen bonds. This efficient intermolecular coupling causes strong delocalization of molecular vibrations in bulk water. We study intermolecular coupling at the air/water interface and find intermolecular coupling 1) to be significantly reduced and 2) to vary strongly for different water molecules at the interface—whereas in bulk water the coupling is homogeneous. For strongly hydrogen‐bonded OH groups, coupling is roughly half of that of bulk water, due to the lower density in the near‐surface region. For weakly hydrogen‐bonded OH groups that absorb around 3500 cm^?1, which are assigned to the outermost, yet hydrogen‐bonded OH groups pointing towards the liquid, coupling is further reduced by an additional factor of 2. Remarkably, despite the reduced structural constraints imposed by the interfacial hydrogen‐bond environment, the structural relaxation is slow and the intermolecular coupling of these water molecules is weak.     

Efficient and Selective Formation of Unsaturated Carboxylic and Phenylacetic Acids from Diketene

A nickel catalyst promotes the multicomponent coupling reaction of diketene, an alkyne, and Me₂Zn to provide 3‐methylene‐4‐hexenoic acids in excellent yields. Under similar conditions, the combination of the nickel catalyst and Et₂Al(OEt) promotes a cycloaddition reaction involving dimerization of an alkyne to furnish phenylacetic acids. In the presence of PPh₃, a formal [2+2+1+1] cycloaddition reaction proceeds to afford regioisomeric phenylacetic acids via cleavage of the C?C bond.     

Photoinduced reactions—LXIX : The photochemical transposition of 2,6-di-t-butylphenols through their ketone tautomers

2,6-Di-t-butylphenol and its 4-substituted derivatives (1) have been shown to undergo novel photochemical transposition to isomeric phenols 2 and 3, being accompanied by de-t-butylation to give 4. Involvement of the triplet excited state of 1 was confirmed by sensitization and quenching experiments. Evidence is presented for the initial tautomerization of 1 to the ketonic tautomers which undergo further photochemical transformation to the products.     

Fluorescent properties of coumarins with dual functions constructed by two sequential reactions

A series of coumarins with two aryl moieties was constructed from 3-azide-6-bromocoumarin scaffold by means of two sequential reactions, Huisgen 1,3-cycloaddition and Suzuki-Miyaura coupling reactions. Evaluation of their fluorescence properties indicated that the mode of fluorescent change by substituted group on each aryl group would be different. So this structure could be promising candidates as multi-analyte type fluorescent sensors, whose mode of spectroscopic changes, such as fluorescence intensity, and absorption or fluorescence maximum wavelength, are different for each analyte.     

Non-Kolmogorovian Approach to the Context-Dependent Systems Breaking the Classical Probability Law

There exist several phenomena breaking the classical probability laws. The systems related to such phenomena are context-dependent, so that they are adaptive to other systems. In this paper, we present a new mathematical formalism to compute the joint probability distribution for two event-systems by using concepts of the adaptive dynamics and quantum information theory, e.g., quantum channels and liftings. In physics the basic example of the context-dependent phenomena is the famous double-slit experiment. Recently similar examples have been found in biological and psychological sciences. Our approach is an extension of traditional quantum probability theory, and it is general enough to describe aforementioned contextual phenomena outside of quantum physics.     

Ramification in the division fields of an elliptic curve

We study the ramification in the division fields of an elliptic curve. Applications on the class number of quadratic fields and on elliptic curves with prime power conductor are given.     

On homogeneous solutions of Einstein's field equations

In the first part of this paper we describe a formalism capable of finding all homogeneous solutions of Einstein's field equations with any arbitrary energy-impulse tensor. In the second part we find all homogeneous vacuum solutions.