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.     

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.     

Stereoselective coupling reaction of dimethylzinc and alkyne toward nickelacycles

Ni catalyst promotes the three-component coupling reaction of vinyloxacyclopropane, alkyne, and dimethylzinc to provide 2,5-heptadienyl alcohol in high yields. Vinylcyclopropane also participates in a similar three-component coupling reaction to afford dimethyl (α-heptadienyl)malonate with excellent E-stereoselectivity.     

Synthesis,isolation, and characterization of polytitanasiloxanes and zirconasiloxanes by the hydrolytic cocondensation of tetraethoxysilane and titanium or zirconium tetraisopropoxide

Polytitanasiloxanes and polyzirconasiloxanes were synthesized through the hydrolytic cocondensation of tetraethoxysilane (TEOS) and tetraisopropoxytitanium (TPT) or tetraisopropoxyzirconium (TPZ) 2‐propanol adduct (process A) and through the reaction of partially hydrolyzed TEOS with TPT or TPZ (process B) and were isolated as acetylacetonato derivatives stable against self‐condensation. In both processes, acetylacetone was added to provide acetylacetonato derivatives of polytitanasiloxanes and polyzirconasiloxanes. In process A, titanium‐ or zirconium‐rich polymetallasiloxanes were formed during the initial stage of the process, whereas the molar ratio of silicon to titanium or zirconium was gradually increased up to almost unity with an increasing reaction time. In process B, the molar ratio gradually increased below and above unity as the molar ratio of water to TEOS increased. When the acetylacetonato derivatives of polymetallasiloxanes were subjected to heat treatment, the titania or zirconia component was crystallized. The crystallization temperature increased as the silica content and the molar ratio of water to TEOS increased, and this demonstrated that the crystallization was dependent on the sequence in the main chain of the polymetallasiloxanes. The ²⁹Si NMR spectra of the polymetallasiloxanes led to the idea that the backbone metallasiloxane linkages consisted of random and block sequences for processes A and B, respectively. © 2005 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 43: 763–772, 2005