Initial value/boundary value problems for fractional diffusion-wave equations and applications to some inverse problems

We consider initial value/boundary value problems for fractional diffusion-wave equation: , where 0<α?2, where L is a symmetric uniformly elliptic operator with t-independent smooth coefficients. First we establish the unique existence of the weak solution and the asymptotic behavior as the time t goes to ∞ and the proofs are based on the eigenfunction expansions. Second for α∈(0,1), we apply the eigenfunction expansions and prove (i) stability in the backward problem in time, (ii) the uniqueness in determining an initial value and (iii) the uniqueness of solution by the decay rate as t→∞, (iv) stability in an inverse source problem of determining t-dependent factor in the source by observation at one point over (0,T).     

Approximate controllability for fractional diffusion equations by interior control

We consider the approximate controllability by interior control of a partial differential equation with time derivatives of non-integer order. First, we prove the well-posedness of the inhomogeneous problem for the controlled system. Next, we study the dual system and show a weak type of unique continuation property. Finally, we prove the approximate controllability.     

Experimental and theoretical study on gas-phase ion/molecule reactions of silver trimer cation, Ag3+, with 12-crown-4

The reaction mechanisms of silver trimer cation, Ag3+, with 12-crown-4 (12C4) were studied experimentally and theoretically. Using a cylindrical ion trap time-of-flight mass spectrometer, gas-phase ion/molecule reactions of Ag3+ with 12C4 were observed. Metal-ligand complexes of [Ag(12C4)]+, [Ag3(12C4)]+ and [Ag3(12C4)2]+, and of [Ag(12C4)2]+ and [Ag3(12C4)3]+, were observed as the reaction intermediates and terminal products, respectively. The formations of the [Ag12C4]+ and [Ag(12C4)2]+ complexes indicated that the neutral dimer (Ag2) had been eliminated from the trimer cation. From the results of ab initio calculations at the HF/LanL2DZ level of theory and the experiments, it is suggested that three 12C4 molecules can attach to Ag3+ through consecutive reactions and that neutral Ag2 can be easily eliminated from [Ag3(12C4)]+.     

C3-symmetric trisimidazoline-catalyzed enantioselective bromolactonization of internal alkenoic acids

A method for conducting enantioselective bromolactonization reactions of trisubstituted alkenoic acids, using the C(3)-symmetric trisimidazoline 1 and 1,3-dibromo-5,5-dimethyl hydantoin as a bromine source, has been developed. The process generates chiral δ-lactones that contain a quaternary carbon. The results of studies probing geometrically different olefins show that (Z)-olefins rather than (E)-olefins are favorable substrates for the process. The method is not only applicable to acyclic olefin reactants but can also be employed to transform cyclic trisubstituted olefins into chiral spirocyclic lactones. Finally, the synthetic utility of the newly developed process is demonstrated by its application to a concise synthesis of tanikolide, an antifungal marine natural product.     

Diastereoselective hydroformylation of 2,5-cyclohexadienyl-1-carbinols with catalytic amounts of a reversibly bound directing group

A phosphinite plays a role as a reversibly bound directing group for the regio- and diastereoselective hydroformylation of 2,5-cyclohexadienyl-1-carbinols. Of the two alkene functions only one was functionalized through hydroformylation to form a synthetically attractive quaternary carbon center leaving the second alkene function for potential further functionalization.     

Kinetic study of proton-transfer reactions of phenylnitromethanes. Implication for the origin of nitroalkane anomaly

Measurements of rate constants and substituent effects for three important elementary steps of proton-transfer reactions of phenylnitromethane were reported. The Hammett ρ values for the deprotonation of ArCH(2)NO(2) with OH(-), protonation of ArCH═NO(2)(-) with H(2)O, and protonation of ArCH═NO(2)(-) with HCl were determined in aqueous MeOH at 25 °C. Comparison of these experimentally observed ρ values with those calculated at B3LYP/6-31G* revealed that aci-nitro species (ArCH═NO(2)H), which is formed on the O-protonation of ArCH═NO(2)(-), does not lie on the main route of the proton-transfer reaction. Analysis of the Br?nsted plot implies that the proton-transfer reaction of most XC(6)H(4)CH(2)NO(2) exhibits nitroalkane anomaly, but not for p-NO(2)C(6)H(4)CH(2)NO(2), and that the transition state charge imbalance is an origin of anomaly.     

Cationic polymerization of formaldehyde in liquid carbon dioxide. Part II: A kinetic study of the polymerization

The kinetic behavior on the polymerization of formaldehyde with and without acidic catalyst, in liquid carbon dioxide, in the temperature range of 30 to 50°C. was investigated. In the polymerization without catalyst both the polymer yield and the degree of polymerization increased with reaction time and also with rising temperature. With acidic catalyst, such as acetic acid and dichloroacetic acid, both the polymer yield and the degree of polymerization increased more than that in the polymerization without catalyst. The overall rate of polymerization with and without acidic catalyst was expressed by the first-order rate equation with respect to monomer concentration. From the results it was concluded that the polymerizations belonged to a type of successive polymerization with rapid initiation and no termination. The rate constant and the activation energy of each elementary process of polymerization were estimated on the basis of the results.     

Concise total synthesis of (-)-spongotine A

The first asymmetric total synthesis of spongotine A is described. The oxidative synthesis of the imidazoline/ketone unit from keto aldehyde and diamine is a key step in this synthesis. The absolute stereochemistry of the asymmetric center of natural spongotine A is revealed as the (S)-configuration.