Asymmetric synthetic study of macrolactin analogues

We designed two aromatic analogues 1a and 1b of macrolactin A with expectation of enhancing biological activity and metabolical stability. As a result of retrosynthetic analysis of these compounds 1a-b, two synthetic strategies have been examined. The first strategy includes the enantioselective addition of nonadienyl anion, derived from 3, to aldehyde 4 as a key step. The second one includes epimerization of ynone 7 to (E,E)-conjugated dienone 31 and subsequent diastereoselective hydride-reduction of 31. Although the former route furnished no desired target, the latter one was revealed to work well for the synthesis of 1. Unfortunately, the aimed (2Z,4E)-analogue 1a could not be synthesized due to an epimerization of the (2Z)-olefin into the (2E)-olefin. However, these methods could be applied to the total asymmetric synthesis of the (2E,4E)-analogue 1b. Overall, control of all of the four stereocenters was achieved by means of asymmetric and diastereoselective reactions without using any chiral natural sources.     

Electron transfer-initiated asymmetric photocyclization of chiral auxiliary-substituted N-acyl-α-dehydro(1-naphthyl)alaninamides to the corresponding 3,4-dihydrobenzo[f]quinolinone derivatives

Photoinduced electron transfer reactions of the title N-acyl-α-dehydronaphthylalaninamides [(Z)-1] with (S)-1-phenylethylamino and (S)-alaninamide auxiliary groups in methanol containing a tertiary amine were shown to form (R,S)- and (S,S)-3,4-dihydrobenzo[f]quinolinone derivatives (2) in excess at rt, respectively. The magnitude of diastereomeric excess (de) was varied in the range of −5-26% for (R,S)-2 and 16-92% for (S,S)-2, depending on the chiral auxiliary and reaction temperature. The mechanism of asymmetric induction in the photocyclization process eventually affording diastereomeric 2 was discussed based on solvent, tertiary amine, chiral auxiliary and temperature effects on the de value as well as on MM2 and PM5 calculations for the diastereomeric enol intermediates.     

Global behavior of the branch of positive solutions to a logistic equation of population dynamics

We consider the nonlinear problem arising in population dynamics:

where is a constant and is a positive parameter. We establish the crucial asymptotic formula for the branch of positive solutions in -framework as , where ( ). Especially, for the original logistic equation, namely the case where and , we obtain not only the asymptotic expansion formula for but also the remainder estimate. Such a formula for the bifurcation branch seems to be new.

     

Asymptotic Behavior of Bifurcation Branch of Positive Solutions for Semilinear Sturm–Liouville Problems

We consider the nonlinear eigenvalue problem

Two new dimeric coumarins isolated from Murraya exotica

Bismurrangatin and murramarin A, two new coumarins, were isolated from the vegetative branches of Murraya exotica. Murramarin A is a rare type of bicoumarin that connects two coumarin moieties by orthoester structure. The structures were elucidated based on spectroscopic methods, especially by 2D-NMR experiments.     

Photophysical and photochemical processes of 9,10-dihydro-9-silaphenanthrene derivatives: photochemical formation and electronic structure of 9-silaphenanthrenes

Photophysical and photochemical processes of 9-methyl- and 9-phenyl-9,10-dihydro-9-silaphenanthrene derivatives have been studied at room temperature and 77 K in comparison with the carbon analogue, 9,10-dihydrophenanthrene. These 9,10-dihydro-9-silaphenanthrene derivatives show smaller fluorescence quantum yield and remarkably larger Stokes shifts than those of the carbon analogue. In contrast, their phosphorescence quantum yields are two times larger than those of the carbon analogue, although the absolute value is not so large (approximately 0.1). Reaction products and intermediates produced by the 266 nm light photolysis have been studied, and it has been confirmed that 9-methyl- and 9-phenyl-9-silaphenanthrenes have been photochemically formed in methylcyclohexane at 77 K, in addition to the formation of radical cations of 9,10-dihydro-9-silaphenanthrene derivatives and the carbon-centered radical: 9-hydro-9-silaphenanthrenyl radical.     

Three-term asymptotics for the boundary layers of semilinear elliptic eigenvalue problems

We consider the nonlinear eigenvalue problem −Δu=λ f(u) in Ω u=0 on ∂Ω, where Ω is a ball or an annulus in R^N (N ≥ 2) and λ > 0 is a parameter. It is known that if λ >> 1, then the corresponding positive solution u_λ develops boundary layers under some conditions on f. We establish the asymptotic formulas for the slope of the boundary layers of u_λ with the exact second term and the ‘optimal’ estimate of the third term.     

Precise asymptotic formulas for variational eigencurves of semilinear two-parameter elliptic eigenvalue problems

We consider the two-parameter nonlinear eigenvalue problem?−Δu = μu − λ(u + u ^p + f(u)), u > 0 in Ω, u = 0 on ∂Ω,?where p>1 is a constant and μ,λ>0 are parameters. We establish the asymptotic formulas for the variational eigencurves λ=λ(μ,α) as μ→∞, where α>0 is a normalizing parameter. We emphasize that the critical case from a viewpoint of the two-term asymptotics of the eigencurve is p=3. Moreover, it is shown that p=5/3 is also a critical exponent from a view point of the three-term asymptotics when Ω is a ball or an annulus. This sort of criticality for two-parameter problems seems to be new. Received: February 9, 2002; in final form: April 3, 2002?Published online: April 14, 2003     

Crystallization-based optical resolution of 1,1′-binaphthalene-2,2′-dicarboxylic acid via 1-phenylethylamides: control by the molecular structure and dielectric property of solvent

In the recrystallization of a diastereomeric mixture of amides (RS_a,S)-1 formed from racemic 1,1′-binaphthalene-2,2′-dicarboxylic acid and (S)-1-phenylethylamine, either of the diastereomers crystallizes out as a diastereomerically pure form, depending on the solvent employed; sterically undemanding solvents, acetone, dichloromethane, and acetonitrile, afford crystals formulated as (S_a,S)-1·solvent with an exception of ethanol, which affords (R_a,S)-1·EtOH, while sterically bulkier solvents afford (R_a,S)-1 including no solvent. The stereoselectivity can be rationalized by the crystal structures. A dielectrically controlled resolution (DCR) can also be carried out by using mixed solvents, which contain, for example, 25 vol % of acetone and varying ratios of hexane and 1-propanol in total 75 vol %; (S_a,S)-1·acetone is deposited as crystals from the solvents with a dielectric constant (ε) range 8.9 ? ε ? 10.2, while (R_a,S)-1 is deposited from the solvents with 14.8 ? ε ? 20.3.