First determination of the absolute stereochemistry of a naturally occurring 1,1'-biphenanthrene, (--)-blestriarene C,and its unexpected photoracemization

A naturally occurring 1,1'-biphenanthrene, blestriarene C, was prepared and its absolute stereochemistry was determined to be Sa-(-) by an empirical method, during which the compound was found to undergo rapid photoracemization even under ambient light exposure.     

Precise Spectral Asymptotics for the Dirichlet Problem − u″(t) + g(u(t)) = λsinu(t)

We consider the nonlinear eigenvalue problem on an interval−u″(t)+g(u(t))=λsinu(t),u(t)>0,t∈I:=(−T,T),u(±T)=0,where λ > 0 is a parameter and T > 0 is a constant. It is known that if λ ? 1, then the corresponding solution has boundary layers. In this paper, we characterize λ by the boundary layers of the solution when λ ? 1 from a variational point of view. To this end, we parameterize a solution pair (λ, u) by a new parameter 0 < ?< T, which characterizes the boundary layers of the solution, and establish precise asymptotic formulas for λ(?) with exact second term as ? → 0. It turns out that the second term is a constant which is explicitly determined by the nonlinearity g.     

Synthesis of a proposed isomer of F420 having α-glutamyl bonding

A proposed isomer of redox coenzyme F₄₂₀, having α? glutamyl bonding, has been synthesized from 8-benzyloxy-10-D-ribityl-5-deazaflavin and α-L-glutamyl-L-glutamic acid moiety, by the phosphite triester approach followed by deprotection procedures.     

Variational method for precise asymptotic formulas for nonlinear eigenvalue problems

We consider the nonlinear eigenvalue problem motivated by the perturbed elliptic sine-Gordon equation where p >1 is a constant and λ ∈ R is an eigenvalue parameter. Our aim is to clarify the asymptotic relationship between L ^p+1-norm, L ^∞-norm of the solutions and λ when these norms are large. To this end, we consider an associated variational problem with this equation on a manifold new parameter), and obtain a solution pair . We establish the precise asymptotic formulas for .     

Precise Spectral Asymptotics for Logistic Equations of Population Dynamics

The semilinear elliptic eigenvalue problem with superlinearpure power nonlinearity is considered. This problem is treatedfrom the standpoint of L²-theory and the precise asymptoticformula for the eigenvalue parameter = () as is established,where is the L²-norm of the solution u associated with . 2000Mathematics Subject Classification 35P30 (primary), 35J60 (secondary).     

Nodal and asymptotic properties of solutions to nonlinear elliptic eigenvalue problems on general level sets

We establish some nodal and asymptotic properties of the solutions of nonlinear elliptic eigenvalue problems obtained by Ljusternik-Schnirelman theory on general level sets.     

New asymptotic formula for eigenvalues of nonlinear Sturm-Liouville problems

We study the nonlinear Sturm-Liouville problem

Synthetic studies of salinosporamide A through the intramolecular hydroamidation of alkynes

Rhodium-catalyzed intramolecular hydroamidation of alkynes was carried out to construct the synthetic intermediates of a proteasome inhibitor, salinosporamide A. Several alkynyl formamides were synthesized and subjected to the hydroamidation reaction. Some derivatives with a methoxymethyl (MOM) or 2-methoxy-2-propyl (MOP) group near the reaction site were converted to the corresponding lactams in excellent yields.     

Synthesis of biologically active (-)-dehydroiso-β-lapachone and the determination of its absolute configuration

Synthesis of dehydoriso-β-lapachone (1) in both racemic and enantioenriched forms is achieved starting from reduced naphthoquinone equivalents. As for the synthesis of enantioenriched dehydroiso-β-lapachone, introduction of the asymmetric center was carried out by catalytic asymmetric epoxidation of the unfunctionalized trisubstituted olefin using Shi epoxidation diketal catalyst. The construction of isopropenylfurano-1,2-(β)-naphthoquinone was carried out by acidic ring-opening reaction of the epoxynaphthalene and the following diammonium cerium(IV) nitrate (CAN) oxidation. The absolute configuration of naturally occurring (-)-dehydroiso-β-lapachone was finally determined as (R) by comparing the measured optical rotation value of the synthetic (R)-dehydroiso-β-lapachone.     

Synthesis of dinuclear boron complexes of sulfinylcalix[4]arenes: Syn/Anti stereocontrol by the arrangement of the sulfinyl functions

Stereocontrol in the synthesis of dinuclear metal complexes of sulfinylcalix[4]arenes 2 has been achieved by the arrangement of sulfinyl functionalities. Thus, the treatment of the(rtct) isomer of 2 (2(rtct)) with an excess of Et(3)B affords syn dinuclear boron complex 4, while a similar treatment of rctt and rcct isomers 2(rctt) and 2(rcct) yields anti dinuclear complexes 5 and 6, respectively.