Asymptotic behavior of eigenvalues of two-parameter nonlinear Sturm-Liouville problems

The nonlinear two-parameter Sturm-Liouville problemu ^"+μg(u)=λf(u) is studied for μ, λ>0. By using Ljusternik-Schnirelman theory on the general level set developed by Zeidler, we shall show the existence of ann-th variational eigenvalue λ=λ_n(μ). Furthermore, for specialf andg, the asymptotic formula of λ₁(μ)) as μ→∞ is established.     

New synthesis of 5-amino-5-deazaflavin derivatives by direct coupling of 5-deazaflavins and amines

5-Amino-5-deazaflavin derivatives are newly synthesized by direct coupling of 5-deazaflavins and amines. Some of them revealed potential activity toward tumor cells such as L1210 or KB cells.     

Synthetic studies on macrolactin A by using a (diene)Fe(CO)3 complex

The stereoselective synthesis of the two segments 3 and 4 of macrolactin A 1 is described. Macrolactin A is a 24-membered polyene macrolide antibiotic, which is of interest due to a strong activity against B16-F10 murine tumor cell and HIV-1 virus. The key step of the synthesis is the 1,2-migration reaction of a (diene)Fe(CO)₃ complex with a introduction of the thiol group to construct the unstable (E,Z)-conjugated dienic moiety (C8-C11).     

Synthesis of all stereoisomers of sulfinylcalix[4]arenes

All four stereoisomers of p-tert-butylsulfinylcalix[4]arene [4(rccc), 4(rcct), 4(rctt), and 4(rtct)], arising from the disposition of the four sulfinyl groups with respect to the mean plane of the four bridging sulfur atoms, have been prepared via oxidation of p-tert-butylthiacalix[4]arene (2) or its tetra-O-benzyl ethers 5 of defined conformations. Thus, treatment of 2 with 4.4 molar equiv of NaBO(3).4H(2)O gave the rtct and rctt isomers in 27% and 17% yields, respectively, while oxidation of cone 5 (5(C)) and partial cone 5 (5(PC)) proceeded stereoselectively to give, after debenzylation of the resulting tetrasulfoxides 12 and 15, the rccc and rcct isomers in 56% and 28% yields, respectively, based on 5. The sulfinylcalix[4]arenes 4 were treated with iodomethane in the presence of a base to give the corresponding tetramethyl ethers 16, the structures of which in regard to the disposition of the sulfinyl groups and the conformation of the phenol units were determined by X-ray crystallography. Also reported is the synthesis of all four conformational isomers of tetra-O-benzyl ether of 2 (5(C), 5(PC), 5(1,2-A), and 5(1,3-A)).     

Asymptotic expansion of the boundary layers of the perturbed simple pendulum problems

We consider the nonlinear eigenvalue problem on an interval

     

Asymmetric total synthesis of rhinacanthin A

Starting from a reduced lapachol compound, the total synthesis of rhinacanthin A in both racemic and enantioenriched forms is achieved in eight steps without forming any undesired β-lapachone derivatives. For the synthesis of enantioenriched rhinacanthin A, the introduction of the asymmetric center was carried out by using the catalytic asymmetric epoxidation of an unfunctional trisubstituted olefin using Shi’s epoxidation diketal catalyst. The acidic treatment of a derived enantioenriched epoxynaphthol and the following CAN oxidation afforded the target molecule with high enantiomeric purity.     

Inverse bifurcation problems for diffusive Holling–Tanner population model

We consider the equation which is called Holling–Tanner population model where is a bifurcation parameter and are unknown constants. In this paper, we determine the unknown constants from the asymptotic behavior of the bifurcation curve , where .     

Two-Parameter Eigenvalue Problems in Nonlinear Second Order Differential Equations

Two-parameter nonlinear second order differential equations are studied. By using a variational method we characterize the variational eigenvalues μ = μ(λ) and study the properties of μ(λ). Furthermore, asymptotic formulas of μ(λ) as λ → ±∞ are established.     

Unique inclusion properties of crystalline powder p-tert-butylthiacalix[4]arene toward alcohols and carboxylic acids

Powdery crystals of p-tert-butylthiacalix[4]arene (2) selectively include EtOH from 1:1 mixtures of MeOH-EtOH and EtOH-PrOH, and EtCO(2)H from HCO(2)H-EtCO(2)H. On the other hand, no acid is included from HCO(2)H-MeCO(2)H, even though MeCO(2)H is included from the neat acid. The origins of these phenomena are discussed based on X-ray analysis of inclusion crystals prepared separately by crystallization.