Double catalytic enantioselective Michael addition reactions of tertiary nucleophile precursors—tertiary/quaternary and quaternary/quaternary carbon–carbon bond formations

Enantioselective Michael addition reactions of tertiary nucleophile precursors, such as substituted malononitriles and cyclic 1,3-diketones, can be successfully activated by the metal complexes derived from R,R-DBFOX/Ph chiral ligand and cationic metal salts. With this method, the enantioselective tertiary/quaternary and quaternary/quaternary carbon–carbon bond formations can be achieved. Use of alcohol solvents is essential for the success, and ,β-unsaturated amides of 3,5-dimethylpyrazole are much better acceptors than those of 2-oxazolidinone.     

Synthesis and Biological Activities of Simplified Analogs of the Natural PKC Ligands,Bryostatin‐1 and Aplysiatoxin

Protein kinase C (PKC) isozymes play central roles in signal transduction on the cell surface and could serve as promising therapeutic targets of intractable diseases like cancer, Alzheimer's disease, and acquired immunodeficiency syndrome (AIDS). Although natural PKC ligands like phorbol esters, ingenol esters, and teleocidins have the potential to become therapeutic leads, most of them are potent tumor promoters in mouse skin. By contrast, bryostatin‐1 (bryo‐1) isolated from marine bryozoan is a potent PKC activator with little tumor‐promoting activity. Numerous investigations have suggested bryo‐1 to be a promising therapeutic candidate for the above intractable diseases. However, there is a supply problem of bryo‐1 both from natural sources and by organic synthesis. Recent approaches on the synthesis of bryo‐1 have focused on its simplification, without decreasing the ability to activate PKC isozymes, to develop new medicinal leads. Another approach is to use the skeleton of natural PKC ligands to develop bryo‐1 surrogates. We have recently identified 10‐methyl‐aplog‐1 ( 26 ), a simplified analog of tumor‐promoting aplysiatoxin (ATX), as a possible therapeutic lead for cancer. This review summarizes recent investigations on the simplification of natural PKC ligands, bryo‐1 and ATX, to develop potential medicinal leads.     

Compatibility of local and global Langlands correspondences

We prove the compatibility of local and global Langlands correspondences for , which was proved up to semisimplification in M. Harris and R. Taylor, The Geometry and Cohomology of Some Simple Shimura Varieties, Ann. of Math. Studies 151, Princeton Univ. Press, Princeton-Oxford, 2001. More precisely, for the -dimensional -adic representation of the Galois group of an imaginary CM-field attached to a conjugate self-dual regular algebraic cuspidal automorphic representation of , which is square integrable at some finite place, we show that Frobenius semisimplification of the restriction of to the decomposition group of a place of not dividing corresponds to by the local Langlands correspondence. If is square integrable for some finite place we deduce that is irreducible. We also obtain conditional results in the case .

     

Phenomenology of boiling: A coupled map lattice model

A minimal model for boiling is proposed. With increasing temperature of a bottom plate, the model shows three successive phases; conduction, nucleate, and film boiling. In the nucleate regime the heat flux increases with the temperature of the bottom plate, while it decreases in the film boiling regime. In the boiling phase, the maximum Lyapunov exponent is positive, implying that the boiling phenomena are spatiotemporally chaotic.     

Mass spectra of 5-fluorouracil derivatives. N-1-substituted sulfonyl derivatives

The electron impact mass spectra of 1-sulfonyl substituted derivatives of 5-fluorouracil were investigated. The substituents were CH₃SO₂ (compound I), CH₃(CH₂)₃SO₂ (II), C₆H₅SO₂ (III) and p-CH₃C₆H₄SO₂ (IV).     

A latent process model for the pricing of corporate securities

We propose a structural model with a joint process of tangible assets (marker) and firm status for the pricing of corporate securities. The firm status is assumed to be latent or unobservable, and default occurs when the firm status process reaches a default threshold at the first time. The marker process is observable and assumed to be correlated with the latent firm status. The recovery upon default is a fraction of tangible assets at the time of default. Our model can evaluate both the corporate debt and equity to fit their market prices in a unified framework. When the two processes are perfectly correlated, our model is reduced to the seminal Black–Cox model. Numerical examples are given to support the usefulness of our model. A previous version of this paper was presented at the Tsukuba–Stanford workshop held at Stanford University on March 2006. The authors are grateful to participants of the workshop for helpful discussions.