A preconditioner for constrained and weighted least squares problems with Toeplitz structure

We study methods for solving the constrained and weighted least squares problem min _x by the preconditioned conjugate gradient (PCG) method. HereW = diag (₁, , _m ) with _{1 m} 0, andA ^T = [T ₁ ^T , ,T _k ^T ] with Toeplitz blocksT _l R ^{n × n} ,l = 1, ,k. It is well-known that this problem can be solved by solving anaugmented linear 2 × 2 block linear systemM +Ax =b, A ^T = 0, whereM =W ^–1. We will use the PCG method with circulant-like preconditioner for solving the system. We show that the spectrum of the preconditioned matrix is clustered around one. When the PCG method is applied to solve the system, we can expect a fast convergence rate.Research supported by HKRGC grants no. CUHK 178/93E and CUHK 316/94E.     

Enantioselective total synthesis of (+)-gigantecin: exploiting the asymmetric glycolate aldol reaction

The enantioselective synthesis of the potent, selective, cytotoxic, annonaceous acetogenin, (+)-gigantecin, has been completed. An asymmetric glycolate aldol serves to establish the stereocenters at C13,14 and at C21,22. A Carreira asymmetric acetylide addition is used to establish the C17 stereocenter.     

Oxidative reactivity of S-nitrosoglutathione with Hantzsch 1,4-dihydropyridine

[formula: see text] S-Nitrosoglutathione oxidized 4-substituted Hantzsch 1,4-dihydropyridines in CH3CN/H2O or CH3CN/phosphate aqueous buffer solution to give aromatic products in various yields.