Local and superlinear convergence for truncated iterated projections methods

Least change secant updates can be obtained as the limit of iterated projections based on other secant updates. We show that these iterated projections can be terminated or truncated after any positive number of iterations and the local and the superlinear rate of convergence are still maintained. The truncated iterated projections method is used to find sparse and symmetric updates that are locally and superlinearly convergent. A part of this paper was presented at the Third International Workshop on Numerical Analysis, IIMAS, University of Mexico, January 1981 and ORSA-TIMS National Meeting, Houston, October 1981.     

Synthesis of 3,5-O-Benzylidene-2-deoxy-L-riboaldose from 5,5-Dihydroxy-2-phenyl-1,3-dioxane

The asymmetric alkylation of 2-phenyl-1,3-dioxan-5-one was achieved via the RAMP-hydrazone. Regeneration of the ketone followed by setreoselective reduction and ozonolysis, gave the protected 2-deoxy-L-ribose, 3,5-O-benzyldiene-2-deoxy-L-erythro-pentoaldose with 98% e.e. Removal of the benzylidene yielded the unnatural 2-deoxy-L-ribose.     

Concise syntheses of three ω-3 polyunsaturated fatty acids

The synthesis of the three ω-3 polyunsaturated fatty acids, eicosatetraenoic acid (3), docosapentaenoic acid (4), and stearidonic acid (5) has been achieved using eicosapentaenoic acid or docosahexaenoic acid as the starting materials.     

On diagonally structured problems in unconstrained optimization using an inexact super Halley method

We consider solving the unconstrained minimization problem using an iterative method derived from the third order super Halley method. Each iteration of the super Halley method requires the solution of two linear systems of equations. We show a practical implementation using an iterative method to solve the linear systems. This paper introduces an array of arrays (jagged) data structure for storing the second and third derivative of a multivariate function and suitable termination criteria for the (inner) iterative method to achieve a cubic rate of convergence. Using a jagged compressed diagonal storage of the Hessian matrices and for the tensor, numerical results show that storing the diagonals are more efficient than the row or column oriented approach when we use an iterative method for solving the linear systems of equations.     

Four-component relativistic Kohn-Sham theory

A four-component relativistic implementation of Kohn-Sham theory for molecular systems is presented. The implementation is based on a nonredundant exponential parametrization of the Kohn-Sham energy, well suited to studies of molecular static and dynamic properties as well as of total electronic energies. Calculations are presented of the bond lengths and the harmonic and anharmonic vibrational frequencies of Au(2), Hg(2+)(2), HgAu(+), HgPt, and AuH. All calculations are based on the full four-component Dirac-Coulomb Hamiltonian, employing nonrelativistic local, gradient-corrected, and hybrid density functionals. The relevance of the Coulomb and Breit operators for the construction of relativistic functionals is discussed; it is argued that, at the relativistic level of density-functional theory and in the absence of a vector potential, the neglect of current functionals follows from the neglect of the Breit operator.     

Tetrasubstituted phenanthrolines as highly potent, water-soluble, and selective g-quadruplex ligands

Small molecules capable of stabilizing the G-quadruplex (G4) structure are of interest for the development of improved anticancer drugs. Novel 4,7-diamino-substituted 1,10-phenanthroline-2,9-dicarboxamides that represent hybrid structures of known phenanthroline-based ligands have been designed. An efficient synthetic route to the compounds has been developed and their interactions with various G4 sequences have been evaluated by F?rster resonance energy transfer (FRET) melting assays, fluorescent intercalator displacement (FID), electrospray ionization mass spectrometry (ESI-MS), and circular dichroism (CD) spectroscopy. The preferred compounds have high aqueous solubility and are strong and potent G4 binders with a high selectivity over duplex DNA; thus, they represent a significant improvement over the lead compounds. Two of the compounds are inhibitors of HeLa and HT1080 cell proliferation.     

Stereoselective total synthesis of ieodomycin C

A concise stereoselective synthesis of the marine natural product ieodomycin C (3) has been achieved from commercially available pyridinium-1-sulfonate (8) in eight linear steps and 14% overall yield. The key synthetic steps included a B-alkyl Suzuki–Miyaura cross-coupling reaction and an Evans–Nagao acetate aldol reaction. The same synthetic sequence was used for preparing the enantiomer of ieodomycin C (3). Our efforts confirmed the structure of the antibacterial natural product 3.     

Quadratic response functions in the relativistic four-component Kohn-Sham approximation

A formulation and implementation of the quadratic response function in the adiabatic four-component Kohn-Sham approximation is presented. The noninteracting reference state is time-reversal symmetric and formed from Kramers pair spinors, and the energy density is gradient corrected. Example calculations are presented for the optical properties of disubstituted halobenzenes in their meta and ortho conformations. It is demonstrated that correlation and relativistic effects are not additive, and it is shown that relativity alone reduces the mubeta-response signal by 62% and 75% for meta- and ortho-bromobenzene, respectively, and enhances the same response by 17% and 21% for meta- and ortho-iodobenzene, respectively. Of the employed functionals, CAM-B3LYP shows the best performance and gives hyperpolarizabilities beta distinctly different from B3LYP.