Solving a class of multiplicative programming problems via c-programming

In this note we show that many classes of global optimization problems can be treated most satisfactorily by classical optimization theory and conventional algorithms. We focus on the class of problems involving the minimization of the product of several convex functions on a convex set which was studied recently by Kunoet al. [3]. It is shown that these problems are typical composite concave programming problems and thus can be handled elegantly by c-programming [4]–[8] and its techniques.     

Practical syntheses of [1,3,5]‐triazine dendritic molecules on solid supports

A practical and divergent synthesis of supported [1,3,5]‐triazine dendritic molecules on Wang resin, PEGA resin, SynPhase? Lanterns, and silica gel is described. The alkylamine linkers used allow derivatization with functionality for both synthetic (e.g., supported reagent and scavenger activity) and chemical biology applications. The use of supported intermediates allows differentiation of symmetric linkers without the need for protecting group chemistry. The synthetic route uses inexpensive, readily available starting materials in a straightforward and scaleable strategy. © 2006 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 44: 2248–2259, 2006     

Synthesis of 3-formyltetronic acid and enamine derivatives

The first reported synthesis of 3-formyltetronic acid and its conversion to enamine derivatives is described. 3-Dimethylaminomethylene-2,4-dioxotetrahydrofuran derivatives were also prepared by treatment of tetronic acids with dimethylformamide diethyl acetal. Nmr spectral studies are included.     

Hypericin-Induced Phototoxicity in Cultured Fibroblasts and Swine Erythrocytes

Hypericin is a naturally occurring photosensitizer, whose presence in plants has been responsible for cutaneous phototoxicity in grazing animals. The photosensitizing properties of this agent have recently been exploited in models for anti-tumor and anti-viral activity. The cytotoxicity of hypericin and light was assessed in 3T3 mouse fibroblasts using the MTT [3-(4, 5-dimethylthiazol-2-yl)-2, 5-diphenyl tetrazolium bromide)] assay and the lactate dehydrogenase (LDH) leakage assay. Membrane damage was assessed in swine erythrocytes using hemolysis, potassium (K⁺) leakage and formation of lipid hydroperoxides. Concentration- and light-dependent decreases in fibroblast viability were seen starting at hypericin concentrations of 1.25 μM and light power flux levels of 24 J/cm² using a visible light source and at 0.417 μM hypericin and a similar light dose using a solar simulator, No LDH leakage was observed at hypericin concentrations up to 30 μM and visible light up to 144 J/cm². Light-and/or concentration-dependent increases in hemolysis, K⁺ leakage and formation of lipid hydroperoxides in red blood cell (RBC) membranes were observed, but at concentrations and light doses much greater than those required to induce cytotoxicity in fibroblasts. Lipid peroxidation and hemolysis occurred at 15 μM hypericin and 24 J/cm² (visible light source). Potassium ion leakage occurred at concentrations and light levels as low as 5 μM and 12 J/cm² or 15 μM and 4.8 J/cm² (visible light source) but was still a less sensitive indicator than fibroblast cytotoxicity. Evidence for both type I and type II reactions was shown in RBC membranes by TLC analysis of cholesterol products. In the absence of light, hypericin appears to be relatively nontoxic in the models tested.     

Nitrile ylide dimerization: investigation of the carbene reactivity of nitrile ylides

A series of novel hexaaryl diazatrienes 5 ("nitrile ylide dimers") were synthesized directly from the corresponding diaryl ketimines 12 and dichlorotoluenes 13 in a facile one-pot synthesis. The carbene character of the nitrile ylides was investigated by varying the substituents on the aromatic ring adjacent to the carbene center. The isolation of the corresponding carbene dimers as stable crystalline materials with absorption maxima (lambda(max)) from 363 to 422 nm was shown to be promoted by the absence of strongly electron-withdrawing substituents. The crystal structures indicate that the E-isomers were isolated when phenyl, 3-methylphenyl, and 3-chlorophenyl substituents are present at the carbene carbon; the Z-isomer was isolated when the more sterically hindered 2,4,6-trimethylphenyl substituent (Mes) is present. The (1)H NMR spectra of the E-isomers demonstrate the nonequivalence of the aromatic rings, in which two of the aromatic rings of the imine moiety are pseudoaxial and the remaining aromatic rings are pseudoequatorial. The reactions proceed via the intermediate nitrile ylides 1 generated by the base-promoted 1,1-elimination of HCl from the intermediate chloroimine 14. The nitrile ylide was also generated by 1,3-elimination of HCl from the imidoyl chloride 18, confirming common pathways via the nitrile ylide as the dimer products obtained from these different routes were identical. The strongly electron-withdrawing 4-nitrophenyl substituent promotes the linear carbanion character of the 1,3-dipole and no dimer is formed.     

Proton and carbon-13 nuclear magnetic resonance spectroscopy and conformational aspects of 5,6,7,8-tetrahydro-4-chromanone derivatives

The 25 MHz ¹³C and 350 MHz ¹H-nmr spectra of the title compounds are reported. Conformational equilibria in variously substituted 5,6,7,8-tetrahydrochromanones are discussed. Compounds bearing a t-butyl group at the 6 position appear to be conformationally homogenous.     

Synthesis of 1H-imidazo[1,2-a]imidazole

The synthesis and structure analysis of the unknown 1H-imidazo[1,2-a]imidazole ( 1 ) is described. The preparation involves alkylation of 2-aminoimidazole with bromoacetaldehyde diethyl acetal and subsequent hydrolysis and cyclization with hydrochloric acid. The structure was characterized by mass spectrometry and by ¹H-, ¹⁵N- and ¹³C-nmr of 1 and by ¹H-nmr of its 1-benzyl derivative 8 . An independent synthesis of 8 was accomplished via cyclization of 2-(N-dichloroethyl-N-benzyl)aminoimidazole ( 11 ).     

New Explanation for Ligand Bending in Transition Metal Tris(dithiolate) Complexes

The results of Fenske-Hall molecular orbital calculations are reported for the trigonal prismatic complexes Mo(S(2)C(2)H(2))(3) and Mo(S(2)C(6)H(4))(3). Both complexes exhibit a bend of the S-C-C-S ligand plane away from the S-Mo-S plane. A series of calculations which systematically follow the changes in electronic structure as the bend angle alpha is varied between 0 and 30 degrees indicates that the bend can be attributed to a second order Jahn-Teller distortion. The driving force for this distortion, which allows mixing between a set of ligand pi orbitals and the metal d(z)()()2 orbital, should be greatest for d(0) systems. In these systems the bent geometry leads to the stabilization of the doubly occupied HOMO. The driving force for ligand bending should be lower in systems having more or fewer electrons (e.g. Re(S(2)C(2)Ph(2))(3) or V(S(2)C(2)Ph(2))(3), respectively). While the steric bulk of the dithiolate ligands in the latter complexes may also influence the degree of ligand bending, this is probably a secondary effect.     

Influence of the coordination number of nitrogen on the structure of 6aλ4-thia-1,3,4,6-tetraazapentalenic systems. Crystal structure analyses of 3-(2-pyridylimino)-3H-[1,2,4]thiadiazolo[4,3-a]pyridine and its 1-methylated salt

Structural data were obtained by X-ray crystallography for the title compounds which show that they are essentially planar and exhibit an approximately linear N2-S1-N8 arrangement. In compound 3 the separation between the sulfur atom and the pyridine nitrogen atom (2.61 Å) is larger than the Huggins constant energy distance (2.58 Å), suggesting that there is little or no bonding between them. The methylated salt 4 , on the contrary, has a closer S…N(pyridine) distance (2.19 Å) with an estimated bond dissociation energy of 6 kcal/mole.     

Synthesis, structure, and kinetics and stereochemistry of base-catalyzed hydrolysis of meso- and rac-[Co2(tmpdtne)Cl2]4+, bis(pentaamine) complexes devoid of deprotonatable NH centers

The bis(pentadentate) ligand tmpdtne binds two Co(II) centers, and the entity is readily oxidized to the dicobalt(III) derivative [Co(2)(tmpdtne)Cl(2)](4+) which has been separated into two isomeric forms. NMR studies establish these as meso and rac isomers arising from the different or same absolute configurations for the asym configuration about each Co(III) center. Each dinuclear ion base hydrolyses to the dihydroxo derivative [Co(2)(tmpdtne)(OH)(2)](4+) with retained asym configurations about each metal ion and also retained rac or meso configurations. The kinetics for the stepwise loss of the two Cl(-) ligands is uniphasic, and data are presented to show that the loss of the first chloride is rate determining and is followed by very rapid intramolecular and loss of the second Cl(-) via a hydroxo-bridged species to yield the observed dihydroxo derivative. Meso and rac forms of the latter have been crystallized. The X-ray crystal structure of the rac-dihydroxo complex is reported, and it establishes the configurations of all the complexes reported. The (1)H NMR spectra for the hydroxo ions show very high field Co-OH resonances (ca. delta-0.5 ppm) not observed previously for such ions, and this result is discussed in the context of published (1)H NMR data for bridged Co-OH-Co species. The base hydrolysis kinetics for the dichloro ions are first order in [OH(-)], and deprotonation at an alpha-CH(2) center (alpha to a pyridyl) is identified as the source of the catalysis, since there is no NH center available for deprotonation on the ligand. These data further support the new pseudoaminate base hydrolysis mechanism first reported in 2003. The values of k(OH) for the second-order base-catalyzed reaction are ca. 4.0 M(-1) s(-1) for both the rac and meso isomers, and these results are discussed in terms of the increased acidities of these 4+ cations compared to their 2+ ion counterparts.