Properties of the Central Points in Linear Programming Problems

In this paper we list several useful properties of central points in linear programming problems. We study the logarithmic barrier function, the analytic center and the central path, relating the proximity measures and scaled Euclidean distances defined for the primal and primal–dual problems. We study the Newton centering steps, and show how large the short steps used in path following algorithms can actually be, and what variation can be ensured for the barrier function in each iteration of such methods. We relate the primal and primal–dual Newton centering steps and propose a primal-only path following algorithm for linear programming.     

Massenspektrometrische Untersuchung aromatischer Halogenide der Summenformel C9H11Cl: Mechanismus der Äthylen-Abspaltung aus dem Ion [M ? Cl]+˙

By investigation of isomeric ²H- and ¹³C-labelled C₉H₁₁ Cl-compounds it has been shown that the ion [M ? Cl]⁺ is transformed mainly to the ion [C₇H₇]⁺ via C₂H₄-elimination from alkyl-substituted tropylium-ions. Phenyl-cyclopropane-cations play only a small part, if at all, in this fragmentation process.     

Biosynthesis of isoprenoids. purification and properties of IspG protein from Escherichia coli

[Structure: see text]. The IspG protein is known to catalyze the transformation of 2-C-methyl-d-erythritol 2,4-cyclodiphosphate into 1-hydroxy-2-methyl-2-(E)-butenyl 4-diphosphate in the nonmevalonate pathway of isoprenoid biosynthesis. We have found that the apparent IspG activity in the cell extracts of recombinant Escherichia coli cells as observed by a radiochemical assay can be enhanced severalfold by coexpression of the isc operon which is involved in the assembly of iron-sulfur clusters. The recombinant protein was isolated by affinity chromatography under anaerobic conditions. With a mixture of flavodoxin, flavodoxin reductase, and NADPH as the reducing agent, stringent assay methods based on photometry or on 13C NMR detection of multiply 13C-labeled substrate/product ratios afforded catalytic activities greater than 60 nmol mg(-1) min(-1) for the protein "as isolated" (i.e., without reconstitution of any kind). Lower apparent activities were found using photoreduced deazaflavin as an artifactual electron donor, whereas dithionite was unable to serve as an artificial electron donor. The apparent Michaelis constant for 2-C-methyl-D-erythritol 2,4-cyclodiphosphate was 700 microM. The enzyme was inactivated by EDTA and could be reactivated by Mn2+. The pH optimum was at 9.0. The protein contained 2.4 iron ions and 4.4 sulfide ions per subunit. The replacement of any of the three conserved cysteine residues afforded mutant proteins which were devoid of catalytic activity and contained less than 6% of Fe2+ and less than 23% of S2- as compared to the wild-type protein. Sequence comparison indicates that putative IspG proteins of plants, the apicomplexan protozoan Plasmodium falciparum, and bacteria from the Bacteroidetes/Chlorobi group contain an insert of about 170-320 amino acid residues as compared with eubacterial enzymes.     

Elektronenstossinduzierte Fragmentierung von Acetylenverbindungen—IV: Mechanistische Betrachtungen zur Bildung des Benztropyliumkations aus den Chlormethyl-Naphthalinen und 1-Chlor-Phenyl-(5)-Penten-(2)-in-(4)

Mass spectroscopic investigations of ²H- and ¹³C-labelled derivatives of e.g. 1-, 2-chloro-methyl-naphthalene and 1-chloro-phenyl(5)-pentene-(2)-in-(4) show that the [C₁₁H₉]⁺ ion, which gives [C₉H₇]⁺ by acetylene elimination, has the structure of a benztropylium cation. Model considerations show that the formation of this cation [C₁₁H₉]⁺ through a common transition state with a three-membered ring is very probable.     

A Stereospecific Synthesis of (E,Z)-α, β-γ, δ-Diunsaturated Aldehydes,Ketones, and Esters Using the Benary Reaction

The reaction between (Z)-1-alkenyllithium and (E)-β-(N, N-dialkylamino)-α, β-alkenals, (E)-β-(N, N-dialkylamino)-α, β-alkenones or (E)-β-(N, N-dialkylamino)-α, β-alkenoic esters yields mainly (E, Z)-α, β-γ, δ-diunsaturated aldehydes, ketones, or esters and is therefore highly stereospecific.     

Synthesis of (-)-2s,3s, 11s,12r-2,3,11,12-tetraphenyl[18]crown-6

The synthesis of ( - ) 2S,3S,11S,12R-2, 3,11,12-tetraphenyl [18]-crown-6 from (-)-1S,2S-hydrobenzoin and meso-hydrobenzoin is described. Chemical shifts and vicinal coupling constants of the benzylic protons in the 2 S, 3 S and 11 S,12 R substructures in the free ligands and in complexes with KSCN and 1-phenylethylammonium bromides and a brief discussion of the related conformational changes are also presented. A detailed procedure for the resolution of racemic hydrobenzoin is given.