A strong bound on the integral of the central path curvature and its relationship with the iteration-complexity of primal-dual path-following LP algorithms

The main goals of this paper are to: i) relate two iteration-complexity bounds derived for the Mizuno-Todd-Ye predictor-corrector (MTY P-C) algorithm for linear programming (LP), and; ii) study the geometrical structure of the LP central path. The first iteration-complexity bound for the MTY P-C algorithm considered in this paper is expressed in terms of the integral of a certain curvature function over the traversed portion of the central path. The second iteration-complexity bound, derived recently by the authors using the notion of crossover events introduced by Vavasis and Ye, is expressed in terms of a scale-invariant condition number associated with m × n constraint matrix of the LP. In this paper, we establish a relationship between these bounds by showing that the first one can be majorized by the second one. We also establish a geometric result about the central path which gives a rigorous justification based on the curvature of the central path of a claim made by Vavasis and Ye, in view of the behavior of their layered least squares path following LP method, that the central path consists of long but straight continuous parts while the remaining curved part is relatively “short”. R. D. C. Monteiro was supported in part by NSF Grants CCR-0203113 and CCF-0430644 and ONR grant N00014-05-1-0183. T. Tsuchiya was supported in part by Japan-US Joint Research Projects of Japan Society for the Promotion of Science “Algorithms for linear programs over symmetric cones” and the Grants-in-Aid for Scientific Research (C) 15510144 of Japan Society for the Promotion of Science.     

Arylmagnesiation of alkynes catalyzed cooperatively by iron and copper complexes

Iron and copper complexes cooperatively catalyzed the arylmagnesiation of unfunctionalized alkynes including dialkylacetylenes, where the presence of both iron and copper catalysts is essential for high yields of 2-aryl-1-alkenylmagnesium bromides.     

5-[4-(1-Hydroxyethyl)phenyl]-10,15,20-triphenylporphyrin as a probe of the transition-state conformation in hydrolase-catalyzed enantioselective transesterifications

5-[4-(1-Hydroxyethyl)phenyl]-10,15,20-triphenylporphyrin (1a) and zinc porphyrin 1b were designed and synthesized to experimentally examine the validity of the transition-state model previously proposed for the lipase-catalyzed kinetic resolution of secondary alcohols. The lipases from Pseudomonas cepacia (lipase PS), Candida antarctica (CHIRAZYME L-2), Rhizomucor miehei (CHIRAZYME L-9), and Pseudomonas aeruginosa (lipase LIP) exhibited excellent enantioselectivity (E >100 at 30 degrees C). Subtilisin Carlsberg from Bacillus licheniformis (ChiroCLEC-BL) also showed high enantioselectivity for 1a (E = 140 at 30 degrees C), and the thermodynamic parameters were determined: DeltaDeltaH = -6.8 +/- 0.8 kcal mol(-1), DeltaDeltaS = -13 +/- 3 cal mol(-1) K(-1). Lipases and subtilisin showed R- and S-preference for 1, respectively. The mechanisms underlying the experimental observations are explained in terms of the transition-state models. The large secondary alcohol 1 is a powerful tool for investigating the conformation of the transition state of the enzyme-catalyzed reactions. The fact that 1 was resolved with high enantioselectivity strongly suggests that the gauche conformation, but not the anti conformation, is taken in the transition state, in agreement with the transition-state models involving the stereoelectronic effect.     

Palladium-catalyzed direct arylation of aryl(azaaryl)methanes with aryl halides providing triarylmethanes

Direct arylation of aryl(azaaryl)methanes with aryl halides takes place at the benzylic position in the presence of a hydroxide base under palladium catalysis to yield triarylmethanes.     

Studies of Japanese lacquer: Urushiol dimerization by the coupling reaction between urushiol quinone and a triolefinic component of urushiol

Previously, the formation of urushiol quinone from urushiol was demonstrated in the laccase-catalyzed oxidation process of the sap of the Japanese lacquer tree (Rhus vernicifera D.C.) or of lacquer formed from it. This paper presents the results of the investigation on the participation of urushiol quinone in the oxidative polymerization and crosslinking of the sap or the lacquer. The polymeric urushiol was obtained by the fractionation of the mildly oxidized sap (Japanese lacquer), and a specific dimeric urushiol was isolated from it by thin-layer chromatography (TLC). Structural analysis of the dimer illustrated that it has a conjugated triene structure and may be formed by a coupling reaction between urushiol quinone and a triolefinic component of urushiol. Further support for this was given by the spectroscopic study of the reaction between 4-tert-butyl-o-quinone and the triolefinic component of dimethylurushiol, and by the isolation and identification of the coupling product between them.     

New synthetic method for orsellic acid type macrolides by intramolecular alkylation of protected cyanohydrin. The synthesis of (±)-zearalenone.

Zearalenone was synthesized by a general cyclization method of orsellic acid type macrolides having ketone moiety using the intramolecular alkylation of the protected cyanohydrin. This alkylation tolerates the presence of ester group and requires short reaction time.     

Catalytic asymmetric epoxidation of alpha,beta-unsaturated esters using an yttrium-biphenyldiol complex

We succeeded in a catalytic asymmetric epoxidation reaction of alpha,beta-unsaturated esters via a conjugate addition of an oxidant using 2-10 mol % of the yttirium-chiral biphenyldiol catalyst. A variety of substrates with beta-aryl and beta-alkyl substituents were epoxidized efficiently, yielding the corresponding alpha,beta-epoxy esters in up to 97% yield and 99% ee.     

Structural Insights into Rice Straw Pretreated by Hot-Compressed Water in Relation to Enzymatic Hydrolysis

Pretreatment-induced structural alteration is critical in influencing the rate and extent of enzymatic saccharification of lignocellulosic biomass. The present work has investigated structural features of rice straw pretreated by hot-compressed water (HCW) from 140 to 240 °C for 10 or 30 min and enzymatic hydrolysis profiles of pretreated rice straw. Compositional profiles of pretreated rice straw were examined to offer the basis for structural changes. The wide-angle X-ray diffraction analysis revealed possible modification in crystalline microstructure of cellulose and the severity-dependent variation of crystallinity. The specific surface area (SSA) of pretreated samples was able to achieve more than 10-fold of that of the raw material and was in linear relationship with the removal of acetyl groups and xylan. The glucose yield by enzymatic hydrolysis of pretreated materials correlated linearly with the SSA increase and the dissolution of acetyl and xylan. A quantitatively intrinsic relationship was suggested to exist between enzymatic hydrolysis and the extraction of hemicellulose components in hydrothermally treated rice straw, and SSA was considered one important structural parameter signaling the efficiency of enzymatic digestibility in HCW-treated materials in which hemicellulose removal and lignin redistribution happened.     

Supramolecular Approaches towards Ordered Polymer Materials

Controlled organization of polymer chains into ordered structures is highly important to tune or enhance the properties of the polymeric materials. A supramolecular approach using host–guest chemistry has allowed rational design of chain assemblies with many functional properties. Nanoporous materials with ordered channel structures are particularly useful for attaining precise assemblies of polymer chains through nanoconfinement.