AnO(\sqrt n L) iteration potential reduction algorithm for linear complementarity problems

This paper proposes an interior point algorithm for a positive semi-definite linear complementarity problem: find an (x, y)∈? ²ⁿ such thaty=Mx+q, (x,y)?0 andx ^T y=0. The algorithm reduces the potential function $$f(x,y) = (n + \sqrt n )\log x^T y - \sum\limits_{i = 1}^n {\log x_i y_i } $$ by at least 0.2 in each iteration requiring O(n ³) arithmetic operations. If it starts from an interior feasible solution with the potential function value bounded by \(O(\sqrt n L)\) , it generates, in at most \(O(\sqrt n L)\) iterations, an approximate solution with the potential function value \( - O(\sqrt n L)\) , from which we can compute an exact solution in O(n ³) arithmetic operations. The algorithm is closely related with the central path following algorithm recently given by the authors. We also suggest a unified model for both potential reduction and path following algorithms for positive semi-definite linear complementarity problems.     

Inventory of <Superscript>129</Superscript>I in brackish lake sediments adjacent to a spent nuclear fuel reprocessing plant in Japan

In this study, four fruit’s seed samples as Punica granatum L., Citrus medica var. limonum, Malus domestica L. and Citrus vulgaris Risso were prepared from Arak’s markets. They were analyzed using instrumental neutron activation method (INAA). In this method, Tehran research reactor as a neutron source and relative INAA method has been used as the analysis method and to record gamma ray spectrum, the high purity germanium detector was used. Pomegranate seeds had the highest number of essential elements. Apple seeds and sour orange seeds contain the highest levels of Mg and K, Respectively.     

Enantioselective carbonyl-ene-type cyclization of α-ketoester and 2-substituted vinylsilane catalyzed by a chiral Cu-BOX complex

We developed an enantioselective carbonyl-ene-type cyclization using 2-substituted vinylsilane as a nucleophilic ene moiety catalyzed by a chiral copper-BOX complex. This reaction is the first example of enantioselective carbonyl-ene cyclization using a 1,2-disubstituted olefin. This methodology gave chiral indenols with a tetrasubstituted carbon.     

Columnar Liquid Crystals from a Giant Macrocycle Mesogen

Columnar liquid crystals composed of a giant macrocyclic mesogen were prepared. The giant macrocyclic mesogen has a square hollow with a 2.5 nm diagonal, which was bounded by diindolo[3,2‐b:2′,3′‐h]carbazole (diindolocarbazole) moieties as the edges and bis(salicylidene)‐o‐phenylenediamine (salphen) moieties as the corners. The shape and size of the macrocycle were directly observed by scanning tunneling microscopy (STM). Each side of the bright square in the STM image corresponds to a diindolocarbazole moiety, and the length of the sides was consistent with the result of the single crystal analysis of diindolocarbazole. Finally, we successfully obtained a giant macrocycle with long and branched side chains, which exhibited a rectangular columnar LC phase over a wide temperature range. To the best of our knowledge, it contained the largest discrete inner space of any thermotropic columnar liquid crystal composed of macrocyclic mesogens.     

Encapsulation of Hb into unsaturated lipid vesicles and γ-ray polymerization

A carbonyl hemoglobin (HbCO) solution was stirred with a mixed powder of polymerizable 1,2-bis(2,4-octadecadienoyl)-sn-glycero-3-phosphocholine (DODPC), cholesterol and stearic acid (7/7/2 by mol). The mixture was extruded through polycarbonate membrane filters (final pore size = 0.2 μm Ø). The average diameter of the resulting vesicles was 203 ± 39 nm. The [Hb]/[Lipid] ratio (the weight ratio of Hb in vesicle to lipid) increased with the Hb concentration, and decreased with the NaCl concentration. A maximum [Hb]/[lipid] ratio was observed at pH 6.9, which was the same as the isoelectric point of Hb. The vesicles were stabilized by γ-irradiation (⁶⁰Co) because the bilayer lipids bound each other to yield polyphospholipids. Denaturation of Hb by γ-irradiation was not detected. These polyphospholipid vesicles encapsulating Hb were stable even against the freeze–thaw cycles and the freeze-drying procedure.     

Rh(I)-catalyzed ring-closing reaction of allenynes: selective construction of cycloheptene, bicyclo[5.3.0]decadienone, and bicyclo[5.2.0]nonene frameworks

Highly selective formation of cycloheptene, bicyclo[5.3.0]decadienone, and bicyclo[5.2.0]nonene skeletons from tri- and tetrasubstituted allenynes has been achieved via a Rh(I)-catalyzed ring-closing reaction and proper choice of substrate and/or reaction conditions.     

A facile preparation of 4-(1-Acetyl-4(1H)-pyridylidene)-2-oxazohn-5-ones

4-(1-Acetyl-4(1H)-pyridylidene)-2-oxazolin-5-ones were prepared by the reaction of acylglycines with pyridine and acetic anhydride under oxygen. Acidic and alkaline hydrolysis of 2-oxazolin-5-ones provided oxazole derivatives, pyridine derivatives, and carboxylic acids.     

Preparation and characterization of aqueous colloids of Pt-Ru nanoparticles

A synthetic method for platinum-ruthenium (PtRu) nanoparticles in aqueous media is proposed. This method employs citric acid as a capping agent and NaBH(4) as a reducing agent with the aid of pH control. The number-averaged size of the PtRu nanoparticles was ca. 2 nm. The crystal phase and chemical composition of the nanoparticles was investigated by X-ray diffraction measurement and scanning transmission electron microscopy coupled with energy-dispersive X-ray spectroscopy analysis, which indicated that the nanoparticles mainly consisted of an alloy of Pt and Ru. Electrochemical measurement showed that the PtRu nanoparticles had catalytic activity for methanol oxidation.