ε-optimality criteria for convex programming problems via exact penalty functions

In this paper, we present-optimality criteria for convex programming problems associated with exact penalty functions. Several authors have given various criteria under the assumption that such convex problems and the associated dual problems can be solved. We assume the solvability of neither the convex problem nor the dual problem. To derive our criteria, we estimate the size of the penalty parameter in terms of an-solution for the dual problem.     

Synthesis of methylpyridine derivatives—XXXIIIChem. Pharm. Bull.25, 203 (1977).: Phosphonylation and chlorination of methylpyridine and 3-nitro-methylpyridine derivatives

Novel phosphonylation of the active Me group of pyridine derivatives is described.Reaction of 2 (and 4) -methylpyridine (3 and 5) with PCl₅ in POCl₃ gave 2 (and 4) -trichloromethylpyridine (4 and 6). Similarly, reaction of 4 (and 6) methyl-3-nitropyridine (7 and 9) afforded the corresponding trichloromethyl derivative (8 and 10). However, the similar reaction of 2-methyl-3-nitropyridine (11) gave dichloro-(3-nitro-2-pyridyl)-methylphosphonic dichloride (12).Mechanisms of the formation of these products are discussed.     

Fluorous reverse-phase silica gel-supported Lewis acids as recyclable catalysts in water

Fluorous reverse-phase silica gel (FRPSG)-supported Lewis acids which have fluorous ligands acted as effective catalysts of Baeyer-Villiger and Diels-Alder reactions in water. Direct esterification of carboxylic acid with alcohol in organic media was also catalyzed. The FRPSG-supported Lewis acids could be recycled by simple filtration after the reaction.     

Synthesis and crystal structure of ionic multicomponent complex: ([Cr(I)(PhH)(2)].+))(2)[Co(II)TPP(C(60)(CN)(2))]-[C(60)(CN)(2)](.-).3(o-C(6)H(4)Cl(2)) containing C(60)(CN)(2).- radical anion and sigma-bonded diamagnetic Co(II)TPP(C(60)(CN)(2)) -anion

The ionic multicomponent complex complex: ([Cr(I)(PhH)(2)].+))(2)[Co(II)TPP(C(60)(CN)(2))]-[C(60)(CN)(2)](.-).3(o-C(6)H(4)Cl(2)) (Co(II)TPP: cobalt (II) tetraphenylporphyrin; Cr(PhH)(2): bis(benzene)chromium; o-C(6)H(4)Cl(2): o-dichlorobenzene) containing CoTPP(C(60)(CN)(2)- anion and C(60)(CN)(2).- radical anion was obtained. The complex has the cage structure with channels, which accommodate Cr(I)(PhH)(2)(.+) and o-C(6)H(4)Cl(2) molecules. For the first time the sigma-bonding of Co(II)TPP to the fullerene radical anion with the essentially shortened Co.C(C(60)(CN)(2)) contact of 2.282 A is observed. The sigma-bonding results in the diamagnetism of Co(II)TPP(C(60)(CN)(2))(-) anion. The nonbonded C(60)(CN)(2)(.-) radical anion retains both the C(2)(v)symmetry and the shape of the molecule. The length of the C(triple bond)N bonds is 1.141 and 1.152 A.     

Robust and simple interface for microchip electrophoresis-mass spectrometry

A robust and simple interface for microchip electrophoresis-mass spectrometry (MCE-MS) was developed using a spray nozzle connected to the exit of the separation channel of the microchip. The spray nozzle was attached to the microchip using a polyether ether ketone screw without adhesive, thus allowing easy replaced. Sample injection and electrophoretic separation was performed by control of the voltage only. The analysis of a few basic drugs was performed using the optimized MCE-MS system. The separation was improved by using a high-viscosity separation buffer and a spray nozzle with a small bore size. This system was also applied to the separation of peptides and protein-trypsin digests. Sample adsorption was minimized by adding acetonitrile to the separation buffer when using a quartz microchip.     

Chain-growth polycondensation for well-defined aramide. Synthesis of unprecedented block copolymer containing aramide with low polydispersity

Poly(p-benzamide) with a defined molecular weight and a low polydispersity and a block copolymer containing this well-defined aramide was synthesized. Phenyl 4-aminobenzoate, which would yield poly(p-benzamide), did not polymerize under the conditions of chain-growth polycondensation. However, phenyl 4-(4-octyloxybenzylamino)benzoate (1b) polymerized at room temperature in the presence of base and phenyl 4-nitrobenzoate (2) as an initiator in a chain-growth polycondensation manner to give well-defined aromatic polyamides having the 4-octyloxybenzyl groups as a protecting group on nitrogen in an amide. It was confirmed by a model reaction that deprotection of this protecting group proceeded completely with trifluoroacetic acid (TFA) without breaking the amide linkage. The utility of this approach to poly(p-benzamide) with a low polydispersity was demonstrated by the synthesis of block copolymers. Thus, phenyl 4-(octylamino)benzoate (1a) polymerized in the presence of 2 and base, followed by addition of 1b and base to the reaction mixture of the prepolymer to yield the block copolymer of 1a and 1b with a controlled molecular weight and a low polydispersity. The block copolymer was treated with TFA, resulting in a soluble block copolymer of poly(N-octyl-p-benzamide) and poly(p-benzamide). The SEM images of the supramolecular assemblies of the block copolymer showed mum-sized bundles and aggregates of flake structures.     

On the classification of weighing matrices and self‐orthogonal codes

We provide a classification method of weighing matrices based on a classification of self‐orthogonal codes. Using this method, we classify weighing matrices of orders up to 15 and order 17, by revising some known classification. In addition, we give a revised classification of weighing matrices of weight 5. A revised classification of ternary maximal self‐orthogonal codes of lengths 18 and 19 is also presented. © 2011 Wiley Periodicals, Inc. J Combin Designs 20:40–57, 2012     

Three‐arm star block copolymers of aromatic polyether and polystyrene from chain‐growth condensation polymerization,atom transfer radical polymerization,and click reaction

Well‐defined (AB)₃ type star block copolymer consisting of aromatic polyether arms as the A segment and polystyrene (PSt) arms as the B segment was prepared using atom transfer radical polymerization (ATRP), chain‐growth condensation polymerization (CGCP), and click reaction. ATRP of styrene was carried out in the presence of 2,4,6‐tris(bromomethyl)mesitylene as a trifunctional initiator, and then the terminal bromines of the polymer were transformed to azide groups with NaN₃. The azide groups were converted to 4‐fluorobenzophenone moieties as CGCP initiator units by click reaction. However, when CGCP was attempted, a small amount of unreacted initiator units remained. Therefore, the azide‐terminated PSt was then used for click reaction with alkyne‐terminated aromatic polyether, obtained by CGCP with an initiator bearing an acetylene unit. Excess alkyne‐terminated aromatic polyether was removed from the crude product by means of preparative high performance liquid chromatography (HPLC) to yield the (AB)₃ type star block copolymer (M_n = 9910, M_w/M_n = 1.10). This star block copolymer, which contains aromatic polyether segments with low solubility in the shell unit, exhibited lower solubility than A₂B or AB₂ type miktoarm star copolymers. In addition, the obtained star block copolymer self‐assembled to form spherical aggregates in solution and plate‐like structures in film. © 2012 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem, 2012     

Large electro‐optic activity and enhanced temporal stability of methacrylate‐based crosslinking hyperbranched nonlinear optical polymer

A methacrylate‐based crosslinking hyperbranced polymers have been synthesized through initiator‐fragment incorporation radical polymerization and used for the temperature stable electro‐optic (EO) polymer application. This polymer consists of methyl methacrylate, 2‐metacryloxyethyl isocyanate, and ethylene glycol dimethacrylate (EGDMA) monomers. The use of EGDMA as a bifunctional unit resulted in the solvent‐soluble crosslinking hyperbranched chain, so that the EO polymer enhanced glass transition temperatures. A phenyl vinylene thiophene vinylene bridge nonlinear optical chromophore was attached to the polymer backbone as the side‐chain by a post‐functionalization reaction. The loading concentration of the chromophore was varied between 30 and 50 wt % by simply changing the mixing ratio of the precursor polymer to the chromophore. The synthesized EO polymers produced optical quality films with a light propagation loss of 0.61 dB/cm in a slab waveguide at 1.31 μm. The electrically poled film had an EO coefficient (r₃₃) of 139 pm/V at 1.31 μm. The EO crosslinking hyperbranced polymer had a high‐glass transition temperature of 170 °C, and exhibited excellent temporal stability of the EO activity at 85 °C for 500 h. © 2012 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem, 2012