On the rate of convergence of solutions in free boundary problems via penalization

The rate of convergence of approximate solutions via penalization for free boundary problems are concerned. A key observation is to obtain global bounds of penalized terms which give necessary estimates on integrations by the nonlinear adjoint method by L.C. Evans.     

New Synthetic Method for Bicyclic Compounds Through a Sequence of Ene-Type Chlorination,Palladium Catalyzed Dehydrochlorination,and Intramolecular Diels-Alder Reaction

A sequence of ene-type chlorination, palladium catalyzed dehydrochlorination, and the intramolecular Diels-Alder reaction afforded a new method for conversion of prenyl derivatives into bicyclic compounds.     

Design and synthesis of 2-(1,3-dialkoxy-2-methylpropan-2-yl)-1,3-diarylpropanes as tethering units for folded H-stacking polymers

1,3-Diarylpropenes 9 having a 1,3-dialkoxy-2-methylpropan-2-yl group were designed as tethering monomers for folded H-stacking polymers, and were readily synthesized from 2-ethoxymethylidene malonate in four- or five-steps, including a facile sequential addition–elimination–addition reaction of benzyl zinc reagents. The preference for the closed (stacked) conformation in the resulting 2-substituted 1,3-diarylpropanes 9 was evaluated using MM2 calculations, ¹H NMR analyses, and fluorescence measurements. Copolymerization of the resulting monomers 9 with compounds containing π-units provided polymers with blue-shifted UV-absorptions both in solution and as films, compared with that of a model compound containing a single π-unit. This optical property is unique to H-aggregated π-units.     

Determination of the phase boundary of GaP using in situ high pressure and high-temperature X-ray diffraction

The high pressure behavior of gallium phosphide, GaP, has been examined using the synchrotron X-ray diffraction technique in a diamond anvil cell up to 27?GPa and 900?K. The transition from a semiconducting to a metallic phase was observed. This transition occurred at 22.2?GPa and room temperature, and a negative dependence of temperature of this transition was found. The transition boundary was determined to be P (GPa)?=?22.6???0.0014?×?T (K).     

Synthesis and radical polymerization of styrene‐based monomer having a five‐membered cyclic carbonate structure

A styrene‐based monomer having a five‐membered cyclic carbonate structure, 4‐vinylbenzyl 2,5‐dioxoran‐3‐ylmethyl ether (VBCE), was prepared by lithium bromide‐catalyzed addition of carbon dioxide to 4‐vinylbenxyl glycidyl ether (VBGE). Radical polymerization of the obtained VBCE was carried out using 2,2′‐azobisisobutyronitrile as an initiator. PolyVBCE with number‐averaged molecular weight higher than 13,800 was obtained by a solution polymerization in N,N‐dimethylformamide, N,N‐dimethylacetamide, dimethyl sulfoxide, and methyl ethyl ketone. The glass transition temperature and 5 wt % decomposition temperature of the polyVBCE were determined to be 52 and 305 °C by differential scanning calorimetry and thermal gravimetry analysis, respectively. It was confirmed that a polymer consisting of the same VBCE repeating unit can be also obtained via chemical modification of polyVBGE, that is, a lithium‐bromide‐catalyzed addition of carbon dioxide to a polyVBGE prepared from a radical polymerization of VBGE. Further copolymerization of VBCE with styrene gave the corresponding copolymer in a high yield. © 2012 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem, 2012     

Synthesis of Unsaturated Nitriles from Trisubstituted Olefins Via Ene-Type Chlorination

Unsaturated nitriles have been synthesized from trisubstituted olefins via ene-type chlorination and regioselective substitution with cyanide ion followed by double bond migration.     

Preparation of open tubular solid-phase extraction column with 5-amino-8-hydroxyquinoline-modified gold nanoparticle phase for the enrichment of heavy metal ions.

A 5-amino-8-hydroxyquinoline (AHQ)-modified gold nanoparticle (GNP) layer was fabricated on an inner wall of a silica capillary column by alternatively passing a citrate-stabilized GNP solution and an AHQ solution in a repeating fashion. The observations by a field emission scanning electron microscope showed that the thickness of the resulting GNP layer was about 0.15 microm. This column was then used as an open tubular solid-phase extraction column for cadmium, followed by electrothermal atomic absorption spectrometric determination. The detection limit of 0.009 ng ml(-1) was obtained.     

Scanning tunneling microscopy observation of initial growth of Sn and Ge1−xSnx layers on Ge(0 0 1) substrates

We have investigated the initial growth of Sn and Ge_1−xSn_x layers on Ge(0 0 1) surface by using scanning tunneling microscopy. After the growth of a 0.035 ML-thick Sn layer at room temperature, Sn clusters lining vertically to a dimer row was observed. In the case of the 0.035-0.018 ML-thick Sn growth at 250 °C, the characteristic surface reconstruction with the step-edge undulation like a comb was observed. In the growth of a Ge_0.994Sn_0.006 layer at 250 °C, the multilayer polynuclear growth with a lot of two-dimensional small domain was observed. These surface reconstructions should be accounted for by the large compressive stress induced in the surface layer due to the incorporation of Sn atoms.