Strongly Focused Gravitational Waves

This paper contains a new proof of the formation of trapped spheres, in vacuum spacetimes, by the focusing of gravitational waves, from generic data. The first such result was obtained by Christodoulou (Zurich: Eur Math Soc, 2009). We exploit the same physical mechanism, but give a logically independent construction of these spacetimes.     

A parameter robust Petrov–Galerkin scheme for advection–diffusion–reaction equations

In this paper, a singularly perturbed convection diffusion boundary value problem, with discontinuous diffusion coefficient is examined. In addition to the presence of boundary layers, strong and weak interior layers can also be present due to the discontinuities in the diffusion coefficient. A priori layer adapted piecewise uniform meshes are used to resolve any layers present in the solution. Using a Petrov–Galerkin finite element formulation, a fitted finite difference operator is shown to produce numerical approximations on this fitted mesh, which are uniformly second order (up to logarithmic terms) globally convergent in the pointwise maximum norm.     

Multivalent Recognition of Concanavalin A by {Mo132} Glyconanocapsules—Toward Biomimetic Hybrid Multilayers

Herein, we consider Müller’s spherical, porous, anionic, molybdenum oxide based capsule, (NH₄)₄₂‐ [{(Mo^VI)Mo^VI₅O₂₁(H₂O)₆}₁₂{Mo^V₂O₄(CH₃COO)}₃₀]?10 CH₃COONH₄? 300 H₂O≡(NH₄)₄₂? 1 a ?crystal ingredients≡ 1 , {Mo₁₃₂}, as an effective sugar‐decorated nanoplatform for multivalent lectin recognition. The ion‐exchange of NH₄⁺ ions of 1 with cationic‐sugars, D ‐mannose‐ammonium chloride ( 2 ) or D ‐glucose‐ammonium chloride ( 3 ) results in the formation of glyconanocapsules (NH₄)_42?n 2 _n? 1 a and (NH₄)_42?m 3 _m? 1 a . The Mannose (NH₄)_42?n 2 _n? 1 a capsules bind selectively Concanavalin A (Con A) in aqueous solution, giving an association avidity constant of ${K{{{\rm multi}\hfill \atop {\rm a}\hfill}}}$ =4.6×10⁴ M ^?1 and an enhancement factor of β=K${{{{\rm multi}\hfill \atop {\rm a}\hfill}}}$ /K${{{{\rm mono}\hfill \atop {\rm ass}\hfill}}}$ =21.9, reminiscent of the formation of “glycoside clusters” on the external surface of glyconanocapsule. The glyconanocapsules (NH₄)_42?n 2 _n? 1 a and (NH₄)_42?m 3 _m? 1 a self‐assemble in “hybrid multilayers” by successive layer‐by‐layer deposition of (NH₄)_42?n 2 _n? 1 a or (NH₄)_42?m 3 _m? 1 a and Con A. These architectures, reminiscent of versatile mimics of artificial tissues, can be easily prepared and quantified by using quartz crystal microgravimetry (QCM). The “biomimetic hybrid multilayers” described here are stable under a continual water flow and they may serve as artificial networks for a greater depth of understanding of various biological mechanisms, which can directly benefit the fields of chemical separations, sensors or storage‐delivery devices.     

Facile and convenient synthesis of aryl hydrazines via copper-catalyzed C–N cross-coupling of aryl halides and hydrazine hydrate

An efficient and convenient method for the synthesis of aryl hydrazines has been developed via copper-catalyzed cross-coupling of aryl bromides and hydrazine with a readily accessible ligand and water as a solvent. The multigram scale procedure is applicable to aryl bromides bearing both moderately electron-donating and electron-withdrawing substituents in the aromatic nucleus. No column chromatography is required to obtain aryl hydrazine hydrochlorides in good yields.     

Activity coefficients at infinite dilution of organic solutes in the ionic liquid 1-butyl-3-methylimidazolium hexafluoroantimonate using gas–liquid chromatography at T = (313.15, 323.15, and 333.15) K

Activity coefficients at infinite dilution were determined for 27 solutes: n-alkanes, alk-1-enes, alk-1-ynes, cycloalkanes, alkylbenzenes, alcohols, and ketones in the ionic liquid 1-butyl-3-methylimidazolium hexafluoroantimonate, [BMIM][SbF₆], by gas–liquid chromatography at three different temperatures, T = (313.15, 323.15, and 333.15) K. The results are compared to published data on related compounds. The partial molar excess enthalpy values at infinite dilution were calculated from the experimental data over the same temperature range. Selectivities and capacities at infinite dilution were calculated for the hexane/benzene and methanol/benzene systems from experimental infinite dilution activity coefficients and compared to the literature values for related ionic liquids, as well as to data on industrial molecular solvents.     

Phosphorinane and Enol Rings in One Molecule. Evidence for Reciprocal Stabilization of Half-Chair Conformations

Abstract.

The X-ray crystal structure of 2-(2′,4′-dioxo-3′-pentyl)-5,5-dimethyl-2-oxo-1,3,2-dioxaphosphorinane (2) reveals significant half-chair distortion of the axially oriented cisenol ring. The molecule also undergoes in-plane deformations. R(O...O) = 2.410 Å in the enol moiety indicates a very strong hydrogen bonding. The enol content, δ_OH and thermodynamic parameters for the axial-equatorial conformational and keto-enol equilibriums were obtained from ¹H, ³¹P NMR and IR measurements in comparison with the planar 4,6-dimethyl isomer (1) containing equatorially oriented enol ring. The X-ray single crystal structure of 5,5-dimethyl-2-(methoxycarbonyl-3′-oxo-2′-butyl)-2-oxo-1,3,2-dioxaphosphorinane (3) reveals the unusual half-chair conformation of the dioxaphosphorinane cycle disposed a trans-enol ring substituent. ¹H, ³¹P NMR and IR solution data support the same structure displays a strong conformational preference while the minor forms are chair conformers with an axial or equatorial cis-enol ring.     

NOTE: Synthesis and Characterization of a Poly(acrylamide) with Pendant 1,4-piperazine-2,5-dione Moieties via Post-polymerization Cyclization

A poly(acrylamide) was synthesized from N ^α -Boc-N ^? -acrolyl-l-lysylglycine methyl ester via radical polymerization. This polymer typically had Mn ～ 100,000 g/mol, Mw ～ 300,000 g/mol, and a T_g of 93°C. Removal of Boc with TFA and cyclization with DABCO? in DMSO at 65°C afforded a soluble piperazinedione-containing polymer that had a T_g of 157°C and thermal stability up to 300°C. These results demonstrate a viable and efficient synthetic route to piperazinedione-containing polyacrylamides of high molecular weight. Related polymers that incorporate substituted indane moieties could be useful high T_g materials for fabrication of LC and NLO devices.