Sharp Estimates of the Distance from a Fixed Point to the Frontier of a Hele-Shaw Flow

We discuss the global shape of a Hele–Shaw flow which is produced by the injection of fluid into the narrow gap between two parallel planes. We translate the problem into a problem concerning the shape of a quadrature domain of a finite positive measure for subharmonic functions and give sharp estimates of the distance from a fixed point to the frontier of the flow.     

Molecular-shape selectivity tuned by donor–acceptor type copolymers as organic phase in reversed-phase high-performance liquid chromatography

The copolymer with a terminal reactive group (copoly-VP₁₇MA₁₂) was newly designed and prepared by selecting 4-vinylpyridine (VP) as an electron-donating monomer and methyl acrylate (MA) as an electron-accepting monomer. Copoly-VP₁₇MA₁₂ was grafted onto porous silica particles by a silanol coupling reaction with the terminal group. Individually, poly-VP₁₅ and poly-MA₂₀ with a terminal reactive group were also synthesized and co-grafted onto silica (Sil-cograft-VP₁₅MA₂₀) to compare the effect of the copolymer-grafted (Sil-copoly-VP₁₇MA₁₂) and polymer co-grafted stationary phases in HPLC separation. All the polymers were characterized by ¹H NMR and FT-IR analysis before grafting on silica. Polymer grafting was confirmed by diffuse reflectance infrared Fourier transform (DRIFT), elemental analysis and thermogravimetric analysis (TGA). The intra- and intermolecular interaction between monomer units in copolymer-grafted and polymer co-grafted systems, respectively was observed by DRIFT measurement. The detailed chromatographic study revealed using PAHs as solutes that remarkably higher selectivity for planar/non-planar discrimination was observed with the copolymer-grafted phase than with the co-grafted stationary phase. In this paper, it is also discussed that the selectivity enhancement by copolymer-grafting in the Sil-copoly-VP₁₇MA₁₂ phase can be brought through intramolecular interaction between VP and MA.     

Radical reactions initiated by the photochemical cleavage of carbon-indium bonds of organoindium compounds

Intra- and intermolecular reactions of carbon-centered radicals generated by photolysis of organoindium compounds were examined. The photolysis of vinylindium compounds and indium acetylides provided vinyl and alkynyl radicals, respectively, which were trapped with ethyl iodoacetate giving the corresponding β,γ-unsaturated esters. Allylic indium compounds, prepared from 8-bromo- or 8-iodooct-1,6-dienes and powdered indium metal, underwent an intramolecular radical cyclization to afford the 5-exo-trig product.     

A note on stationarity of types over models in simple theories

We investigate stationarity of types over models in simple theories. In particular, we show that in simple theories with finite SU‐rank, any complete type over a model having Cantor‐Bendixson rank is stationary. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Poly-intercalators Carrying Threading Intercalator Moieties as Novel DNA Targeting Ligands

Threading intercalators are a novel class of intercalators that carry two substituents along the diagonal positions of an aromatic ring. These substituents are projecting out in DNA grooves when bound to DNA. Poly-intercalators carrying threading intercalating parts are quite novel and were recently found to show a unique DNA binding behavior. We review herein two types of poly-intercalators. First, tris-intercalators carrying a threading intercalator part in the middle of the molecule are described. These intercalators appear to intercalate into double stranded DNA in a special binding manner, which we call the penetrating mode, in which all the three intercalating units are arranged linearly with one of them penetrating into the DNA ladder. We synthesized two tris-intercalators ( 3 and 4) of this type and studied their binding behavior for double stranded DNA. All the experimental results were consistent with the proposed penetrating mode. Another type of threading poly-intercalators is a macrocyclic bis-threading intercalator ( 5). We found that this compound can bis-intercalate to double stranded DNA when the base pairing is disrupted temporarily to form a complex with a unique structure like a catenane. On the basis of a study of the interaction of such intercalators we envisage that DNA is a flexible and dynamic entity. These novel families of poly-intercalators will expand the scope of DNA poly-intercalation chemistry with possible medicinal applications.     

The first hetero-bifunctionalization of the secondary face of beta-cyclodextrin: selective and efficient conversion of the A-ring of a 2A,2B-disulfonate to 2A,3A-epoxymannoside

The A-ring of 2(A),2(B)-O,O-di(mesitylenesulfonyl)-beta-cyclodextrin was converted to 2(A),3(A)-epoxymannoside without affecting the other sulfonylated residue, which affords the first approach to hetero-bifunctionalization at the secondary hydroxyl side of cyclodextrins.