Tree-length equals branch-length

The graph parameter tree-length, which is defined in terms of Robertson-Seymour’s tree decomposition, was introduced by Dourisboure and Gavoille [Y. Dourisboure, C. Gavoille, Tree-decompositions with bags of small diameter, Discrete Math. 307 (2007) 2008-2029], and has recently been studied. In this paper, we introduce a new graph parameter branch-length, which is defined in terms of Robertson-Seymour’s branch decomposition. We also prove the equivalence between tree-length and branch-length.     

The range of maps on classical insertion theorems

A classical insertion theorem due to Kat??tov?CTong (or Dowker?CKat??tov, Michael) reads that ? can be a test space for the range of maps on the insertion theorem which characterizes the domain to be normal (or normal and countably paracompact, perfectly normal). It is known that the range ? in the Kat??tov?CTong insertion theorem is not necessarily replaced by a non-trivial separable Banach lattice. We show that the range ? in the Dowker?CKat??tov and Michael insertion theorems can be replaced by any non-trivial separable Banach lattice.     

Graft polymerization of polysilsesquioxane containing chloromethylphenyl groups by atom transfer radical polymerization

Polysilsesquioxane with phenyl and chloromethylphenyl groups (PCPSQ) was prepared readily from phenyltrimethoxysilane and [2‐(chloromethylphenyl)ethyl]trimethoxysilane under acidic conditions. Polymerization with chloromethylphenyl groups on PCPSQ with methyl methacrylate (MMA) was conducted in the presence of a catalytic amount of copper(I) bromide and (−)‐sparteine. Atom transfer radical polymerization yielded a graft polymer (PCPSQ‐g‐MMA) efficiently, and no gelation was observed. The process was also applied to the preparation of graft block copolymers on PCPSQ with several methacrylate monomers. An advantage of the graft hybrid polymers was shown in improved thermal behavior. © 2004 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 42: 4212–4221, 2004     

Chiral initiator-induces self-disproportionation of enantiomers via achiral chromatography: application to enantiomer separation of racemate

We report here the theoretical design and proof of principle of the first example of a conceptually new approach for the preparation of enantiomerically pure compounds from the racemates by chiral initiator-induced Self-Disproportionation of Enantiomers (SDE) via achiral chromatography.     

A mass spectrometric method to determine activities of enzymes involved in polyamine catabolism

An analytical method for the determination of three polyamines (putrescine, spermidine, and spermine) and five acetylpolyamines [N¹-acetylspermidine (N¹AcSpd), N⁸-acetylspermidine (N⁸AcSpd), N¹-acetylspermine, N¹,N⁸-diacetylspermidine, and N¹,N¹²-diacetylspermine] involved in the polyamine catabolic pathway has been developed using a hybrid tandem mass spectrometer. Heptafluorobutyryl (HFB) derivatives of these compounds and respective internal standards labeled with stable isotopes were analyzed simultaneously by TOF MS, based on peak areas appearing at appropriate m/z values. The isomers, N¹AcSpd and N⁸AcSpd were determined from their fragment ions, the acetylamidopropyl and acetylamidobutyl groups, respectively, using MS/MS with ¹³C₂-N¹AcSpd and ¹³C₂-N⁸AcSpd which have the ¹³C₂-acetyl group as an internal standard. The TOF MS method was successfully applied to measure the activity of enzymes involved in polyamine catabolic pathways, namely N¹-acetylpolyamine oxidase (APAO), spermine oxidase (SMO), and spermidine/spermine N¹-acetyltransferase (SSAT). The following natural substrates and products labeled with stable isotopes considering the application to biological samples were identified; for APAO, [4,9,12-¹⁵N₃]-N¹-acetylspermine and [1,4,8-¹⁵N₃]spermidine (¹⁵N₃-Spd), respectively; for SMO, [1,4,8,12-¹⁵N₄]spermine and ¹⁵N₃-Spd, respectively; and for SSAT, ¹⁵N₃-Spd and [1,4,8-¹⁵N₃]-N¹-acetylspermidine, respectively.     

Interaction between the Heme and a G-Quartet in a Heme-DNA Complex

The structure of a complex between heme(Fe(3+)) and a parallel G-quadruplex DNA formed from a single repeat sequence of the human telomere, d(TTAGGG), has been characterized by (1)H NMR. The study demonstrated that the heme(Fe(3+)) is sandwiched between the 3'-terminal G-quartets of the G-quadruplex DNA. Hence, the net +1 charge of the heme(Fe(3+)) in the complex is surrounded by the eight carbonyl oxygen atoms of the G-quartets. Interaction between the heme Fe(3+) and G-quartets in the complex was clearly manifested in the solvent (1)H/(2)H isotope effect on the NMR parameters of paramagnetically shifted heme methyl proton signals, and interaction of the heme Fe(3+) with the eight carbonyl oxygen atoms of the two G-quartets was shown to provide a strong and axially symmetric ligand field surrounding the heme Fe(3+), yielding a heme(Fe(3+)) low-spin species with a highly symmetric heme electronic structure. This finding provides new insights as to the design of the molecular architecture and functional properties of various heme-DNA complexes.     

Electrically induced lipid migration in non-lamellar phase

Inverted hexagonal blocks of 1,2-dioleoyl-sn-glycero-3-phosphoethanolamine (DOPE) lipid adsorbed on a polyethyleneimine (PEI)-coated surface in deionized water transformed its shape upon the application of an electric field, forming lipid objects in a variety of shapes (e.g. lines with a width of 10-50μm). The phenomenon was driven by the electrophoresis, because the zwitterionic lipid, DOPE turned out to be highly negatively charged in deionized water. The interaction between DOPE and the PEI surface stabilized the system, assuring a lifetime over several weeks for the formed structures after the electric field was switched off. The free-drawing of microscopic objects (lines, crosses, and jelly fish) was also achieved by controlling the direction of the lipid movement with the field direction.     

Electronic structures of single-walled carbon nanotubes encapsulating ellipsoidal C70

The molecular orientation of ellipsoidal C(70) in single-walled carbon nanotubes (SWCNTs) depends on the tube diameter (d(t)). Photoluminescence (PL) studies reveal that the fullerene encapsulation effects on the optical transition energy of SWCNTs are significantly different for C(70) and C(60) at d(t) = 1.405-1.431 nm. This indicates that the transition from the "lying" alignment to the "standing" alignment occurs at d(t) ≈ 1.41 nm and the electronic states of SWCNTs are very sensitive to the interspacing between the encapsulated molecules and the SWCNTs. The present findings suggest that the electronic structure of SWCNTs is tunable not only by alternating the encapsulated molecules but also by controlling their molecular orientations, thus paving the way for development of novel SWCNT-based devices.