Photochemical Preparation of Highly Water-Soluble Pendant [60]Fullerene-Aminopolymers

Abstract— In order to introduce fullerene cages into an aqueous environment, pendant [60]fullerene-poly(propionylethyle-neimine-co-ethyleneimine) was prepared photochemical-ly. The pendant polymer is highly water soluble, with equivalent aqueous solubilities of the polymer-bound [60]fullerene much higher than the solubility of [60]ful-lerene in toluene. The photochemical reaction between [60]fullerene and secondary amine moieties in the ami-nopolymers likely follows a photoinduced electron transfer-proton transfer mechanism. The pendant polymer structures, which are represented by dehydrogenated di-and tetra-aminofullerene linkages, were characterized by use of proton and 13C NMR, Fourier transform-infrared spectroscopy, gel-permeation chromatography and optical spectroscopic methods.     

Architectural effects on the stability limits of ABC block copolymers

The random phase approximation has been used to extend the Leibler theory for the stability limit of a homogeneous melt of A–B diblock copolymers to examine the onset of microphase and macrophase separation in a variety of ABC block copolymer systems. The stability limit is located by the divergence of the collective structure factor of the melt. We introduce and analyze three models for ABC block copolymers: linear triblocks, random comb copolymers where a fixed number of A and B teeth are placed randomly along a C backbone, and statistical comb copolymers, with A or B teeth spaced regularly, but with sequences constructed using a two parameter Markov process. We compute order-disorder stability boundaries for the segregation strength parameter _χABN at threshold as a function of _χACN, _χBCN, composition, and other model parameters, and compare the results for the three different architectural models. An interesting “reentrant order-disorder transition” is located in several model phase diagrams, and is associated with a peculiar situation in which more incompatibility causes less segregation. In the case of statistical combs, macrophase separation into two liquid phases can be favored over microphase separation. © 1997 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 35: 849–864, 1997     

Electrochemistry of 6-methyl-5,6,7,8-tetrahydropterin

The electrochemical oxidation of 6-methyl-5,6,7,8-tetrahydropterin (6-MTHP), the most effective of the synthetic aromatic amino acid hydroxylase pseudo cofactors, has been studied in aqueous solution over a wide pH range at a pyrolytic graphite electrode. The first electrooxidation of 6-WTHP occurs by a quasi-reversible 2e-2H⁺ reaction giving an unstable quinonoid-dihydropterin. The latter undergoes a first order chemical follow-up reaction yielding 6-methyl-7,8-dihydropterin (6-MDHP). At pH values ?5.6 6-MDHP forms an equilibrium mixture of a covalently hydrated species and non-hydrated species. The covalently hydrated form of 6-MDHP is electrooxidized in a 2e-2H⁺ quasi-reversible reaction to another unstable quinonoid that appears to undergo a two-step rearrangement to 6-methylpterin. Non-hydrated 6-MDHP is electrooxidized at the most positive potential in an irreversible 2e-2H⁺ reaction giving 6-methylpterin.     

Stereochemistry of the thermal isomerizations of (2S,3R-methoxymethyl-2,3-dideuterio-1-(dideuteriomethylene)cyclopropane

The (2S,3R) isomer of 2-methoxymethyl-2,3-dideuterio-1-(dideuteriomethylene)cyclopropane has been synthesized and heated at 198.8°: from the experimentally observed mol fractions of the eight isomers of 2,3,α,α,- and 2,3,3,α - tetradeuterio - 2 - methoxymethyl - 1 - methylenecyclopropane in the pyrolysis product mixture have been derived rate constants for seven distinct modes of isomerization. One-center thermal epimerizations at C(2) and C(3) and the C(2)C(3) two-center epimerization are of kinetic importance. Only two of four observable stereochemical modes for carbon [1,3] shifts are seen: there is inversion of stereochemistry at the migrating C atom, while the C(3)H trans to C(2)-CH₂OCH₃ in starting material becomes syn 4 : 1 C(α)-H in the [1,3] shift product. Stereomutation at C(2) does not occur along the reaction coordinate for [1,3] carbon shifts.     

Synthesis and structural characterisation of a novel tris-methylene bridged compound (NO) 4Fe2 Se(μ-CH2)3

The tris-methylene bridged compound (NO)₄Fe₂Se(μ-CH₂)₃ has been isolated. It has been characterised by IR and ¹H, ¹³C, and ⁷⁷Se NMR spectroscopy. Its structure has been determined by single-crystal X-ray diffraction methods. The structure consists of a heavy atom triangle consisting of one Se and two Fe atoms. The Fe-Fe and the two Fe-Se edges are bridged by methylene groups.     

Some Asymptotic ith Ramsey numbers

Let G be a graph with chromatic number χ(G) and let t(G) be the minimum number of vertices in any color class among all χ(G)-vertex colorings of G. Let H′ be a connected graph and let H be a graph obtained by subdividing (adding extra vertices to) a fixed edge of H′. It is proved that if the order of H is sufficiently large, the ith Ramsey number r_i(G, H) equals $\text{[}\text{((χ(G)?1)(|}\text{H}\text{|?1)+t(G)?1)}\text{i}\text{]+1}$.     

Overconvergent modular sheaves and modular forms for GL 2/F

Given a totally real field F and a prime integer p which is unramified in F, we construct p-adic families of overconvergent Hilbert modular forms (of non-necessarily parallel weight) as sections of, so called, overconvergent Hilbert modular sheaves. We prove that the classical Hilbert modular forms of integral weights are overconvergent in our sense. We compare our notion with Katz’s definition of p-adic Hilbert modular forms. For F = ?, we prove that our notion of (families of) overconvergent elliptic modular forms coincides with those of R. Coleman and V. Pilloni.     

Overlap Cycles for Steiner Quadruple Systems

Steiner quadruple systems are set systems in which every triple is contained in a unique quadruple. It is well known that Steiner quadruple systems of order v, or SQS(v), exist if and only if . Universal cycles, introduced by Chung, Diaconis, and Graham in 1992, are a type of cyclic Gray code. Overlap cycles are generalizations of universal cycles that were introduced in 2010 by Godbole, et al. Using Hanani's SQS constructions, we show that for every with there exists an SQS(v) that admits a 1‐overlap cycle.     

Composition Operators on the Lipschitz Space of a Tree

The Lipschitz space ${\mathcal{L}}$ of an infinite tree T rooted at o is defined as the space consisting of the functions ${f : T \rightarrow \mathbb{C}}$ such that $$\beta_f = {\rm sup}\{|f(v) - f(v^-)| : v \in T\backslash\{o\}, \,v^- {\rm parent \, of \,} v\}$$ is finite. Under the norm ${\|f\|_\mathcal{L} = |f(o)|+\beta_f,\mathcal{L}}$ is a Banach space. In this article, the functions φ mapping T into itself whose induced composition operator ${C_{\varphi} : f \mapsto f \circ \varphi}$ on the Lipschitz space is bounded, compact, or an isometry, are characterized. Specifically, it is shown that the symbols of the bounded composition operators are the Lipschitz maps of T into itself viewed as a metric space under the edge-counting distance. The symbols inducing compact operators have finite range while those inducing isometries on ${\mathcal{L}}$ are precisely the onto maps fixing the root and whose images of neighboring vertices coincide or are themselves neighboring vertices. Finally, the spectrum of the operators ${C_\varphi}$ that are isometries is studied in detail.     

A short proof that N 3 is not a circle containment order

A partially ordered set P is called a circle containment order provided one can assign to each xP a circle C _x so that . We show that the infinite three-dimensional poset N ³ is not a circle containment order and note that it is still unknown whether or not [n]³ is such an order for arbitrarily large n.