Exact Solutions for Large Amplitude Waves in Dispersive and Dissipative Systems

This paper describes some applications of a transformation which takes a system of two, first order, quasilinear, partial differential equations in two dependent and two independent variables into a similar system. Typically, the equations govern wave propagation in dispersive and dissipative systems. It is shown that certain nonlinear equations which are of current practical interest can be transformed into linear equations.     

Laterally stabilized complexes of DNA with linear reducible polycations: strategy for triggered intracellular activation of DNA delivery vectors.

Target-specific DNA delivery requires vectors that combine stability in the biological milieu, receptor-mediated uptake into target cells, and intracellular activation to mediate transgene expression. This is achieved here using polymer-coated vectors based on plasmid DNA complexed with a reductively degradable polycation (RPC), designed for intercellular degradation. The RPC were prepared by oxidation of the terminal cysteinyl thiol groups of Cys(Lys)10Cys. The complexes were coated and surface-cross-linked using multivalent reactive copolymers of N-(2-hydroxypropyl)methacrylamide (PHPMA), providing a unique combination of steric and reversible lateral stabilization, known to promote extended circulation in the bloodstream. Coated complexes containing RPC exhibited lateral stabilization that was reversible by treatment with 2.5 mM dithiothreitol, releasing free DNA after incubation with a polyanion. In contrast, coated complexes containing nonreducible poly(l-lysine) (PLL) were not destabilized by reduction. The biological usefulness of this trigger mechanism was examined by measuring transfection activity in human retinoblast 911 cells of coated complexes, based on PLL or RPC, targeted to cell surface receptors by covalent linkage of basic fibroblast growth factor. The levels of transgene expression observed for RPC-based targeted vectors indicated efficient intracellular activation, authenticating the concept that lateral stabilization introduced by surface coating with PHPMA can be reversed by intracellular reduction.     

Counting negative eigenvalues of a Hilbert-Schmidt operator via sign changes of a determinant

In this paper a continuous analogue of the Jacobi-Sturm rule for counting the number of negative eigenvalues of a Hermitian matrix is derived.     

Subgraphs of large connectivity and chromatic number in graphs of large chromatic number

For each pair k, m of natural numbers there exists a natural number f(k, m) such that every f(k, m)-chromatic graph contains a k-connected subgraph of chromatic number at least m.     

A counterexample to the rank-coloring conjecture

It has been conjectured by C. van Nuffelen that the chromatic number of any graph with at least one edge does not exceed the rank of its adjacency matrix. We give a counterexample, with chromatic number 32 and with an adjacency matrix of rank 29.     

Organic ions in the gas phase—XXI. Competitive primary loss of C2H4 and CO from 1-tetralone under electron impact

Competing primary reactions by which 1-tetralone loses C₂H₄ and CO give rise to a doublet at mass 118 in the high-resolution mass spectrum corresponding to 96·4% C₈H₆O⁺ and 3·6% C₉H₁₀⁺, respectively. Study of the remainder of the spectrum however, suggests that these intensities constitute a poor measure of the relative importance of the two reaction paths. The C₉H₁₀⁺ ion evidently degrades more readily than C₈H₆O⁺, since an estimated 26% of the ions arising in these paths involve primary loss of CO. This estimate is supported by voltage dependence of the intensity distribution between the members of the doublet. As ionizing voltage is decreased, the intensity distribution is constant to about 20 volts, but between 20 and 10 volts the value for C₉H₁₀⁺ rises smoothly from about 3.5% to about 25%.     

r-tuple colorings of uniquely colorable graphs

An r-tuple coloring of a graph is one in which r colors are assigned to each point of the graph so that the sets of colors assigned to adjacent points are always disjoint. We investigate the question of whether a uniquely n-colorable graph can receive an r-tuple coloring with fewer than nr colors. We show that this cannot happen for n=3 and r=2 and that for a given n and r to establish the conjecture that no uniquely n-colorable graph can receive an r-tuple coloring from fewer than nr colors it suffices to prove it for on a finite set of uniquely n-colorable graphs.     

Reactions of aliphatic aldehydes under electron-impact

The mass spectra of hexanal, heptanal and nonanal variously labeled with deuterium confirm γ-hydrogen migration and β cleavage as the mechanism leading to [C₂H₄O]⁺˙ and [M ? C₂H₄O]⁺˙, although the data on the latter are complicated by contributions from other, related paths. In addition, they show that three other major primary decomposition products, [M ? C₂H₄]⁺˙, [M ? H₂O]⁺˙ and [C₃H₅O]⁺, all arise in large part by processes involving γ-hydrogen migration to the oxygen atom. The ethylene lost to yield the first of these products consists of the α and β methylene groups. The loss of ethylene most likely occurs by way of a cyclobutanol intermediate, which, via alternative reaction paths, may well contribute to the yields of the other two products as well. These findings further extend the range of parallelism between photochemical and electron-impact-induced reactions.