In situ sulfonation of alkyl benzene self-assembled monolayers: product distribution and kinetic analysis

The sulfonation of aromatic rings held at the surface of a covalently anchored self-assembled monolayer has been analyzed in terms of the rates and isomer distribution of the sulfonation process. The observed product distributions are similar to those observed in solution, though the data obtained suggest that the reaction rate and the ortho/para product ratio depend on the length of the tether anchoring the aryl ring to the monolayer interface. It was also found that the interface becomes progressively more disordered and the observed reaction rates decrease as the reaction progresses. There is no evidence for a bias in favor of reaction at the more exposed para-position nor is there evidence for an enhanced reaction rate due to the increased disorder and/or improved wetting as the reaction proceeds. This is the first detailed study of electrophilic aromatic substitution at a monolayer interface. It introduces new approaches to the spectroscopic analysis of reactions on self-assembled monolayers and provides a new general approach to the analysis of isomeric product distribution in such a setting.     

Many‐particle Dirac identities for arbitrary elementary spins

The eigenvalues of arbitrary conjugacy class‐sums of the symmetric group, within subspaces that contain irreducible representations with at most k rows, are considered. Explicit expressions for these eigenvalues in terms of the eigenvalues of single‐cycle class‐sums with cycle lengths up to k are obtained. © 2000 John Wiley & Sons, Inc. Int J Quant Chem 78: 407–411, 2000     

Asymptotic behavior of two-electron expectation values in two-electron excited states

Singly-excited states of the two-electron atom cease being bound when $Z\to 1$ (from above), the outer orbital becoming infinitely diffuse. The asymptotic relations$\underset{Z\to 1}{\lim }?{(Z?1)}^k〈{(1sns)}^{1,3}S\left|r_{12}^k\right|{(1sns)}^{1,3}S〉=〈(n?1)s^{(0)}\left|r^k\right|(n?1)s^{(0)}〉,$ where $k=?1,1,2,3,?$, are demonstrated to hold. Here, $(n?1)s^{(0)}$ is a hydrogenic s orbital with principal quantum number $(n?1)$. New, more nuanced light is shed on the already challenged dogma that the Pauli principle keeps the electrons further apart in the triplet than in the corresponding singlet.     

Beyond realistic considerations: modeling conceptions and controls in task examples with simple word problems

Using simple word problems, we analyze possible teacher conceptions on the process of problem solving, its goals and the choices that a problem solver can make in problem mathematization. We identify several possible teacher conceptions that would be responsible for the different didactical contracts that teachers create in the mathematics class. Using especially chosen and designed task examples, we demonstrate the diagnosis of teacher own controls in solving problems and in evaluating problem solutions. We also discuss characteristics of task examples that might promote a shift from a problem solving perspective to a modeling perspective that goes beyond merely accepting alternative solutions due to realistic considerations. This shift in perspective would be exhibited through a new understanding of the process of fitting mathematical models in problem situations.     

The Hardness of 3-Uniform Hypergraph Coloring

We prove that coloring a 3-uniform 2-colorable hypergraph with c colors is NP-hard for any constant c. The best known algorithm [20] colors such a graph using O(n^1/5) colors. Our result immediately implies that for any constants k ≥ 3 and c₂ > c₁ > 1, coloring a k-uniform c₁-colorable hypergraph with c₂ colors is NP-hard; the case k = 2, however, remains wide open. This is the first hardness result for approximately-coloring a 3-uniform hypergraph that is colorable with a constant number of colors. For k ≥ 4 such a result has been shown by [14], who also discussed the inherent difference between the k = 3 case and k ≥ 4. Our proof presents a new connection between the Long-Code and the Kneser graph, and relies on the high chromatic numbers of the Kneser graph [19,22] and the Schrijver graph [26]. We prove a certain maximization variant of the Kneser conjecture, namely that any coloring of the Kneser graph by fewer colors than its chromatic number, has ‘many’ non-monochromatic edges. * Research supported by NSF grant CCR-9987845. † Supported by an Alon Fellowship and by NSF grant CCR-9987845. ‡ Work supported in part by NSF grants CCF-9988526 and DMS 9729992, and the State of New Jersery.     

Inside Cover: Cognitive‐Performance Recovery of Alzheimer's Disease Model Mice by Modulation of Early Soluble Amyloidal Assemblies (Angew. Chem. Int. Ed. 11/2009)

The accumulation of amyloid‐β (Aβ) as amyloid fibril deposits may play a central role in the pathogenesis of Alzheimer's disease, which is among the most common diseases of the 21st century. E. Gazit and co‐workers describe in their Communication on page 1981 ff. a novel Aβ fibrilization inhibitor, whose mechanism of action is based on targeting aromatic recognition modules together with a unique C^α‐methylation β‐breakage strategy. We thank Tal Mazor for the graphical assistance with the cover.

     

Undirected forest constraints

We present two constraints that partition the vertices of an undirected n-vertex, m-edge graph \(\mathcal {G}=( \mathcal {V}, \mathcal {E})\) into a set of vertex-disjoint trees. The first is the resource-forest constraint, where we assume that a subset \(\mathcal {R}\subseteq \mathcal {V}\) of the vertices are resource vertices. The constraint specifies that each tree in the forest must contain at least one resource vertex. This is the natural undirected counterpart of the tree constraint (Beldiceanu et al., CP-AI-OR’05, Springer, Berlin, 2005), which partitions a directed graph into a forest of directed trees where only certain vertices can be tree roots. We describe a hybrid-consistency algorithm that runs in \(\mathop {\mathcal {O}}(m+n)\) time for the resource-forest constraint, a sharp improvement over the \(\mathop {\mathcal {O}}(mn)\) bound that is known for the directed case. The second constraint is proper-forest. In this variant, we do not have the requirement that each tree contains a resource, but the forest must contain only proper trees, i.e., trees that have at least two vertices each. We develop a hybrid-consistency algorithm for this case whose running time is \(\mathop {\mathcal {O}}(mn)\) in the worst case, and \(\mathop {\mathcal {O}}(m\sqrt{n})\) in many (typical) cases.     

Two-dimensional nonlinear beam shaping

We develop a technique for two-dimensional arbitrary wavefront shaping in quadratic nonlinear crystals by using binary nonlinear computer generated holograms. The method is based on transverse illumination of a binary modulated nonlinear photonic crystal, where the phase matching is partially satisfied through the nonlinear Raman-Nath process. We demonstrate the method experimentally showing a conversion of a fundamental Gaussian beam pump light into three Hermite-Gaussian and three Laguerre-Gaussian beams in the second harmonic. Two-dimensional binary nonlinear computer generated holograms open wide possibilities in the field of nonlinear beam shaping and mode conversion.     

Orbital correspondence analysis in maximum symmetry: Formulation and conceptual framework

A recently proposed method for the analysis of the course of chemical reactions, based on the maximal use of available symmetry, is formulated as a set of procedural rules. The application of these rules is illustrated with a simple prototype reaction: CH₂+C₂H₄ fcyclo-C₃H₆. They are then derived, using the formalism of time-dependent perturbation theory within the Born-Oppenheimer approximation, thus bringing out the method's underlying assumptions and its relation to the widely used Woodward-Hoffmann procedure.