Dubrovin valuation rings and Henselization

Supported in part by the National Science Foundation     

Singular terms of helicity amplitudes at one loop in QCD and the soft limit of the cross sections of multi-parton processes

We describe a general method that enables us to obtain all the singular terms of helicity amplitudes of n-parton processes at one loop. The algorithm uses helicity amplitudes at tree level and simple color algebra. We illustrate the method by calculating the singular part of the one-loop helicity amplitudes of all 2 → 3 parton subprocesses. The results are used to derive the soft gluon limit of the cross sections of all 2 → 4 parton scattering subprocesses which provide a useful initial condition for the angular ordering approximation to coherent multiple soft gluon emission, incorporated in existing Monte Carlo simulation programs.     

Pushing Squares Around

We study dynamic self-reconfiguration of modular metamorphic systems. We guarantee the feasibility of motion planning in a rectangular model consisting of square modules that are allowed to slide along or rotate about one another. That is, we show that any two connected configurations of the same number of modules can be transformed into each other by a sequence of moves so that all intermediate configurations are connected. This settles a conjecture formulated in [6].     

Baer orderings with noninvariant valuation ring

We construct division algebras with involution containing a Baer ordering with noninvariant order ring. This gives a negative answer to a question of Holland, whether the order ring is always invariant under inner automorphisms. Furthermore, we give examples of any index. Previously, the only known examples of division algebras containing Baer orderings were of index 2 ⁿ or of indexp forp a prime of the form 4m + 3. Supported in part by the National Science Foundation.     

A result on sets,with applications to vector optimization

In this paper there is stated a result on sets in ordered linear spaces which can be used to show that some properties of the sets are inherited by their convex hulls under suitable conditions. As applications one gives a characterization of weakly efficient points and a duality result for nonconvex vector optimization problems.     

Click chemistry in materials synthesis. III. Metal‐adhesive polymers from Cu(I)‐catalyzed azide–alkyne cycloaddition

1,2,3‐Triazole‐based polymers generated from the Cu(I)‐catalyzed cycloaddition between multivalent azides and acetylenes are effective adhesive materials for metal surfaces. The adhesive capacities of candidate mixtures of azide and alkyne components were measured by a modified peel test, using a customized adhesive tester. A particularly effective tetravalent alkyne and trivalent azide combination was identified, giving exceptional strength that matches or exceeds the best commercial formulations. The addition of Cu catalyst was found to be important for the synthesis of stronger adhesive polymers when cured at room temperature. Heating also accelerated curing rates, but the maximum adhesive strengths achieved at both room temperature and high temperature were the same, suggesting that crosslinking reaches the same advanced point in all cases. Polytriazoles also form adhesives to aluminum, but copper is bound more effectively, presumably because active Cu(I) ions may be leached from the surface to promote crosslinking and adhesion. © 2007 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 45: 5182–5189, 2007     

Symmetric Hilbert spaces arising from species of structures

Symmetric Hilbert spaces such as the bosonic and the fermionic Fock spaces over some lsquo;one particle space’ are formed by certain symmetrization procedures performed on the full Fock space. We investigate alternative ways of symmetrization by building on Joyal's notion of a combinatorial species. Any such species F gives rise to an endofunctor of the category of Hilbert spaces with contractions mapping a Hilbert space to a symmetric Hilbert space with the same symmetry as the species F. A general framework for annihilation and creation operators on these spaces is developed, and compared to the generalised Brownian motions of R. Speicher and M. Bożejko. As a corollary we find that the commutation relation with admits a realization on a symmetric Hilbert space whenever f has a power series with infinite radius of convergence and positive coefficients. Received: 7 April 2000; in final form: 28 November 2000 / Published online: 19 October 2001     

The Lifting Model for Reconfiguration

Given a pair of start and target configurations, each consisting of n pairwise disjoint disks in the plane, what is the minimum number of moves that suffice for transforming the start configuration into the target configuration? In one move a disk is lifted from the plane and placed back in the plane at another location, without intersecting any other disk. We discuss efficient algorithms for this task and estimate their number of moves under different assumptions on disk radii. We then extend our results for arbitrary disks to systems of pseudodisks, in particular to sets of homothetic copies of a convex object.     

Semicarbazones and thiosemicarbazones,XII: Crystal structure of salicylaldehyde semicarbazone

Summary The crystal and molecular structure of salicylaldehyde semicarbazone was obtained by single crystal X-ray diffraction. The O atom of the semicarbazone fragment isanti to the N atom of the hydrazinic group. The distribution of bond lengths in the semicarbazone fragment indicates delocalization of the -electrons. The crystal structure is stabilized by intra- and intermolecular hydrogen bonds.

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Semicarbazone und Thiosemicarbazone, 12. Mitt.: Die Kristallstruktur des Salicylaldehyd-Semicarbazons

Zusammenfassung Die Kristallstruktur und die molekulare Struktur des Salicylaldehyd-Semicarbazons wurde über Einkristall-Röntgenstreuung ermittelt. Das O-Atom des Semicarbazonteils stehtanti zum N-Atom der Hydrazin-Gruppierung. Die Bindungslängen in der Semicarbazoneinheit zeigen eine Delokalisierung der -Elektronen an. Die Geometrie der Verbindung wird durch stabilisierende intra- und intermolekulare Wasserstoffbrückenbindungen bestimmt.