AN INVARIANT FOR HYPERGRAPHS

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Order-preserving representations of the partitions on the finite set

A partial ordering is defined for monotone projections f: N → N, N = {1, 2,…, n}, such that the class of these mappings is a lattice which is isomorphic to the partition lattice. Thus a partition can be uniquely represented by an element of this class of mappings and the partial ordering of partitions is preserved. Algorithms for computing the join and meet of given partitions are presented.     

Inclusive η production at high pT at the ISR

The inclusive η production cross section at the CERN ISR has been measured for p_T values of up to 11 GeV/c. We find that the $\text{η}\text{π}{}^0$ cross-section ratio has an average value of 0.55 ± 0.07 and varies little with p_T.     

Nonlinear optics in radiatively cooled vapors

We consider the use of a radiatively cooled resonant vapor as a media for 3rd order nonlinear optics processes. The 3rd order nonlinear refractive index coefficient due to both steady state saturation of the atomic polarizability and electrostrictive induced density changes are computed for a radiatively cooled vapor with sodium as an example. For pump detuning on the order of the natural linewidth the electrostrictive and saturation induced nonlinear refractive index coefficients are comparable and several orders of magnitude greater than the highest values yet reported. At pump detunings larger than the natural linewidth the electrostrictive mechanism is shown to dominate in the steady state.     

Monodromy fields on ℤ2

Lattice monodromy fields are defined and the massive scaling regime is controlled.     

Scaling relations for implantation of size-selected Au,Ag, and Si clusters into graphite

The deposition of size-selected clusters represents a new route to the fabrication of truly nanometer-scale surface architectures, e.g., nanopores. We report a systematic experimental study, coupled with molecular dynamics simulations, of the implantation depths of size-selected Au7, Ag7, and Si7 clusters in the model graphite substrate. For impact energies between 1.0 and 5.5 keV, we find that the implantation depth scales linearly with the momentum of the clusters for all three types of cluster. This "universal" behavior is consistent with a (viscous) retarding force proportional to the velocity of the cluster, akin to Stokes's law.     

A new reactivity-based one-pot synthesis of N-acetyllactosamine oligomers

Poly-N-acetyllactosamine oligomer is a type-2 glycan core from which a number of important bioactive glycoconjugates are assembled in vivo. Development of an effective synthesis of N-acetyllactosamine oligomers will therefore provide a new chemoenzymatic entry to this class of complex saccharides. This paper describes the design and synthesis of thioglycoside building blocks, determination of their relative reactivity values, and demonstration of their use in the programmable one-pot synthesis of various N-acetyllactosamine oligomers. Through a combination of segment condensation, the strategy allows for the preparation of larger oligosaccharides with minimal protecting group manipulation, as illustrated in the synthesis of an octasaccharide in a very short period of time.