Nilpotence and finite H-spaces

Zabrodsky asked when is the iterated commutator mapX ⁿ →X for a connected associative H-spaceX a null map. In this paper we reduce this question to a cohomological question and answer it in several cases. Supported by an NSF Presidential Young Investigator award and the Sloan Foundation.     

Infrared-induced reactivity of N2O on small gas-phase rhodium clusters

Far- and mid-infrared multiple photon dissociation spectroscopy has been employed to study both the structure and surface reactivity of isolated cationic rhodium clusters with surface-adsorbed nitrous oxide, Rh(n)N(2)O(+) (n = 4-8). Comparison of experimental spectra recorded using the argon atom tagging method with those calculated using density functional theory (DFT) reveals that the nitrous oxide is molecularly bound on the rhodium cluster via the terminal N-atom. Binding is thought to occur exclusively on atop sites with the rhodium clusters adopting close-packed structures. In related, but conceptually different experiments, infrared pumping of the vibrational modes corresponding with the normal modes of the adsorbed N(2)O has been observed to result in the decomposition of the N(2)O moiety and the production of oxide clusters. This cluster surface chemistry is observed for all cluster sizes studied except for n = 5. Plausible N(2)O decomposition mechanisms are given based on DFT calculations using exchange-correlation functionals. Similar experiments pumping the Rh-O stretch in Rh(n)ON(2)O(+) complexes, on which the same chemistry is observed, confirm the thermal nature of this reaction.     

High resolution laser spectroscopy of the titanium monohalides, TiCl and TiBr

The electronic spectra of the titanium monohalides, TiCl and TiBr, have been investigated in the blue-violet region using a laser ablation molecular beam spectrometer. Five subbands assigned as ⁴Γ_5/2-X⁴Φ_3/2 (0, 0), ⁴Γ_5/2-X⁴Φ_3/2 (1, 1), ⁴Γ_5/2-X⁴Φ_5/2 (0, 0), ⁴Γ_7/2-X⁴Φ_5/2 (0, 0) and ⁴Γ_7/2-X⁴Φ_7/2 (0, 0) were observed and recorded at both low and high-resolution for titanium monochloride. A Hund’s case (a) rotational analysis has been carried out for the ⁴⁸Ti³⁷Cl and ⁴⁸Ti³⁵Cl isotopic species, and polynomial analyses for these, as well as the ⁴⁶Ti³⁵Cl, ⁴⁷Ti³⁵Cl, ⁴⁹Ti³⁵Cl, and ⁵⁰Ti³⁵Cl isotopologues have been completed. The same spectral region yielded several molecular transitions for titanium monobromide, 10 of which were recorded at high resolution. Six of these have been attributed to a ⁴Γ-X⁴Φ electronic transition at 23 484 cm⁻¹, while the remaining four have been assigned to a second ⁴Γ-X⁴Φ electronic transition at 23 613 cm⁻¹. A Hund’s case (a) global analysis has been carried out for the ⁴⁸Ti⁷⁹Br and ⁴⁸Ti⁸¹Br isotopologues.     

Note on a family of economical sixth order finite difference methods for non-linear 2-point boundary value problems

In this note the sixth order method of Chawla [1] is generalized to give a parameterized family of methods.     

Non-specific binding in the affinity chromatography of chymotrypsin

The strong and specific binding of chymotrypsin on chromatographic columns containing agarose substituted with N--amino Caproyl- -tryptophan methyl ester is abolished when the -amino groups on the surface of the enzyme are reacted with acetic anhydride. Because the catalytic properties of the acetylated chymotrypsin are identical to those of the underivatized enzyme, it is concluded that the high affinity of chymotrypsin for this column is not due solely to biospecific inhibitor binding, which is by itself very weak, but requires reinforcement through weak non-specific interactions with the column support. It is postulated that these non-specific interactions include electrostatic interactions between agarose matrix and positively charged lysyl residues on the enzyme. The results demonstrate for the first time that residues on the surface of an enzyme not associated with its active site can play an important role in some chromatographic systems previously thought to be based on purely biospecific interactions.     

Synthesis of protected racemic β,γ-unsaturated-α-amino acids via γ-phenylseleno-α,β-unsaturated esters

Oxidative rearrangement of γ-phenylseleno-α,β-unsaturated esters ($\text{1}$) with the N-chlorosuccinimide/N,N-diisopropylethylamine/alkyl carbamate reagent combination affords preparatively useful yields of protected β,γ-unsaturated-α-amino acids ($\text{2}$).     

Peripheral and ADI hopscotch methods for two dimensional parabolic and elliptic equations with a mixed term

The peripheral and ADI hopscotch methods are extended to solve problems in two space dimensions with a mixed derivative term. The method is compared numerically with existing hopscotch methods.     

The adsorption of nitric oxide on W(110) at 300 K: An electron spectroscopic study

Nitric oxide adsorbs dissociatively onto W(110) at 300 K. The simplest interpretation requires adsorption into three states. In the first of these N and O penetrate the surface. In the second state N and O form an overlay er on the W(110) surface. The third state also involves surface penetration but this is deeper than for state 1. The adsorbate stoichiometry was 1:1 throughout adsorption at 300 K. The occupancy of each state was similar after a 300 L exposure when the total amount adsorbed exceeded 17 (±2) × 10¹⁸ atoms m^?2.     

Extremal bipartite subgraphs of cubic triangle-free graphs

A cubic triangle-free graph has a bipartite subgraph with at least 4/5 of the original edges. Examples show that this is a best possible result.