New results for virial coefficients of hard spheres inD dimensions

We present new results for the virial coefficientsB _k for κ<- 10 for hard spheres in dimensionsD = 2,..., 8.     

On the spectral picture of an irreducible subnormal operator II

In this paper we show that the spectral picture of an irreducible subnormal operator may be arbitrarily prescribed subject only to certain natural necessary conditions. This completes work begun by the second author.

     

On the cover time of random walks on graphs

This article deals with random walks on arbitrary graphs. We consider the cover time of finite graphs. That is, we study the expected time needed for a random walk on a finite graph to visit every vertex at least once. We establish an upper bound ofO(n ²) for the expectation of the cover time for regular (or nearly regular) graphs. We prove a lower bound of (n logn) for the expected cover time for trees. We present examples showing all our bounds to be tight.Mike Saks was supported by NSF-DMS87-03541 and by AFOSR-0271. Jeff Kahn was supported by MCS-83-01867 and by AFOSR-0271.     

High-throughput purification of combinatorial libraries I: a high-throughput purification system using an accelerated retention window approach

We have developed a high-throughput purification system to purify combinatorial libraries at a 50-100-mg scale with a throughput of 250 samples/instrument/day. We applied an accelerated retention window method to shorten the purification time and targeted one fraction per injection to simplify data tracking, lower QC workload, and simplify the postpurification processing. First, we determined the accurate retention time and peak height for all compounds using an eight-channel parallel LC/UV/MS system, and calculated the specific preparative HPLC conditions for individual compounds. The preparative HPLC conditions include the compound-specific gradient segment for individual compounds with a fixed gradient slope and the compound-specific UV or ELSD threshold for triggering a fraction collection device. A unique solvent composition or solvent strength was programmed for each compound in the preparative HPLC in order to elute all compounds at the same target time. Considering the possible deviation of the predicted retention time, a 1-min window around the target time was set to collect peaks above a threshold based on UV or ELSD detection. Dual column preparative instruments were used to maximize throughput. We have purified more than 500 000 druglike compounds using this system in the past 3 years. We report various components of this high-throughput purification system and some of our purification results.     

Vector-spinor space and field equations

Generalizing the work of Einstein and Mayer, it is assumed that at each point of space-time there exists a vector-spinor space with N_v vector dimensions and N_s spinor dimensions, where N_v=2k and N_s=2 ^k, k3. This space is decomposed into a tangent space with4 vector and4 spinor dimensions and an internal space with N_v–4 vector and N_s–4 spinor dimension. A variational principle leads to field equations for geometric quantities which can be identified with physical fields such as the electromagnetic field, Yang-Mills gauge fields, and wave functions of bosons and fermions.     

Signal amplification and detection via a supramolecular allosteric catalyst

The design of a supramolecular allosteric catalyst system for catalytic signal amplification and detection is presented. The catalyst was switched "on" by the introduction of an analyte that also behaves as an allosteric activator. Concentrations of Cl- ions as low as 800 nM were catalytically amplified and detected. The signal was transduced via a pH-sensitive fluorescent probe and observed visually using a laboratory, handheld UV lamp and by spectrophotometry. Furthermore, the allosteric effect was quantified using gas chromatography for a range of Cl- concentrations. This three-part detection scheme involving analyte binding, allosteric catalyst activation, and signal transduction represents a new approach to small-molecule detection.     

Electronically-coupled MM quadruply-bonded complexes of molybdenum and tungsten

The reaction of M2(O2CBu(t))4 (M = Mo, W) with a dicarboxylic acid in toluene yields compounds of general formula [M2]-O2C-X-CO2-[M2] ([M2] = M2(O2CBu(t))3; X = conjugated spacer). The M2 units are electronically coupled via interactions between the M2 delta and dicarboxylate pi* orbitals, and the magnitude of this coupling is revealed by electronic structure calculations and spectroscopic data. These compounds show intense metal to ligand charge transfer (MLCT) absorptions in the visible region of the electronic spectrum that are temperature and solvent dependent. Evidence of electronic coupling is seen in their cyclic voltammograms, which show two successive one-electron oxidations. The extent of electronic coupling in the mixed valence radical cations [M2]-O2C-X-CO2-[M2]+, generated by oxidation with one equivalent of AgPF6 or FeCp2PF6, is evaluated by EPR and UV-vis-NIR spectroscopic data, and delocalized behavior is observed in compounds with W2 units separated by up to 13.6 angstroms. The simplicity of the frontier M2 orbital interactions with the bridge pi orbitals provides a convenient system with which to study electron transfer in mixed valence systems, as compared to the extensively studied, but more complicated, dinuclear t(2g)6/t(2g)5 mixed valence compounds. Oligomeric and polymeric compounds incorporating M2 units have also been synthesized, having general formula [M2(O2CR)2(O2C-Thio-CO2)]n (Thio = n-hexyl substituted ter- and quinque-thiophenes). They can be deposited as thin films by spin coating, and show photoluminescence and electroluminescence. These metallo-polythiophenes show potential for application in electronic materials. (     

Peptide tic-tac-toe: heterotrimeric coiled-coil specificity from steric matching of multiple hydrophobic side chains

Specific coiled-coil heterotrimers result from steric matching of hydrophobic core side chains. A 2:1 heterotrimer is formed by peptides containing alanine or cyclohexylalanine, respectively, at a central core residue. Detailed thermodynamic analysis reveals that the designed complex is considerably more stable than the corresponding alanine homotrimer (deltaT(m) = 25 degrees C, deltadeltaG(unf) = 4.5 kcal/mol), while control complexes with naphthylalanine or cyclopropylalanine peptides are much less stable. However, the cyclohexylalanine homotrimer is of comparable stability to the 2:1 complex, prompting an investigation of multiply substituted peptides. A specific 1:1:1 heterotrimer is formed from three independent peptide strands, each bearing one large (cyclohexylalanine) and two small (alanine) side chains at the same three core positions but in different order. The combined impact of three substitutions improves specificity to the point where each pure peptide and all pairwise equimolar mixtures form significantly less stable complexes (deltaTm = 22-24 degrees C). The capacity for specific complex formation governed by multiple unnatural core side chains should facilitate design of numerous new peptide assemblies.