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.     

Interaction between Ti-gel and silver, copper, as well as nickel compounds under ultrasound irradiation

Ag-TiO₂, Cu-TiO₂ and Ni-TiO₂ were prepared by sonication. The interactions of Ti-gel with silver, copper and nickel ions under ultrasound irradiation are very different, although these ions can be dispersed very well in titania. The results of EDXA and XRD analysis indicate that Ti-gel does not react with AgCl and crystallizes unaffectedly to form rutile. M(OH)₂ (M = Cu and Ni), on the other hand, favors polycondensation with Ti-gel and affects the crystallization of Ti-gel. CuO favors stabilization of the anatase phase. Ni²⁺ ions tend to incorporate more easily into titania than Cu²⁺ ions do when the samples are calcined. TEM, and BET were also used to characterize the samples.     

Role of Cell Surface Lipopolysaccharides in Escherichia coli K12 adhesion and transport

The influence of bacterial surface lipopolysaccharides (LPS) on cell transport and adhesion has been examined by use of three mutants of Escherichia coli K12 with well-characterized LPS of different lengths and molecular composition. Two experimental techniques, a packed-bed column and a radial stagnation point flow system, were employed to investigate bacterial adhesion kinetics onto quartz surfaces over a wide range of solution ionic strengths. Although the two systems capture distinct deposition (adhesion) mechanisms because of their different hydrodynamics, similar deposition kinetics trends were observed for each bacterial strain. Bacterial deposition rates were directly related to the electrostatic double layer interaction between the bacteria and quartz surfaces, in qualitative agreement with classic Derjaguin-Landau-Verwey-Overbeek (DLVO) theory. However, DLVO theory does not fully explain the deposition behavior for the bacterial strain with the lengthy, uncharged O-antigen portion of the LPS. Neither the length nor the charge characteristics of the LPS molecule directly correlated to deposition kinetics, suggesting a complex combination of cell surface charge heterogeneity and LPS composition controls the bacterial adhesive characteristics. It is further suggested that bacterial deposition behavior is determined by the combined influence of DLVO interactions, LPS-associated chemical interactions, and the hydrodynamics of the deposition system.     

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.