Untangling two systems of noncrossing curves

We consider two systems (α₁, …, α_m) and (β₁, …,β_n) of simple curves drawn on a compact two-dimensional surface M with boundary.     

A Simple Near-Infrared Fluorescent Probe for the Detection of Peroxynitrite

Herein, we report the evaluation and synthesis of a reaction based fluorescent probe DCM-Bpin for the detection of Peroxynitrite (ONOO−). DCM-Bpin exhibits selective fluorescence off-on response for ONOO⁻ over other reactive oxygen species, including H₂O₂. Moreover, DCM-Bpin is biocompatible and has been used to visualize exogenous ONOO⁻ in HeLa cells.     

Capillary gas chromatographic analysis of amino acids in blood and protein hydrolysates as tert.-butyldimethylsilyl derivatives

A method is given for a one-step derivatization and gas chromatography of amino acids in blood and protein hydrolysates. Blood samples are partially purified by solvent extraction. Protein hydrolysates are neutralized with a triethylamine solution. Then tert.-butyldimethylsilyl derivatives of the amino acids are prepared in a one-step procedure and separated on a 30-m fused-silica SE-30 capillary column. Except for tryptophan and cystine, amino acids are eluted within 30 min. Amino acids are derivatized more rapidly than their corresponding trimethylsilyl derivatives and do not degrade on the long fused-silica columns.     

Application of mass spectrometry to the study of fluoropolymers. III. Polyperfluorobut-2-yne

Mass spectra of the volatile fractions from polyperfluorobut-2-yne have been obtained. The polymer appears to be thermally stable up to 300°C and molecules containing up to 12 monomer units have been identified. A regular structure is indicated by the mass spectrum which is characterized by unusually intense doubly charged ions. The endgroups are readily identified, and a conjugated polyolefin structure is indicated.     

Rotational Dynamics of Adamantanecarboxylic Acid in Complex with β-cyclodextrin

The reorientation of 1-adamantanecarboxylic acid (AdCA) within the β-cyclodextrin (β-CD) cavity is investigated by means of multiple-field ¹³C NMR relaxation. The dissociation constant describing the complexation equilibrium is determined using translational diffusion measurements for the guest during a titration by the host in D₂O/DMSO solvent mixture. The changes in apparent diffusion properties of AdCA during the titration are at 25 °C well described assuming the formation of a 1:1 complex, whereas at 0 °C the data indicate the presence of a 2:1 (guest:host) complex. The ¹³C NMR relaxation parameters for the AdCA molecule bound inside the β-CD cavity are extracted. Despite the high association constant, indicating a strong interaction between the two molecules, the guest molecule is quite mobile. The reorientation of the bound AdCA at 25 °C can be described by either the Lipari–Szabo or the axially symmetric rotational diffusion model. The motion is extremely anisotropic: the adamantyl group rotates fast around the β-CD symmetry axis, inside its cylindrical cavity. At lower temperature, the relaxation properties are no longer possible to explain using these models. Instead, the data are analyzed using extended, three-step spectral density of Clore et al. [J. Am. Chem. Soc. 112, 4989 (1990)].     

Non-equilibrium behavior of sticky colloidal particles: beads,clusters and gels

To understand the non-equilibrium behavior of colloidal particles with short-range attraction, we studied salt-induced aggregation of lysozyme. Optical microscopy revealed four regimes: bicontinuous texture, beads, large aggregates, and transient gelation. The interaction of a metastable liquid-liquid binodal and an ergodic to non-ergodic transition boundary inside the equilibrium crystallization region can explain our findings.     

The Kinetics of Ester-Ester Exchange Reactions by Mass Spectrometry

The kinetics of ester-ester exchange reactions between poly(ethy1ene adipate) and poly(trimethy1ene adipate) have been studied by mass spectrometric techniques. Reactions were carried out in the absence of catalyst and solvent. Rate constants for the exchange reaction and corresponding Arrhenius parameters are given.     

When is water not water? Exploring water confined in large reverse micelles using a highly charged inorganic molecular probe

The interior water pool of aerosol OT (AOT) reverse micelles tends toward bulk water properties as the micelle size increases. Thus, deviations from bulk water behavior in large reverse micelles are less expected than in small reverse micelles. Probing the interior water pool of AOT reverse micelles with a highly charged decavanadate (V(10)) oligomer using (51)V NMR spectroscopy shows distinct changes in solute environment. For example, when an acidic stock solution of protonated V(10) is placed in a reverse micelle, the (51)V chemical shifts show that the V(10) is deprotonated consistent with a decreased proton concentration in the intramicellar water pool. Results indicate that a proton gradient exists inside the reverse micelles, leaving the interior neutral while the interfacial region is acidic.     

Eventual Positivity of Hermitian Algebraic Functions and Associated Integral Operators∗

Quillen proved that repeated multiplication of the standard sesquilinear form to a positive Hermitian bihomogeneous polynomial eventually results in a sum of Hermitian squares, which was the first Hermitian analogue of Hilbert’s seventeenth problem in the nondegenerate case. Later Catlin-D’Angelo generalized this positivstellensatz of Quillen to the case of Hermitian algebraic functions on holomorphic line bundles over compact complex manifolds by proving the eventual positivity of an associated integral operator. The arguments of Catlin-D’Angelo involve subtle asymptotic estimates of the Bergman kernel. In this article, the authors give an elementary and geometric proof of the eventual positivity of this integral operator, thereby yielding another proof of the corresponding positivstellensatz.