Air-stable liquid clathrates. 1. Crystal structure of [NBu4][Br3] and reactivity of the [NBu4][Br3]·5 C6H6 liquid clathrate

[NBu₄][Br₃] interacts with C₆H₆ to form an air-stable liquid clathrate. The tribromide anion reacts with phenol to give para-bromophenol in>95% yield. The HBr which is generated in the reaction combines with the Br^– anion to form [Br-H-Br]^–. The latter forms the basis for a new liquid clathrate, [NBu₄][Br-H-Br]·n C₆H₆. The parent salt, [NBu₄][Br₃], crystallizes in the monoclinic space group C2/c witha=12.983(5),b=10.380(7),c=16.222(6) Å,=93.93(3)°, andD _c =1.47 g cm^–3 forZ=4. The final R value is 0.068 based on 787 observed reflections.     

Sensitivity and stability analysis for nonlinear programming

We give a brief overview of important results in several areas of sensitivity and stability analysis for nonlinear programming, focusing initially on qualitative characterizations (e.g., continuity, differentiability and convexity) of the optimal value function. Subsequent results concern quantitative measures, in particular optimal value and solution point parameter derivative calculations, algorithmic approximations, and bounds. Our treatment is far from exhaustive and concentrates on results that hold for smooth well-structured problems.Research supported by National Science Foundation Grant ECS-86-19859 and Grant N00014-89-J-1537 Office of Naval Research.     

Perturbed variations of penalty function methods

Penalty function techniques are well known perturbation methods for solving mathematical programming problems. We define new classes of penalty functions by introducing simple perturbations of classical penalty functions or, equivalently, perturbations of the given problem. Motivation is a recently developed method called Projective SUMT, proposed by McCormick, based on solving the differential equation associated with a barrier function minimizing trajectory. We show that this trajectory-following algorithm is a simple variation of classical SUMT (Sequential Unconstrained Minimization Technique). This leads to numerous additional interpretations, simplified convergence results, duality relationships and extensions. Like SUMT, Projective SUMT is closely related to the approach of Karmarkar.Research supported by Grant ECS-86195859 and NSF N00014-85-K-0052, Office of Naval Research.     

The computation of characteristic classes of lattice gauge fields

AGL(p,C)-valued lattice gauge fieldu on a simplicial complex determines a principalGL(p,C)-bundle if the plaquette products are sufficiently small with respect to the maximum distortion coefficient of the transporters. A representative cocyclec _q for theq ^th Chern class of can be computed on each 2q-simplex by takingc _q() to be the intersection number of a certain singular 2q-cubeM with a Schubert-type variety _q in the space of allp×p matrices. This reduces to the solution of polynomial equations with coefficients coming fromu and thus avoids numerical integration or cooling-type procedures. An application of this method is suggested for the computation of the topological charge of anSU(3)-valued lattice gauge field on a 4-complex.Partially supported by NSF grant DMS 8607168Partially supported by PSC-CUNY and by NSF grant DMS 8805485     

Investigating the interface of superhydrophobic surfaces in contact with water

Neutron reflectivity (NR) is used to probe the solid, liquid, vapor interface of a porous superhydrophobic (SH) surface submerged in water. A low-temperature, low-pressure technique was used to prepare a rough, highly porous organosilica aerogel-like film. UV/ozone treatments were used to control the surface coverage of hydrophobic organic ligands on the silica framework, allowing the contact angle with water to be continuously varied over the range of 160 degrees (superhydrophobic) to <10 degrees (hydrophilic). NR shows that the superhydrophobic nature of the surface prevents infiltration of water into the porous film. Atomic force microscopy and density functional theory simulations are used in combination to interpret the NR results and help establish the location, width, and nature of the SH film-water interface.     

Factors affecting the market penetration of biomass-derived liquid transportation fuels

Applied Biochemistry and Biotechnology - The market for liquid transportation fuels in the United States is about 610×109 L (160×109 gal) annually, with gasoline accounting for about...     

Dendritic molecular capsules for hydrophobic compounds

Reichardt's dye, a highly solvatochromic dye, was encapsulated within poly (glycerol succinic acid) ([Gn]-PGLSA-OH) dendrimers to investigate the interior environment of these dendritic macromolecules. The absorption maximum for the encapsulated Reichardt's dye in water was indicative of a relatively high dielectric constant present within the dye/dendrimer complex. (1)H NMR of the encapsulated complex showed the presence of aromatic protons from Reichardt's dye along with the aliphatic protons of the dendrimer. Additionally, there were substantial changes in T(1) and T(2) times of the encapsulated dye when compared with the free dye, and (1)H NOESY spectra for the complex showed a significant number of intermolecular NOE cross-peaks. These data reveal the close through-space proximity of the dye to the dendrimer and the restricted motion of the encapsulated dye. To demonstrate the potential use of these macromolecules as drug delivery vehicles, the poorly water-soluble anticancer drug 10-hydroxycamptothecin (10HCPT) was encapsulated within a carboxylated PGLSA dendrimer ([G4]-PGLSA-COONa). Cytotoxicity assays with human breast cancer cells showed a significant reduction of cell viability, demonstrating that 10HCPT retains activity upon encapsulation.