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.     

Production and characterisation of polyclonal antibodies to a derivative of 3-amino-2-oxazolidinone, a metabolite of the nitrofuran furazolidone

Polyclonal antibodies were produced to detect 3-amino-2-oxazolidinone (AOZ), a stable metabolite of the nitrofuran antibiotic furazolidone, following derivatisation with o-nitrobenzaldehyde. A carboxyphenyl derivative of AOZ was prepared, purified and conjugated to immunogenic carrier protein. Six antisera were produced from the immunisation of seven rabbits using various immunogen doses and time-scales. IC₅₀ values, as determined by competitive enzyme-linked immunosorbent assay (ELISA) suggested that reducing immunogen dose from 0.3 to 0.05 mg, while lengthening rest periods between booster immunisations from 2 to 8 weeks, increased the sensitivity of the antibodies to 3-{[(2-nitrophenyl)methylene]amino}-2-oxazolidinone (NPAOZ) from 3.8 to 0.3 μg l⁻¹. An IC₅₀ of 0.065 μg l⁻¹ (AOZ in the form of NPAOZ) was achieved with antiserum R670 by altering ELISA conditions. This antibody was highly specific for NPAOZ and did not cross-react with various nitrofuran metabolites, their nitrophenyl derivatives or a range of veterinary drugs. Antibody R670 is suitable for incorporation into an immunoassay for AOZ with sufficient sensitivity to satisfy current criteria for monitoring of veterinary drug residues. This is the first publication of an antibody for detection of a nitrofuran metabolite.