Hybrid methods for large sparse nonlinear least squares

Hybrid methods are developed for improving the Gauss-Newton method in the case of large residual or ill-conditioned nonlinear least-square problems. These methods are used usually in a form suitable for dense problems. But some standard approaches are unsuitable, and some new possibilities appear in the sparse case. We propose efficient hybrid methods for various representations of the sparse problems. After describing the basic ideas that help deriving new hybrid methods, we are concerned with designing hybrid methods for sparse Jacobian and sparse Hessian representations of the least-square problems. The efficiency of hybrid methods is demonstrated by extensive numerical experiments.This work was supported by the Czech Republic Grant Agency, Grant 201/93/0129. The author is indebted to Jan Vlek for his comments on the first draft of this paper and to anonymous referees for many useful remarks.     

Synthesis and characterization of surface-aminated polypyrrole–silica nanocomposites

 Two synthetic routes to surface-aminated polypyrrole–silica nanocomposite particles have been investigated. Route 1 involved the initial synthesis of homopolypyrrole – silica particles as described previously, followed by surface amination using 3-aminopropyltriethoxy-silane. In Route 2 aminated polypyrrole–silica particles were synthesized directly by copolymerising an N-substituted aminopyrrole comonomer with pyrrole in the presence of an ultrafine silica sol. Both types of aminated particles were characterized in terms of their particle size and morphology, long-term colloid stability and degree of amination using transmission electron microscopy, disc centrifuge photosedimentometry and zeta potential measurements, respectively. Received: 19 May 1998 Accepted: 15 June 1998     

The effects of pH, ionic strength and buffer concentration of mobile phase onR F of acidic compounds in ion-pair TLC

Summary The effects of some factors important in ion-pair, high-performance liquid chromatography were studied in ion-pair, thin-layer chromatography. Tetramethyl and cetyltrimethylammonium salts were used as ion-pairing reagents. As stationary phases, silica gel and chemically bonded reversed-layers (C₁₈) were used. Layers were impregnated with ion-pairing reagent prior to chromatography. In some cases the stationary phase was treated with buffer at different concentrations. The mobile phase contained methanol and water, in one set of experiments buffer, salt for adjustment of ionic strength and ion-pairing reagent were added. The migration behaviour of different benzoic acids was studied. Several problems of ion-pair thin-layer chromatography are discussed. Passed away on 13^th of April, 1998 Presented at: Balaton Symposium on High-Performance Separation Methods, Siófok, Hungary, September 3–5, 1997.     

β‐Cyclodextrin Duplexes That Are Connected through Two Disulfide Bonds: Potent Hosts for the Complexation of Organic Molecules

New tubular host molecules, which are composed of two β‐cyclodextrin macrocycles that are connected through two disulfide bonds, have been prepared by the air‐promoted oxidation of 6^I,6^IV‐dideoxy‐6^I,6^IV‐disulfanyl‐β‐cyclodextrin in aqueous solution. This reaction leads to three products: monomeric intramolecular disulfide and two dimeric species, which are termed as “non‐eclipsed” and “eclipsed” cyclodextrin duplexes. Oxidation at a concentration of the starting thiol of 0.1 mM gave the intramolecular disulfide as the major product whereas a concentration in the millimolar range afforded the dimeric species as the dominant products. The tubular structure of the “non‐eclipsed” isomer was unequivocally determined by X‐ray analysis. The binding affinities of the duplexes to a wide range of compounds, including fluorescent dyes and clinically used drugs Imatinib and Esomeprazol, were studied in water by ITC. For most guest compounds, the experimentally determined K_a values were in the range 10⁷–10⁸ M ^?1. These binding affinities are significantly higher than those found in the literature for analogous complexes with native cyclodextrins. In cases of binding of neutral or anionic guest molecules cyclodextrin duplexes outperformed cucurbiturils. A complex between a duplex and Nile blue was used to investigate its ability to penetrate the cytoplasmic membrane of HeLa cells. We found that the complex accumulated in the cell membrane but did not pass into cytosol. Importantly, the complex did not decompose to a significant extent under high dilution in the cellular environment.     

Synthesis and Complexation properties of N,N’-bis(calix[4]Arenoxyacetyl)Hydrazine Derivative

Heating of p-tert-butylcalix[4]arene bearing acethydrazide moiety at the lower rim in MeCN or PrⁱOH (EtOH) affords the corresponding N,N’-bis(calix[4]arenoxyacetyl)hydrazine derivative. The hydrazinolysis of mono(methoxycarbonylmethoxy)-p-tert-butylcalix[4]-arene in benzene or refluxing biscalixarene hydrazide in benzene in the presence of hydrazine hydrate produces the mixture of 1,2- and 1,3-(N,N’-diacetylhydrazine)-p-tert-butylcalix[4]arenes.     

Studying the characteristics of the photosensitive elements of photodetector matrices based on Si Pt: Si by means of induced potential and transmission electron microscopy

The prospects for the combined use of scanning and transmission electron microscopy in studying defects in the matrix elements of the infrared photodetectors are considered. It is shown that combining these techniques allows us to fully realize the potential of high-voltage transmission microscopy for detecting defects that impair matrix parameters.