On the convergence of the exponential multiplier method for convex programming

In this paper, we analyze the exponential method of multipliers for convex constrained minimization problems, which operates like the usual Augmented Lagrangian method, except that it uses an exponential penalty function in place of the usual quadratic. We also analyze a dual counterpart, the entropy minimization algorithm, which operates like the proximal minimization algorithm, except that it uses a logarithmic/entropy proximal term in place of a quadratic. We strengthen substantially the available convergence results for these methods, and we derive the convergence rate of these methods when applied to linear programs.Research supported by the National Science Foundation under Grant DDM-8903385, and the Army Research Office under Grant DAAL03-86-K-0171.     

Effects of concentrated matrices on the determination of trace levels of platinum and gold in aqueous samples using solvent extraction—Zeeman effect graphite furnace atomic absorption spectrometry and inductively coupled plasma—mass spectrometry

Two methods of determining trace levels of platinum and gold in aqueous solutions with high concents of total dissolved solids were investigated. The first involves preconcentration and separation of the precious metals from the interfering matrix by solvent extraction, followed by graphite furnace atomic absorption spectrometry (GFAAS) with Zeeman effect background correction. The direct determination of Pt and Au in solutions of high ionic strength by GFAAS is not desirable because of interference between elements in the matrix and the analyte, increased imprecision of analysis, greatly increased background absorbance leading to increased detection limits and rapid deterioration of the graphite tube. All the extraction methods for gold examined in this study resulted in decreased imprecision, increased sensitivity and lower background absorbance compared with direct measurements on the aqueous solution. All techniques also exhibited good recoveries (> 8%) and reproducibilities (relative standard deviation < 10%). The highest sensitivities for gold extraction from distilled water were obtained for dibutyl sulfide (DBS)—toluene and the lowest for cyanide—dibutyl ketone. The degree of extraction of Au was, however, dependent on the composition of the solution, indicating that standard and sample matrices should be closely matched even when employing solvent extraction. Solvent extraction was generally less successful for Pt. In order to obtain an acceptable imprecision in the Pt extractions, it was found that the use of SnCl₂ as a labilizing agent is essential for most of the techniques investigated.The second method was direct measurement by inductively coupled plasma mass spectrometry (ICP—MS). ICP—MS offers the advantages of a very low detection limit (100 ng l^?1 or better) without preconcentration and a large dynamic range. However, severe matrix effects can occur in concentrated solutions. Whereas high concentrations in solution of both sodium perchlorate and sodium chloride decrease the sensitivity, the presence of sulfide and natural organic (fulvic) acid increase the sensitivity for Pt and Au by a factor of up to 4. Sulfate, on the other hand, decreases the sensitivity of ICP-MS for Pt. The method of standard additions or isotope dilution is recommended for routine use to circumvent this problem, especially when the nature of the matrix is unknown or cannot be easily matched in the standards.     

Anisotropic local motions and location of amide protons in proteins

A new method has been developed to obtain dynamic and structural information about peptide planes in proteins by a combination of measurements of weak short-range cross-correlation rates R(H(N)N/NC') that are due to concerted fluctuations of the H(N)-N and N-C' dipole-dipole interactions and stronger long-range cross-correlation rates R(C'H(N)/H(N)N) and R(NH(N)/H(N)C(alpha)). The rates were interpreted using the axially symmetric Gaussian axial fluctuation model (GAF). The oscillation amplitudes as well as the positions of H(N) atoms with respect to peptide planes in ubiquitin were determined. Most N-H(N) bonds were found not to lie exactly along the bisector of the N-C' and N-C(alpha) bonds but to be slightly tilted toward the carbon-terminal side of the peptide.     

High-resolution electron spin resonance spectroscopy of XeF* in solid argon. The hyperfine structure constants as a probe of relativistic effects in the chemical bonding properties of a heavy noble gas atom

Xenon fluoride radicals were generated by solid-state chemical reactions of mobile fluorine atoms with xenon atoms trapped in Ar matrix. Highly resolved electron spin resonance spectra of XeF* were obtained in the temperature range of 5-25 K and the anisotropic hyperfine parameters were determined for magnetic nuclei 19F, 129Xe, and 131Xe using naturally occurring and isotopically enriched xenon. Signs of parallel and perpendicular hyperfine components were established from analysis of temperature changes in the spectra and from numerical solutions of the spin Hamiltonian for two nonequivalent magnetic nuclei. Thus, the complete set of components of hyperfine- and g-factor tensors of XeF* were obtained: 19F (Aiso=435, Adip=1249 MHz) and 129Xe (Aiso=-1340, Adip=-485 MHz); g(parallel)=1.9822 and g(perpendicular)=2.0570. Comparison of the measured hyperfine parameters with those predicted by density-functional theory (DFT) calculations indicates, that relativistic DFT gives true electron spin distribution in the 2Sigma+ ground-state, whereas nonrelativistic theory underestimates dramatically the electron-nuclear contact Fermi interaction (Aiso) on the Xe atom. Analysis of the obtained magnetic-dipole interaction constants (Adip) shows that fluorine 2p and xenon 5p atomic orbitals make a major contribution to the spin density distribution in XeF*. Both relativistic and nonrelativistic calculations give close magnetic-dipole interaction constants, which are in agreement with the measured values. The other relativistic feature is considerable anisotropy of g-tensor, which results from spin-orbit interaction. The orbital contribution appears due to mixing of the ionic 2Pi states with the 2Sigma+ ground state, and the spin-orbit interaction plays a significant role in the chemical bonding of XeF*.     

A single-site model for divalent transition and heavy metal adsorption over a range of metal concentrations

Metal adsorption data over a range of surface coverages typically are characterized by curvilinear metal adsorption isotherms. These isotherms generally have a slope of 1 at low surface coverage and a shallower slope at higher surface coverages. The curvature of metal adsorption isotherms with increasing surface coverage is frequently interpreted in terms of sequential adsorption onto different types of surface sites, multinuclear surface complexation, or nonideality of metal adsorption. We demonstrate that the curvature of metal adsorption isotherms can also be attributed to changes in surface charge and potential that depend on the predominant type of metal surface complex. A single-site extended triple-layer model is used to reinterpret previously studied metal adsorption isotherms and pH edges for a wide variety of metals (Cd2+, Co2+, Cu2+, Pb2+, and Zn2+) and solids (goethite, hydrous ferric oxide, corundum, and magnetite) in different electrolyte solutions (NaNO3 and NaClO4). Only metal adsorption on ferrihydrite at very low surface coverages is not consistent with the single-site triple-layer model. This discrepancy might be explained if ferrihydrite is in fact not a single phase but a mixture of two or more phases. Metal surface coverages ranging from 10(-4) to 10.2 mmol/m2 on the other minerals can be accounted for with a single-site extended triple-layer model if appropriate metal adsorption reactions are chosen. In addition, several examples suggest that, within the context of the model, surface complexation schemes can be established that describe metal adsorption over both a wide range of surface coverage and a wide range of ionic strength.     

Formation of supported size-controlled nanoparticles of sulfated zirconia

Methods of the preparation of catalysts for alkane skeletal isomerization based on uniform nanoparticles of sulfated zirconia anchored to different supports were investigated. These catalysts were characterized by using the ICP, HRTEM and BET techniques. The activities of the catalysts in the reaction of n-butane isomerization were measured and compared with those of bulk catalysts.     

2-Azabicyclo[2.2.1]heptane-3-carboxylic acid - A bicyclic proline

Diels-Alder reaction of cyclopentadiene and methyl N-carbobenzyloxy-2-iminoacetate generated in situ from methyl 2-chloro-N-carbobenzyloxyglycinate by triethylamine gave the N-carbobenzyloxy unsaturated bicyclic proline ester. This was converted in two steps to 2-azabicylo[2.2.1]heptane-3-carboxylic acid. In contrast to N-carbobenzyloxy-L-proline methyl ester, the corresponding bicyclic proline ester was resistant to hydrolysis catalyzed by carboxypeptidase Y.     

Local dense structural heterogeneities in liquid water from ambient to 300 MPa pressure: evidence for multiple liquid-liquid transitions.

Difference and double-difference near-infrared DO-D and HO-H stretching overtone (2nuOD and 2nuOH) spectroscopy and a rigorous (physically substantiated) band deconvolution technique were applied to reveal three different kinds of inherent (interstitial) structures of liquid water, which determine its high density (compared to ice lh under ambient conditions), its compressibility (under hydrostatic pressure, up to 300MPa), and its high fragility (manifested under temperature variation). Our data processing allowed the rigorous discrimination of up to six vibrational components. On the basis of an extensive comparative analysis combined with available structural data (X-ray and neutron scattering) and molecular dynamics (MD) simulations for liquid water, as well as with experimental and computed data for small non-tetrahedrally arranged water clusters, the major four components could be ascribed to: i) The basic lh icelike substructure; ii) the temperature-dependent remote interstitial "defects" due to tetrahedral displacements (primarily responsible for transport properties); iii) the interstitial "defects" most probably arranged in quasiplanar noncyclic tetramers (totally absent in the ice structure); and iv) the interstitial "defects" formed with increasing pressure, probably arranged in cubic water octamers and composed of two pairs of noncyclic and cyclic tetramer fragments. The latter structures include, essentially, bent hydrogen bonds stabilized by resonance effects.     

Fast reduction of a copper center in laccase by nitric oxide and formation of a peroxide intermediate

The rapid reduction of one of the copper atoms (type 2) of tree laccase by nitric oxide (NO) has been detected. Addition of NO to native laccase in the presence of oxygen leads to EPR changes consistent with fast reduction and slow reoxidation of this metal center. These events are paralleled by optical changes that are reminiscent of formation and decay of the peroxide intermediate in a fraction of the enzyme population. Formation of this species is only possible if the trinuclear copper cluster (type 2 plus type 3) is fully reduced. This condition can only be met if, as suggested previously, a fraction of the enzyme contains both type 3 coppers already reduced before addition of NO. Our data are consistent with this assumption. We have suggested recently that fast reduction of copper is the mechanism by which NO interacts with the oxidized dinuclear center in cytochrome c oxidase. The present experiments using laccase strongly support this view and suggest this reaction as a general mechanism by which copper proteins interact with NO. In addition, this provides an unexploited way to produce a stable peroxide intermediate in copper oxidases in which the full complement of copper atoms is present. This enables the O-O scission step in the catalytic cycle to be studied by electron addition to the peroxide derivative through the native electron entry site, type 1 copper.     

Catalytic Reduction of Hydrazine to Ammonia with MoFe(3)S(4)-Polycarboxylate Clusters. Possible Relevance Regarding the Function of the Molybdenum-Coordinated Homocitrate in Nitrogenase

The catalytic function of the previously synthesized and characterized [(L)MoFe(3)S(4)Cl(3)](2)(-)(,3)(-) clusters (L = tetrachlorocatecholate, citrate, citramalate, methyliminodiacetate, nitrilotriacetate, thiodiglycolate) and of the [MoFe(3)S(4)Cl(3)(thiolactate)](2)(4)(-) and [(MoFe(3)S(4)Cl(4))(2)(&mgr;-oxalate)](4)(-) clusters in the reduction of N(2)H(4) to NH(3) is reported. In the catalytic reduction, which is carried out at ambient temperature and pressure, cobaltocene and 2,6-lutidinium chloride are supplied externally as electron and proton sources, respectively. In experiments where the N(2)H(4) to the [(L)MoFe(3)S(4)Cl(3)](n)()(-) catalyst ratio is 100:1, and over a period of 30 min, the reduction proceeds to 92% completion for L = citrate, 66% completion for L = citramalate, and 34% completion for L = tetrachlorocatecholate. The [Fe(4)S(4)Cl(4)](2)(-) cluster is totally inactive and gives only background ammonia measurements. Inhibition studies with PEt(3) and CO as inhibitors show a dramatic decrease in the catalytic efficiency. These results are consistent with results obtained previously in our laboratory and strongly suggest that N(2)H(4) activation and reduction occur at the Mo site of the [(L)MoFe(3)S(4)Cl(3)](2)(-)(, 3)(-) clusters. A possible pathway for the N(2)H(4) reduction on a single metal site (Mo) and a possible role for the carboxylate ligand are proposed. The possibility that the Mo-bound polycarboxylate ligand acts as a proton delivery "shuttle" during hydrazine reduction is considered.