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.     

A role of non-hydrogen framework vibrational modes in formation of ferroelectric properties of H-bonded K3H(SO4)2-like materials

An effect of molecular vibrational modes within the dimers [O₃AO–(H/D)OAO₃]³⁻ on behavior of H-bond protons or deuterons is studied theoretically for H-bonded antiferroelectrics and quantum paraelectrics of the M₃(H/D)(AO₄)₂ family (M=alkali metal, A=S, Se). The ‘heavy’ reorganization modes in D-species of this family and both reorganization and promoting modes in corresponding H-analogues are examined. It is shown that the analysis with due regard for the reorganization modes results in insignificant decreasing of the effective tunneling frequency of light nuclei. Hence the reasonable estimations of the critical temperature of the low-temperature phase transition in M₃D(AO₄)₂ materials are available only with additional corrections related to potential profiles of a deuteron. It is noted that in the limits of the proposed model the promoting mode in the case of H-species can favor, in principle, the increasing as well as the decreasing of effective proton level splitting.     

Use of the wittig reaction for synthesizing 2-deoxy-L-glucose

Conclusions The Wittig reaction was carried out between 2,3:4,5-diisopropylidene-al-L-arabinose and tolyloxy-methylenetriphenylphosphorane, and 2-deoxy-L-glucose was synthesized in a high yield.Translated from Izvestiya Akademii Nauk SSSR, Seriya Khimicheskaya, No. 4, pp. 892–895, April, 1970.     

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*.     

Microcalorimetric Study of Water Adsorption on Initial and Polyfluoroalkylated Silicas

Water adsorption on initial and modified Silochrom samples was studied by the adsorption calorimetry. Integral heats of immersional wetting by water were measured simultaneously. It was shown that hydroxyl groups both free and sterically screened by a modifier remain on the modified Silochrom surface. Concentrations of these groups and OH groups chemically interacted with the modifier were estimated. The heat of reaction of water molecules with a free surface OH groups of modified sorbents was determined (≈60 kJ/mol). It was found that the modifying layers of the sorbents are getting loose under the effect of adsorbed water, and water molecules gain access to the sterically screened OH groups; the heat of water interaction with these groups is 54–55 kJ/mol. The energy is consumed for getting the modifying layers loose and the rupture of point contacts between Aerosil particles of the secondary structure of both initial and modified Silochrom that significantly affects the heat of immersion, the differential heat of adsorption, the form of the heat release curve, and the dependence of the differential heat on the adsorption value.     

Ion-exchange equilibria and exchange heats on clinoptilolite involving singly-charged cations

Isotherms and integral heats of exchange of alkali metal, ammonium, and silver cations on sodium clinoptilolite were measured. Exchange involving K₊, NH₄ ⁺, Cs⁺, and Ag⁺ displacing cations was found to be exothermic for all occupancies of the clinoptilolite exchange sites. Exchange was exothermic for Li₊ cations up to = 0.15. The dependence of the differential ion-exchange heats on was determined. Clinoptilolite was found to have two types of exchange sites with different heats of ion exchange. The experimental data were used to calculate the selectivity coefficients, thermodynamic constants, and ion-exchange entropy. These findings are discussed relative to the differences in the cation properties and structural features of clinoptilolite.A. V. Dumanskii Institute of Colloid Chemistry and the Chemistry of Water, National Academy of Sciences of Ukraine, 42 Prospekt Akademika Vernadskogo, 252680 Kiev-142, Ukraine. Translated from Teoreticheskaya i Éksperimental'naya Khimiya, Vol. 32, No. 5, pp. 315–319, September–October, 1996. Original article submitted February 12, 1996.