The Newton modified barrier method for QP problems

The Modified Barrier Functions (MBF) have elements of both Classical Lagrangians (CL) and Classical Barrier Functions (CBF). The MBF methods find an unconstrained minimizer of some smooth barrier function in primal space and then update the Lagrange multipliers, while the barrier parameter either remains fixed or can be updated at each step. The numerical realization of the MBF method leads to the Newton MBF method, where the primal minimizer is found by using Newton's method. This minimizer is then used to update the Lagrange multipliers. In this paper, we examine the Newton MBF method for the Quadratic Programming (QP) problem. It will be shown that under standard second-order optimality conditions, there is a ball around the primal solution and a cut cone in the dual space such that for a set of Lagrange multipliers in this cut cone, the method converges quadratically to the primal minimizer from any point in the aforementioned ball, and continues, to do so after each Lagrange multiplier update. The Lagrange multipliers remain within the cut cone and converge linearly to their optimal values. Any point in this ball will be called a hot start. Starting at such a hot start, at mostO(In In ^-1) Newton steps are sufficient to perform the primal minimization which is necessary for the Lagrange multiplier update. Here, >0 is the desired accuracy. Because of the linear convergence of the Lagrange multipliers, this means that onlyO(In ^-1)O(In In ^-1) Newton steps are required to reach an -approximation to the solution from any hot start. In order to reach the hot start, one has to perform Newton steps, wherem characterizes the size of the problem andC>0 is the condition number of the QP problem. This condition number will be characterized explicitly in terms of key parameters of the QP problem, which in turn depend on the input data and the size of the problem.Partially supported by NASA Grant NAG3-1397 and National Science Foundation Grant DMS-9403218.     

Uncertainty of the Thermal Conductivity Measurement Using the Transient Hot Wire Method

This work deals with uncertainty analysis of the thermal conductivity measurement using the transient hot wire method. The characterization is made from a sample of low-density, polyethylene BRALEN SA 200-22. The utilized experimental data are obtained from the test measurements performed on the air at room temperature. The sources of measurement errors are analyzed and the uncertainty of the measured value of the thermal conductivity is evaluated. The analysis shows that in the present case the uncertainty of the thermal conductivity measurement is about ±3.3% for 68% confidence level.This revised version was published online in November 2005 with corrections to the Cover Date.     

One-dimensional rigorous hole theory of fluids: Internally constrained ensembles

A hole in a fluid is specified in a well-defined manner. The concentration of holes is a thermodynamic property of the fluid and we derive this concentration in three different ensembles for a one-dimensional fluid of hard rods. The thermodynamics of these rigorously defined holes is developed, and the properties of holes are explored. The ensemble in which the concentration of holes is maintained fixed exhibits dramatic properties. Finally, pair correlation functions for hard rods in the various ensembles are computed. Contrary to a frequently made assumption, the equilibrium number of holes is found to never be proportional to the probability of finding a single hole in the fluid. Constraining the concentration of holes as well as the density leads to dramatic structural effects prominently displayed by the pair correlation function. The ensemble in which the concentration of holes is fixed is an example of an internally constrained metastable system.     

Inner shell structure of heavy atoms

The inner-shell structure of some heavy atoms is examined using a self-consistent relativistic local density method. Ar(K), Kr(K) and Xe (K,L ₁,L ₂ andL ₃) binding energies and {ie863-1} (hyper-satellite) energies of Tl, Hg and Tm are calculated. The results are compared with available experimental data. A part of this work was presented byMPD at the Trieste International Symposium on “Core level excitations in atoms, molecules and solids,” 22–26 June 1981, Extended Abstracts (ed.) E Tosatti, ICTP Report No. 89/81 p. 11.     

Hole Burning and Fluorescence Spectra of Sol-Gel Derived Sm2+-Doped Glasses

Sm2+-doped glasses in the system of Al2O3-SiO2 were prepared by sol-gel processing of metal alkoxides and reacting with H2 gas at 800°C. The hole burning properties of these glasses were investigated. The holes were burned in the 7F0 5D0 line of the Sm2+ ions using a DCM dye laser at 77 K. The hole depth increased with increasing the laser irradiation time, reaching up to 15% of the total intensity within a few hundred seconds. The hole width was 3 cm–1 full width at half maximum. Fluorescence line narrowing spectra of the 5D0 7 F1 transition were analyzed to study the local structure surrounding the Sm2+ ion. It is concluded that the Sm2+ ions are closely coordinated with nine oxygens of the AlO6 group in aluminosilicate glasses and that the addition of Al3+ ions into glass induces an increase in the coordination number of the Sm2+.     

Rapid determination of panaxynol in a traditional Chinese medicine of Saposhnikovia divaricata by pressurized hot water extraction followed by liquid-phase microextraction and gas chromatography-mass spectrometry

Panaxynol is a bioactive component in traditional Chinese medicines (TCMs), such as Saposhnikovia divaricata and Panax ginseng. In the work, two solvent-free sample techniques of pressurized hot water extraction (PHWE) and headspace liquid-phase microextraction (HS-LPME) were combined and developed for the determination of panaxynol in a TCM of S. divaricata. Panaxynol in the TCM samples from different growing areas was extracted by PHWE in dynamic mode, followed by extraction and concentration with HS-LPME and analysis with gas chromatography-mass spectrometry (GC-MS). The PHWE and HS-LPME parameters were optimized and the method validations were studied. Panaxynol in S. divaricata from four different growing areas was quantitatively analyzed by internal standard method. These results have shown that PHWE-LPME-GC-MS is a simple, rapid, efficient and low-cost method for the determination of panaxynol in TCMs and is a potential tool for TCM quality assessment.     

Effects of pressure and solvent on the diffusion of aromatic compounds through polymers

The diffusion of six azo and five anthraquinone derivatives through nylon 6, poly(ethylene terephthalate) and secondary cellulose acetate films were studied under high hydrostatic pressures of up to 3000 bar and at temperatures 80–130 °C, by analyzing the diffusion profiles yielded in a stacked multiple film, placed in the solution of the diffusant. It was found that the diffusion coefficient,D, of the diffusant decreased with increasing pressure, giving a linear relationship between InD and the pressure, the slope of which gave the activation volume for the diffusion,V . It was revealedV increased linearly with increasing intrinsic molecular volume of the diffusant,V _w , the slopes being different between the azo and the anthraquinone derivatives. The ratio ofV toV _w (V /V _w ) ranged from 0.13 to 0.93, depending in a sensitive manner on the degree of swelling of the polymer matrix which in turn was varied by the solvent. The overall results could be explained in accordance with the formulation,V _{f, local} +V =V _w , whereV _{f, local} represents the free volume contribution. It was proposed thatV _w is increased by solvation when the solvent is good for the diffusant.     

Eu<Superscript>3+</Superscript>-fluorescence properties in nano-crystallized SnO<Subscript>2</Subscript>-SiO<Subscript>2</Subscript> glass-ceramics

Fluorescence and spectral hole burning properties of Eu³⁺ ions were studied in nanocrystals-precipitated SnO₂-SiO₂ glasses. The glasses were prepared to contain various amount of Eu₂O₃ using the sol-gel method, in which SnO₂ nanocrystals were precipitated by heating in air. In the glasses containing Eu₂O₃ less than 1%, the Eu³⁺ ions were preferentially doped in the SnO₂ nanocrystals and their fluorescence intensities were enhanced by the energy transfer due to the recombination of electrons and holes excited in SnO₂ crystals. The SnO₂ nanocrystals-precipitated glasses exhibited the persistent spectral holes with the depth of ∼25% of the total fluorescence intensities of the Eu³⁺ ions. With the increasing Eu₂O₃ concentration, the amount of SnO₂ nanocrystals decreased and the Sn⁴⁺ ions formed the random glass structure together with the silica network. This structure change induced the fluorescence intensities and the hole depth to decrease.     

Application of Hot Press Sintering to Na2O-B2O3-SiO2 Gels Containing Quantum Dots for Lowering of Densification Temperature

Na₂O-B₂O₃-SiO₂ (NBS) gels containing a large amount of CdS quantum-dots (10 wt%) were densified using the hot press (HP) sintering method. By HP treatment, full-densification temperature could be lowered by about 40°C than that of the normal non-pressing (NP) heat treatment. Exciton absorption of CdS quantum-dots in HP-sample showed a large blue shift compared with that in the NP sample, and the size-distribution of CdS dots remained very sharp, with a mean particle diameter d = 3.66 nm and a standard deviation of = 0.72. HP pressure had a large effect on the reduction of sintering temperature and time, resulting in the suppression of the aggregation and growth of CdS quantum-dots in NBS glasses.     

Formation of different products during photo-catalytic reaction on TiO<Subscript>2</Subscript> suspension in water with and without 2-propanol under diverse ambient conditions

Studies on photo-catalytic reduction of CO₂ using TiO₂ photo-catalyst (0.1%, w/v) as a suspension in water was carried out at 350 nm light. CO₂ from both commercially available source, as well as generated in situ through 2-propanol oxidation, was used for this study. The photolytic products such as hydrogen (H₂), carbon monoxide (CO) andmethane (CH₄) generated were monitored in TiO₂ suspended aqueous solution with and without a hole scavenger, viz., 2-propanol. Similar photolytic experiments were also carried out with varying ambient such as air, O₂, N₂ and N₂O. The yields of CO and CH₄ in all these systems under the present experimental conditions were found to be increasing with light exposure time. H₂ yield in N₂-purged systems containing 2-propanol was found to be more as compared to the without 2-propanol system. The rate of H₂ production in N₂-purged aqueous solutions containing 0.1% TiO₂ suspension were evaluated to be 0.226 and 5.8 μl/h, without and with 0.5 M 2-propanol, respectively. This confirmed that 2-propanol was an efficient hole scavenger and it scavenged photo-generated holes (h⁺), allowing its counter ion, viz., e⁻, to react with water molecule/H⁺ to yield more H₂. The formation of both CO and CH₄ in the photolysis of CO₂-purged aqueous solutions containing suspended TiO₂ in absence of 2-propanol reveal that the generation of CH₄ is taking place mainly through CO intermediate. In presence of air/O₂, the yield of H₂ in the system without 2-propanol was observed to be negligible as compared to the system containing 2-propanol in which low yield of H₂ was obtained with a formation rate of approx. 0.5 μl/h.