Lyapunov stability on fiber bundles

In this paper we develop a theory of Lyapunov stability for generalized flows on principal and associated bundles. We present a study of Lyapunov stability and attraction in the total space of a principal bundle by means of the action of the structure group.We also relate limit sets, prolongations, prolongational limit sets, attracting sets and stable sets in the total space of an associated bundle to the corresponding concepts in the fibers.     

A comparative study of the optical properties of Fe3+ in ordered LiGa5O8 and LiAl5O8

Measurements are reported on the fluorescence and excitation spectra of Fe³⁺-doped LiGa₅O₈ in the ordered phase. Spectral determinations were made with powder samples containing 0.01 to 1% atomic weight of Fe³⁺, within the temperature range 300 K to 25 K. A comparison is presented between the optical properties of trivalent iron in lithium gallate and in lithium aluminate, LiAl₅O₈, both in their ordered phases. The best fit with crystal field parameters B, C, and Dq, yields the following values for these parameters: Dq = 906 cm^-1, B = 594 cm^-1, and C = 3 737 cm^-1. As is the case with LiAl₅O₈:Fe³⁺, the Stokes shift in LiGa₅O₈:Fe³⁺ is very large, 3 624 cm^-1, although somewhat smaller than the 4 300 cm^-1 seen in LiAl₅O₈:Fe³⁺.     

Using duality to solve generalized fractional programming problems

In this paper we explore the relations between the standard dual problem of a convex generalized fractional programming problem and the partial dual problem proposed by Barros et al. (1994). Taking into account the similarities between these dual problems and using basic duality results we propose a new algorithm to directly solve the standard dual of a convex generalized fractional programming problem, and hence the original primal problem, if strong duality holds. This new algorithm works in a similar way as the algorithm proposed in Barros et al. (1994) to solve the partial dual problem. Although the convergence rates of both algorithms are similar, the new algorithm requires slightly more restrictive assumptions to ensure a superlinear convergence rate. An important characteristic of the new algorithm is that it extends to the nonlinear case the Dinkelbach-type algorithm of Crouzeix et al. (1985) applied to the standard dual problem of a generalized linear fractional program. Moreover, the general duality results derived for the nonlinear case, yield an alternative way to derive the standard dual of a generalized linear fractional program. The numerical results, in case of quadratic-linear ratios and linear constraints, show that solving the standard dual via the new algorithm is in most cases more efficient than applying directly the Dinkelbach-type algorithm to the original generalized fractional programming problem. However, the numerical results also indicate that solving the alternative dual (Barros et al., 1994) is in general more efficient than solving the standard dual.This research was carried out at the Econometric Institute, Erasmus University Rotterdam, the Netherlands and was supported by the Tinbergen Institute Rotterdam     

Rapid determination of 2,3,7,8-tetrachlorodibenzo-p-dioxin in water samples by using solid-phase microextraction followed by gas chromatography with tandem mass spectrometry

A rapid and simple method of using solid-phase microextraction was developed for determination of 2,3,7,8-tetrachlorodibenzo-p-dioxin (2,3,7,8-TCDD) in water samples. In this method, the target analyte is extracted from the sample into the polymeric coating of the fused-silica fiber. After exposure, the fiber is thermally desorbed in the heated injection port of the gas chromatograph, and a chromatographic analysis is performed by using low-resolution tandem mass spectrometry. Parameters that may affect the extension of the microextraction process, such as sampling mode, sample volume, temperature, agitation, and sampling time, were studied. Extraction efficiencies for 3 coating fibers were investigated: 100 microm poly(dimethylsiloxane) (PDMS), 65 microm PDMS-divinylbenzene, and 75 microm carboxen-PDMS. Linearity was evaluated (R = 0.999) for a 250-fold concentration range from the fg/mL to the pg/mL level. The 2,3,7,8-TCDD was detected at the fg/mL level when the headspace over the water sample was sampled for 60 min; the limit of detection obtained was better than that of Method 8280B of the U.S. Environmental Protection Agency. The proposed method performed well when applied to the analysis of tap water, lake water, and seawater samples.     

Substituent Effects in π-Hole Regium Bonding Interactions Between Au(p-X-Py)2 Complexes and Lewis Bases: An ab initio Study

Long range substituent effects in regium bonding interactions involving Au(I) linear complexes are investigated for the first time. The Au(I) atom is coordinated to two para-substituted pyridine ligands. The interaction energy (RI-MP2/def2-TZVP level of theory) of the π-hole regium bonding assemblies is affected by the pyridine substitution. The Hammett's plot representations for several sets of Lewis bases have been carried out and, in all cases, good regression plots have been obtained (interaction energies vs. Hammett's σ parameter). The Bader's theory of “atoms-in-molecules” has been used to evidence that the electron density computed at the bond critical point that connects the Au-atom to the electron donor can be used as a measure of bond order in regium bonding. Several X-ray structures retrieved from the Cambridge Structural Database (CSD) provide experimental support to the existence of π-hole regium bonding in [Au(Py)₂]⁺ derivatives.     

Heat capacity of pure and doped V2O3 single crystals

Heat capacities have been measured for single crystals of V₂O₃, either pure or doped with 1 and 1.4 mole% Cr₂O₃ and Al₂O₃ over the temperature range 100–700°K. V₂O₃ undergoes a fairly sharp transition at low temperatures (～170°K) but fails to exhibit any thermal anomaly above 300°K. The thermal behavior of (M_xV_1?x)₂O₃, M = Cr, Al, is manifested by two transitions: one at low temperatures, 170–180°K for x = 0.01 and 180–190°K for x = 0.014, and the other at high temperatures. For x = 0.01, the high-temperature (HT) anomaly extended over the range 325–345°K (Cr-doped V₂O₃) and 345–365°K (Al-doped V₂O₃), respectively. The corresponding ranges for x = 0.014 were found to be 260–280°K and 270–290°K, respectively. Further, the HT anomaly was characterized by a large hysteresis (～50°K). The values of lattice heat capacity of pure and doped V₂O₃ were, however, found to be almost the same and could be empirically represented by the Debye (D)?Einstein (E) function $\text{D}\text{(}\text{580}\text{T}\text{) + 4}\text{E}\text{(}\text{θ}\text{T}\text{)}$ with θ values 430°K (T = 100–230°K) and 465°K (T > 230°K), respectively. Further, the enthalpy change ΔH associated with the HT anomaly in doped V₂O₃ (80 ≤ ΔH ≤ 510 J/mole) was 5–10 times smaller than the ΔH corresponding to the lower-temperature transition. The results cited here appear incompatible with the Mott transition model that has been invoked to explain the HT anomaly.     

Elemental composition of freshwater sponges Drulia uruguayensis and Drulia cristata collected in the Tapajós River

Sponges are aquatic, predominantly marine animals, but are also represented by several families that inhabit freshwater environments. All freshwater sponges are included in the Demospongiae class and so have skeletons composed of silicious spicules. Because they are filter feeders, they have high potential for bioaccumulation of metals, with various implications and applications in environmental chemistry. This study describes the inorganic chemical composition of two Amazonian species of freshwater sponges: Drulla cristata and Drulla uruguayensis, using energy dispersive X‐ray fluorescence. In both species, the major constituent was silicon (36.75% and 36.05%, respectively), followed by aluminum. Elements such as sulfur, chlorine, copper, and titanium were selectively accumulated and were detected only in the species D. cristata, suggesting its use in environmental characterization studies. Copyright © 2012 John Wiley & Sons, Ltd.     

Single‐wall carbon nanotube interactions with copper‐oxamato building block of molecule‐based magnets probed by resonance Raman spectroscopy

The electronic interactions between the [Cu(opba)]²⁻ anions (where opba is orthophenylenebis (oxamato)) and single‐wall carbon nanotubes (SWCNTs) were investigated by resonance Raman spectroscopy. The opba can form molecular magnets, and the interactions of opba with SWCNTs can produce materials with very different magnetic/electronic properties. It is observed that the electronic interaction shows a dependence on the SWCNT diameter independent of whether they are metallic or semiconducting, although the interaction is stronger for metallic tubes. The interaction also is dependent on the amount of complex that is probably adsorbed on the carbon surface of the SWCNTs. Some charge transfer can be also occurring between the metallic complex and the SWCNTs. Copyright © 2012 John Wiley & Sons, Ltd.