QSym over Sym has a stable basis

We prove that the subset of quasisymmetric polynomials conjectured by Bergeron and Reutenauer to be a basis for the coinvariant space of quasisymmetric polynomials is indeed a basis. This provides the first constructive proof of the Garsia-Wallach result stating that quasisymmetric polynomials form a free module over symmetric polynomials and that the dimension of this module is n!.     

Direct determination of sodium,potassium, chromium and vanadium in biodiesel fuel by tungsten coil atomic emission spectrometry

High levels of sodium and potassium can be present in biodiesel fuel and contribute to corrosion, reduced performance and shorter engine lifetime. On the other hand, trace amounts of chromium and vanadium can increase the emission of pollutants during biodiesel combustion. Sample viscosity, immiscibility with aqueous solutions and high carbon content can compromise biodiesel analyzes. In this work, tungsten filaments extracted from microscope light bulbs are used to successively decompose biodiesel's organic matrix, and atomize and excite the analytes to determine sodium, potassium, chromium and vanadium by tungsten coil atomic emission spectrometry (WCAES). No sample preparation other than simple dilution in methanol or ethanol is required. Direct analysis of 10-μL sample aliquots using heating cycles with less than 150 s results in limits of detection (LOD) as low as 20, 70, 70 and 90 μg kg⁻¹ for Na, K, Cr and V, respectively. The procedure's accuracy is checked by determining Na and K in a biodiesel reference sample and carrying out spike experiments for Cr and V. No statistically significant differences were observed between reference and determined values for all analytes at a 95% confidence level. The procedure was applied to three different biodiesel samples and concentrations between 6.08 and 95.6 mg kg⁻¹ for Na and K, and between 0.22 and 0.43 mg kg⁻¹ for V were obtained. The procedure is simple, fast and environmentally friendly. Small volumes of reagents, samples and gases are used and no residues are generated. Powers of detection are comparable to other traditional methods.     

Cobalt as chemical modifier to improve chromium sensitivity and minimize matrix effects in tungsten coil atomic emission spectrometry

Cobalt is used as chemical modifier to improve sensitivity and minimize matrix effects in Cr determinations by tungsten coil atomic emission spectrometry (WCAES). The atomizer is a tungsten filament extracted from microscope light bulbs. A solid-state power supply and a handheld CCD-based spectrometer are also used in the instrumental setup. In the presence of 1000 mg L⁻¹ Co, WCAES limit of detection for Cr (λ = 425.4 nm) is calculated as 0.070 mg L⁻¹; a 10-fold improvement compared to determinations without Co modifier. The mechanism involved in such signal enhancement is similar to the one observed in ICP OES and ICP-MS determinations of As and Se in the presence of C. Cobalt increases the population of Cr⁺ by charge transfer reactions. In a second step, Cr⁺/e⁻ recombination takes place, which results in a larger population of excited-state Cr atoms. This alternative excitation route is energetically more efficient than heat transfer from atomizer and gas phase to analyte atoms. A linear dynamic range of 0.25–10 mg L⁻¹ and repeatability of 3.8% (RSD, n = 10) for a 2.0 mg L⁻¹ Cr solution are obtained with this strategy. The modifier high concentration also contributes to improving accuracy due to a matrix-matching effect. The method was applied to a certified reference material of Dogfish Muscle (DORM-2) and no statistically significant difference was observed between determined and certified Cr values at a 95% confidence level. Spike experiments with bottled water samples resulted in recoveries between 93% and 112%.     

Picosecond excitonic luminescence in ZnO and other wide-gap semiconductors

Radiative lifetimes of free-atom transitions, scaled by ω³ for comparison at 368 nm, are not faster than about 6.9 ns. BaF₂ core-valence luminescence, scaled in the same way from 220 to 368 nm, corresponds to 4.1 ns. In contrast, excitonic transitions in wide-gap semiconductors display subnanosecond radiative lifetimes, and in particular ZnO has radiative lifetimes measured at 50–300 ps for D^o,X and 400–900 ps for free excitons. The “giant oscillator strength” corresponding to these lifetimes can be explained by theories developed initially for defect-bound excitons, then quantum wells, and nanoparticles. An exciton is a coherent array of N dipoles, where N is the number of sites covered by coherent translational motion of the exciton. This is not essentially a phenomenon of multiple excitons, but applies as well to single-exciton decay. It differs in that regard from the more familiar Dicke giant dipole of N coherently excited atoms lacking translational periodicity. The phenomenon suggests possibilities for achieving ultrafast scintillators and high light yield.     

Compositions with the euler and carmichael functions

Let ϕ and λ be the Euler and Carmichael functions, respectively. In this paper, we establish lower and upper bounds for the number of positive integers n ≤ x such that ϕ(λ(n)) = λ(ϕ(n)). We also study the normal order of the function ϕ(λ(n))/λ(ϕ(n)).     

Photosensitized tetrahydropyran transfer

THP ethers were formed cleanly during photolysis of 3,4-dihydro-2 H-pyran, an alcohol, and catalytic 1,5-dichloro-9,10-anthraquinone with use of visible light. The reaction could be conducted under ambient fluorescent lighting or with sunlight as well as in a Rayonet reactor. The scope and mechanism are discussed.     

Luminescence and Stimulated Emission in Zinc Oxide Nanoparticles,Films, and Crystals

ZnO has attracted attention as a candidate material for ultraviolet light-emitting devices. Its 3.37 -eV band gap is comparable to that of GaN, and single crystal substrates can be grown. Control of p-type conductivity in ZnO is under study in several laboratories including ours. We report streak camera measurements of time-resolved luminescence and stimulated emission excited in single crystal, film, and particle samples under excitation by 300 fs laser pulses at temperatures from 17 K to 295 K. We also describe p-n junctions formed by control of oxygen pressure in reactive sputtering of ZnO films, and results of introducing nitrogen during reactive sputtering.     

Continua of local minimizers in a non-smooth model of phase transitions

In this paper, we study critical points of the functional $$J_{\epsilon}(u):=\frac{\epsilon^2}{2} \int\limits_0^1|u_x|^2{\rm {d}}x+\int\limits_0^1F(u){\rm {d}}x, u \,\in W^{1,2}{(0,1)}, \quad \quad \quad(1)$$ where ${F : \mathbb {R}\rightarrow \mathbb {R}}$ is assumed to be a double-well potential. This functional represents the total free energy in models of phase transition and allows for the study of interesting phenomena such as slow dynamics. In particular, we consider a non-classical choice for F modeled on ${F(u)=|1-u^2|^{\alpha}}$ where 1?<????<?2. The discontinuity in F??? at ±1 leads to the existence of multiple continua of critical points that are not present in the classical case ${F \in C^2}$ . We prove that the interior points of these continua are local minima. The energy of these local minimizers is strictly greater than the global minimum of ${J_{\epsilon}}$ . In particular, the existence of these continua leads to an alternative explanation for the slow dynamics observed in phase transition models.