Convex polynomial and spline approximation in C[−1, 1]

We prove that a convex functionf C[–1, 1] can be approximated by convex polynomialsp _n of degreen at the rate of ₃(f, 1/n). We show this by proving that the error in approximatingf by C² convex cubic splines withn knots is bounded by ₃(f, 1/n) and that such a spline approximant has anL third derivative which is bounded by n³₃(f, 1/n). Also we prove that iff C²[–1, 1], then it is approximable at the rate ofn ^–2 (f, 1/n) and the two estimates yield the desired result.Communicated by Ronald A. DeVore.     

Apparent Molar Volume, Heat Capacity, and Conductance of Lithium Bis(trifluoromethylsulfone)imide in Glymes and Other Aprotic Solvents

Lithium bis(trifluoromethylsulfone)imide (LiTFSI) is a promising electrolyte for high-energy lithium batteries due to its high solubility in most solvents and electrochemical stability. To characterize this electrolyte in solution, its conductance and apparent molar volume and heat capacity were measured over a wide range of concentration in glymes, tetraethylsulfamide (TESA), acetonitrile, -butyrolactone, and propylene carbonate at 25°C and were compared with those of LiClO₄ in the same solvents. The glymes or n(ethylene glycol) dimethyl ethers (nEGDME), which have the chemical structure CH₃–O–(CH₂–CH₂–O) _n –CH₃ for n = 1 to 4, are particularly interesting since they are electrochemically stable, have a good redox window, and are analogs of the polyethylene oxides used in polymer-electrolyte batteries. TESA is a good plasticizer for polymer-electrolyte batteries. Whenever required, the following properties of the pure solvents were measured: compressibilities, expansibilities, temperature and pressure dependences of the dielectric constant, acceptor number, and donor number. These data were used in particular to calculate the limiting Debye-Hückel parameters for volumes and heat capacities. The infinite dilution properties of LiTFSI are quite similar to those of other lithium salts. At low concentrations, LiTFSI is strongly associated in the glymes and moderately associated in TESA. At intermediate concentrations, the thermodynamic data suggests that a stable solvate of LiTFSI in EGDME exists in the solution state. At high concentrations, the thermodynamic properties of the two lithium salts approach those of the molten salts. These salts have a reasonably high specific conductivity in most of the solvents. This suggests that the conductance of ions at high concentration in solvents of low dielectric constant is due to a charge transfer process rather than to the migration of free ions.     

Polynomial approximation inL p (0<p<1)

We prove that forf∈L _p , 0<p<1, andk a positive integer, there exists an algebraic polynomialP _n of degree ≤n such that $$\left\| {f - P_n } \right\|_p \leqslant C\omega _k^\varphi \left( {f,\frac{1}{n}} \right)_p $$ whereω _k ^? (f,t)p is the Ditzian-Totik modulus of smoothness off inL _p , andC is a constant depending only onk andp. Moreover, iff is nondecreasing andk≤2, then the polynomialP _n can also be taken to be nondecreasing.     

Local atomic and electronic structure in the LiVPO4(F,O) tavorite-type materials from solid-state NMR combined with DFT calculations

⁷Li, ³¹P, and ¹⁹F solid-state nuclear magnetic resonance (NMR) spectroscopy was used to investigate the local arrangement of oxygen and fluorine in LiVPO₄F_1-yO_y materials, interesting as positive electrode materials for Li-ion batteries. From the evolution of the 1D spectra versus y, 2D ⁷Li radiofrequency-driven recoupling (RFDR) experiments combined, and a tentative signal assignment based on density functional theory (DFT) calculations, it appears that F and O are not randomly dispersed on the bridging X position between two X–VO₄–X octahedra (X = O or F) but tend to segregate at a local scale. Using DFT calculations, we analyzed the impact of the different local environments on the local electronic structure. Depending on the nature of the VO₄X₂ environments, vanadium ions are either in the +III or in the +IV oxidation state and can exhibit different distributions of their unpaired electron(s) on the d orbitals. Based on those different local electronic structures and on the computed Fermi contact shifts, we discuss the impact on the spin transfer mechanism on adjacent nuclei and propose tentative signal assignments. The O/F clustering tendency is discussed in relation with the formation of short V^IVO vanadyl bonds with a very specific electronic structure and possible cooperative effect along the chain.     

Effect of particle polydispersity on particle concentration measurement by using laser Doppler anemometry

Measurement of particle concentration by laser Doppler anemometry (LDA) is studied on a vertical air jet seeded by a powder disperser with controlled particle and air flow rates. Particle arrival rate is utilized to retrieve particle number densities from conventional LDA operation. The effect of polydisperse nature of the particles is assessed. Comparisons between measured and estimated particle number densities suggest that only a certain portion of the particle population with a particle size to fringe spacing ratio around unity can be detected. Results indicate that reliable measurement of absolute particle concentration is possible for a particle population of narrow size distribution with an average diameter equivalent to fringe spacing. Present number density measurement technique which is useful for practical purposes with conventional LDA systems is found to yield physically reasonable profiles in both laminar and turbulent regimes.     

Reactivity study of 1H-thieno[3,2-d][1,3]oxazine-2,4-dione toward the synthesis of bicyclic 3,4-dihydro-1H-thieno[3,2-e][1,4]diazepine-2,5-dione analogues

A series of 10 optically pure 3,4-dihydro-1H-thieno[3,2-e][1,4]diazepine-2,5-dione derivatives has been synthesized in 41-75% yields on treatment of 1H-thieno[3,2-d][1,3]oxazine-2,4-dione with different natural alpha-amino acids.     

TCF selenium preconcentration in geological materials for determination at sub-mugg(-1) with INAA (Se/TCF-INAA)

In geological samples, Se concentration ranges from 1 × 10⁻⁹ g g⁻¹ up to 1 × 10⁻³ g g⁻¹. The analytical difficulty at low concentration (<1 μg g⁻¹), is one of the main reasons why the geological cycle of Se is poorly known. The analytical method that consisted of preconcentration of Se with thiol cotton fiber (TCF) followed by graphite furnace atomic absorption spectrometry (GFAAS) has been modified by finishing with instrumental neutron activation analysis (INAA). The modified technique involves sample dissolution (HF-HNO₃-H₂O₂) and evaporation to dryness at low temperature (55-60 °C) to avoid selenium volatilization. Se^VI is converted to Se^IV by adding 6 M HCl to the dry residuum and the solution is then heated in a covered boiling bath (95-100 °C). The solution is diluted to obtain 0.6 M HCl and then collected on TCF. The TCF is placed in a polyethylene vial for irradiation in the SLOWPOKE II reactor (Montréal) for 30 s at a neutron flux of 10¹⁵ m⁻² s⁻¹. The 162 keV peak of ^77mSe (half-life 17.36 s) is read for 20 s after a decay of 7 s. The amount of sample to be dissolved is controlled by two competing effects. To obtain low detection limits, a larger amount of sample should be dissolved. On the other hand, the TCF could become saturated with chalcophile elements when large sample is used. Sulfur is a good indicator of the amount of Se and chalcophile elements present. In S poor sample (<100 μg g⁻¹) 3.0 g of sample was used and the L_D was ∼2 ng g⁻¹. In S high samples (>1.5% S) 0.05 g of sample was used and the L_D was ∼120 ng g⁻¹. The present work also includes suggested Se concentration for eight international geological reference materials (IGRM) that compare favorably with literature values.     

A new biolistic intradermal injector

We present a novel intradermal needle-free drug delivery device which exploits the unsteady high-speed flow produced by a miniature shock tube to entrain drug or vaccine particles onto a skin target. A first clinical study of pain and physiological response of human subjects study is presented, comparing the new injector to intramuscular needle injection. This clinical study, performed according to established pain assessment protocols, demonstrated that every single subject felt noticeably less pain with the needle-free injector than with the needle injection. Regarding local tolerance and skin reaction, bleeding was observed on all volunteers after needle injection, but on none of the subjects following powder injection. An assessment of the pharmacodynamics, via blood pressure, of pure captopril powder using the new device on spontaneously hypertensive rats was also performed. It was found that every animal tested with the needle-free injector exhibited the expected pharmacodynamic response following captopril injection. Finally, the new injector was used to study the delivery of an inactivated influenza vaccine in mice. The needle-free device induced serum antibody response to the influenza vaccine that was comparable to that of subcutaneous needle injection, but without requiring the use of an adjuvant. Although no effort was made to optimize the formulation or the injection parameters in the present study, the novel injector demonstrates great promise for the rapid, safe and painless intradermal delivery of systemic drugs and vaccines.