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1.
2.
We prove a direct theorem for shape preservingL
p
-approximation, 0p, in terms of the classical modulus of smoothnessw
2(f, t
p
1
). This theorem may be regarded as an extension toL
p
of the well-known pointwise estimates of the Timan type and their shape-preserving variants of R. DeVore, D. Leviatan, and X. M. Yu. It leads to a characterization of monotone and convex functions in Lipschitz classes (and more general Besov spaces) in terms of their approximation by algebraic polynomials.Communicated by Ron DeVore. 相似文献
3.
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. 相似文献
4.
Dany Brouillette Gérald Perron Jacques E. Desnoyers 《Journal of solution chemistry》1998,27(2):151-182
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. 相似文献
5.
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. 相似文献
6.
7.
Tahya Bamine Edouard Boivin Christian Masquelier Laurence Croguennec Elodie Salager Dany Carlier 《Magnetic resonance in chemistry : MRC》2020,58(11):1109-1117
7Li, 31P, and 19F solid-state nuclear magnetic resonance (NMR) spectroscopy was used to investigate the local arrangement of oxygen and fluorine in LiVPO4F1-yOy 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 VIVO vanadyl bonds with a very specific electronic structure and possible cooperative effect along the chain. 相似文献
8.
Carole Yaacoub Rim Wehbe Yahya Salma Dany El-Obeid Romeo El Bersaoui Bruno Coutard Ziad Fajloun 《Molecules (Basel, Switzerland)》2022,27(5)
Bee venom (BV) is one of the most remarkable natural products that has been a subject of studies since ancient times. Recent studies have shown that Apis mellifera syriaca venom possesses antibacterial as well as cytotoxic effects on cancer cell lines. The venom contains a variety of bioactive molecules—mainly melittin (MEL) and phospholipase A2 (PLA2), as well as other compounds that are not well characterized. In this work, we continue the biological characterization of A. mellifera syriaca venom by testing its anticoagulant effect on human plasma using the prothrombin time (PT) test, as well as assessing its proteolytic activity. In addition, the cytotoxicity of the crude venom—and of its two main components, MEL and PLA2—was tested on HeLa cancer cell lines for the first time. The results obtained showed the capacity of A. mellifera syriaca venom to increase clotting time, thereby proving its anticoagulant effect. Moreover, the venom did not demonstrate a significant proteolytic activity unless administrated at concentrations ≥ 5 mg/mL. Finally, we showed that crude A. mellifera syriaca venom, along with MEL, exhibit a strong in vitro cytotoxic effect on HeLa cancer cell lines, even at low concentrations. In summary, our findings could serve as a basis for the development of new natural-based drug candidates in the therapeutic field. 相似文献
9.
10.
Prof. Dany Leviatan 《Mathematische Zeitschrift》1972,124(3):208-212