Chebyshev polynomials of the second kind via raising operator preserving the orthogonality

It is well known that monic orthogonal polynomial sequences \(\{T_n\}_{n\ge 0}\) and \(\{U_n\}_{n\ge 0}\), the Chebyshev polynomials of the first and second kind, satisfy the relation \(DT_{n+1}=(n+1)U_n\) (\(n\ge 0\)). One can also easily check that the following “inverse” of the mentioned formula holds: \({\mathcal {U}}_{-1}(U_n)=(n+1)T_{n+1}\) (\(n\ge 0\)), where \({\mathcal {U}}_\xi =x(xD+{\mathbb {I}})+\xi D\) with \(\xi \) being an arbitrary nonzero parameter and \({\mathbb {I}}\) representing the identity operator. Note that whereas the first expression involves the operator D which lowers the degree by one, the second one involves \({\mathcal {U}}_\xi \) which raises the degree by one (i.e. it is a “raising operator”). In this paper it is shown that the scaled Chebyshev polynomial sequence \(\{a^{-n}U_n(ax)\}_{n\ge 0}\) where \(a^2=-\xi ^{-1}\), is actually the only monic orthogonal polynomial sequence which is \({\mathcal {U}}_\xi \)-classical (i.e. for which the application of the raising operator \({\mathcal {U}}_\xi \) turns the original sequence into another orthogonal one).     

Expressions of dissipated powers and stored energies in poroelastic media modeled by {u,U} and {u,P} formulations

This paper is devoted to the rigorous obtention of the energy balance in porous materials. The wave propagation in the porous media is described by Biot-Allard's {u,U} and {u,P} formulations. The paper derives the expressions for stored kinetic and strain energies together with dissipated energies. It is shown that, in the case of mixed formulations, these expressions do not correspond to the real and imaginary parts of the variational formulations. A quantitative convergence analysis of finite element scheme is then undertaken with the help of these indicators. It is shown that the order of convergence of these indicators for linear finite-element is one and that they are then well fitted to check the validity of finite-element models.     

Novel synthesis of 3-cyano-2-pyridones derivatives catalyzed by Au–Co/TiO2

Research on Chemical Intermediates - The current work described a new and highly selective method for the synthesis of substituted 3-cyano-2-pyridones scaffolds using gold-cobalt supported on TiO2...     

Chitosan-Based Materials for the Removal of Nickel Ions from Aqueous Solutions

Russian Journal of Physical Chemistry A - Sorption of Ni(II) ions from liquid effluents utilizing chemically modified chitosan; (vanillin, polymer I) and (ortho-vanillin, polymer II) is studied...     

Radical copolymerization of chlorotrifluoroethylene with 4‐bromo‐3,3,4,4‐tetrafluorobut‐1‐ene

The radical copolymerization of chlorotrifluoroethylene (CTFE) with 3,3,4,4‐tetrafluoro‐4‐bromobut‐1‐ene (BTFB) initiated by tert‐butylperoxypivalate is presented. The microstructures of the obtained copolymers are determined by means of NMR spectroscopies and elemental analysis and show that random copolymers were obtained. A wide range of poly(CTFE‐co‐BTFB) copolymers is synthesized, containing from 17 to 89 mol % of CTFE. In all the cases, CTFE is the less reactive of both comonomers. T_d^10% values, ranging from 163 up to 359 °C, are dependent on the BTFB content. These variations of thermal property are attributed to the increase in the number of C‐H and C‐Br bonds breakdown when the BTFB molar percentage in the copolymer is higher. T_g values range from 19 to 39 °C and a decreasing trend is observed when increasing the amount of BTFB in the copolymer. This observation arises from the higher flexibility of the copolymer when increasing the number of fluorobrominated lateral chains. These original fluoropolymers bearing reactive pendant bromo groups are suitable candidates for various applications. © 2014 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2014 , 52, 1714–1720     

N-isopropylsulfinylimines as useful intermediates in the synthesis of chiral amines: expeditive asymmetric synthesis of the calcimimetic (+)-NPS R-568

An efficient and high-yielding approach for the asymmetric synthesis of calcimimetic (+)-NPS R-568 (1) has been developed. The key step of the synthesis is the highly diastereoselective addition of methyl Grignard to the (SS,E)-N-(3-methoxybenzylidene)-2-propanesulfinamide [5(S)], which afforded a single diastereoisomer in high yield in short reaction time.     

Isobaric metabolite interferences and the requirement for close examination of raw data in addition to stringent chromatographic separations in liquid chromatography/tandem mass spectrometric analysis of drugs in biological matrix

In addition to matrix effects, common interferences observed in liquid chromatography/tandem mass spectrometry (LC/MS/MS) analyses can be caused by the response of drug-related metabolites to the multiple reaction monitoring (MRM) channel of a given drug, as a result of in-source reactions or decomposition of either phase I or II metabolites. However, it has been largely ignored that, for some drugs, metabolism can lead to the formation of isobaric or isomeric metabolites that exhibit the same MRM transitions as parent drugs. The present study describes two examples demonstrating that interference caused by isobaric or isomeric metabolites is a practical issue in analyzing biological samples by LC/MS/MS. In the first case, two sequential metabolic reactions, demethylation followed by oxidation of a primary alcohol moiety to a carboxylic acid, produced an isobaric metabolite that exhibits a MRM transition identical to the parent drug. Because the drug compound was rapidly metabolized in rats and completely disappeared in plasma samples, the isobaric metabolite appeared as a single peak in the total ion current (TIC) trace and could easily be quantified as the drug since it was eluted at a retention time very close to that of the drug in a 12-min LC run. In the second example, metabolism via the ring-opening of a substituted isoxazole moiety led to the formation of an isomeric product that showed an almost identical collision-induced dissociation (CID) MS spectrum as the original drug. Because two components were co-eluted, the isomeric product could be mistakenly quantified and reported by data processing software as the parent drug if the TIC trace was not carefully inspected. Nowadays, all LC/MS data are processed by computer software in a highly automated fashion, and some analysts may spend much less time to visually examine raw TIC traces than they used to do. Two examples described in this article remind us that quality data require both adequate chromatographic separations and close examination of raw data in LC/MS/MS analyses of drugs in biological matrix.     

A sensitive nitrite sensor using an electrode consisting of reduced graphene oxide functionalized with ferrocene

A composite consisting of chitosan containing azidomethylferrocene covalently immobilized on sheets of reduced graphene oxide was drop-casted on a polyester support to form a screen-printed working electrode that is shown to enable the determination of nitrite by cyclic voltammetry and chronoamperometry. Both reduction and oxidation of nitrite can be accomplished due to the high electron-transfer rate of this electrode. Under optimal experimental conditions (i.e. an applied potential of 0.7 V vs. Ag/AgCl in pH 7.0 solution), the calibration plot is linear in the 2.5 to 1450 μM concentration range, with an ~0.35 μM limit of detection (at a signal-to-noise ratio of 3). The sensor was successfully applied to the determination of nitrite in spiked mineral water samples, with recoveries ranging between 95 and 101 %.

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Graphical abstract We describe the design of ferrocene-functionalized reduced graphene oxide electrode and its electrocatalytic properties towards the determination of nitrite. Compared to a reduced graphene oxide electrode, the sensor exhibits enhanced electrocatalytic activity towards both oxidation and reduction of nitrite.