Second degree classical forms

A form (linear functional) u is called regular if there exists a sequence of polynomials {P_n}_n≥0, deg P_n = n which is orthogonal with respect to u. Such a form is said to be of second degree if there are polynomials B and C such that the Stieltjes function satisfies a relation of the form BS²(u) + CS(u) + D = 0.Classical forms correspond to classical orthogonal polynomials: sequences of polynomials whose derivatives also form an orthogonal sequence. In this paper, the authors determine all the classical forms which are of second degree. They show that Hermite, Laguerre and Bessel forms are not of second degree. Only Jacobi forms which satisfy a certain condition possess this property.     

Synthesis and structure determination of a new layered zincophosphate: [H2N2C6H16]0.5[Zn2(PO4)(HPO4)(H2O)]·H2O

The synthesis and crystal structure of a new microporous zincophosphate are described. [H₂N₂C₆H₁₆]_0.5[Zn₂(PO₄)(HPO₄)(H₂O)]·H₂O crystallizes in the triclinic space group P1¯ with a = 8.822(4), b = 9.236(4), c = 8.451(3) Å, = 67.19(3), = 91.32(3), = 111.10(3)°, V = 586.7(4) ų and Z = 2. This new material consists of infinite two-dimensional anionic layers alternated with planes containing organic diprotonated templates, N, N, N, N-tetramethylethylenediamine [H₂N₂C₆H₁₆]²⁺ molecules. The framework structure is built up of ZnO₄, ZnO₃OH₂, PO₄, and PO₃OH tetrahedra, linked through oxygen vertices. The presence of terminal OH₂ and OH groups, leads to an open structure containing four- and eight-rings. The organic molecules are interconnected to the framework through hydrogen bonds.     

Synthesis and X-ray structure of p-tolyl phenylthioglyoxylate

The title compound (C₁₅H₁₂O₂S) is triclinic witha=7.077(10),b=8.825(2),c=11.068(2) Å, =106.66(3)^o, Z=2, and space group P. The significant structural features lies in the two carbonyl groups of the thioglyoxylate which are oriented antiperiplanar to each other [–168.2(2)^o]. The central C(8)–C(9) bond is 1.553(3) Å. The phenyl rings are twisted with respect to the carbonyl groups. Short contacts are present between S and O(1) [2.652(2) Å] and also between S and O(2) [2.758(2) Å].     

Relative Gorenstein Dimensions

In the last years (Gorenstein) homological dimensions relative to a semidualizing module C have been subject of several works as interesting extensions of (Gorenstein) homological dimensions. In this paper, we extend to the noncommutative case the concepts of G _C -projective module and dimension, weakening the condition of C being semidualizing as well. We prove that indeed they share the principal properties of the classical ones and relate this new dimension with the classical Gorenstein projective dimension of a module. The dual concepts of G _C -injective modules and dimension are also treated. Finally, we show some interesting interactions between the class of G _C -projective modules and the Bass class associated to C on one side, and the class of G\({_{C^{\vee}}}\) -injective modules (C ^∨ = Hom _R (C, E) where E is an injective cogenerator in R-Mod) and the Auslander class associated to C in the other.     

Continued Fractions and Transcendence of Formal Power Series Over a Finite Field

The aim of this paper was to establish a new transcendence criterion for a class of quasi-periodic continued fractions of formal power series over a finite field depending only on the length of specific blocks appearing in the sequence of partial quotients.     

Spectral discretization of a model for organic pollution in waters

We are interested in a mixed reaction diffusion system describing the organic pollution in stream‐waters. In this work, we propose a mixed‐variational formulation and recall its well‐posedness. Next, we consider a spectral discretization of this problem and establish nearly optimal error estimates. Numerical experiments confirm the interest of this approach. Copyright © 2016 John Wiley & Sons, Ltd.     

Experimental study of a confined premixed metal combustor: Metal flame stabilization dynamics and nitrogen oxides production

This work presents a study of a magnesium/air combustion process in the context of innovative zero carbon dioxide (CO₂) energy carriers for reducing global warming effects. In order to analyze more deeply the confined combustion of magnesium under fluctuating overpressure conditions (0 to 24 hPa) and the generated gaseous by-products, magnesium/air flames have been realized in a combustion chamber with a conical bluff-body as flame holder and different contraction ratios diaphragms at the exit duct. Sieved magnesium samples with two size-fractions were tested: 20–50?µm and 50–70?µm. The gaseous emissions of nitrogen oxides (NO_x) and dioxygen (O₂) were analyzed with on-line infrared, ultraviolet and paramagnetic analyzers. A flame pulsating behavior was clearly observed from light emission intensity (monitored by a photodiode) and pressure fluctuations (monitored by a pressure sensor); the frequencies obtained ranged between 3 and 10?Hz. The frequency of the pulsation exhibited strong dependence on the geometric configuration of the chamber: a contraction diaphragm divided by two the frequency level of the fluctuations in the studied range of maximum overpressure. Such fluctuations may probably be the consequence of periodic perturbations of the recirculation zone behind the bluff-body. These periodic perturbations are themselves caused by strong periodic overpressure variations due to stiff contraction downstream responding to gas velocity fluctuations. This feed-back-loop mechanism was considered in this study. NO_x emissions produced through the thermal pathway were analyzed for equivalence ratios ranging from 0.29 to 1. The representation of NO_x versus equivalence ratio exhibited a parabolic shape with a maximum for an equivalence ratio of 0.4. Moreover, NO_x emissions of this metal combustor have shown a similar order of magnitude than current internal combustion engines.     

Purification and Properties of a Thermostable Xylanase GH 11 from Penicillium occitanis Pol6

An extracellular, endo-??-1,4-xylanase was purified to homogeneity from the culture filtrate of the filamentous fungus Penicillium occitanis Pol6, grown on oat spelt xylan. The purified enzyme (PoXyn2) showed a single band on SDS?CPAGE with an apparent molecular weight of 30?kDa. The xylanase activity was optimal at pH?3.0 and 65?°C. The specific activity measured for oat spelt xylan was 2,368?U?mg^?1. The apparent K _m and V _max values were 8.33?mg?ml^?1 and 58.82???mol?min^?1?ml^?1, respectively, as measured on oat spelt xylan. Thin-layer chromatography experiments revealed that purified PoXyn2 degrades xylan in an endo-fashion releasing xylobiose as main end product. The genomic DNA and cDNA encoding this protein were cloned and sequenced. This PoXyn2 presents an open reading frame of 962?bp, not interrupted by any introns and encoding for a mature protein of 320 amino acids and 29.88?kDa.     

Sustainable potable water production from conventional solar still during the winter season at Algerian dry areas: energy and exergy analysis

Journal of Thermal Analysis and Calorimetry - The Algeria Sahara suffers from the scarcity of drinking water. Solar distillation is one of the simplest and generally inexpensive techniques to solve...     

Surface Modification of Halogenated Polymers. 7. Local Reduction of Poly(tetrafluoroethylene) and Poly(chlorotrifluoroethylene) by a Scanning Electrochemical Microscope in the Feedback Mode

Fluoropolymers have been reduced locally by the radical anion of a redox mediator electrogenerated at a microelectrode operating in the configuration of a scanning electrochemical microscope. Approach curves with different redox mediators were used to investigate the reduction mechanism of the fluoropolymer. Different factors are discussed, such as the monomer reduction mechanism, the kinetic control by the surface modification growth, and the conductivity of the modified surface. The fluoropolymers' reduction parallels the trends observed in organic electrochemistry in solution within the haloalkane series.