A Convenient Method for the Synthesis of bis-Trifluoroethyl Phosphonoacetates

bis-Trifluoroethyl phosphonoacetates were easily obtained by condensation of bis-trifluoroethyl alkylphosphonates with alkyl chloroformates in the presence of 2 equivalents of lithium hexamethyldisilazane (LiHMDS).     

The Chemistry of L-Ascorbic and D-Isoascorbic Acids. 3: Efficient Syntheses of Pure R- and S- 1,2-O-Isopropylidene-1,2,4-Butanetriols1

Both enantiomers of 1,2-0-isopropylidene-1,2,4-butanetriol were prepared by two different and simple methods starting from readily available L-ascorbic and D-isoascorbic acids.     

SYNTHÈSE D'HÉTÉROCYCLES α-PHOSPHONIQUES. NOUVEAUX DÉVELOPPEMENTS

Abstract

On rélise la synthése d'hétérocycles α-phosphoniques par condensation de bis-nucléophiles-1,2, -1,3 et -1,4 avec des énamines β-phosphoniques 2 portant un groupe fonctionnel [C(O)R, C(O)OC₂H₅, CN]. Avec la guanidine. l'acétamidine, la S-méthyl-isothiourée et l'acéomalonimide on prépare les diétho[xacute]yphosphinyl-4 pyrimidines 5 et 8 avec des redements supérieurs á 50%. Les hydrazines substitutées conduisent aux diéthoxyphosphinyl-4 pyrazoles 11 α plus de 90%. Avec l'hydroxylamine, on obtient par déshydratation spontanée de l'intermédiaire réactionnel l'énol du β-cétophosphonate α-nitrile 18. Dans le cas de l'orthophényléne diamine la réaction ne donne pas la diazépine 23 mais évolue vers la régénération du β-cétophosphonate de départ par élimination de benzimidazole.

Synthesis of α-phosphonic heterocycles is described by condensation of 1,2- 1,3- or 1,4-bis-nucleophiles with β-phosphonic enamines 2 bearing a functional group. From guanidine and analogs 4-diethoxyphosphinyl pyrimidines 5 and 8 are obtained with yields up to 50%. Substituted hydrazines give 4-dietho-xyphosphinyl pyrazoles 11 with very good yields. With hydroxylamine a spontaneous dehydration gives the enolic form 18 of a β-ketophosphonate α-nitrile. Orthophenylene diamine is a special example in fact the departure β-ketophosphonate is recovered with benzimidazole elimination.     

Perturbed Recurrence Relations

In this paper, we give some new relations between two families of polynomials defined by three-term recurrence relations. These relations allow us to study how some properties of a family of orthogonal polynomials are affected when the coefficients of the recurrence relation are perturbed. In the literature some methods are already available. However, most of them are only effective for small perturbations. In order to show the sharpness of our method, we compare it with Gronwall's classical method in the case of large perturbations. Using our tool, we also give a relation between the differential equation satisfied by a family of orthogonal polynomials and its perturbed family. Some explicit results are obtained for Chebyshev polynomials of the second kind.     

Development of an ultra-performance liquid chromatography-mass spectrometry method for the detection of lipophilic marine toxins

A rapid method for the detection of marine toxins was developed using an ultra-performance liquid chromatography (UPLC) system coupled to a latest generation mass spectrometry (MS) system. The analysis of 21 lipophilic marine toxins was achieved on an Acquity C18 column using a water-acetonitrile gradient with a cycle time of 6.6 min, reducing analysis time by more than a factor two compared to HPLC while maintaining peak resolution. Linear ranges, limits of detection and limits of quantification were established for okadaic acid (OA), pectenotoxin-2, azaspiracid-1 (AZA1), yessotoxin, gymnodimine and 13-desmethylspirolide C. The method was found to be accurate when using a triplicate methanolic extraction. Matrix effects were assessed by standard addition of OA and AZA1 in extracts of raw and heat-treated flesh of mussels and oysters. For the analysis of AZA1, the UPLC-MS method was always prone to signal suppression, while for OA analysis signal suppression was observed in extracts of raw shellfish flesh and signal enhancement in extracts of heat-treated flesh. Matrix effects occurring in the method presented are diminished compared to previous studies.     

Statistics of the deformation of the front of a tunnel-crack propagating in some inhomogeneous medium

We present a statistical analysis of some geometrical features of the front of a tensile tunnel-crack propagating quasistatically, according to some Paris-type law, in some elastic solid with spatially varying Paris constant. The work is based on an earlier formula of the authors, which provides the first-order change of the distribution of the mode I stress intensity factor along the front of a tunnel-crack, arising from some small but otherwise arbitrary in-plane perturbation of this front. The quantities studied include the power spectrum and the autocorrelation function of the deviation of the two parts of the front from reference straight lines, the autocorrelation function of the derivative of this deviation in the direction of the crack front, the mean squared fluctuation of the deviation, and its correlation distance. The various measures of the magnitude of the deviation of the front from straightness are all found to increase in time at a considerable rate, which means in some sense that the “wavyness” of the front continuously grows. However, the correlation distance of the deviation also increases, which mitigates the preceding conclusion, since it means in another sense that the crack front tends to “straighten back” in time. Also, comparisons are made with the cases of a semi-infinite crack propagating quasistatically or dynamically, using some results of Rice and coworkers for the latter case. The rate of growth of the various measures of the magnitude of the deviation from straightness is much larger for the tunnel-crack than for the semi-infinite one. This is because the finite width of the tunnel-crack induces a “destabilizing” effect of the straight configuration of the front for sinusoidal perturbations with large wavelengths, which is typical of such finite crack geometries.     

Reaction sintering and microstructural evolution in metakaolin-metastable alumina composites

Fine needles of mullite grains were obtained successfully in a compact and low porous matrix using solid state sintering. We treated high-grade kaolin and sand-rich kaolin at 750 °C to amorphous metakaolins, and bauxite at 1,000 °C to metastable alumina. By designing a stochiometric composition of mullite, each amorphous metakaolin was added to metastable alumina. Fine grains of mullite with almost complete crystallization were obtained from 1,350 °C in a case of amorphous metakaolin from high-grade kaolin and at 1,550 °C in the other case where amorphous metakaolin is from sand-rich kaolin. The difference in the temperatures of mullitization was linked to the late dissolution of silica from the cristobalite and quartz phases which were still present in the sand-rich metakaolin sample at 1,350 °C. The use of metastable alumina and metakaolin instead of kaolin to design the mullite matrix allows the increase in number of mullite nucleation sites. This results to high densification and crystallization, fine grain size, and high mechanical properties of the final matrix.     

Some Cubic Birth and Death Processes and their Related Orthogonal Polynomials

The orthogonal polynomials with recurrence relation (λ,_n +μ_n-z)F_n(z) = μ_n+1F_n+1(z)+λ_n-1F_n-1(z) with two kinds of cubic transition rates λ_n and μ_n, corresponding to indeterminate Stieltjes moment problems, are analyzed. We derive generating functions for these two classes of polynomials, which enable us to compute their Nevanlinna matrices. We discuss the asymptotics of the Nevanlinna matrices in the complex plane.     

Learning to Solve Mathematical Application Problems: A Design Experiment With Fifth Graders

Recent research has shown that many upper elementary school children do not master the skill of solving mathematical application problems. In this design experiment, a learning environment for teaching and learning how to model and solve mathematical application problems was developed and tested in 4 classes of 5th graders. Pupils were taught a series of heuristics embedded in an overall metacognitive strategy for solving mathematical application problems. Meanwhile, pupils of 7 control classes followed regular mathematics classes. The implementation and effectiveness of the experimental learning environment were tested in a study with a pretest-posttest-retention test design with an experimental and a control group. The results indicate that the intervention had a positive effect on different aspects of pupils' mathematical modeling and problem-solving abilities.