Classification Des Ideaux a Droite De A1(k)

Les études récentes sur les idéaux àdroite de A₁(k), la première algèbre de Weyl surun corps algébriquement clos et de caractéristiquenulle k, nous montrent que : pour tout idéal I 0 àdroite de A₁(k), il existe x Q = frac(A₁(k)), et V V telsque : I = xD(R, V) o V est l'ensemble des sous-espaces primairementdécomposables de k[t] = R, et D(R, V), l'idéalà droite {d A₁(k/d(R V}. Dans cet article nous montreronsprincipalement que: pour tout 0 I idéal à droitede A₁(k, !n N, (x, ) Q^* x Aut_k(A₁(k)) : I = x(D(R, O(X_n))),où X_n est la courbe d'algèbre des fonctions régulières: O(X_n = k+tⁿ⁺¹k[t]. La forme des idéaux décriteci-dessus permet de voir dans une hypothèse de Letzteret Makar-Limanov, pour deux courbes algébriques affinesX et X' on a : D(XD(X') co dim D(X = co dim D(X'). Recent studies on right ideals of the first Weyl algebra A₁(k)over an algebraic closed field k with characteristic zero showthat: for each right ideal I 0 of A₁(k), there exist x Q =fracA₁(k)) and a primary decomposable sub-space V of k[t] suchthat I=xD(R,V), where D(R,V) : = {d A₁(k)/d(R) V} is a rightideal of A₁(k). In this paper, we show that for all right idealsI 0 of A₁(k), !n N, (x, ) Q^* x Aut_k(A₁(k)) : I = x(D(R, O(X_n))),where X_n denotes the affine algebraic curve with ring of regularfunctions O(X_n=k+tⁿ⁺¹k[t]. With ideals as described above, onecan easily see, under a hypothesis given by Letzter and Makar-Limanov,that for two affine algebraic curves X and X', D(X)D(X') codim D(X) = co dim D(X'). 2000 Mathematics Subject Classification16S32.     

Purification and Biochemical Characterization of Polyphenol Oxidases from Embryogenic and Nonembryogenic Cotton (<Emphasis Type="Italic">Gossypium hirsutum</Emphasis> L.) Cells

Polyphenol oxidases (PPOs) were isolated from cell suspensions of two cultivars of cotton (Gossypium hirsutum L.), and their biochemical characteristics were studied. PPO from Coker 312, an embryogenic cultivar, showed a highest affinity to catechol 20 mM, and PPO from R405-2000, a nonembryogenic cultivar, showed a highest affinity to 4-methylcatechol 20 mM. The optimal pH for PPO activity was 7.0 and 6.0 for Coker 312 and R405-2000, respectively. The enzyme had an optimal temperature of 25 °C and was relatively stable at 20–30 °C. Reducing sodium metabisulfite, ascorbic acid, dithiothreitol, SnCl₂, and FeCl₃ markedly inhibited PPO activity, whereas its activity was highly enhanced by Mg²⁺, Ca²⁺, and Mn²⁺ and was moderately inhibited by Ba²⁺, Cu²⁺, and Zn²⁺. The analysis revealed a single band on the sodium dodecyl sulfate polyacrylamide gel electrophoresis which corresponded to a molecular weight of 55 kDa for Coker 312 and 42 kDa for R405-2000.     

Synthesis of Novel Substituted Indazoles via Nucleophilic Substitution of Hydrogen (SNH)

New four‐substituted indazoles 4a–e were synthesized by regioselective nucleophilic substitution of hydrogen of N‐alkyl‐7‐nitroindazoles 2a,b with arylacetonitriles 3a–c . Compounds 4a–e were reacted with arylsulfonyl chloride in pyridine to give some new indazole linked sulfonamides with good yields. The S_NH at position C‐4 of 7‐nitroindazole with arylacetonitrile is confirmed by X‐ray diffraction analysis of compounds 4e and 6a .     

Purification and Characterization of Cell Suspensions Peroxidase from Cotton (<Emphasis Type="Italic">Gossypium hirsutum</Emphasis> L.)

Two peroxidases, cPOD-I and rPOD-II, have been isolated and purified from cotton cell suspension and their biochemical characteristics studied. rPOD-II from R405-2000, a non-embryogenic cultivar, has higher activity than cPOD-I derived from Coker 312, which developed an embryogenic structure. The cPOD-I and rPOD-II had molecular mass of 39.1 and 64 kDa respectively, as determined by SDS-PAGE. Both enzymes showed high efficiency of interaction with the guaiacol at 25 mM. The optimal pH for cPOD-I and rPOD-II activity was 5.0 and 6.0, respectively. The enzyme had an optimum temperature of 25 °C and was relatively stable at 20–30 °C. The isoenzymes were highly inhibited by ascorbic acid, dithiothreitol, sodium metabisulfite, and β-mercaptoethanol. Their activities were highly enhanced by Al³⁺, Fe³⁺, Ca²⁺, and Ni²⁺, but they were moderately inhibited by Mn²⁺ and K⁺. The enzyme lost 50% to 62% of its activity in the presence of Zn²⁺ and Hg²⁺.     

Determination of the Glyphosate Content in Liquid and Dry Formulations by HPLC-UV: Pre-column Derivation with 9-Fluorenylmethyl Chloroformate (FMOC)

Chromatographia - Monitoring the glyphosate content of glyphosate-based herbicides requires simple, inexpensive and accessible analytical methods. The objective of this work was to determine by...     

On the Automorphism Group of the First Weyl Algebra

Let A ₁: = 𝕜[t, ?] be the first algebra over a field 𝕜 of characteristic zero. Let Aut_𝕜(A ₁) be the automorphism group of the ring A ₁. One can associate to each right ideal I of A ₁ a subgroup of Aut_𝕜(A ₁) called the isomorphism subgroup of I. In this article, we show that each such isomorphism subgroup is equal to its normalizer. For that, we study when the isomorphism subgroup of a right ideal of A ₁ contains a given isomorphism subgroup.     

Stability of an erodible bed in various shear flows

The 2D laminar quasi-steady asymptotically simplified and linearized flow with a simplified mass transport of sediments is solved over a slowly erodible bed in various laminar basic shear flow (steady, oscillating or decelerating). The simplified mass transport equation includes the two following phenomena: flux of erosion when the skin friction goes over a threshold value, and a non local effect coming either from an inertial effect or from a slope effect. It is shown that the bed is always unstable for small wave numbers. Examples of long time evolution in various shear régimes are presented, wave trains of ripples are created and merge into a unique bump. This coarsening process is such that the maximum wave length obeys a power law with time.     

Effet dispersif de la loi d'Exner menant à l'équation de Benjamin–Ono : ondulations d'un sol meubleExner's law dispersive effects leading to Benjamin–Ono equation: waves over an erodible bed

The flow over an erodible bed is revisited supposing that the flux of sediments is proportional to the slip velocity of the potential flow. This gives a linear Benjamin–Ono equation which is numerically solved, this solution is favorably compared to a selfsimilar approached solution. To cite this article: P.-Y. Lagrée et al., C. R. Mecanique 331 (2003).     

Ultra-Fast Continuous-Flow Photo-Thiol-Ene Functionalization of Conformation-Controlled Cinchona Alkaloids

In this work, we describe ultra-fast continuous flow photo-thiol-ene reactions on cinchona alkaloids derivatives through a control of the reactive conformation in solution. Flow thiol-ene reactions proceed at 32 °C under light irradiation at 365 nm and require only 2.5 minutes of residence time to reach completion. The short path length of the tubular flow photochemical reactor, which maximizes and homogenizes the photon flux, associated to the fine tuning of the reactive conformation of cinchona alkaloids in solution are the main reasons for the high rates observed. The predominant conformation in solution of cinchona alkaloids was adjusted through the substitution of the hydroxyl group at C9 by a phenyl carbamate function.