Convergence in variation of the laws of multiple stable integrals

Multiple stable integrals generalize Wiener–Itô integrals, their construction being based upon a generalized LePage representation. This approach allows one to study their behaviour. We are interested in this Note in the continuity for total variation norm of the laws of these integrals I_d(f) with respect to f. To cite this article: J.-C. Breton, C. R. Acad. Sci. Paris, Ser. I 338 (2004).     

A First Order Sufficient Condition for Optimality in Nonsmooth Optimization

We derive a simple sufficient condition for a point a∈S?X be a local minimum of f: X → R on S. This condition is of the first order in its nature and takes into account the derivative (or some generalization of it) in a neighborhood of a. Applications like a sufficient condition for (a, b)∈ S × T ? X × Y be a saddle-point of a bivariate function f: X × Y ? R are also proposed.     

Pupils learning algebra with DERIVE

This article deals with the use of computer algebra systems in mathematics secondary education. First, we present the global framework of a research project carried out in France with pupils of grades 9 to 12, from 1993 through 1995. Then we focus on a specific part of this project concerning two grade 9 classes of different mathematical ability taught by the same teacher. We briefly present the aims and organisation of DERIVE's use in the two classes, before embarking with more details on a specific topic: systems of linear equations. Finally, we present the data provided by the pupils' answers to a questionnaire taken at the end of the academic year; we use them for investigating pupils' assumptions about DERIVE's potential for mathematics learning, and compare these representations with those emerging from the entire population.     

Dynamics of a bilayer membrane with membrane-solvent partial slip boundary conditions

We discuss the dynamics of a bilayer membrane with partial slip boundary conditions between the monolayers and the bulk fluid. Using Onsager’s variational principle to account for the associated dissipations, we derive the coupled dynamic equations for the membrane height and the excess lipid density. The newly introduced friction coe?cients appear in the renormalized fluid viscosities. For ordinary lipid bilayer membranes, we find that it is generally justified to ignore the e?ects of permeation and parallel slip at the membrane surface.     

Synthesis of Delta(1)-1,2-diazetines via a Diels-Alder cycloaddition approach

[reaction: see text] A novel method for the synthesis of Delta(1)-1,2-diazetines is presented. Diels-Alder cycloaddition of dienophile 4 with five dienes afforded cycloadducts in good to excellent yields. Four of the obtained cycloadducts were converted to the corresponding diazetines.     

Evaluation of Energy Balance in a Batch and Circulating Non-thermal Plasma Reactors During Organic Pollutant Oxidation in Aqueous Solution

Plasma Chemistry and Plasma Processing - This work presents the treatment of an organic waste solution using gliding arc plasma in moist air, which is an excellent source of oxidizing species....     

Synthesis of a stereochemically defined 1,2-diazetine N,N'-dioxide and a study of its thermal decomposition

Diazetine dioxide 1a has been synthesized in a single step via oxidation of meso-2,3-diphenyl-1,2-ethanediamine with dimethyldioxirane, albeit in low yield (7%). Thermal decomposition of 1a afforded predominantly either trans-stilbene or diphenyl glyoxime depending on solvent, temperature, and the presence of an amine catalyst. Reaction in chloroform at 69 degrees C favored elimination of NO and formation of trans-stilbene. The stereospecific formation of trans-stilbene suggests a mechanism of decomposition in which C-N bond cleavage leads to a diradical intermediate stabilized by the phenyl group. Bond rotation followed by cleavage of the second C-N bond accounts for the trans-stilbene. At 25 degrees C in chloroform, while trans-stilbene was still the major product, some diphenyl glyoxime was also observed (4% yield). However, 1a as a solution in chloroform in the presence of Et3N, or 1a as a solution in DMSO-d6, afforded predominantly diphenyl glyoxime. These results are interpreted in terms of two closely competing reactions subject to the effects of entropic contributions.     

Alternative synthetic routes to N-methyl-1,2,4-triazoline-3,5-dione (MeTAD) and other triazolinedione derivatives

N-Methyl-1,2,4-triazoline-3,5-dione (MeTAD) is a powerful electrophile and a versatile synthetic reagent. In this Letter we describe two methods for the synthesis of N-methylurazole, the direct precursor to MeTAD, on gram scales and in good yields. Both methods provide pure urazole while avoiding the necessity of large scale purification via column chromatography or recrystallization. One of the methods proved to be amenable for the synthesis of derivatives other than N-methyl.