Design Method for Optical Waveguide Filters Having Corrugation Structures by Corrugation Width Modulation

A method to design a corrugated optical waveguide filter by modulating the corrugation width profile is proposed. This method is based on combined applications of the Fourier transformation and the F-matrix formalism. The method achieves the spatial profile of the corrugation width required to design a filter with any specified spectral profile of the reflection coefficient. The idea of the technique is that the spatial variation of the effective refractive index can be transformed, with the help of the F-matrix formalism, to variation of the corrugation width while maintaining a constant amplitude of the refractive index variation. Two examples are given applying the technique to the design of optical waveguide filters with reflectivity profiles of two- and four-rejection bands.     

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].     

Callosal connections of dorsal versus ventral premotor areas in the macaque monkey: a multiple retrograde tracing study

Background  

The lateral premotor cortex plays a crucial role in visually guided limb movements. It is divided into two main regions, the dorsal (PMd) and ventral (PMv) areas, which are in turn subdivided into functionally and anatomically distinct rostral (PMd-r and PMv-r) and caudal (PMd-c and PMv-c) sub-regions. We analyzed the callosal inputs to these premotor subdivisions following 23 injections of retrograde tracers in eight macaque monkeys. In each monkey, 2–4 distinct tracers were injected in different areas allowing direct comparisons of callosal connectivity in the same brain.     

Invariance des probabilités de retour sur des groupes localement compacts

We construct an asymptotic invariant for locally compact separable, compactly generated unimodular groups. If G is such a group and if F is a symmetric bounded density on it with second order moment (with respect to a word metric), we show that the asymptotic behavior of $n?F^{1(2n)}(e)$ does not depend on the choice of the density F. As an example we show that the asymptotic of the return probabilities on $\mathrm{sol}(K)$ where K is a p-field behaves like $\exp (?t^{(1/3)})$. In the case where $K={\mathbb{Q}}_p$ this answers a question of Pittet and Saloff-Coste published recently by Mustapha. To cite this article: D. Gretete, C. R. Acad. Sci. Paris, Ser. I 342 (2006).     

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.     

Elements with generalized bounded conjugation orbits

For a pair of linear bounded operators and on a complex Banach space , if commutes with then the orbits of under are uniformly bounded. The study of the converse implication was started in the 1970s by J. A. Deddens. In this paper, we present a new approach to this type of question using two localization theorems; one is an operator version of a theorem of tauberian type given by Katznelson-Tzafriri and the second one is on power-bounded operators by Gelfand-Hille. This improves former results of Deddens-Stampfli-Williams.     

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.