Weyl Pseudo-Differential Operator and Wigner Transform on the Poincaré Disk

The purpose of this paper is to investigate some relations between the kernel of a Weyl pseudo-differential operator and the Wigner transform on Poincaré disk defined in our previous paper [11]. The composition formula for the class of the operators defined in [11] has not been proved yet. However, some properties and relations, which are analogous to the Euclidean case, between the Weyl pseudo-differential operator and the Wigner transform have been investigated in [11]. In the present paper, an asymptotic formula for the Wigner transform of the kernel of a Weyl pseudo-differential operator as 0 is given. We also introduce a space of functions on the cotangent bundle T ^* D whose definition is based on the notion of the Schwartz space on the Poincaré disk. For an S ¹-invariant symbol in that space, we obtain a formula to reproduce the symbol from the kernel of the Weyl pseudo-differential operator.     

Crystal Phases of TiO2 Ultrafine Particles Prepared by Laser Ablation of Solid Rods

Titanium dioxide ultrafine particles (UFPs) are produced by pulsed laser ablation of titanium or titanium dioxide (anatase and rutile) rods in an atmosphere of He or O₂/He mixture. The collected UFPs on cellulose membrane filters at the exit of the ablation chamber are analyzed by X-ray diffraction (XRD) and transmission electron microscopy (TEM). The TiO₂ particles produced are composed of very small particles (diameter: 10–50nm) that are completely anatase, irrespective of the rod material, and relatively large particles (diameter: 100nm–1m) that are a mixture of anatase and rutile. The large particles consist of the direct strip-off fragments coming from the rod surface. The particles obtained from the laser ablation on TiO₂ rods in an atmosphere of He contains gray particles that are supposed to be amorphous TiO₂ (x < 2). In the presence of O₂ in the ablation chamber, these oxygen defects in amorphous TiO₂ are stabilized and anatase UFPs are formed. These results suggest that the crystal phase of the products can be controlled by adjusting the rod material and the gases used in the ablation process.     

A Characterization of Some Minihypers and its Application to Linear Codes

Any {f,r- 2+s; r,q}-minihyper includes a hyperplane in PG(r, q) if fr-1 + s 1 + q – 1 for 1 s q – 1, q 3, r 4, where i = (qi + 1 – 1)/ (q – 1 ). A lower bound on f for which an {f, r – 2 + 1; r, q}-minihyper with q 3, r 4 exists is also given. As an application to coding theory, we show the nonexistence of [ n, k, n + 1 – qk – 2 ]q codes for k 5, q 3 for qk – 1 – 2q – 1 < n qk – 1 – q – 1 when k > q – q - \sqrt q + 2$$ " align="middle" border="0"> and for when , which is a generalization of [18, Them. 2.4].     

A versatile route to silylsubstituted ketones by rhodium catalyzed isomerization of silylated allyl alcohols

The rhodium catalyzed isomerization of α-, β-, and γ-silylated allyl alcohols has been successfully applied to the selective synthesis of acylsilane, α-silyl ketones, and β-silyl ketones, respectively.     

Novel synthesis of carbohydrates using electroreduction as key reactions

Glyceraldehyde was transformed to threose, erythrose, and erythrose using electro-reduction as key reactions.     

Spontaneous formation of cadmium hydroxide nanostrands in water

Cadmium hydroxide nanostrands with a diameter of 1.9 nm were spontaneously formed by raising the pH of a dilute Cd(NO3)2 solution. The length reaches a few micrometers and the aspect ratio exceeds 1000. The crystallographic structure was successfully elucidated by high-resolution electron microscopy. The surface of the nanostrands was remarkably positively charged and adsorbed an astonishing number of negatively charged dye molecules.     

Electromagnetically induced diffraction in sodium vapor

By using a sodium atomic vapor we have observed a honeycomb-type multiple-diffraction pattern that was due to a grating induced optically by three noncollinear bichromatic excitation beams. In particular, when the two incident frequencies satisfy the two-photon resonance condition and the atomic density is high, the diffraction is enhanced by electromagnetically induced transparency, and strong Stokes and anti-Stokes components are generated in well-defined directions.     

<Emphasis Type="Italic">p</Emphasis>-Nuclearity in a New Perspective

In this Letter we try to settle some confused points concerning the use of the notion of p-nuclearity in the mathematical and physical literature, pointing out that the nuclearity index in the physicists’ sense vanishes for any p> 1. Our discussion of these issues suggests a new perspective, in terms of ε-entropy and operator spaces, which might permit connections to be drawn between phase space criteria and quantum energy inequalities.Mathematics Subject Classification (2000): 81T05, 47B10, 47L25.