Synthesis of Zn/Al mixed-oxide catalyst for carbonylation of glycerol with urea

Zn/Al mixed oxide was prepared by the coprecipitation or the hydrothermal method under different conditions and used as catalyst for synthesis of glycerol carbonate by carbonylation of glycerol with urea. The physical properties of the prepared Zn/Al mixed oxide particles were investigated, as well as their activity as catalyst in the mentioned synthesis. The dried Zn/Al mixed-oxide particles prepared by the coprecipitation method showed higher activity in synthesis of glycerol carbonate than those prepared by the hydrothermal method. The Zn/Al mixed oxide prepared by the coprecipitation method without NaNO₃ showed the highest catalytic activity in synthesis of glycerol carbonate.     

Wigner function and Bell’s inequalities for even and odd coherent states

The Wigner function and the symplectic tomogram of an entangled quantum state, which is a superposition of the photon’s coherent states (even and odd coherent states), is studied. Photon statistics and violation of Bell’s inequality for the photon state are discussed.     

Gradient-index fiber-optic microprobes for minimally invasive in vivo low-coherence interferometry

We describe the design, construction, and application of what are believed to be the smallest fiber-optic probes used to date during imaging or diagnosis involving low-coherence interferometry (LCI). The probes use novel fiber-optic gradient-index (GRIN) lenses fabricated by a recently developed modified chemical-vapor-deposition (MCVD) process that avoids on-axis aberrations commonly marring MCVD-fabricated GRIN substrate. Fusing GRIN fiber lenses onto single-mode fiber yields automatically aligned all-fiber probes that insert into tissue through hypodermic needles as small as 31-gauge (inner diameter, 127 mum). We demonstrate the use of such probes with LCI by measuring microscopic brain motions in vivo.     

Etude du Systeme Ternaire H2O-Al(NO3)3-Mg(NO3)2 I - Isothermes 15, 25, 30, 40 et 50°C

The solid-liquid equilibria of the ternary system H₂ O-Al(NO₃ )₃ -Mg(NO₃ )₂ were studied at 15, 25, 30, 40 and 50°C by using a synthetic method which allows to determine all the characteristic points of isothermal sections. In all isotherms the liquidus exhibit two curves corresponding to the saturation in Mg(NO₃ )₂ ⋅6H₂ O and Al(NO₃ )₃ ⋅9H₂ O. Neither double salts nor mixed crystals are observed in the temperature and composition field studied. This revised version was published online in July 2006 with corrections to the Cover Date.     

Entropy and information characteristics of qubit states

Shannon entropy, Rényi entropy, and Tsallis entropy are discussed for the tomographic probability distributions of qubit states. Relative entropy and its properties are considered for the tomographic probability distribution describing the states of multi-spin systems. New inequalities for Hermite polynomials are obtained.     

On the Constitutive Equations of Some Weakly‐Textured Materials

(Accepted May 16, 1997)