A theorem on iterations of polynomial maps in several variables

We establish a polynomial version of a theorem obtained by Enflo, Gurarii, Lomonosov and Lyubich for linear operators. As a consequence, we also derive a polynomial version of a result due to Pták.

     

Working group report: Heavy-ion physics and quark-gluon plasma

This is the report of Heavy Ion Physics and Quark-Gluon Plasma at WHEPP-09 which was part of Working Group-4. Discussion and work on some aspects of quark-gluon plasma believed to have created in heavy-ion collisions and in early Universe are reported.     

Synthesis and characterization of SiO2–CrO3, SiO2–MoO3, and SiO2–WO3 mixed oxides produced using the non-hydrolytic sol–gel process

Silica-based mixed oxide xerogels, namely SiO₂–CrO₃, SiO₂–MoO₃, and SiO₂–WO₃, were prepared using the non-hydrolytic sol–gel process. The materials were synthesized using metal chloride:tetraethoxysilane (TEOS) molar ratios of 0.1:2; 0.2:2 and 0.4:2 for each metal chloride and 1:2 SiCl₄:TEOS molar ratio. All of the xerogels containing Cr, Mo or W had considerably greater surface areas than that of SiO₂. The small angle X-ray scattering experiments suggest that the surface roughness of the aggregates in SiO₂–CrO₃ is less than that of SiO₂–MoO₃ and SiO₂–WO₃. The morphological characteristics of the silica-based mixed oxide xerogels were not affected by the nature and amount of metal chloride employed in the synthesis. An irregular morphology was observed for SiO₂–CrO₃, SiO₂–MoO₃ and SiO₂–WO₃, but a lamellar structure was observed for SiO₂. X-ray photoelectron spectroscopy analysis suggests that tungsten species were preferentially distributed on the outmost part of the grain. The resulting particle diameter was shown to be lower for the mixed oxides compared to that of bare silica. Furthermore, the presence of metals (Cr, Mo and W) on silica caused a decrease in the size of the particles as the atomic radii of these metals increased. According to the Fourier transform infrared spectroscopy and Raman, Cr, Mo and W were incorporated within the silica framework.