On divisors of a quadratic form

An approximation is given for the number of divisors of the quadratic formn²+m²+t².Supported by University of the Basque Country.     

Raman study of WO3 thin films

The influence of substrates, thermal treatment and coloration-bleaching cycles on the structure of WO₃ thin films used in electrochromic devices has been investigated by Raman microscopy. Films (2000–8000 Å) were prepared by RF sputtering from a metallic tungsten target at a constant pressure (5 × 10^?3Torr) of pure oxygen or a mixture of Ar20% O₂. They are amorphous, transparent and electrochromic. Thermal treatment at 360°C produces crystallization. Modifications of the WO₃ framework are also induced by coloration-bleaching cycles.     

Taking advantage of the radical character of tris(2,4,6-trichlorophenyl)methyl to synthesize new paramagnetic glassy molecular materials

This paper describes the synthesis of the novel bis[4-(N-carbazolyl)-2,6-dichlorophenyl](2,4,6-trichlorophenyl)methyl radical (2*) and tris[4-(N-carbazolyl)-2,6-dichlorophenyl]methyl radical (3*). A Friedel-Crafts reaction on [4-(N-carbazolyl)-2,6-dichlorophenyl)bis(2,4,6-trichlorophenyl]methyl radical (1*), 2*, and 3* leads to the introduction of acyl chains in the 3- and 6-positions of the carbazolyl moiety without impairment of the radical character of the molecule to give radicals 5*, 6*, and 7*. All of these novel radical adducts are thermally stable, 5* and 6* being amorphous solids by differential scanning calorimetry. Electron paramagnetic resonance spectra of them show a multiplet at low temperature due to the electron-coupling with six aromatic hydrogens. They show electrochemical amphotericity being reduced and oxidized to their corresponding stable anionic and cationic species, respectively. These radical adducts have luminescent properties covering the red spectral band of the emission with high intensities.     

Stability of smectic phases in hard-rod mixtures

Using density-functional theory, we have analyzed the phase behavior of binary mixtures of hard rods of different lengths and diameters. Previous studies have shown a strong tendency of smectic phases of these mixtures to segregate and, in some circumstances, to form microsegregated phases. Our focus in the present work is on the formation of columnar phases which some studies, under some approximations, have shown to become thermodynamically stable prior to crystallization. Specifically we focus on the relative stability between smectic and columnar phases, a question not fully addressed in previous work. Our analysis is based on two complementary perspectives: on the one hand, an extended Onsager theory, which includes the full orientational degrees of freedom but with spatial and orientational correlations being treated in an approximate manner; on the other hand, we formulate a Zwanzig approximation of fundamental-measure theory on hard parallelepipeds, whereby orientations are restricted to be only along three mutually orthogonal axes, but correlations are faithfully represented. In the latter case novel, complete phase diagrams containing regions of stability of liquid-crystalline phases are calculated. Our findings indicate that the restricted-orientation approximation enhances the stability of columnar phases so as to preempt smectic order completely while, in the framework of the extended Onsager model, with full orientational degrees of freedom taken into account, columnar phases may preempt a large region of smectic stability in some mixtures, but some smectic order still persists.     

Brønsted acid−catalyzed synthesis of tetrasubstituted allenes and polysubstituted 2H-chromenes from tertiary propargylic alcohols

A practical and environmentally benign Brønsted acid?catalyzed protocol for the preparation of all-carbon tetrasubstituted allenes, consisting in the direct S_N? addition of tri- or dimethoxy arenes or allyltrimethylsilane to tertiary propargylic alcohols, has been developed. In addition, a straightforward synthesis of densely substituted 2H-chromenes by metal-free tandem allenylation/heterocyclization reaction of methoxyphenols and tertiary alkynols is presented.     

A survey on Cox rings

We survey the construction of the Cox ring of an algebraic variety X and study the birational geometry of X when its Cox ring is finitely generated. Basic notation. Throughout this paper k is an algebraically closed field.     

PROMOTIONAL EFFECT OF Sn ON NO OXIDATION OVER Pt/Al2O3 AS PROMISING GAS EXHAUST CATALYTIC CONVERTER. SELECTIVE Pt AND Sn DISPERSION DETERMINATION

NO oxidation was investigated over Pt-Sn/g-Al₂O₃. The addition of Sn to 1%Pt/g-Al₂O₃ enhances NO oxidation to NO₂. This effect is related to the enhancement of chemisorbed oxygen on the metallic surface produced by Sn.     

Borides and vitreous compounds sintered as high-energy fuels

Boron was chosen as fuel in view of its excellent thermodynamic values for combustion, as compared to traditional fuels. The problem of the boron in combustion is the formation of a surface layer of oxide, which delays the ignition process, reducing the performance of the rocket engine. This paper presents a high-energy fuel for rocket engines. It is composed of sintered boron (borides and carbides and vitreous compounds) with a reducing chemical agent. Borides and boron carbide were prepared since the combustion heat of the latter is similar to that of the amorphous boron (in: K.K. Kuo (Ed.), Boron-Based Solid Propellant and Solid Fuel, Vol. 427, CRC Press, Boca Raton, FL, 1993). Several chemical reducing elements were used, such as aluminum, magnesium, and coke. As the raw material for boron, different compounds were used: amorphous boron, boric acid and boron oxide.