Finding charm at RHIC

Dileptons produced by hard scatterings, such as heavy quark decays and the Drell-Yan mechanism, probe the gluon and sea quark distributions in hadrons. In nucleus-nucleus collisions, these processes are the thermal ‘back-ground’. To determine the magnitude and behavior of this background, we calculate the hard scattering contribution to next to leading order in perturbative QCD at RHIC. We compare these results to optimistic estimates of thermal dilepton production and find that initial charm production is dominant. However, experimental cuts can reduce the charm background, enhancing thermal information.     

Crystal chemistry and stability of "Li7La3Zr2O12" garnet: a fast lithium-ion conductor

Recent research has shown that certain Li-oxide garnets with high mechanical, thermal, chemical, and electrochemical stability are excellent fast Li-ion conductors. However, the detailed crystal chemistry of Li-oxide garnets is not well understood, nor is the relationship between crystal chemistry and conduction behavior. An investigation was undertaken to understand the crystal chemical and structural properties, as well as the stability relations, of Li(7)La(3)Zr(2)O(12) garnet, which is the best conducting Li-oxide garnet discovered to date. Two different sintering methods produced Li-oxide garnet but with slightly different compositions and different grain sizes. The first sintering method, involving ceramic crucibles in initial synthesis steps and later sealed Pt capsules, produced single crystals up to roughly 100 μm in size. Electron microprobe and laser ablation inductively coupled plasma mass spectrometry (ICP-MS) measurements show small amounts of Al in the garnet, probably originating from the crucibles. The crystal structure of this phase was determined using X-ray single-crystal diffraction every 100 K from 100 K up to 500 K. The crystals are cubic with space group Ia3?d at all temperatures. The atomic displacement parameters and Li-site occupancies were measured. Li atoms could be located on at least two structural sites that are partially occupied, while other Li atoms in the structure appear to be delocalized. (27)Al NMR spectra show two main resonances that are interpreted as indicating that minor Al occurs on the two different Li sites. Li NMR spectra show a single narrow resonance at 1.2-1.3 ppm indicating fast Li-ion diffusion at room temperature. The chemical shift value indicates that the Li atoms spend most of their time at the tetrahedrally coordinated C (24d) site. The second synthesis method, using solely Pt crucibles during sintering, produced fine-grained Li(7)La(3)Zr(2)O(12) crystals. This material was studied by X-ray powder diffraction at different temperatures between 25 and 200 °C. This phase is tetragonal at room temperature and undergoes a phase transition to a cubic phase between 100 and 150 °C. Cubic "Li(7)La(3)Zr(2)O(12)" may be stabilized at ambient conditions relative to its slightly less conducting tetragonal modification via small amounts of Al(3+). Several crystal chemical properties appear to promote the high Li-ion conductivity in cubic Al-containing Li(7)La(3)Zr(2)O(12). They are (i) isotropic three-dimensional Li-diffusion pathways, (ii) closely spaced Li sites and Li delocalization that allow for easy and fast Li diffusion, and (iii) low occupancies at the Li sites, which may also be enhanced by the heterovalent substitution Al(3+) ? 3Li.     

On asymptotically stabilizing the Rikitake two-disk dynamo dynamics

In this paper, we give a method to stabilize asymptotically the nontrivial Lyapunov stable equilibrium states of Rikitake two-disk dynamo dynamics.     

From searching text to querying XML streams

XML data is queried with a limited form of regular expressions, in a language called XPath. New XML stream processing applications, such as content-based routing or selective dissemination of information, require thousands or millions of XPath expressions to be evaluated simultaneously on the incoming XML stream at a high, sustained rate. In its simplest approximation, the XPath evaluation problem is analogous to the text search problem, in which one or several regular expressions need to be matched to a given text. At a finer level, it is related to the tree pattern matching problem. However, unlike the traditional setting, the number of regular expressions here is much larger, while the “text” is much shorter, since it corresponds to the depth of the XML stream. In this paper we examine techniques that have been proposed for XML stream processing and describe a few open problems.     

Solid-state nuclear magnetic resonance investigation of synthetic phlogopite and lepidolite samples

In the present work, our aim is to decipher the cationic ordering in the octahedral and tetrahedral sheets of two Al-rich synthetic materials, namely, phlogopites of nominal composition K(Mg_3-xAl_x)[Al_1+xSi_3-xO₁₀](OH)_yF_2-y and lepidolites in the system trilithionite–polylithionite with composition K (Li_xAl_3-x)[Al_4-2xSi_2xO₁₀](OH)_yF_2-y, by directly probing the aluminium distribution through ²⁷Al and ¹⁷O magic-angle spinning, multiple-quantum magic-angle spinning, and ²⁷Al-²⁷Al double-quantum single-quantum nuclear magnetic resonance (NMR) experiments. Notably, ²⁷Al-²⁷Al double-quantum single-quantum magic-angle spinning NMR spectra, recorded at 9.34 and/or 20.00 T, show the spatial proximity or avoidance of the Al species inside or between the sheets. In both studied minerals, the ensemble of NMR data suggests a preference for ^[4]Al in the tetrahedral sheet to occupy position close to the ^[6]Al of the octahedral sheets.     

Borel-Carathéodory and Fan Type Inequalities for Hilbert Space Bicontractions

This paper deals with some operator versions of the classical Borel–Carathéodory and Ky Fan theorems for analytic functions of complex variable. Our results refer to the functional calculus with analytic functions on the unit bidisk induced by strict bicontractions on a complex Hilbert space.