A general rice formula,palm measures,and horizontal-window conditioning for random fields

In the first main result the mean (m?n)-dimensional Hausdorff measure of the set of crossing points of a level y ? $\text{R}$ⁿ by an m-dimensional continuous random vector field with values in R _ⁿ, m?n, is computed. The second one deals with horizontal-window conditional (Palm) distributions for such random fields. For this purpose, a general concept of Palm measures is introduced, which contains both the ‘stationary’ and the ‘nonstationary’ one.     

Characteristics of queueing systems observed at events and the connection between stochastic intensity and palm probability

This article explores the link between the concepts of stochastic intensity and Palm probability and gives a new proof and useful extensions to the so-called PASTA property of queueing theory.     

Thermal processes of a powder particle in coaxial laser cladding

This paper presents a numerical analysis of the heating, melting and evaporation processes of a single spherical powder particle when irradiated by a CO₂ laser beam in coaxial laser cladding. The power particle has a size ranging from 20 to 200 μm and the intensity of the laser has been varied from 500 to 3000 W. The laser energy, initial powder velocity and size have been shown to have important effects on the temperature profile of the powder stream. It has also been shown that high powder evaporation due to high power laser radiation may induce significant loss in the powder particle mass, to as much as 25% of the initial size at certain conditions in the simulation.     

A note on the conservation law for continuous reflected processes and its application to queues with fluid inputs

In this note we provide a new derivation of a conservation law for stationary continuous reflected processes which arise in the context of fluid queueing models. This readily gives the so-called Little's law for fluid queues as a special case. We then apply the result to compute the Laplace transform of the stationary workload distribution for a queue with fluid ON-OFF inputs in terms of the Palm distribution associated with the beginning of ON periods. This revised version was published online in June 2006 with corrections to the Cover Date.     

Complete and limited substitution of rare-earth elements in apatite silicates La(9-x)Lnx(SiO4)6O1.5

The isomorphous substitution of smaller RE elements (Ln = Nd, Eu, Gd, Ho, Tm, and Yb) for lanthanum in the apatite silicate solid solutions La_9−xLn_x(SiO₄)₆O_1.5 was studied by X-ray powder diffraction and the Rietveld structure refinement, scanning electron microscopy and energy-dispersive X-ray microanalysis. Single-phase samples were prepared by solid-state synthesis at a moderate temperature of 1200 °C using an amorphous SiO₂ nanopowder (10–40 nm) as a reactant. As the atomic number of Ln increases, the complete solubility, 0 ≤ x ≤ 9, found in the systems with Ln = Nd, Eu, Gd, and Ho changes to a limited one for Ln = Tm (0 ≤ x < 1.5) and Yb (0 ≤ x < 1). The distribution of La and smaller Ln over two structurally independent cationic sites is close to statistical. In both cationic polyhedra, Ln(1)O₉ and Ln(2)O₇, the bond lengths Ln – O decrease with x, except the longest bonds Ln(1) – O(3) and Ln(2) – O(1) which increase slightly. The experimental results on the substitution limits agree with the values of the mixing energy, and critical temperature of miscibility calculated in the approximation of a regular solid solution.     

Structural development and kinetic analysis of PbTiO3 powders processed at low-temperature via new sol-gel approach

The synthesis of crystalline lead titanate powder by a generic low-temperature sol-gel approach is developed. Acetoin was added as ligand, instead of the commonly used alkanolamines, to ensure total dissolution of the precursor compounds. The feasibility of the acetoin-Ti isopropoxide complex as a new precursor of PbTiO₃ perovskite particles via sol-gel method has been demonstrated. No excess lead has been introduced. Nanometric PbTiO₃ crystallites have been formed at 400 °C under atmospheric pressure from titanium isopropoxide and lead acetate in alcoholic solution by remarkably low activation energy of crystallization process of 90 kJ mol⁻¹. The powders show tetragonal lattice and dendritic morphology. In addition to the effect of heat-treatment temperature, time, and atmosphere, the sol chemistry particularly influenced the phase composition, particle size, and particle morphology. The use of different ligands significantly modified powder morphology. The extent of the crystallization was quantitatively evaluated by differential thermal analysis and analyzed by Johnson-Mehl-Avrami approach. The crystallization followed two rate regimes depending on the interval of the crystallized fraction.     

Solid-state structural properties of 2,4,6-trimethoxybenzene derivatives, determined directly from powder X-ray diffraction data in conjunction with other techniques

Structural properties of 2,4,6-trimethoxybenzaldehyde, 2,4,6-trimethoxybenzyl alcohol and 2,4,6-trimethoxyacetophenone have been determined directly from powder X-ray diffraction data, using the direct-space Genetic Algorithm (GA) technique for structure solution followed by Rietveld refinement. Structural similarities and contrasts within this family of materials are elucidated. The work illustrates the value of utilizing information from other sources, including spectroscopic data and computational techniques, as a means of augmenting the structural knowledge established from the powder X-ray diffraction data.     

A combined X-ray diffraction and Raman scattering study of the phase transitions in Sr1−xCaxTiO3 (x=0.04, 0.06, and 0.12)

Results of powder X-ray diffraction and Raman scattering studies on the phase transitions in Sr_1−xCa_xTiO₃ (SCT) are presented for x=0.04, 0.06 and 0.12 in the temperature range 8-473 K. It is proposed that the space group of SCT in the composition range 0.06?x?0.35 is Imma with a⁰b^-b^- tilt system and not I4/mcm with a⁰a⁰c^- tilt system, as assumed by earlier workers. The lowering of the crystal symmetry from I4/mcm to Imma is supported by the observation of additional Raman lines, in agreement with the factor group analysis for the Imma space group. The structural E_g mode, characteristics of the non-cubic phase, is shown to be present even in the cubic phases of x=0.06 and x=0.12 but not of x=0.04 indicating the change in the local structure of the cubic phase of SCT for x?0.06. The presence of symmetry forbidden TO₂ mode in the Raman spectra of the cubic phase of SCT for x<0.06 and its absence for x?0.06 provides yet another characteristic feature distinguishing the I4/mcm and Imma space groups. The implications of the change in the tilt system from a⁰a⁰c^- to a⁰b^-b^- on the development of the polar order is also discussed.     

Ternary Alkali Metal Transition Metal Acetylides

The first alkali metal transition metal acetylides of general composition A₂M⁰C₂ (A = Na ? Cs, M⁰ = Pd, Pt) were obtained by solid state reactions of alkali metal acetylides with palladium and platinum. They are characterized by chains, which are separated by alkali metal ions. Analogous chains also separated by alkali metal ions are the characteristic structural feature of acetylides of composition AM^IC₂, which are accessible by reacting AC₂H with M^II in liquid ammonia (A = Li ? Cs, M^I = Cu, Ag, Au). Despite their structural similarities they possess different properties, as acetylides of composition A₂M⁰C₂ are semiconductors with very small indirect band gaps and slightly extended C–C distances compared to a C–C triple bond, whereas acetylides of composition AM^IC₂ show a typical salt‐like behavior with C–C distances close to the expected value for a C–C triple bond of 120 pm. But with the help of simple chemical models these differences can be made plausible. Furthermore, it is shown that only by a combination of different methods (powder diffraction with X‐rays and neutrons, solid state NMR spectroscopy, Raman spectroscopy) it was possible to characterize this new class of compounds structurally and chemically.     

Intercalation of cyclic ketones into vanadyl phosphate

Intercalation compounds of vanadyl phosphate with cyclic ketones (cyclopentanone, cyclohexanone, 4-methylcyclohexanone, and 1,4-cyclohexanedione) were prepared from corresponding propanol or ethanol intercalates by a molecular exchange. The intercalates prepared were characterized using powder X-ray diffraction and thermogravimetric analysis. The intercalates are stable in dry environment and decompose slowly in humid air. Infrared and Raman spectra indicate that carbonyl oxygens of the guest molecules are coordinated to the vanadium atoms of the host layers. The local structure and interactions in the cyclopentanone intercalate have been suggested on the basis of quantum chemical calculations.