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Some asymptotic expansions non necessarily related to the central limit theorem are discussed. After observing that the smoothing inequality of Esseen implies the proximity, in the Kolmogorov distance sense, of the distributions of the random variables of two random sequences satisfying a sort of general asymptotic relation, two instances of this observation are presented. A first example, partially motivated by the the statistical theory of high precision measurements, is given by a uniform asymptotic approximation to $(g(X+ μ_n))_{n ın \mathbbm{N}}$, where $g$ is some smooth function, $X$ is a random variable having a moment and a bounded density and $(μ_{n})_{n ın \mathbbm{N}}$ is a sequence going to infinity; the multivariate case as well as the proofs and a complete set of references will be published elsewhere. We next present a second class of examples given by a randomization of the interesting parameter in some classical asymptotic formulas, namely, a generic Laplace's type integral, by the sequence $(μ_n X)_{n ın \mathbbm{N}}$, $X$ being a Gamma distributed random variable. Finally, a simulation study of this last example is presented in order to stress the quality of asymptotic approximations proposed.

Indium molybdenum oxide thin films were deposited using different radio-frequency sputtering units on glass substrates at room temperature from an In 2O 3 (95 wt.%): Mo (5 wt.%) target. The film thickness ranges between 160 and 275 nm. The chamber volume of Unit-1 was ̃2.4 times larger than that of Unit-2. Apart from the chamber volume, a significant difference between the two units was the sputtering pressure. The films were characterized by their structural, morphological, optical, and electrical properties. A strong reflection from (222) plane was obtained for the ̃275 nm thick films deposited in Unit-1. The films deposited with <275 nm thickness and those deposited in Unit-2 are close to amorphous with a small crystalline fraction. The surface of the films deposited in Unit-1 is comprised of randomly arranged crystallites, which is restructured with the increasing film thickness to become a well defined "rice field" like structure (275 nm thick). The films deposited in Unit-2 are comprised of many holes on the surface that is presumably due to back sputtering. The average visible transmittance calculated in the wavelength between 400 and 800 nm ranges from 70 to 82%. The optical band gap is found to vary between 3.80 and 3.86 eV. The lowest bulk resistivity of the films deposited in Unit-1 was increased from ̃4.06×10 -3 to 4.07×10 -1ωcm when deposited in Unit-2. The carrier concentration was decreased from 1.31×10 20 to 1.03×10 18 cm -3 but the Hall mobility increased from 11.7 to 15.0 cm2 V -1 s -1. © 2009 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

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Indium molybdenum oxide (IMO) thin films were deposited by RF magnetron sputtering on glass substrates at room temperature. The deposition and argon partial pressures were maintained at 6.0 × 10-1 Pa and 3.0 × 10-1 Pa, respectively. The oxygen partial pressure (OPP) was varied in the range 1.0-6.0 × 10-3 Pa. The films were sputtered at 40 W for 30 min using the target consisted In2O3 (98 wt%): Mo (2 wt%). The films are polycrystalline with a slight preferential orientation along (2 2 2) plane. The crystallinity is increased with the increasing OPP. The negative sign of Hall coefficient confirmed the n-type conductivity. A maximum mobility ∼19 cm2 V-1 s-1 is obtained for the films deposited with OPP of 3.6 × 10-3 Pa. The average visible transmittance calculated in the wavelength ranging 500-800 nm is ranging between 2% and 77%. The optical band gap calculated from the absorption data is varied between 3.69 and 3.91 eV. A striking feature is that the work function of the films is wide ranging 4.61-4.93 eV. A possibility of using the produced IMO films as transparent conducting oxide in photovoltaic applications such as organic solar cells is discussed in this article. © 2008 Elsevier Ltd. All rights reserved.

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We prove a higher order asymptotic formula for traces of finite block Toeplitz matrices with symbols belonging to Hölder-Zygmund spaces. The remainder in this formula goes to zero very rapidly for very smooth symbols. This formula refines previous asymptotic trace formulas by Szegő and Widom and complement higher order asymptotic formulas for determinants of finite block Toeplitz matrices due to Böttcher and Silbermann.

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Thin films of molybdenum doped indium oxide (IMO) were deposited on glass at room temperature using an in-built three-source RF magnetron sputtering. The films were studied as a function of oxygen volume percentage (O2 vol. %; ranging from 0.0 to 17.5%) in the sputtering chamber. The as-deposited amorphous films were crystallized on post-annealing. The as-deposited films are low conducting and Hall coefficients were undetectable; whereas post-annealed films possess fairly high conductivity. The lowest transmittance (11.96% at 600 nm) observed from the films deposited without oxygen increased to a maximum of 88.01% (3.5 O2 vol. %); whereas this transmittance was decreased with the increasing O2 vol. % to as low as 81.04% (15.6 O2 vol. %); a maximum of 89.80% was obtained from the films annealed at 500 °C in open air (3.5 O2 vol. %). The optical band gap of 3.80 eV obtained from the films deposited without oxygen increased with increasing O2 vol. % to as high as 3.91 eV (17.5 O2 vol. %). A maximum of 3.92 eV was obtained from the films annealed at 300 °C in N2:H2 gas atmosphere (17.5 O2 vol. %). © 2008 Elsevier Ltd. All rights reserved.

Indium molybdenum oxide thin films radio-frequency sputtered at room temperature on glass were studied as a function of oxygen volume percentage. The as-deposited films were post-annealed in the temperature range of 300-500 °C in oxidizing (open air) and reducing (N2:H2 gas) atmospheres for 1 h. The as-deposited amorphous films become crystalline on post-annealing irrespective of the annealing conditions. In most cases, the (2 2 2) diffraction line is emerged as the high intensive peak. The films annealed at ≥400 °C in N2:H2 show a carrier concentration >1020 cm-3. The better electrical properties are obtained for the films post-annealed at 300 °C. The optical transmittance of the as-deposited films varies between 10% and 85% depending on the deposition and annealing conditions. Atomic force microscope analysis reveal that the films annealed at 300 °C are composed of closely packed crystallites (size of which varies between 5 nm and 150 nm) whose size varies noticeably when the annealing temperature is raised to 400 °C. On the other hand, the surface of the films annealed at 500 °C becomes rougher, with the RMS roughness varying between 2.00 nm and 16.97 nm. The surface of the films deposited in the presence of oxygen shows metal like features when annealed at ≥400 °C in N2:H2 that is attributed to the segregation of indium. Further, the segregation of In is substantiated from the scanning electron microscope analysis of these samples. © 2008 Elsevier B.V. All rights reserved.

The theory of domain decomposition is described and used to divide the variable domain of a diatomic molecule into separate regions which are solved independently. This approach makes it possible to use fast Krylov methods in the broad interior of the region while using explicit methods such as Gaussian elimination on the boundaries. As is demonstrated by solving a number of model problems, these methods enable one to obtain solutions of the relevant partial differential equations and eigenvalue equations accurate to six significant figures with a small amount of computational time. Since the numerical approach described in this article decomposes the variable space into separate regions where the equations are solved independently, our approach is very well-suited to parallel computing and offers the long term possibility of studying complex molecules by dividing them into smaller fragments that are calculated separately.