Traité d'analyse /

t. 1. Intégrales simples et multiples. Lʼéquation de Laplace et ses applications. Développments in séries. Applications géométriques du calcul infinitésimal.

Œuvres complètes de Regnard.

Mode of access: Internet.

Journal de l'École polytechnique.

Cahiers 7-10 were originally intended to comprise "Mécanique philosophique, par R. Prony" in 5 parts, but only the first 3 parts were published, forming cah. 7-8. Later, Prony's work was withdrawn from the series and in its place "Leçons de mathématiques données à l'École normale en 1795" by Legrange and Laplace were published as cah. 7-8.

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Thesis (Master's)--University of Washington, 2016-06

Mechanical alloying of MoSi2 with ternary alloying elements. Part 1: Experimental

Phase evolution during the mechanical alloying of Mo and Si elemental powders with a ternary addition of Al, Mg, Ti or Zr was monitored using X-ray diffraction. Rietveld analysis was used to quantify the phase proportions. When Mo and Si are mechanically alloyed in the absence of a ternary element, the tetragonal C11b polymorph of MoSi2 (t-MoSi2) forms by a self-propagating combustion reaction. With additional milling, the tetragonal phase transforms to the hexagonal C40 structure (h-MoSi2). The mechanical alloying of Al, Mg and Ti additions with Mo and Si tend to promote a more rapid transformation of t-MoSi2 to h-MoSi2. In high concentrations, the addition of these ternary elements inhibits the initial combustion reaction, instead promoting the direct formation of h-MoSi2. The addition of Zr tends to stabilise the tetragonal phase.

Diffusion modeling of percutaneous absorption kinetics: 3. Variable diffusion and partition coefficients, consequences for stratum corneum depth profiles and desorption kinetics

Stratum corneum (SC) desorption experiments have yielded higher calculated steady-state fluxes than those obtained by epidermal penetration studies. A possible explanation of this result is a variable diffusion or partition coefficient across the SC. We therefore developed the diffusion model for percutaneous penetration and desorption to study the effects of either a variable diffusion coefficient or variable partition coefficient in the SC over the diffusion path length. Steady-state flux, lag time, and mean desorption time were obtained from Laplace domain solutions. Numerical inversion of the Laplace domain solutions was used for simulations of solute concentration-distance and amount penetrated (desorbed)-time profiles. Diffusion and partition coefficients heterogeneity were examined using six different models. The effect of heterogeneity on predicted flux from desorption studies was compared with that obtained in permeation studies. Partition coefficient heterogeneity had a more profound effect on predicted fluxes than diffusion coefficient heterogeneity. Concentration-distance profiles show even larger dependence on heterogeneity, which is consistent with experimental tape-stripping data reported for clobetasol propionate and other solutes. The clobetasol propionate tape-stripping data were most consistent with the partition coefficient decreasing exponentially for half the SC and then becoming a constant for the remaining SC. (C) 2004 Wiley-Liss, Inc.

Full S matrix calculation via a single real-symmetric Lanczos recursion: The Lanczos artificial boundary inhomogeneity method

We present an efficient and robust method for the calculation of all S matrix elements (elastic, inelastic, and reactive) over an arbitrary energy range from a single real-symmetric Lanczos recursion. Our new method transforms the fundamental equations associated with Light's artificial boundary inhomogeneity approach [J. Chem. Phys. 102, 3262 (1995)] from the primary representation (original grid or basis representation of the Hamiltonian or its function) into a single tridiagonal Lanczos representation, thereby affording an iterative version of the original algorithm with greatly superior scaling properties. The method has important advantages over existing iterative quantum dynamical scattering methods: (a) the numerically intensive matrix propagation proceeds with real symmetric algebra, which is inherently more stable than its complex symmetric counterpart; (b) no complex absorbing potential or real damping operator is required, saving much of the exterior grid space which is commonly needed to support these operators and also removing the associated parameter dependence. Test calculations are presented for the collinear H+H-2 reaction, revealing excellent performance characteristics. (C) 2004 American Institute of Physics.

Magnetosomal matrix: ultrafine structure may template biomineralization of magnetosomes

The organic matrix surrounding bullet-shaped, cubo-octahedral, D-shaped, irregular arrowhead-shaped, and truncated hexa-octahedral magnetosomes was analysed in a variety of uncultured magnetotactic bacteria. The matrix was examined using low- (80 kV) and intermediate- (400 kV) voltage TEM. It encapsulated magnetosomes in dehydrated cells, ultraviolet-B-irradiated dehydrated cells and stained resin-embedded fixed cells, so the apparent structure of the matrix does not appear to be an artefact of specimen preparation. High-resolution images revealed lattice fringes in the matrix surrounding magnetite and greigite magnetosomes that were aligned with lattice fringes in the encapsulated magnetosomes. In all except one case, the lattice fringes had widths equal to or twice the width of the corresponding lattice fringes in the magnetosomes. The lattice fringes in the matrix were aligned with the {311}, {220}, {331}, {111} and {391} related lattice planes of magnetite and the {222} lattice plane of greigite. An unidentified material, possibly an iron hydroxide, was detected in two immature magnetosomes containing magnetite. The unidentified phase had a structure similar to that of the matrix as it contained {311}, {220} and {111} lattice fringes, which indicates that the matrix acts as a template for the spatially controlled biomineralization of the unidentified phase, which itself transforms into magnetite. The unidentified phase was thus called pre-magnetite. The presence of the magnetosomal matrix explains all of the five properties of the biosignature of the magnetosomal chain proposed previously by Friedmann et al. and supports their claim that some of the magnetite particles in the carbonate globules in the Martian meteorite ALH84001 are biogenic. Two new morphologies of magnetite magnetosomes are also reported here (i.e. tooth-shaped and hexa-octahedral magnetosomes). Tooth-shaped magnetite magnetosomes elongated in the [110] direction are reported, and are distinct from arrowhead-shaped and bullet-shaped magnetosomes. Elongation of magnetite magnetosomes in the [110] direction has not been reported previously. A Martian hexa-octahedral magnetite particle was previously characterized by Thomas-Keptra et al. and compared with truncated hexa-octahedral magnetite magnetosomes. Hexa-octahedral magnetite magnetosomes with the same morphology and similar sizes and axial ratios as those reported by Thomas-Keptra et al. are characterized here. These observations support their claim that ALH84001 contains evidence for a past Martian biota.

Existence of solutions for p(x)-Laplacian problems on a bounded domain

In this paper we study the following p(x)-Laplacian problem: -div(a(x)&VERBAR;&DEL; u&VERBAR;(p(x)-2)&DEL; u)+b(x)&VERBAR; u&VERBAR;(p(x)-2)u = f(x, u), x ε &UOmega;, u = 0, on &PARTIAL; &UOmega;, where 1< p(1) &LE; p(x) &LE; p(2) < n, &UOmega; &SUB; R-n is a bounded domain and applying the mountain pass theorem we obtain the existence of solutions in W-0(1,p(x)) for the p(x)-Laplacian problems in the superlinear and sublinear cases. © 2004 Elsevier Inc. All rights reserved.

Grain refinement of Mg-Al(-Mn) alloys by SiC additions

The addition of SiC particles effectively grain refined a range of Mg-Al alloys. The greatest reductions in grain size were found for the alloys with lower Al contents. The presence of Mg2Si in the microstructure after that SiC addition, and consideration of phase equilibria suggested that the SiC transforms to Al4C3, and this is the actual nucleant. The addition of Mn poisoned the grain refining effect of the SiC addition, probably due to the formation of less potent Al-Mn-carbides. (c) 2006 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.

Indexing and integrating multiple features for WWW images

In this paper, we present a novel indexing technique called Multi-scale Similarity Indexing (MSI) to index image's multi-features into a single one-dimensional structure. Both for text and visual feature spaces, the similarity between a point and a local partition's center in individual space is used as the indexing key, where similarity values in different features are distinguished by different scale. Then a single indexing tree can be built on these keys. Based on the property that relevant images have similar similarity values from the center of the same local partition in any feature space, certain number of irrelevant images can be fast pruned based on the triangle inequity on indexing keys. To remove the dimensionality curse existing in high dimensional structure, we propose a new technique called Local Bit Stream (LBS). LBS transforms image's text and visual feature representations into simple, uniform and effective bit stream (BS) representations based on local partition's center. Such BS representations are small in size and fast for comparison since only bit operation are involved. By comparing common bits existing in two BSs, most of irrelevant images can be immediately filtered. To effectively integrate multi-features, we also investigated the following evidence combination techniques-Certainty Factor, Dempster Shafer Theory, Compound Probability, and Linear Combination. Our extensive experiment showed that single one-dimensional index on multi-features improves multi-indices on multi-features greatly. Our LBS method outperforms sequential scan on high dimensional space by an order of magnitude. And Certainty Factor and Dempster Shafer Theory perform best in combining multiple similarities from corresponding multiple features.

Atomic composition profile change of SiGe islands during Si capping

The 6% Ge isocomposition profile change of individual SiGe islands during Si capping at 640 degrees C is investigated by atomic force microscopy combined with a selective etching procedure. The island shape transforms from a dome to a {103}-faceted pyramid at a Si capping thickness of 0.32 nm, followed by the decreasing of pyramid facet inclination with increasing Si capping layer thickness. The 6% Ge isocomposition profiles show that the island with more highly Si enriched at its one base corner before Si capping becomes to be more highly Si intermixed along pyramid base diagonals during Si capping. This Si enrichment evolution inside an island during Si capping can be attributed to the exchange of capped Si atoms that aggregated to the island by surface diffusion with Ge atoms from inside the island by both atomic surface segregation and interdiffusion rather than to the atomic interdiffusion at the interface between the island and the Si substrate. In addition, the observed Si enrichment along the island base diagonals is attempted to be explained on the basis of the elastic constant anisotropy of the Si and Ge materials in (001) plane. (c) 2006 American Institute of Physics.

Direct numerical simulation of turbulent flow and mass transfer around a rotating circular cylinder

Turbulent flow around a rotating circular cylinder has numerous applications including wall shear stress and mass-transfer measurement related to the corrosion studies. It is also of interest in the context of flow over convex surfaces where standard turbulence models perform poorly. The main purpose of this paper is to elucidate the basic turbulence mechanism around a rotating cylinder at low Reynolds numbers to provide a better understanding of flow fundamentals. Direct numerical simulation (DNS) has been performed in a reference frame rotating at constant angular velocity with the cylinder. The governing equations are discretized by using a finite-volume method. As for fully developed channel, pipe, and boundary layer flows, a laminar sublayer, buffer layer, and logarithmic outer region were observed. The level of mean velocity is lower in the buffer and outer regions but the logarithmic region still has a slope equal to the inverse of the von Karman constant. Instantaneous flow visualization revealed that the turbulence length scale typically decreases as the Reynolds number increases. Wavelet analysis provided some insight into the dependence of structural characteristics on wave number. The budget of the turbulent kinetic energy was computed and found to be similar to that in plane channel flow as well as in pipe and zero pressure gradient boundary layer flows. Coriolis effects show as an equivalent production for the azimuthal and radial velocity fluctuations leading to their ratio being lowered relative to similar nonrotating boundary layer flows.

Indexing text and visual features for WWW images

In this paper, we present a novel indexing technique called Multi-scale Similarity Indexing (MSI) to index imagersquos multi-features into a single one-dimensional structure. Both for text and visual feature spaces, the similarity between a point and a local partitionrsquos center in individual space is used as the indexing key, where similarity values in different features are distinguished by different scale. Then a single indexing tree can be built on these keys. Based on the property that relevant images haves similar similarity values from the center of the same local partition in any feature space, certain number of irrelevant images can be fast pruned based on the triangle inequity on indexing keys. To remove the ldquodimensionality curserdquo existing in high dimensional structure, we propose a new technique called Local Bit Stream (LBS). LBS transforms imagersquos text and visual feature representations into simple, uniform and effective bit stream (BS) representations based on local partitionrsquos center. Such BS representations are small in size and fast for comparison since only bit operation are involved. By comparing common bits existing in two BSs, most of irrelevant images can be immediately filtered. Our extensive experiment showed that single one-dimensional index on multi-features improves multi-indices on multi-features greatly. Our LBS method outperforms sequential scan on high dimensional space by an order of magnitude.

Ultrasonic measurement technique of burning metals in normal and reduced gravity

The in situ real time measurement of the regression rate of a melting interface (RRMI) is performed by the ultrasonic measurement system reported here. The RRMI is the rate at which a solid/liquid interface (SLI) moves along a metallic rod while burning in an oxygen-enriched atmosphere and is an important flatnmability indicator. The ultrasonic transducer and associated equipment used to drive the transducer and record the echo signal is described, along with the process that transforms the acquired signals into a RRMI value. Test rods of various metals and geometric shapes were burned at several test conditions in different test facilities. The RRMI results with quantified errors are presented and reviewed. The effect of reduced gravity on burning metals is important to space-applications and RRMI results obtained in a reduced gravity environment are also presented.