2,352 research outputs found

    Necessary and sufficient conditions for the oscillation of higher-order differential equations involving distributed delays

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    In this article, we establish necessary and sufficient conditions for the oscillation of both bounded and unbounded solutions of the differential equation \begin{equation} \bigg[x(t)+\int_{0}^{\lambda}p(t,v)x(\tau(t,v))\,\mathrm{d}v\bigg]^{(n)}+\int_{0}^{\lambda}q(t,v)x(\sigma(t,v))\,\mathrm{d}v=\varphi(t)\quad\text{for } t \geq t_{0},\notag \end{equation} where nNn\in\mathbb{N}, t0,λR+t_{0},\lambda\in\mathbb{R}^{+}, pC([t0,)×[0,λ]R)p\in C([t_{0},\infty)\times[0,\lambda] \mathbb{R}), qC([t0,)×[0,λ],R+)q\in C([t_{0},\infty)\times[0,\lambda],\mathbb{R}^{+}), τC([t0,)×[0λ],R)\tau\in C([t_{0},\infty)\times[0 \lambda],\mathbb{R}) with limtinfv[0,λ]τ(t,v)=\lim_{t\to\infty}\inf_{v\in[0,\lambda]}\tau(t,v)=\infty and supv[0,λ]τ(t,v)t\sup_{v\in[0,\lambda]}\tau(t,v)\leq t for all tt0t\geq t_{0}, σC([t0,)×[0,λ],R)\sigma\in C([t_{0},\infty)\times[0,\lambda],\mathbb{R}) with limtinfv[0,λ]σ(t,v)=\lim_{t\to\infty}\inf_{v\in[0,\lambda]}\sigma(t,v)=\infty, and φC([t0,),R)\varphi\in C([t_{0},\infty),\mathbb{R}). We also give illustrating examples to show the applicability of these results

    On the formaldehyde release of wood particles

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    The emission of formaldehyde from softwood particles, as measured by the flask method (EN 717-3), depends highly on the particle size. Therefore, no definite value for the formaldehyde release from wood can be given

    Applying Reflection Tomography in the Postmigration Domain to Multifold Ground-Penetrating Radar Data

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    Acquisition and processing of multifold ground-penetrating radar (GPR) data enable detailed measurements of lateral velocity variability. The velocities constrain interpretation of subsurface materials and lead to significant improvement in image accuracy when coupled with prestack depth migration (PSDM). Reflection tomography in the postmigration domain was introduced in the early 1990s for velocity estimation in seismic reflection. This robust, accurate method is directly applicable in multifold GPR imaging. At a contaminated waste facility within the U.S. Department of Energy’s Hanford site in Washington, the method is used to identify significant lateral and vertical velocity heterogeneity associated with infilled waste pits. Using both the PSDM images and velocity models in interpretation, a paleochannel system that underlies the site and likely forms contaminant migration pathways is identified

    Airborne multi-axis DOAS measurements of atmospheric trace gases on CARIBIC long-distance flights

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    A DOAS (<i>Differential Optical Absorption Spectroscopy</i>) instrument was implemented and operated onboard a long-distance passenger aircraft within the framework of the CARIBIC project (<i>Civil Aircraft for the Regular Investigation of the atmosphere Based on an Instrument Container</i>). The instrument was designed to keep weight, size and power consumption low and to comply with civil aviation regulations. It records spectra of scattered light from three viewing directions (nadir, 10° above and below horizon) using a miniaturized telescope system. The telescopes are integrated in the main pylon of the inlet system which is mounted at the belly of the aircraft. Fibre bundles transmit light from the telescopes to spectrograph-detector units inside the DOAS container instrument. The latter is part of the removable CARIBIC instrument container, which is installed monthly on the aircraft for a series of measurement flights. <br><br> During 30 flight operations within three years, measurements of HCHO, HONO, NO<sub>2</sub>, BrO, O<sub>3</sub> and the oxygen dimer O<sub>4</sub> were conducted. All of these trace gases except BrO could be analysed with a 30 s time resolution. HONO was detected for the first time in a deep convective cloud over central Asia, while BrO, NO<sub>2</sub> and O<sub>3</sub> could be observed in tropopause fold regions. Biomass burning signatures over South America could be seen and measurements during ascent and descent provided information on boundary layer trace gas profiles (e.g. NO<sub>2</sub> or HCHO)

    Einfluss der Aufschlusstemperatur auf die morphologischen Eigenschaften von TMP aus Kiefernholz

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    Chips from pine wood were subjected to thermomechanical pulping (TMP) at 140 and 180 degrees C for 5 minutes, whereas the cooked chips were defibrated using a single disk pressurized refiner at the same temperatures (140 and 180 degrees C). The fibres were tested for some of their morphological properties including fibre length, fibre width, cell-wall thickness. Moreover, the fine fibre fraction (zero fibres) and the content of splinters were also estimated. The results reveal, that increasing the temperature during thermomechanical pulping decreases the fibre length, the cell width and the fibre wall thickness. It also increases the amount of fine fibres and increases the curl factor

    Provenance and geochemistry of exotic clasts in conglomerates of the Oligocene Torehina Formation, Coromandel Peninsula, New Zealand

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    Non-marine pebble to cobble conglomerates of the lower Torehina Formation (Oligocene) crop out along western Coromandel Peninsula and overlie, with strong angular discordance, continental-margin metasedimentary rocks (Manaia Hill Group) of Mesozoic (Late Jurassic to ?Early Cretaceous) age. The conglomerates contain provenance information that identifies a pre-Oligocene depositional history obscured by the unconformable juxtaposition of these Tertiary and Mesozoic strata. Most clasts in the lower Torehina Formation are visually similar to local bedrock lithologies, including metamorphosed sandstones and argillites, but are kaolinitic and contain more detrital and authigenic chert, quartz, and potash feldspar. Local derivation of these clasts seems unlikely. By comparing geochemical ratios with those defined for continental margin sandstones, and well characterised New Zealand tectonic terranes, we interpret the majority of clasts in the lower Torehina Formation to have been derived from a dissected orogen, with mixtures of felsic and volcanogenic-derived sediment. The most likely sources are the Waipapa and Torlesse Terranes. The remaining 20–30% of the clasts in the lower Torehina Formation were originally friable, are coarse grained, and appear to be lithologically exotic relative to known metamorphosed sandstones in basement terrane sources on North Island. Some clasts contain coal laminae and particles, and all contain detrital kaolinite as lithic fragments and matrix. Such characteristics imply a non-marine to marginal-marine source containing sediment derived from strongly weathered granite or granodiorite. Mechanical fragility implies a likely proximal, easily erodible source. We propose that this group of clasts was derived from an Upper Cretaceous sedimentary cover, either part of a locally developed basin fill or part of a once regionally extensive cover on North Island. Either case defines a more widely distributed Cretaceous source than found today

    An embedding scheme for the Dirac equation

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    An embedding scheme is developed for the Dirac Hamiltonian H. Dividing space into regions I and II separated by surface S, an expression is derived for the expectation value of H which makes explicit reference to a trial function defined in I alone, with all details of region II replaced by an effective potential acting on S and which is related to the Green function of region II. Stationary solutions provide approximations to the eigenstates of H within I. The Green function for the embedded Hamiltonian is equal to the Green function for the entire system in region I. Application of the method is illustrated for the problem of a hydrogen atom in a spherical cavity and an Au(001)/Ag/Au(001) sandwich structure using basis sets that satisfy kinetic balance.Comment: 16 pages, 5 figure
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