26,546 research outputs found

    Differential equations for the cuspoid canonical integrals

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    Differential equations satisfied by the cuspoid canonical integrals I_n(a) are obtained for arbitrary values of n≥2, where n−1 is the codimension of the singularity and a=(ɑ_1,ɑ_2,...,ɑ_(n−1)). A set of linear coupled ordinary differential equations is derived for each step in the sequence I_n(0,0,...,0,0) →I_n(0,0,...,0,ɑ_(n−1)) →I_n(0,0,...,ɑ_(n−2),ɑ_(n−1)) →...→I_n(0,ɑ_2,...,ɑ_(n−2),ɑ_(n−1)) →I_n(ɑ_1,ɑ_2,...,ɑ_n−2,ɑ_(n−1)). The initial conditions for a given step are obtained from the solutions of the previous step. As examples of the formalism, the differential equations for n=2 (fold), n=3 (cusp), n=4 (swallowtail), and n=5 (butterfly) are given explicitly. In addition, iterative and algebraic methods are described for determining the parameters a that are required in the uniform asymptotic cuspoid approximation for oscillating integrals with many coalescing saddle points. The results in this paper unify and generalize previous researches on the properties of the cuspoid canonical integrals and their partial derivatives

    Bonding of reusable surface insulation with low density silicone foams

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    The development and evaluation of a reduced density, high reliable foamed bond strain isolation system for attaching reusable surface insulation to the space shuttle structure are reported. Included are data on virgin materials as well as on materials that received 100 cycles of exposure to 650 F for approximately 20 minutes per cycle. Room temperature vulcanizing silicon elastomers meet all the requirments for an adhesive bonding system

    Traditional Biocidal Replacement Viability of Microcrystalline Silver Chloride

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    The antimicrobial effects of silver ions and silver chloride nanoparticles have been well established while the efficacy of microcrystalline silver chloride has been less studied. Certex-AM, a microcrystalline silver chloride product produced by Cerion, Rochester, NY, was tested for its antimicrobial properties as a possible replacement for traditional biocidal techniques used in water cooling towers. The minimum inhibitory concentration (MIC) of the compound was determined using a microtiter broth assay. The compound was found to have inhibitory effects on bacterial growth for all tested organisms at concentrations greater than 9 ppm. Additional testing simulating a water cooling system showed the effectiveness of reducing an established wild population at concentrations of 10 ppm of the microcrystalline silver chloride. Certex-AM was found to be a promising replacement for traditional biocides as well as for other applications. Introduction of effective antimicrobial compounds such as this could reduce the pathogenic risk to humans associated with water cooling towers
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