d=1 P ( m ∑ i=1 Ai[d] ≤ ξp ) = 1− n ∏ d=1 P (∑m i=1 Ai[d] m ≤ ξp m ) = 1− n ∏ d=1 P ( Ā[d] ≤ ξp m ) = 1− n ∏ d=1 P ( Ā[d]− µd σd√ m ≤ ξp m − µd σd√ m ) = 1− n ∏ d=1 P ( Z ≤ [ ξp m − µd ] √ m σd ) = 1− [...] on):Let xi, i ∈ {1, . . . ,m} be m independent samples drawn from a population X with values in the range[a, b]. Let Qm = 1 m ∑ i xi be the sample mean. Then, when m ≥ (b−a)2ln(q′) 2ǫ2 , we have Pr{Qm [...] − 2mǫ2 (b− a)2 ) ≤ q′. Therefore, − 2mǫ2 (b− a)2 ≤ ln (q′) =⇒ m ≥ (b− a)2ln ( 1 q′ ) 2ǫ2 . (2) Note that0 < q′ < 1, 0 < ǫ < 1 and both are parameters determined by the user. For example, ifb− a = 5, q′ …

TU Dortmund -- Computer Science VIII

Springer , 2015. Buss/etal/2015a Buss, Jens and Ahnen, M.L. and Balbo, M. and Bergmann, M. and Biland, Adrian and Bockermann, Christian and Bretz, Thomas and Brügge, K. A. and Dorner, Daniela and Einecke [...] Thordsen/Schubert/2022b Erik Thordsen and Erich Schubert. On Projections to Linear Subspaces . In Similarity Search and Applications, SISAP, 2022. Abbasi/etal/2021a R. Abbasi and M. Huennefeld and K. Morik [...] Bause/etal/2021a Franka Bause and David B. Blumenthal and Erich Schubert and Nils M. Kriege. Metric Indexing for Graph Similarity Search . In Similarity Search and Applications - 14th International Conference …

Characterization of Sprays Generated by the Expansion of Emulsions with Liquid Carbon Dioxide

Symbols used AE [m2] total area of all inlet cross-sections d [m] droplet diameter D [m] nozzle diameter rKE [m] mean inlet radius v [m s–1] velocity We [–] Weber number Greek symbols b [] angle of i [...] through a second orifice with a low length-to-diameter ratio, enabling a rapid decrease of the pressure, resulting in the evaporation of the liquid CO2 and a breakup of the water drop- lets. A schematic [...] through the expansion nozzle under the assumption of a constant density. For a density of the emulsion of 869 kg m–3, a mean outlet velocity of 85 m s–1 can be calcu- lated, which is higher than the measured …