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      Cover image for Many-body Quantum Tunneling of Ultracold Bosonic Gases: Quantum Phase Transitions, Bosonic Josephson Junctions, and Mott Switch Atomtronics
      1. 
      Cover image for Realizing Fractional Derivatives of Elementary and Composite Functions through the Generalized Euler's Integral Transform and Integer Derivative Series: Building the Mathematical Framework to Model the Fractional Schrödinger Equation in Fractional Spacetime
      2. 
      Cover image for Liouville's equation and radiative acceleration in general relativity
      3. 
      Liouville's equation and radiative acceleration in general relativity
      by 
      Keane, Aidan J., author.
      http://gateway.proquest.com/openurl?url_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:dissertation&res_dat=xri:pqm&rft_dat=xri:pqdiss:10867978
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      Excerpt: 
      particle, neglecting the influence of any gravitational force on the particle. The saturation velocity is