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Measurement of ratios of branching fractions and<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>C</mml:mi><mml:mi>P</mml:mi></mml:math>-violating asymmetries of<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msup><mml:mi>B</mml:mi><mml:mo>±</mml:mo></mml:msup><mml:mo>→</mml:mo><mml:msup><mml:mi>D</mml:mi><mml:mo>*</mml:mo></mml:msup><mml:msup><mml:mi>K</mml:mi><mml:mo>±</mml:mo></mml:msup></mml:math>decays
We report a study of ${B}^{\ifmmode\pm\else\textpm\fi{}}\ensuremath{\rightarrow}{D}^{*}{K}^{\ifmmode\pm\else\textpm\fi{}}$ decays with ${D}^{*}$ decaying to $D{\ensuremath{\pi}}^{0}$ or $D\ensuremath{\gamma}$, using $383\ifmmode\times\else\texttimes\fi{}{10}^{6}$ $B\overline{B}$ pairs collected at the $\mathit{\ensuremath{\Upsilon}}(4S)$ resonance with the BABAR detector at the SLAC PEP-II $B$ Factory. The $D$ meson decays under study include a non-$CP$ mode $({K}^{\ifmmode\pm\else\textpm\fi{}}{\ensuremath{\pi}}^{\ensuremath{\mp}})$, $CP$-even modes $({K}^{\ifmmode\pm\else\textpm\fi{}}{K}^{\ensuremath{\mp}},{\ensuremath{\pi}}^{\ifmmode\pm\else\textpm\fi{}}{\ensuremath{\pi}}^{\ensuremath{\mp}})$, and $CP$-odd modes …