  Idealized glass transitions are discussed within a novel mode-coupling theory
(TMCT) proposed by Tokuyama(Physica A 395,31(2014)). This is done in order to
identify common grounds with and differences to the conventional mode-coupling
theory (MCT). It is proven that both theories imply the same scaling laws for
the transition dynamics, which are characterized by two power-law decay
functions and two diverging power-law time scales. However, the values for the
corresponding anomalous exponents calculated within both theories differ from
each other. It is proven that the TMCT, contrary to the MCT, does not describe
transitions with continuously vanishing arrested parts of the correlation
functions. It is also demonstrated for a schematic model that the TMCT neither
leads to the MCT scenarios for transition-line crossings nor for the appearance
of higher-order glass-transition singularities.
