8,424 research outputs found
Dynamical spacetimes in conformal gravity
The conformal gravity remarkably boosts our prehension of gravity theories.
We find a series of dynamical solutions in the -conformal gravity,
including generalized Schwarzschild-Friedmann-Robertson-Walker (GSFRW), charged
generalized Schwarzschild-Friedmann-Robertson-Walker (CGSFRW), especially
rotating Friedmann-Robertson-Walker (RFRW), charged rotating
Friedmann-Robertson-Walker (CRFRW), and a dynamical cylindrically symmetric
solutions. The RFRW, CRFRW and the dynamical cylindrically symmetric solutions
are never found in the Einstein gravity and modified gravities. The GSFRW and
CGSFRW solutions take different forms from the corresponding solutions in the
Einstein gravity.Comment: 13 pages, no fi
On gradual-impulse control of continuous-time Markov decision processes with multiplicative cost
In this paper, we consider the gradual-impulse control problem of
continuous-time Markov decision processes, where the system performance is
measured by the expectation of the exponential utility of the total cost. We
prove, under very general conditions on the system primitives, the existence of
a deterministic stationary optimal policy out of a more general class of
policies. Policies that we consider allow multiple simultaneous impulses,
randomized selection of impulses with random effects, relaxed gradual controls,
and accumulation of jumps. After characterizing the value function using the
optimality equation, we reduce the continuous-time gradual-impulse control
problem to an equivalent simple discrete-time Markov decision process, whose
action space is the union of the sets of gradual and impulsive actions
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