8,424 research outputs found

    Dynamical spacetimes in conformal gravity

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    The conformal gravity remarkably boosts our prehension of gravity theories. We find a series of dynamical solutions in the W2W^2-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

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    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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