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    A metal–organic framework/α-alumina composite with a novel geometry for enhanced adsorptive separation

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    The development of a metal–organic framework/α-alumina composite leads to a novel concept: efficient adsorption occurs within a plurality of radial micro-channels with no loss of the active adsorbents during the process. This composite can effectively remediate arsenic contaminated water producing potable water recovery, whereas the conventional fixed bed requires eight times the amount of active adsorbents to achieve a similar performance

    Causality Problem in a Holographic Dark Energy Model

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    In the model of holographic dark energy, there is a notorious problem of circular reasoning between the introduction of future event horizon and the accelerating expansion of the universe. We examine the problem after dividing into two parts, the causality problem of the equation of motion and the circular logic on the use of the future event horizon. We specify and isolate the root of the problem from causal equation of motion as a boundary condition, which can be determined from the initial data of the universe. We show that there is no violation of causality if it is defined appropriately and the circular logic problem can be reduced to an initial value problem.Comment: 5 page

    On Resource-bounded versions of the van Lambalgen theorem

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    The van Lambalgen theorem is a surprising result in algorithmic information theory concerning the symmetry of relative randomness. It establishes that for any pair of infinite sequences AA and BB, BB is Martin-L\"of random and AA is Martin-L\"of random relative to BB if and only if the interleaved sequence ABA \uplus B is Martin-L\"of random. This implies that AA is relative random to BB if and only if BB is random relative to AA \cite{vanLambalgen}, \cite{Nies09}, \cite{HirschfeldtBook}. This paper studies the validity of this phenomenon for different notions of time-bounded relative randomness. We prove the classical van Lambalgen theorem using martingales and Kolmogorov compressibility. We establish the failure of relative randomness in these settings, for both time-bounded martingales and time-bounded Kolmogorov complexity. We adapt our classical proofs when applicable to the time-bounded setting, and construct counterexamples when they fail. The mode of failure of the theorem may depend on the notion of time-bounded randomness
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