Cooperation between the fog and the cloud in mobile cloud computing environments could offer improved offloading services to smart mobile user equipment (UE) with computation intensive tasks. In this paper, we tackle the computation offloading problem in a mixed fog/cloud system by jointly optimizing the offloading decisions and the allocation of computation resource, transmit power and radio bandwidth, while guaranteeing user fairness and maximum tolerable delay. This optimization problem is formulated to minimize the maximal weighted cost of delay and energy consumption (EC) among all UEs, which is a mixed-integer non-linear programming problem. Due to the NP-hardness of the problem, we propose a low-complexity suboptimal algorithm to solve it, where the offloading decisions are obtained via semidefinite relaxation and randomization and the resource allocation is obtained using fractional programming theory and Lagrangian dual decomposition. Simulation results are presented to verify the convergence performance of our proposed algorithms and their achieved fairness among UEs, and the performance gains in terms of delay, EC and the number of beneficial UEs over existing algorithms. Index Terms-Computation offloading, cloud computing, fog computing, resource allocation, min-max fairness.

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Here, we report a general catalytic manifold for the selective C-C bond scission of ketones via the exploitation of the ligand-to-metal charge transfer (LMCT) excitation mode. Through a cooperative utilization of Lewis acid catalysis and LMCT catalysis, the C-C bond of ketones could be selectively and effectively cleaved, enabling the installation of different functionalities at each carbon of the cleaved C-C bond through a sequential and orthogonal manner. This reaction manifold serves as a photocatalytic alternative to the Norrish type I reaction with the combination of visible light and inexpensive cerium salts. Under operationally simple conditions, a wide range of acyclic and cyclic ketones, from simple strained cyclobutanones to complex androsterone with less strained cyclopentanone moiety, could be successfully transformed into versatile chemical building blocks.

The intermediacy of alkoxy radicals in ceriumcatalyzed C−H functionalization via H-atom abstraction has been unambiguously confirmed. Catalytically relevant Ce(IV)−alkoxide complexes have been synthesized and characterized by X-ray diffraction. Operando electron paramagnetic resonance and transient absorption spectroscopy experiments on isolated pentachloro Ce(IV) alkoxides identified alkoxy radicals as the sole heteroatom-centered radical species generated via ligand-tometal charge transfer (LMCT) excitation. Alkoxy-radical-mediated hydrogen atom transfer (HAT) has been verified via kinetic analysis, density functional theory (DFT) calculations, and reactions under strictly chloride-free conditions. These experimental findings unambiguously establish the critical role of alkoxy radicals in Ce-LMCT catalysis and definitively preclude the involvement of chlorine radical. This study has also reinforced the necessity of a high relative ratio of alcohol vs Ce for the selective alkoxy-radical-mediated HAT, as seemingly trivial changes in the relative ratio of alcohol vs Ce can lead to drastically different mechanistic pathways. Importantly, the previously proposed chlorine radical−alcohol complex, postulated to explain alkoxy-radicalenabled selectivities in this system, has been examined under scrutiny and ruled out by regioselectivity studies, transient absorption experiments, and high-level calculations. Moreover, the peculiar selectivity of alkoxy radical generation in the LMCT homolysis of Ce(IV) heteroleptic complexes has been analyzed and back-electron transfer (BET) may have regulated the efficiency and selectivity for the formation of ligand-centered radicals.

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