We present several algorithms that solve the single-source shortestpath problem using CUDA. We have run them on a database, composed of hundreds of large graphs represented by adjacency lists and adjacency matrices, achieving high speedups regarding a CPU implementation based on Fibonacci heaps. Concerning correctness, we outline why our solutions work, and show that a previous approach [10] is incorrect.

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A new copper vanadate Cu1.1V4O11 phase has been isolated by both chemical and electrochemical removal of Cu from the mother Cu2.33V4O11 phase, and its electrochemical performance in Li cells has been studied. The removal of copper was shown to occur in a topotactic manner, resulting in a stacking of [V4O11] n layers linked by differently coordinated copper ions. This new phase reversibly reacts with 5 Li, leading to a capacity of about 260 mAh/g, through a process involving a reversible displacement reaction entailing to the growth/disappearance of Cu dendrites. However, in contrast to what was observed for Cu2.33V4O11, this reversible copper extrusion/insertion process was shown neither to involve all of the Cu atoms (solely 0.8 out of the 1.1) nor lead to an amorphization of the electrode in its discharged sate. Structural considerations are put forward to account for such observed differences.

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Abstract. In recent times, many constants in Banach spaces have been defined and/or studied. Relations and inequalities among them (sometimes very complicated) have been indicated. But not much effort has been devoted to organize all connections, also because the literature on the subject is growing at an always bigger rate. Here we give some new connections which better the insight on some of them. In particular, we improve a known inequality between the von Neumann-Jordan and James constants.

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