A connected dominating set in a graph is a subset of vertices such that every vertex is either in the subset or adjacent to a vertex in the subset and the subgraph induced by the subset is connected. A minimum-connected dominating set is such a vertex subset with minimum cardinality. An application in ad hoc wireless networks requires the study of the minimum-connected dominating set in unit-disk graphs. In this paper, we design a (1 ؉ 1/s)-approximation for the minimum-connected dominating set in unit-disk graphs, running in time n O ((s log s) 2 ).
Solid-state lithium batteries (SSBs) promise high energy and power densities, as well as enhanced safety, owing to the use of Li metal and nonflammable solid-state electrolytes.
c-LLZO) is a promising Li + ion conductor for applications as a ceramic solid electrolyte in next generation high safety lithium batteries. The sintering temperature of c-LLZO is usually higher than 1100 °C, where Li-loss is severe, especially in conventional air ambient sintering method. Covering the green body with "mother powder" is often adopted for compensating the Li-loss. The mother powder having the same composition as the green body cannot be repeatedly use, which raises the cost of the c-LLZO ceramics. A self-compensating Li-loss method without mother powder is proposed and investigated to prepare high-quality c-LLZO ceramics. In this method, excess lithium is added to c-LLZO green pellets to self-compensate Li-loss at high temperature. The impact of different amounts of excess Li and crucible material, such as Pt, MgO, Al 2 O 3 , and ZrO 2 is studied. With optimized such sintering method, Ta doped LLZO pellets with 10% excess Li can be well sintered inside low-cost MgO crucible without mother powder at 1250 °C for only 40 min and laboratory scale production is demonstrated. The ceramics have relative densities of ∼96%, conductivities of ∼6.47 × 10 −4 S cm −1 and critical current density of 1.15 mA cm −2 at 25 °C, which is fundamental for further researches on solid-state batteries.
A newly designed gel-ceramic multi-layer electrolyte has been used as the separator and electrolyte for lithium sulfur (Li-S) batteries. The Li-S cells, free of the shuttle effect, exhibit superior electrochemical performance. With almost no self-discharge, the cell demonstrates an initial discharge specific capacity of up to 725 mA h g(-1) and remains at 700 mA h g(-1) after 300 cycles at the C/2 rate.
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