The lithium-sulfur battery is the subject of much recent attention due to the high theoretical energy density, but practical applications are challenged by fast decay owing to polysulfide shuttle and electrode architecture degradation. A comprehensive study of the sulfur host microstructure design and the cell architecture construction based on the MXene phase (Ti3C2Tx nanosheets) is performed, aiming at realize stable cycling performance of Li–S battery with high sulfur areal loading. The interwoven KB@Ti3C2Tx composite formed by self-assembly of MXene and Ktejen black, not only provides superior conductivity and maintains the electrode integrality bearing the volume expansion/shrinkage when used as the sulfur host, but also functions as an interlayer on separator to further retard the polysulfide cross-diffusion that possibly escaped from the cathode. The KB@Ti3C2Tx interlayer is only 0.28 mg cm−2 in areal loading and 3 μm in thickness, which accounts a little contribution to the thick sulfur electrode; thus, the impacts on the energy density is minimal. By coupling the robust KB@Ti3C2Tx cathode and the effective KB@Ti3C2Tx modified separator, a stable Li–S battery with high sulfur areal loading (5.6 mg cm−2) and high areal capacity (6.4 mAh cm−2) at relatively lean electrolyte is achieved.

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This paper aims to build an estimate of an unknown density of the data with measurement error as a linear combination of functions of a dictionary. Inspired by penalization approach, we propose the weighted Elastic-net penalized minimal L2-distance method for sparse coefficients estimation, where the weights adaptively coming from sharp concentration inequalities. The optimal weighted tuning parameters are obtained by the first-order conditions holding with high-probability. Under local coherence or minimal eigenvalue assumptions, non-asymptotical oracle inequalities are derived. These theoretical results are transposed to obtain the support recovery with high-probability. Then, the issue of calibrating these procedures is studied by some numerical experiments for discrete and continuous distributions, it shows the significant improvement obtained by our procedure when compared with other conventional approaches. Finally, the application is performed for a meteorology data set. It shows that our method has potency and superiority of detecting the shape of multi-mode density compared with other conventional approaches.