Polymeric dielectrics have attracted intensive attention worldwide because of their huge potential for advanced energy storage capacitors. Thus far, various effective strategies have been developed to improve the inherent low energy densities of polymer dielectrics. However, enhanced energy density is always accompanied by suppressed discharge efficiency, which is detrimental to practical applications and deserves considerable concern. Targeting at achieving simultaneous high energy density and high discharge efficiency, the unique design of asymmetric all-polymer trilayer composite consisting of a transition layer sandwiched by a linear dielectric layer and a nonlinear dielectric layer is herein reported. It is demonstrated that the nonlinear dielectric layer offers high energy density, while the linear dielectric layer provides high discharge efficiency. Especially, the transition layer can effectively homogenize the electric field distribution, resulting in greatly elevated breakdown strength and improved energy density. In particular, a high efficiency of 89.9% along with a high energy density of 12.15 J cm −3 are concurrently obtained. The asymmetric trilayer all-polymer design strategy represents a new way to achieve high-performance dielectric energy storage materials.

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We develop a toolbox for proving decouplings into boxes with diameter smaller than the canonical scale. As an application of this new technique, we solve three problems for which earlier methods have failed. We start by verifying the small cap decoupling for the parabola. Then we find sharp estimates for exponential sums with small frequency separation on the moment curve in R 3 . This part of the work relies on recent improved Kakeya-type estimates for planar tubes, as well as on new multilinear incidence bounds for plates and planks.We also combine our method with the recent advance on the reverse square function estimate, in order to prove small cap decoupling into square-like caps for the two dimensional cone.The Appendix by Roger Heath-Brown contains an application of the new exponential sum estimates for the moment curve, to the Riemann zeta-function.

Two‐dimensional (2D) transition metal dichalcogenide has attracted significant attention recently due to its unique electrical and optical properties. However, MoS2 nanosheets fabricated by traditional methods exhibit poor electrical performance due to the existence of the 1T metal phase. A solution‐processable pure 2H semiconductor phase MoS2 nanosheet for use as the functional layer of high‐performance memristors is presented. The resulting memristor based on a Ag/MoS2/Pt structure exhibits excellent resistive switching properties including high endurance and multilevel retention. Moreover, the power consumption and programming current of the SET operation can be as low as 7.35 nW and 100 nA, respectively. Interestingly, it is demonstrated that the resistance of the Ag/MoS2/Pt device can be bidirectionally modulated over a wide range (pulse number >500) with an approximately linear trend. Furthermore, the accuracy of pattern recognition with handwritten data can reach 90.37%. This work provides a simple and practical method for the realization of fabrication of pure 2H‐MoS2 and application in biological neural computing systems.