Quantitative unique continuation for the heat equations with inverse square potential

Abstract

In this paper, we investigate the unique continuation properties for multi-dimensional heat equations with inverse square potential in a bounded convex domain Ω of . We establish observation estimates for solutions of equations. Our result shows that the value of the solutions can be determined uniquely by their value on an open subset ω of Ω at any given positive time L.

Gallium Nitride Based Electrode for High‐Temperature Supercapacitors

“…Interestingly, the curves of the GaN/NCO-2 exhibit an inverted V-shape, which directly indicates the heterostructures' existence between GaN and NCO NSs. [27] In terms of the M-S formula (Supporting Information), the electron concentration of porous GaN is calculated to be 6.1 × 10 22 cm −3 . It is a satisfactory substrate with congenital conductivity for rapid charge transfer.…”

Highly electron-deficient ultrathin Co nanosheets supported on mesoporous Cr2O3 for catalytic hydrogen evolution from ammonia borane

“…S18 †). 68 Combining characterization results of photocurrent and EIS with catalytic activity under visible light irradiation, it highlights that the semiconductor type and photoelectric properties of the support have limited influence on the activity of the catalyst and improving the difference in electron density between the support and active sites by strong interaction is more important.…”

Tröger's base derived 3D-porous aromatic frameworks with efficient exciton dissociation and well-defined reactive site for near-unity selectivity of CO2 photo-conversion

“…For n-type semiconductors, the flatband potential can be approximated as the location of the Fermi level. In general, the conduction band (ECB) potential in the n-type semiconductor is 0.1-0.3 eV above the Fermi level [46]. Therefore, values of ECB could be estimated to be -1.03 (SPF-TB-PAF), -1.04 (TEPE-TB-PAF), and -1.01 V (TEPM-TB-PAF) (V vs. NHE).…”