Continuous dependence for NLS in fractional order spaces

We consider the Cauchy problem for the nonlinear Schr\"odinger equation $iu_t+ \Delta u+ \lambda |u|^\alpha u=0$ in $\R^N$, in the $H^s$-subcritical and critical cases $0<\alpha \le 4/(N-2s)$, where $0<s<N/2$. Local existence of solutions in $H^s$ is well known. However, even though the solution is constructed by a fixed-point technique, continuous dependence in $H^s$ does not follow from the contraction mapping argument. In this paper, assuming furthermore $s<1$, we show that the solution depends continuously on the initial value in the sense that the local flow is continuous $H^s \to H^s$. If, in addition, $\alpha \ge 1$ then the flow is Lipschitz. This completes previously known results concerning the cases $s=0,1,2$.Comment: Corrected typos. Simplified section 4. Results unchange

Biomass-derived three-dimensional porous N-doped carbonaceous aerogel for efficient supercapacitor electrodes

Functionalized carbonaceous materials with hierarchical structure and developed porosity are highly desired in energy storage and conversion fields. In this work, a facile and scalable hydrothermal methodology was established to synthesise three-dimensional (3D) N-doped carbonaceous aerogels using biomass-based starting materials and polypyrrole as N-source. The effect of different calcination temperatures on the structural properties, type and content of N-species and electrochemical performance of the 3D N-doped carbonaceous aerogels were uncovered. Thanks to the combinatorial effect of the appropriate N content and porous structure, the obtained samples exhibited excellent electrochemical performance, in particular, an outstanding specific capacitance of 281.0 F g-1 achieved on the sample calcined at 600 °C. This methodology offers a new fabrication strategy to prepare nanoscale carbonaceous materials with desirable morphology and hierarchical architecture of great potentials for the applications in energy fields

Size-segregated particle number and mass concentrations from different emission sources in urban Beijing

Although secondary particulate matter is reported to be the main contributor of PM2.5 during haze in Chinese megacities, primary particle emissions also affect particle concentrations. In order to improve estimates of the contribution of primary sources to the particle number and mass concentrations, we performed source apportionment analyses using both chemical fingerprints and particle size distributions measured at the same site in urban Beijing from April to July 2018. Both methods resolved factors related to primary emissions, including vehicular emissions and cooking emissions, which together make up 76% and 24% of total particle number and organic aerosol (OA) mass, respectively. Similar source types, including particles related to vehicular emissions (1.6 +/- 1.1 mu gm(-3); 2.4 +/- 1.8 x 10(3) cm(-3) and 5.5 +/- 2.8 x 10(3) cm(-3) for two traffic-related components), cooking emissions (2.6 +/- 1.9 mu gm(-3) and 5.5 +/- 3.3 x 10(3) cm(-3)) and secondary aerosols (51 +/- 41 mu gm(-3) and 4.2 +/- 3.0 x 10(3) cm(-3)), were resolved by both methods. Converted mass concentrations from particle size distributions components were comparable with those from chemical fingerprints. Size distribution source apportionment separated vehicular emissions into a component with a mode diameter of 20 nm ("traffic-ultrafine") and a component with a mode diameter of 100 nm ("traffic-fine"). Consistent with similar day- and nighttime diesel vehicle PM2.5 emissions estimated for the Beijing area, traffic-fine particles, hydrocarbon-like OA (HOA, traffic-related factor resulting from source apportionment using chemical fingerprints) and black carbon (BC) showed similar diurnal patterns, with higher concentrations during the night and morning than during the afternoon when the boundary layer is higher. Traffic-ultrafine particles showed the highest concentrations during the rush-hour period, suggesting a prominent role of local gasoline vehicle emissions. In the absence of new particle formation, our re-sults show that vehicular-related emissions (14% and 30% for ultrafine and fine particles, respectively) and cooking-activity-related emissions (32 %) dominate the particle number concentration, while secondary particulate matter (over 80 %) governs PM2.5 mass during the non-heating season in Beijing.Peer reviewe

The promotion effects of thionation and isomerization on charge carrier mobility in naphthalene diimide crystals

Herein, the promotion effects of thionation and isomerization on the carrier mobility properties of naphthalene diimide and thionated naphthalene diimide crystals were investigated in detail based on the Marcus-Hush theory and quantum-chemical calculations. The thionation of NDIs will improve the charge mobility of both electrons and holes, which is similar to the thionation of PDIs. The compound P only behaves as an n-type organic semiconductor (OSC), whereas the three other thionation structures have higher mobility values and can behave as p-type OSCs. For the cis/trans isomers of the two double-thionation structures, trans-S2 has a larger hole and electron carrier mobility than cis-S2; this is consistent with the experimental results obtained for cis-trans-isomers. A potential strategy for the development of high performance ambipolar OSCs is the substitution of O atoms by S atoms. These results will provide a guide for the design and optimization of OSCs via analysis of the relationship between carrier mobility and molecular crystal structures