Search

We have established the existence and uniqueness of the local solution for (0.1)∂tu+∂x5u−u∂xu=0,00,u(x,0)=φ(x),00,\left\{\begin{array}{ll}{\partial }_{t}u+{\partial }_{x}^{5}u-u{\partial }_{x}u=0,& 0\lt x\lt 1,\hspace{1.0em}t\gt 0,\\ u\left(x,0)=\varphi \left(x),& 0\lt x\lt 1,\\ u\left(0,t)={h}_{1}\left(t),u\left(1,t)={h}_{2}\left(t),\hspace{0.33em}{\partial }_{x}u\left(1,t)={h}_{3}\left(t),& \\ {\partial }_{x}u\left(0,t)={h}_{4}\left(t),\hspace{0.33em}{\partial }_{x}^{2}u\left(1,t)={h}_{5}\left(t),& t\gt 0,\end{array}\right. in the study of Zhao and Zhang [Non-homogeneous boundary value problem of the fifth-order KdV equations posed on a bounded interval, J. Math. Anal. Appl. 470 (2019), 251–278]. A question arises naturally: Can the local solution be extended to a global one? This article will address this question. First, through a series of logical deductions, a global a priori estimate is established, and then the local solution is naturally extended to a global solution.

We have studied four 2D layered perovskites, including OA2PbI4 (RP phase), ODAPbI4 and BDAPbI4 (DJ phase), (GA)MAPbI4 (ACI phase), where OA is [(CmH2m+1)NH3](m = 8), ODA is [NH3(CH2)mNH3](m = 8), BDA is [NH3(CH2)mNH3](m = 4), and GA is [C(NH2)3]; RP, DJ, and ACI means Ruddlesden–Popper, Dion–Jacobson and alternating cations in the interlayer, respectively. The temperature dependence of absorption and photoluminescence (PL) spectra have been measured. From which the average phonon energy (electron-phonon interaction strength) is analyzed as around 34 (80), 47 (184), 50 (402), and 63 (758) with the unit of meV for OA2PbI4, ODAPbI4, BDAPbI4, and (GA)MAPbI4, respectively. Larger phonon energy indicates the involvement of more phonons in organic spacer layer, with the corresponding stronger electron-phonon interaction. Furthermore, ultrafast transient absorption spectroscopy proves that, when the excitation photon energy is serval hundred meV higher than bandgap, the excitons still are the major photoexcitations in OA2PbI4, but polarons are major one in ODAPbI4, BDAPbI4, and (GA)MAPbI4 films, no matter the excitonic transitions dominate the absorption at their band edges. This work proves the organic spacers can regulate electron–phonon interaction then optoelectronic properties in 2D perovskites profoundly, which have implications toward future rational design for relevant devices.

In this paper, we study the initial boundary problem of fifth-order Korteweg-de Vries equation with nonlinear boundary values. First, we establish a so-called sharp boundary trace regularity associated with the linearized fifth-order Korteweg-de Vries equation. Then, aided by the sharp boundary trace regularity, we verify that initial-boundary value problem of fifth-order Korteweg-de Vries equation with nonlinear boundary conditions is locally well-posed when initial and boundary values are properly chosen.

In order to study the influence of the structural parameters of the wound cylindrical honeycomb on the energy absorption characteristics, a finite element simulation model was first established. Then, using the controlled variable method, the influence of the side length of the corrugated sheet, the thickness of the corrugated sheet and the thickness of the flat sheet on the energy absorption characteristics of the honeycomb was systematically studied. Finally, the experiment is carried out and compared with the simulation results. The results show that as the side length of the corrugated sheet decreases, the thickness of the corrugated sheet and the thickness of the flat sheet increase, the average stress and volume ratio energy absorption of the honeycomb can be increased; reducing the side length of the corrugated sheet and increasing the thickness of the corrugated sheet can increase the mass specific energy absorption. The increase in the thickness of the flat sheet can reduce the mass specific energy absorption; the simulation model is accurate, and the results are in good agreement with the experimental results in the honeycomb deformation and energy absorption characteristics. This paper has done a more detailed study on the three parameters that affect the strength of the cylindrical honeycomb, which provides new ideas and theoretical support for the energy-absorbing components of the passive safety protection of rail transit.

Constructing core–shell structure is recognized as an effective approach for the conventional colloidal semiconductor nanocrystals (NCs) to improve their stability and optical performance in optoelectronic applications. It is, however, still a challenge to develop green manufacture for core–shell lead halide perovskite NCs (PeNCs). Herein, an ice‐confined freeze‐thaw strategy using pure water solvent is devised, which results in the surface reconstruction of CsPbBr3 PeNCs thereby formatting the CsPb2Br5 shell on the CsPbBr3 core to achieve core–shell CsPbBr3@CsPb2Br5. The in situ formation of the CsPb2Br5 shell is attributed to the transformation of the intermediate polyhedral structure with the help of amphiphilic 4‐dodecylbenzene sulfonic acid ligand in the precursor solution. The PeNCs show ultrahigh photoluminescence quantum yield of 95%, remarkable stability and humidity‐resistance. Moreover, both light‐emitting diodes and stretchable fluorescence hydrogels based on the PeNCs exhibit a boosted optical performance and excellent operation stability. The organic solvent‐free and recyclability of this strategy pave a novel way to the environmentally friendly and large‐scale manufacture of high‐quality PeNCs for optoelectronic application. [ABSTRACT FROM AUTHOR]

CsPbBr3 nanoparticles with averaged size of 14 and 2.1 nm (named as 14 and 2 nmNP, respectively) are synthesized capping with the ligand of dodecylbenzene sulfonic acid (DBSA). Using ultrafast transient absorption spectroscopy, free carriers in 14 nmNP characterize with the slow thermalization (∼0.76 ps) and long carrier cooling time (∼1 ns), which could be due to the phonon bottleneck effect. On the other hand, excitons are major photoexcitations in 2 nmNP, presenting with fast thermalization (<100 fs) and short cooling time (∼50 ps); this effective energy dissipation in 2 nmNPs can be ascribed to the involvement of phonons in DBSA ligands. In both 14 and 2 nmNP, we find that the photoexcitation accumulation leads to an increase in the bandgap that can be understood by the Burstein–Moss band filling effect. These results provide insights into the intrinsic photophysics of CsPbBr3 perovskite nanocrystals with different confinement effects, supplying direct implications for optoelectronic applications. [ABSTRACT FROM AUTHOR]

We are devoted, in this paper, to the study of the pre-assigned-time drive-response synchronization problem for a class of Takagi–Sugeno fuzzy logic-based stochastic bidirectional associative memory neural networks, driven by Brownian motion, with continuous-time delay and (finitely and infinitely) distributed time delay. To achieve the drive-response synchronization between the neural network systems, concerned in this paper, and the corresponding response neural network systems (identical to our concerned neural network systems), we bring forward, based on the structural properties, a class of control strategies. By meticulously coining an elaborate Lyapunov–Krasovskii functional, we prove a criterion guaranteeing the desired pre-assigned-time drive-response synchronizability: For any given positive time instant, some of our designed controls make sure that our concerned neural network systems and the corresponding response neural network systems achieve synchronization, with the settling times not exceeding the pre-assigned positive time instant. In addition, we equip our theoretical studies with a numerical example, to illustrate that the synchronization controls designed in this paper are indeed effective. Our concerned neural network systems incorporate several types of time delays simultaneously, in particular, they have a continuous-time delay in their leakage terms, are based on Takagi–Sugeno fuzzy logic, and can be synchronized before any pre-given finite-time instant by the suggested control; therefore, our theoretical results in this paper have wide potential applications in the real world. The conservatism is reduced by introducing parameters in our designed Lyapunov–Krasovskii functional and synchronization control. [ABSTRACT FROM AUTHOR]