The authors consider the short time existence for Ricci-Bourguignon flow on manifolds with boundary. If the initial metric has constant mean curvature and satisfies some compatibility conditions, they show the short time existence of the Ricci-Bourguignon flow with constant mean curvature on the boundary. 相似文献
BIT Numerical Mathematics - In this paper, we introduce a novel class of embedded exponential-type low-regularity integrators (ELRIs) for solving the KdV equation and establish their optimal... 相似文献
Conjugated polymers feature promising structure and properties for photocatalytic water splitting. Herein, a hydrolysis strategy was demonstrated to rationally modulate the surface hydrophilicity and band structures of conjugated poly-benzothiadiazoles. High hydrophilicity not only enhances the dispersions of polymeric solids in an aqueous solution but also reduces the absorption energy of water molecules. Besides, both theoretical and experimental results reveal that a more positive valence band potential is generated, which contributes to enhancing the photocatalytic water oxidation performance. Accordingly, the surface-modified conjugated polymers show largely promoted photocatalytic water oxidation activities by deposition of cobalt oxides as cocatalysts. 相似文献
This paper is concerned with the Cauchy problem on the Boltzmann equation without angular cutoff assumption for hard potential in the whole space. When the initial data is a small perturbation of a global Maxwellian, the global existence of solution to this problem is proved in unweighted Sobolev spaces with . But if we want to obtain the optimal temporal decay estimates, we need to add the velocity weight function, in this case the global existence and the optimal temporal decay estimate of the Boltzmann equation are all established. Meanwhile, we further gain a more accurate energy estimate, which can guarantee the validity of the assumption in Chen et al. (0000). 相似文献
Due to narrowband emission and high quantum efficiencies, polycyclic aromatic heterocycles with multi-resonance thermally activated delayed fluorescence (MR-TADF) properties have recently gained considerable attention in the organic optoelectronic field. Albeit their great promise in the full visible region covering from blue to red, MR-TADF emitters with ultraviolet emission have been rarely reported. Through locking the two ortho-positions of a triphenylamine core by sulfone groups, a simple polycyclic aromatic heterocycle, BTPT, was facilely constructed, exhibiting 368 nm ultraviolet emission with a narrow full width at half maximum (FWHM) of 33 nm. Its neat film exhibited distinct TADF property with a main emission peak at 388 nm. Noteworthily, the enantiomeric crystals of BTPT not only demonstrated significant circularly polarized luminescence (CPL) with large luminescence dissymmetry factor in the 10?3 order but also displayed obvious room temperature phosphorescence (RTP). The relationship between this innovative helical unit and unique photophysical properties, including ultraviolet MRTADF, CPL, and RTP, was reasonably revealed.
A stimuli-responsive supramolecular polymer network has been constructed based on the host-guest interactions between the copolymer poly-P[5]A with pendent pillararene units and bis(sulfonium) diction guest G2. The formation mechanism of the supramolecular polymer network has been explored by the intensive study. With the addition of the competitive molecules and heating, the supramolecular polymer network could be dissociated and lead to clear changes in NMR spectroscopy and viscosity property. 相似文献
Expectation values of single electron and interelectronic geometric quantities such as $\langle r\rangle$, $\langle r_{12}\rangle$, $\langle r_<\rangle$, $\langle r_>\rangle$, $\langle \cos\theta_{12}\rangle$ and $\langle \theta_{12}\rangle$ are calculated for doubly excited $2{\rm p}n{\rm p}\,{}^1P^{\,\rm e}\,(3\leq n\leq5),\, 2{\rm p}n{\rm p}\,{}^3\!P^{\,\rm e}\,(2\leq n\leq5)$ and $2{\rm p}n{\rm d}\,{}^{1,3}D^{\,\rm o}\,(3\leq n\leq5)$ states of helium using Hylleraas-$B$-spline basis set. The energy levels converge to at least 10 significant digits in our calculations. The extrapolated values of geometric quantities except for $\langle \theta_{12}\rangle$ reach 10 significant digits as well; $\langle \theta_{12}\rangle$ reaches at least 7 significant digits using a multipole expansion approach. Our results provide a precise reference for future research. 相似文献
Science China Mathematics - This paper studies exact synchronization and asymptotic synchronization problems for a controlled linear system of ordinary differential equations. In this paper, we... 相似文献
Titanium dioxide (TiO2) is regarded as an important prototype photocatalytic material for several decades. The charge carrier kinetics determines the photocatalytic properties of TiO2 materials; this is found to be greatly dependent on electronic structures. It has been revealed that the intrinsic intermediate gap states (intrinsic GSs) play a significant role in charge carrier kinetics that drive the photocatalytic processes of TiO2 materials, which are not well summarized until now. Motivated by this thought, the purpose of this review focuses on physiochemical science of the intrinsic GSs of TiO2 materials and their important role in charge carrier kinetics. We first give a summary on the chemical resources of the intrinsic GSs in TiO2 and their physiochemical nature. Their general energy distribution, charge carrier population, and the associated thermodynamic properties are also elaborated from an overall viewpoint. We further carefully summarize and compare the experimental studies on the energy and the density distribution of the intrinsic GSs and discuss the associated chemical resources and charge carrier localizations. Trapping is the dominant function of intrinsic GSs in the charge carrier kinetics of TiO2 materials. The significant effect of trapping on the transport, recombination, and interfacial transfer of charge carriers are also comprehensive summarized. Furthermore, the effects of charge carrier kinetics on photocatalytic performances are also discussed to some extents. Because of the importance of intrinsic GSs in modulating charge carrier kinetics, it is expected to increase the photocatalytic activity by engineering the intrinsic GSs, not only for TiO2 materials, but also for the other semiconductor photocatalysts. 相似文献