In this paper we study the Cauchy problem of the incompressible fractional Navier-Stokes equations in critical variable exponent Fourier-Besov-Morrey space F Ns(·)p(·),h(·),q(R3)with s(·)=4-2α-3/p(·).We prove global well-posedness result with small initial data belonging to FN4-2α-3/p(·)p(·),h(·)q(R3).The result of this paper extends some recent work. 相似文献
Two Ag(I)-based coordination polymers, namely [Ag2(3,3′-tmbpt)(o-Hbdc)2]·H2O (1) and [Ag8(3,3′-tmbpt)4(1,2,4-Hbtc)4(H2O)] (2) (3,3′-tmbpt?=?1-((1H-1,2,4-triazol-1-yl)methyl)-3,5-bis(3-pyridyl)-1,2,4-triazole, o-H2bdc?=?1,2-benzenedicarboxylic acid and 1,2,4-H3btc?=?1,2,4-benzenetricarboxylic acid), have been synthesized. Single-crystal X-ray diffraction analyses, elemental analyses, infrared spectra, powder X-ray diffraction analyses and thermogravimetric analyses have been carried out to characterize the structures of 1 and 2. Compound 1 shows a (3,4)-connected 2D layered structure with a Schläfli symbol of (42·6)(42·63·8). The intermolecular O–H···O hydrogen-bonding interactions extend the 2D layer into a 3D supramolecular architecture. Compound 2 exhibits a (3,3)-connected double-layered structure with a Schläfli symbol of (4·8·10)2(82·10)2. The intermolecular C–H···O hydrogen-bonding interactions link the double-layers to form a 3D supramolecular architecture. Moreover, there are intramolecular and intermolecular π–π interactions in 1 and 2, which stabilize the whole 3D supramolecular architectures. The band gaps of 1 and 2 are 3.19 and 3.09 eV, respectively, indicating the potential of 1 and 2 as semiconductive materials with wide band gaps. Moreover, 1 and 2 emit intense blue-green light, which may be potential photoactive materials.
Graphic Abstract
Two Ag(I)-based 3D supramolecular coordination polymers constructed from a multidentate N-donor ligand and two aromatic polycarboxylate anions via hydrogen-bonding and π–π interactions have been synthesized and characterized. The band gaps and photoluminescent properties of the compounds have been studied.
Theoretical and Mathematical Physics - By introducing shift relations satisfied by a matrix $$\boldsymbol{r}$$ , we propose a generalized Cauchy matrix scheme and construct a discrete second-order... 相似文献
Asymmetric mode transformation in waveguide is of great significance for on-chip integrated devices with one-way effect, while it is challenging to achieve asymmetric nonlinear-mode-conversion (NMC) due to the limitations imposed by phase-matching. In this work, we theoretically proposed a new scheme for realizing asymmetric NMC by combining frequency-doubling process and periodic PT symmetric modulation in an optical waveguide. By engineering the one-way momentum from PT symmetric modulation, we have demonstrated the unidirectional conversion from pump to second harmonic with desired guided modes. Our findings offer new opportunities for manipulating nonlinear optical fields with PT symmetry, which could further boost more exploration on on-chip nonlinear devices assisted by non-Hermitian optics. 相似文献
In this study, we have provided a facile solution to synthesize well-aligned titanium dioxide nanorods by using hydrothermal reaction. By calcining the materials under different atmospheres and temperatures, a batch of titanium dioxides with excellent oxygen evolution reaction(OER) catalytic efficiency were obtained. This new structured TiO2 photoanode material yields a high photocurrent density of 5.69 mA/cm2 at 1.23 V vs. reversible hydrogen electrode(RHE) under simulated solar light(100 mW/cm2). Surface photovoltage techniques and other measurements were carried out to confirm that the enhanced photoelectrochemical performances were attributed to the synergistic effect of the phase junction and a certain content of surface states, which accelerate the separation and transmission of the photogenerated charges. This material with phase junction and surface states promises a potential application in the field of photoelectric catalysis under solar light. 相似文献