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1.
In this paper, we study the Holder regularity of weak solutions to the Dirichlet problem associated with the regional fractional Laplacian (-△)αΩ on a bounded open set Ω ■R(N ≥ 2) with C(1,1) boundary ■Ω. We prove that when f ∈ Lp(Ω), and g ∈ C(Ω), the following problem (-△)αΩu = f in Ω, u = g on ■Ω, admits a unique weak solution u ∈ W(α,2)(Ω) ∩ C(Ω),where p >N/2-2α and 1/2< α < 1. To solve this problem, we consider it into two special cases, i.e.,g ≡ 0 on ■Ω and f ≡ 0 in Ω. Finally, taking into account the preceding two cases, the general conclusion is drawn. 相似文献
2.
3.
《Wave Motion》2018
The evolution of surface gravity waves is driven by nonlinear interactions that trigger an energy cascade similarly to the one observed in hydrodynamic turbulence. This process, known as wave turbulence, has been found to display anomalous scaling with deviation from classical turbulent predictions due to the emergence of coherent and intermittent structures on the water surface. In the ocean, waves are spread over a wide range of directions, with a consequent attenuation of the nonlinear properties. A laboratory experiment in a large wave facility is presented to discuss the sensitivity of wave turbulence on the directional properties of model wave spectra. Results show that the occurrence of coherent and intermittent structures become less likely with the broadening of the wave directional spreading. There is no evidence, however, that intermittency completely vanishes. 相似文献
4.
This work is concerned with the extension of the Jacobi spectral Galerkin method to a class of nonlinear fractional pantograph differential equations. First, the fractional differential equation is converted to a nonlinear Volterra integral equation with weakly singular kernel. Second, we analyze the existence and uniqueness of solutions for the obtained integral equation. Then, the Galerkin method is used for solving the equivalent integral equation. The error estimates for the proposed method are also investigated. Finally, illustrative examples are presented to confirm our theoretical analysis. 相似文献
6.
Pu Duan Bo Zhi Luke Coburn Christy L. Haynes Klaus Schmidt-Rohr 《Magnetic resonance in chemistry : MRC》2020,58(11):1130-1138
The composition of fluorescent polymer nanoparticles, commonly referred to as carbon dots, synthesized by microwave-assisted reaction of citric acid and ethylenediamine was investigated by 13C, 13C{1H}, 1H─13C, 13C{14N}, and 15N solid-state nuclear magnetic resonance (NMR) experiments. 13C NMR with spectral editing provided no evidence for significant condensed aromatic or diamondoid carbon phases. 15N NMR showed that the nanoparticle matrix has been polymerized by amide and some imide formation. Five small, resolved 13C NMR peaks, including an unusual ═CH signal at 84 ppm (1H chemical shift of 5.8 ppm) and ═CN2 at 155 ppm, and two distinctive 15N NMR resonances near 80 and 160 ppm proved the presence of 5-oxo-1,2,3,5-tetrahydroimidazo[1,2-a]pyridine-7-carboxylic acid (IPCA) or its derivatives. This molecular fluorophore with conjugated double bonds, formed by a double cyclization reaction of citric acid and ethylenediamine as first shown by Y. Song, B. Yang, and coworkers in 2015, accounts for the fluorescence of the carbon dots. Cross-peaks in a 1H─13C HETCOR spectrum with brief 1H spin diffusion proved that IPCA is finely dispersed in the polyamide matrix. From quantitative 13C and 15N NMR spectra, a high concentration (18 ± 2 wt%) of IPCA in the carbon dots was determined. A pronounced gradient in 13C chemical-shift perturbations and peak widths, with the broadest lines near the COO group of IPCA, indicated at least partial transformation of the carboxylic acid of IPCA by amide or ester formation. 相似文献
7.
Two new divalent copper (C1) and zinc (C2) chelates having the formulae [M(PIMC)2] (where M = Cu(II), Zn(II) and PIMC = Ligand [(E)-3-(((3-hydroxypyridin-2-yl)imino)methyl)-4H-chromen-4-one] were obtained and characterized by several techniques. Structures and geometries of the synthesized complexes were judged based on the results of alternative analytical and spectral tools supporting the proposed formulae. IR spectral data confirmed the coordination of the ligands to the copper and zinc centers as monobasic tridentate in the enol form. Thermal analysis, UV-Vis spectra and magnetic moment confirmed the geometry around the copper center to be tetrahedral, square pyramidal and octahedral. Study of the binding ability of the synthesized compounds with Circulating tumor DNA (CT-DNA) bas been evaluated applying UV-Vis spectral titration and viscosity measurements. The copper and zinc oxides were achieved from the copper and zinc nano-particles structures Schiff base complexes as the raw material after calcination for 5 hr at 600°C. On the other hand, synthesized of C1 and C2 NPs were used as suitable precursors to the preparation of CuO and ZnO NPs. Finally, the synthesized of the two complexes exhibited enhanced activity against the tested bacterial (Staphylococcus aureus and Escherichia Coli) and fungal strains (Candida albicans and Aspergillus fumigatus) as compared to HPIMC. Among all these synthesized compounds, C1 exhibits good cleaving ability compared to other newly synthesized C2. 相似文献
8.
Sameerah Jamal 《Journal of Differential Equations》2019,266(7):4018-4026
A manifold that contains small perturbations will induce a perturbed partial differential equation. The partial differential equation that we select is the Poisson equation – in order to explore the interplay between the geometry of the manifold and the perturbations. Specifically, we show how the problem of symmetry determination, for higher-order perturbations, can be elegantly expressed via geometric conditions. 相似文献
9.
We investigate congruence classes and direct congruence classes of m-tuples in the complex projective space ℂP
n
. For direct congruence one allows only isometries which are induced by linear (instead of semilinear) mappings. We establish
a canonical bijection between the set of direct congruence classes of m-tuples of points in ℂP
n
and the set of equivalence classes of positive semidefinite Hermitean m×m-matrices of rank at most n+1 with 1's on the diagonal. As a corollary we get that the direct congruence class of an m-tuple is uniquely determined by the direct congruence classes of all of its triangles, provided that no pair of points of
the m-tuple has distance π/2. Examples show that the situation changes drastically if one replaces direct congruence classes by
congruence classes or if distances π/2 are allowed. Finally we do the same
kind of investigation also for the complex hyperbolic space ℂH
n
. Most of the results are completely analogous, however, there are also some interesting differences.
Received: 15 January 1996 相似文献
10.
Summary. We generalise and apply a refinement indicator of the type originally designed by Mackenzie, Süli and Warnecke in [15] and
[16] for linear Friedrichs systems to the Euler equations of inviscid, compressible fluid flow. The Euler equations are symmetrized
by means of entropy variables and locally linearized about a constant state to obtain a symmetric hyperbolic system to which
an a posteriori error analysis of the type introduced in [15] can be applied. We discuss the details of the implementation of the refinement
indicator into the DLR--Code which is based on a finite volume method of box type on an unstructured grid and present numerical results.
Received May 15, 1995 / Revised version received April 17, 1996 相似文献