In this paper, we study the Cauchy problem for the Benjamin-Ono-Burgers equation \({\partial _t}u - \epsilon \partial _x^2u + {\cal H}\partial _x^2u + u{u_x} = 0\), where \({\cal H}\) denotes the Hilbert transform operator. We obtain that it is uniformly locally well-posed for small data in the refined Sobolev space \({\tilde H^\sigma }(\mathbb{R})\,\,(\sigma \geqslant 0)\), which is a subspace of L2(ℝ). It is worth noting that the low-frequency part of \({\tilde H^\sigma }(\mathbb{R})\) is scaling critical, and thus the small data is necessary. The high-frequency part of \({\tilde H^\sigma }(\mathbb{R})\) is equal to the Sobolev space Hσ (ℝ) (σ ⩾ 0) and reduces to L2(ℝ). Furthermore, we also obtain its inviscid limit behavior in \({\tilde H^\sigma }(\mathbb{R})\) (σ ⩾ 0).
Metronidazole(MTZ) is an important antibiotic, which has been widely applied to cure protozoal and bacterial diseases for human beings or animals. Herein, three novel drug supramolecular crystals constructed by MTZ with 2,5-dihydroxy-benzoic acid(2,5-DHBA)(1), 2,6-dihydroxy-benzoic acid(2,6-DHBA)(2) and 3,5-dihydroxy-benzoic acid(3,5-DHBA)(3), respectively, have been discovered. The hydrogen bonds of N-H···O(O-H···N), C-H···O and O-H···O play important roles in the 3D supramolecular framework formation for crystals 1-3. Interestingly, due to the vary locations of the substituent groups, the two-dimensional layers in crystals 1 or 2 are constructed via intermolecular hydrogen bonds between MTZ and 2,5-DHBA or 2,6-DHBA, while in crystal 3 water molecules play a significant role except the intermolecular hydrogen bonds between MTZ and 3,5-DHBA. In addition, five synthons of I R22(8), II R33(9) in crystal 1, III R12(4), IV R22(8) in crystal 2 and V R22(7) in crystal 3 formed through various hydrogen bonds are founded in this work. Systematic studies of syntheses, crystal structures and thermal analysis are reported. 相似文献
The isothermal decomposition characteristic of the homogeneous high nitrogen austenitic samples prepared by a new multi-stage nitriding process was investigated by SEM and TEM in this paper. Lamellar-structure precipitations arranged on the decomposed austenite grain boundaries (GBs) and the flaky γ′ particles and network-structure precipitations appeared inside of the γ matrix. The extra high Vickers hardness more than 800 HV was found in the 5-h aged samples, which was different from those of the bainitic/martensitic structures in Fe-C alloys. The SAED analysis indicates the γ′ has the coherent relation with the parent γ-Fe[N] phase and the interstitial nitrogen atoms are inclined to aggregate on {1 1 0}γ′/γ planes, which also contributes to the hardness of the matrix. 相似文献