On the Well-posedness of the Schr\"odinger-Korteweg-de Vries system

We prove that the Cauchy problem for the Schr\"odinger-Korteweg-de Vries system is locally well-posed for the initial data belonging to the Sovolev spaces $L^2(\R)\times H^{-{3/4}}(\R)$. The new ingredient is that we use the $\bar{F}^s$ type space, introduced by the first author in \cite{G}, to deal with the KdV part of the system and the coupling terms. In order to overcome the difficulty caused by the lack of scaling invariance, we prove uniform estimates for the multiplier. This result improves the previous one by Corcho and Linares.Comment: 16 page

Global dynamics below the ground state energy for the Klein-Gordon-Zakharov system in the 3D radial case

We consider the global dynamics below the ground state energy for the Klein-Gordon-Zakharov system in the 3D radial case; and obtain the dichotomy between scattering and finite time blow up.Comment: 24 pages. arXiv admin note: substantial text overlap with arXiv:1206.245

Global dynamics below the ground state energy for the Zakharov system in the 3D radial case

We consider the global dynamics below the ground state energy for the Zakharov system in the 3D radial case. We obtain dichotomy between the scattering and the growup.Comment: 28 page

Generalized Strichartz estimates and scattering for 3D Zakharov system

We obtain scattering for the 3D Zakharov system with non-radial small data in the energy space with angular regularity of degree one. The main ingredient is a generalized Strichartz estimate for the Schr\"odinger equation in the space of $L^2$ angular integrability.Comment: 20 page

Global well posedness and inviscid limit for the Korteweg-de Vries-Burgers equation

Considering the Cauchy problem for the Korteweg-de Vries-Burgers equation \begin{eqnarray*} u_t+u_{xxx}+\epsilon |\partial_x|^{2\alpha}u+(u^2)_x=0, \ u(0)=\phi, \end{eqnarray*} where $0<\epsilon,\alpha\leq 1$ and $u$ is a real-valued function, we show that it is globally well-posed in $H^s\ (s>s_\alpha)$, and uniformly globally well-posed in$H^s (s>-3/4)$for all$\epsilon \in (0,1)$. Moreover, we prove that for any$T>0$, its solution converges in$C([0,T]; H^s)$to that of the KdV equation if$\epsilon$ tends to 0.Comment: 35 pages, 0 figur

2,6-Bis(2-hydroxy­ethyl)-8b,8c-diphenyl­perhydro-2,3a,4a,6,7a,8a-hexa­azacyclo­penta­[def]fluorene-4,8-dithione

In the title mol­ecule, C24H28N6O2S2, the dihedral angle between the aromatic ring planes is 42.2 (1)°. In the crystal structure, the hydr­oxy groups are involved in O—H⋯S hydrogen bonding, which links the mol­ecules into corrugated layers propagating parallel to the bc plane

Novel sol-gel synthesis and characterization of oxide nanopowders for solid oxide fuel cells

In this research, three different sol-gel synthesis methods by using cost effective materials, such as sugar + pectin, sodium alginate beads or sodium alginate granules, have been investigated for nanopowders production in Solid Oxide Fuel Cells (SOFCs) application. Materials (cerium gadolinium oxide and nickel oxide) have been selected as model materials. Cerium gadolinium oxide (CGO) is one of the most important electrolyte materials in SOFC due to its high ionic conductivity at 500-800 "C, whilst nickel oxide (NiO) can be reduced into nickel in SOFC fuels (H2 or CH4) as catalyst in anode layer. First of all, a novel sol-gel method has been developed for the production of high purity nanopowders of Ce0.8Gd0.201.9 (CG02) solid solution using maltose or sucrose as an organic chelating agent and pectin for gelation. The results of this investigation indicate that the final particle size of approximately 10 nm can be obtained after calcination of the dried gel at , 500°C for 2 hours in ambient air. Powder X-ray diffraction (XRD) shows that all samples are single phase cubic CGO powders. The mean crystallite sizes calculated from XRD analysis using Rietveld refinement method agree with the morphological features observed by transmission electron microscopy (TEM). The nominal composition of CG02 has been found to be in excellent agreement with that determined by energy dispersive X-ray spectroscopy (EDS) and inductively coupled plasma - atomic emission spectrometry analysis (ICP-AES). The ionic conductivities of Ceo.8Gdo.201.9 samples are measured by AC-impedance which appears reasonably well with the reference data which will qualify the use of this material for SOFC as solid electrolyte and in the fabrication of composite electrodes. On the other hand, another novel and generic sol-gel method has been developed for the production of high purity metal oxide nanopowders using sodium alginate (Na-ALG). This has been demonstrated successfully employing NiO and CGO CG01 (Ce0.9Gd0.1O1.95) and CGO2 (Ce0.8Gd0.201.9) as model materials in this instance. For NiO, the results of this investigation indicate that the final particle size of -20 nm can be obtained after calcination of the predried beads at 500°C for 3 hours in ambient air. XRD shows that the obtained samples are single phase cubic NiO powders. Furthermore, freeze dried and X-ray micro-tomography (XMT) technologies are applied to observe the inside morphology of the Ni-ALG beads. XMT shows that nickel ions have been uniformly cross-linked in the alginate structure and remained stable after freeze drying evidenced by the bright green color of the freeze dried beads. Finally, NiO nanopowders can also be synthesized using Na-ALG granules. Moreover, this alginate method has also been demonstrated successfully employing CGO in two composites designated as CG01 (Ceo.9Gdo.101.95) and CG02 (Ceo.aGdo.201.9), respectively. The results indicate that the nanopowders having a final particle size of -7 nm can be obtained after calcination of ion-exchanged alginate precursor at 500 degC for 2 hours in ambient' air. The chemical structures of Na-ALG solution and CGO beads are analyzed by Fourier transform infrared spectroscopy (FTIR) which indicates that Ce3+/Gd3+ are ion-exchanged with Na+ after gelation. The nominal compositions of CG01 and CG02 have been found to be in excellent agreement with that determined by EDS and ICP-AES. The ionic conductivities of these two samples are measured by AC-impedance which appears reasonably well with the reference data which will also qualify the use of this material for SOFC as solid electrolyte. All of these new sol-gel methods are simple, environmentally friendly and non-toxic routes for a large scale production of high purity single phase nanopowders in a cost effective manner at significantly low temperatures.EThOS - Electronic Theses Online ServiceGBUnited Kingdo

A score of bioavailable strontium isotope archaeology in China: Retrospective and prospective

Bioavailable strontium isotope analysis was proposed for prehistoric human ecology almost 40 years ago and rapidly became one of the most important tools to trace past migratory behaviours. Since its first introduction to China in 2003, this method has greatly improved our understanding of migrations on individual- and community-scales over the past 20 years. This paper summarizes the current state of knowledge regarding identifying non-locals, utilizing animal resources, and strontium isoscapes for China based on empirical data. By incorporating additional baseline data, we updated and extended the current bioavailable strontium isoscape for China and Southeast and South Asia. These data will shed new light on intercultural communications and the spread of customs and technologies. In the future, strontium isotope analysis will involve an integrated provenancing system along with multiple approaches such as various isotopes and different modellings. Correspondingly, the existing isoscape needs to improve its spatial resolution and predictive accuracy to source the non-local archaeological biological remains. Furthermore, advances in analytical techniques allow us to reconstruct lifetime mobility of animals and humans at high temporal resolution