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1.
2.
The barotropic compressible Navier–Stokes equations in an unbounded domain are studied. We prove the unique existence of the solution (u, p) of the system (1.1) in the Sobolev spaceHk + 3 × Hk + 2provided that the derivatives of the data of the problem are sufficiently small, wherek ≥ 0 is any integer. The proof follows from an analysis of the linearized problem, the solvability of the continuity equation, and the Schauder fixed point theory. Similar smoothness results are obtained for a linearized form of (1.1). 相似文献
3.
Pascal Noble 《Archive for Rational Mechanics and Analysis》2007,186(1):53-76
The phenomenon of roll-waves occurs when shallow water flows down open inclined channels. This flow is described by the Saint
Venant’s equations with a friction term due to Chezy. In the case of a flat bottom, their existence (as entropic and periodic
travelling waves) follows from a classical work due to DRESSLER [6].
The aim of this paper is to prove the existence of roll-waves when the bottom is modulated by a small periodic perturbation.
Following JIN and KATSOULAKIS [15], we first compute a Burgers-type equation which possesses “pulsating” roll-waves (the wave
speed oscillates around an average velocity). We prove, in a mathematically rigorous fashion, the existence of these solutions. 相似文献
4.
5.
Polysubstituted indoles can be prepared directly from functionalized nitroalkanes under very mildly acidic conditions in a simple, one-pot, two-stage procedure. 相似文献
6.
In [W.-C. Kuo, C.C.A. Labuschagne, B.A. Watson, Discrete-time stochastic processes on Riesz spaces, Indag. Math. (N.S.) 15 (3) (2004) 435-451], we introduced the concepts of conditional expectations, martingales and stopping times on Riesz spaces. Here we formulate and prove order theoretic analogues of the Birkhoff, Hopf and Wiener ergodic theorems and the Strong Law of Large Numbers on Riesz spaces (vector lattices). 相似文献
7.
Tracy Noble Ricardo Nemirovsky Cara Dimattia Tracey Wright 《International Journal of Computers for Mathematical Learning》2004,9(2):109-167
In this article, we will describe the results of a study of 6th grade students learning about the mathematics of change. The
students in this study worked with software environments for the computer and the graphing calculator that included a simulation
of a moving elevator, linked to a graph of its velocity vs. time. We will describe how the students and their teacher negotiated
the mathematical meanings of these representations, in interaction with the software and other representational tools available
in the classroom. The class developed ways of selectively attending to specific features of stacks of centimeter cubes, hand-drawn
graphs, and graphs (labeled velocity vs. time) on the computer screen. In addition, the class became adept at imagining the
motions that corresponded to various velocity vs. time graphs. In this article, we describe this development as a process
of learning to see mathematical representations of motion. The main question this article addresses is: How do students learn
to see mathematical representations in ways that are consistent with the discipline of mathematics?
This revised version was published online in July 2006 with corrections to the Cover Date. 相似文献
8.
Transport of surface-modified iron nanoparticle in porous media and application to arsenic(III) remediation 总被引:1,自引:0,他引:1
Sushil Raj Kanel Dhriti Nepal Bruce Manning Heechul Choi 《Journal of nanoparticle research》2007,9(5):725-735
The surface-modified iron nanoparticles (S-INP) were synthesized, characterized and tested for the remediation of arsenite
(As(III)), a well known toxic groundwater contaminant of concern. The S-INP material was fully dispersed in the aqueous phase
with a particle size distribution of 2–10 nm estimated from high-resolution transmission electron microscopy (HR-TEM). X-ray
photoelectron spectroscopy (XPS) revealed that an Fe(III) oxide surface film was present on S-INP in addition to the bulk
zero-valent Fe0 oxidation state. Transport of S-INP through porous media packed in 10 cm length column showed particle breakthroughs of 22.1,
47.4 and 60 pore volumes in glass beads, unbaked sand, and baked sand, respectively. Un-modified INP was immobile and aggregated
on porous media surfaces in the column inlet area. Results using S-INP pretreated 10 cm sand-packed columns containing ∼2 g
of S-INP showed that 100 % of As(III) was removed from influent solutions (flow rate 1.8 mL min−1) containing 0.2, 0.5 and 1.0 mg L−1 As(III) for 9, 7 and 4 days providing 23.3, 20.7 and 10.4 L of arsenic free water, respectively. In addition, it was found
that 100% of As(III) in 0.5 mg/L solution (flow rate 1.8 mL min−1) was removed by S-INP pretreated 50 cm sand packed column containing 12 g of S-INP for more than 2.5 months providing 194.4
L of arsenic free water. Field emission scanning electron microscopy (FE-SEM) showed S-INP had transformed to elongated, rod-like
shaped corrosion product particles after reaction with As(III) in the presence of sand. These results suggest that S-INP has
great potential to be used as a mobile, injectable reactive material for in-situ sandy groundwater aquifer treatment of As(III). 相似文献
9.
Andrew D. Abell Bruce M. Clark Kathryn B. Morris Jane M. Taylor 《Journal of mass spectrometry : JMS》1993,28(1):27-29
Positive-ion fast atom bombardment mass spectra of 13 keto acid and keto ester phosphoranes were examined. All compounds gave a protonated molecular ion and characteristic peaks at m/z 303, 279, 262 and 201. 相似文献
10.
Emulsions of perfluorotributylamine (FTBA) and perflubron were evaluated for their utility in 19F echo planar imaging. Fluorine images of the emulsions were obtained in a phantom and two mice that had been predosed. Both agents, but particularly perflubron, show potential for fluorine echo planar studies because of the long spin-spin relaxation times of the CF3 resonances. High resolution thin slice images obtained in as little as 26.6 ms are presented. 相似文献