Higher algebraic K-theory and tangent spaces to Chow groups

This is a reproduction of my thesis. By using higher K-theory(Chern character, cyclic homology, effacement theorem and etc), we provide an answer to a question by Green- Griffiths which says the tangent sequence to Bloch-Gersten-Quillen sequence is Cousin resolution.Comment: 38 pages. Comments are very welcom

Scalar Wave Equation Modeling with Time-Space Domain Dispersion-Relation-Based Staggered-Grid Finite-Difference Schemes

The staggered-grid finite-difference (SFD) method is widely used in numerical modeling of wave equations. Conventional SFD stencils for spatial derivatives are usually designed in the space domain. However, when they are used to solve wave equations, it becomes difficult to satisfy the dispersion relations exactly. Liu and Sen (2009c) proposed a new SFD scheme for one-dimensional (1D) scalar wave equation based on the time-space domain dispersion relation and plane wave theory, which is made to satisfy the exact dispersion relation. This new SFD scheme has greater accuracy and better stability than a conventional scheme under the same discretizations. In this paper, we develop this new SFD scheme further for numerical solution of 2D and 3D scalar wave equations. We demonstrate that the modeling accuracy is second order when the conventional 2M-th-order space-domain SFD and the second order time-domain finite-difference stencils are directly used to solve the scalar wave equation. However, under the same discretization, our 1D scheme can reach 2M-th-order accuracy and is always stable; 2D and 3D schemes can reach 2M-th-order accuracy along 8 and 48 directions, respectively, and have better stability. The advantages of the new schemes are also demonstrated with dispersion analysis, stability analysis, and numerical modeling.National Natural Science Foundation of China 41074100Important National Science & Technology Specific Project of China 2008ZX05024-001Institute for Geophysic

Kinetics and Intermediate Phases in Epitaxial Growth of Fe3O4 Films from Deposition and Thermal Reduction

We have studied the growth of Fe3O4 (111) epitaxial films on Al2O3 (001) substrates using a pulsed laser deposition / thermal reduction cycle using an {\alpha}-Fe2O3 target. While direct deposition onto the Al2O3 (001) substrates results in an {\alpha}-Fe2O3 epilayer, deposition on the Fe3O4 (111) surface results in a {\gamma}-Fe2O3 epilayer. The kinetics of the transitions between Fe2O3 and Fe3O4 were studied by measuring the time constants of the transitions. The transition from {\alpha}-Fe2O3 to Fe3O4 via thermal reduction turns out to be very slow, due to the high activation energy. Despite the significant grain boundaries due to the mismatch between the unit cells of the film and the substrate, the Fe3O4 (111) films grown from deposition/thermal reduction show high crystallinity