Ricci flow on compact K\"ahler manifolds of positive bisectional curvature

We announce a new proof of the uniform estimate on the curvature of solutions to the Ricci flow on a compact K\"ahler manifold $M^n$ with positive bisectional curvature. In contrast to the recent work of X. Chen and G. Tian, our proof of the uniform estimate does not rely on the exsitence of K\"ahler-Einstein metrics on $M^n$, but instead on the first author's Harnack inequality for the K\"ahler-Ricc flow, and a very recent local injectivity radius estimate of Perelman for the Ricci flow.Comment: 4 page

Extraction of spatial information from sterioscopic SAR images

Synthetic Aperture Radar (SAR) is now widely used for generating Digital Elevation Models (DEMs) and has advantages over optical data in terms of availability as it allows all-day and all-weather operations. The stereoscopic SAR method, which allows direct extraction of spatial information in three-dimensional space, has been established for decades. However, the traditional stereoscopic methods developed for SAR data depend on many human operations and need ground control points (GCPs), to set up geometric models. The aims of the thesis are not only to propose a refined rigorous stereoscopic SAR method and a new error model to predict theoretic errors, but also to achieve a higher level of automation and accuracy. By using a weighting matrix, which is derived by considering different observations in the space intersection algorithm, the minimal number of the GCPs required for the refined algorithm is only two. To achieve a high degree of automation, an optimized strategy of parameter selection for the pyramidal image correlation scheme employing a region-growing technique has been proposed. This avoids a trial-and-error approach to produce digital parallax data from the same-side SAR image pairs. A new method to derive GCPs automatically has been developed using a SAR image simulation technique, under the condition that a known DEM chip is available, to minimize human interventions and operator error. The proposed method for providing GCPs and the DEMs generated from space intersection have been incorporated into the procedures for geocoding SAR images to validate the proposed algorithms. The results derived show that the stereoscopic SAR data can be applied to geometric rectification in flat-to-moderate areas, and other applications of extraction of spatial information are promising

Mechanism and Kinetics for the Initial Steps of Pyrolysis and Combustion of 1,6-Dicyclopropane-2,4-hexyne from ReaxFF Reactive Dynamics

We report the kinetic analysis and mechanism for the initial steps of pyrolysis and combustion of a new fuel material, 1,6-dicyclopropane-2,4-hexyne, that has enormous heats of pyrolysis and combustion, making it a potential high-energy fuel or fuel additive. These studies employ the ReaxFF force field for reactive dynamics (RD) simulations of both pyrolysis and combustion processes for both unimolecular and multimolecular systems. We find that both pyrolysis and combustion initiate from unimolecular reactions, with entropy-driven reactions being most important in both processes. Pyrolysis initiates with extrusion of an ethylene molecule from the fuel molecule and is followed quickly by isomerization of the fuel molecule, which induces additional radicals that accelerate the pyrolysis process. In the combustion process, we find three distinct mechanisms for the O2 attack on the fuel molecule: (1) attack on the cyclopropane, ring expanding to form the cyclic peroxide which then decomposes; (2) attack onto the central single bond of the diyne which then fissions to form two C_5H_5O radicals; (3) attack on the alkyne-cyclopropane moiety to form a seven-membered ring peroxide which then decomposes. Each of these unimolecular combustion processes releases energy that induces additional radicals to accelerate the combustion process. Here oxygen has major effects both as the radical acceptor and as the radical producer. We extract both the effective activation energy and the effective pre-exponential factor by kinetic analysis of pyrolysis and combustion from these ReaxFF simulations. The low value of the derived effective activation energy (26.18 kcal/mol for pyrolysis and 16.40 kcal/mol for combustion) reveals the high activity of this fuel molecule