A new model for the double well potential

A new model for the double well potential is presented in the paper. In the new potential, the exchanging rate could be easily calculated by the perturbation method in supersymmetric quantum mechanics. It gives good results whether the barrier is high or sallow. The new model have many merits and may be used in the double well problem.Comment: 3pages, 3figure

Investigation of Partial Discharge in Solid Dielectric under DC Voltage

A partial discharge, or PD, is defined as an electrical discharge that is localized within only a part of the insulation between two separated conductors. Recent research on PD mainly focuses on the study of PD characteristics under AC voltage. Compared with DC, PD under AC is more serious and can be easily detected in terms of PD number. As the results of these concentrated research, the understanding of PD under AC condition has been significantly improved and features extracted from PD measurements have been used to diagnose the insulation condition of many power apparatus. Recently, rapid development in HVDC transmission and power grids connection, and widely applied DC cable and gas-insulated switchgear because of their benefit in long distance usage lead to an increasing concern about PD under DC. However, available study for the condition is little and related research is therefore necessary and essential for understanding the lifetime and reliability of apparatus. <br/

Exceptional del Pezzo hypersurfaces

We compute global log canonical thresholds of a large class of quasismooth well-formed del Pezzo weighted hypersurfaces in $\mathbb{P}(a_{1},a_{2},a_{3},a_{4})$. As a corollary we obtain the existence of orbifold K\"ahler--Einstein metrics on many of them, and classify exceptional and weakly exceptional quasismooth well-formed del Pezzo weighted hypersurfaces in $\mathbb{P}(a_{1},a_{2},a_{3},a_{4})$.Comment: 149 pages, one reference adde

Log canonical thresholds of Del Pezzo Surfaces in characteristic p

The global log canonical threshold of each non-singular complex del Pezzo surface was computed by Cheltsov. The proof used Koll\'ar-Shokurov's connectedness principle and other results relying on vanishing theorems of Kodaira type, not known to be true in finite characteristic. We compute the global log canonical threshold of non-singular del Pezzo surfaces over an algebraically closed field. We give algebraic proofs of results previously known only in characteristic $0$. Instead of using of the connectedness principle we introduce a new technique based on a classification of curves of low degree. As an application we conclude that non-singular del Pezzo surfaces in finite characteristic of degree lower or equal than $4$ are K-semistable.Comment: 21 pages. Thorough rewrite following referee's suggestions. To be published in Manuscripta Mathematic

A compactness theorem for complete Ricci shrinkers

We prove precompactness in an orbifold Cheeger-Gromov sense of complete gradient Ricci shrinkers with a lower bound on their entropy and a local integral Riemann bound. We do not need any pointwise curvature assumptions, volume or diameter bounds. In dimension four, under a technical assumption, we can replace the local integral Riemann bound by an upper bound for the Euler characteristic. The proof relies on a Gauss-Bonnet with cutoff argument.Comment: 28 pages, final version, to appear in GAF

The K\"ahler-Ricci flow with positive bisectional curvature

We show that the K\"ahler-Ricci flow on a manifold with positive first Chern class converges to a K\"ahler-Einstein metric assuming positive bisectional curvature and certain stability conditions.Comment: 15 page

Classification of All Poisson-Lie Structures on an Infinite-Dimensional Jet Group

A local classification of all Poisson-Lie structures on an infinite-dimensional group $G_{\infty}$ of formal power series is given. All Lie bialgebra structures on the Lie algebra {\Cal G}_{\infty} of $G_{\infty}$ are also classified.Comment: 11 pages, AmSTeX fil