An explicit formula for the Webster torsion of a pseudo-hermitian manifold and its application to torsion-free hypersurfaces Dedicated to Professor Sheng GONG on the occasion of his 75th birthday

This paper gives an explicit formula for calculating the Webster pseudo torsion for a strictly pseudoconvex pseudo-hermitian hypersurface. As applications, we are able to classify some pseudo torsion-free hypersurfaces, which include real ellipsoids.     

Towards a θ 13 measurement

Reactor-based antineutrino experiments hold the promise of providing an unambiguous determination of the neutrino mixing angle ?? ₁₃. At present, Daya Bay, Double Chooz and RENO are such experiments being set up for this purpose. In this paper, the status and prospects of these three initiatives are presented.     

反应堆中微子实验的基线优化

介绍了在χ2假设检验中引入本底和系统误差的方法，并通过最大化混合角θ13的测量敏感度对反应堆中微子实验的基线长度进行优化. 考察了对基线有影响的几个因素，包括振荡效应，统计误差，系统误差，本底等. 尽管实验条件可能很不相同，最优基线仍可被确定在一个较小的范围内.     

An explicit formula for the Webster torsion of a pseudo-hermitian manifold and its application to torsion-free hypersurfaces

This paper gives an explicit formula for calculating the Webster pseudo torsion for a strictly pseudoconvex pseudo-hermitian hypersurface. As applications, we are able to classify some pseudo torsion-free hypersurfaces, which include real ellipsoids. Dedicated to Professor Sheng GONG on the occasion of his 75th birthday     

Comparing Nonsmooth Nonconvex Bundle Methods in Solving Hemivariational Inequalities

Hemivariational inequalities can be considered as a generalization of variational inequalities. Their origin is in nonsmooth mechanics of solid, especially in nonmonotone contact problems. The solution of a hemivariational inequality proves to be a substationary point of some functional, and thus can be found by the nonsmooth and nonconvex optimization methods. We consider two type of bundle methods in order to solve hemivariational inequalities numerically: proximal bundle and bundle-Newton methods. Proximal bundle method is based on first order polyhedral approximation of the locally Lipschitz continuous objective function. To obtain better convergence rate bundle-Newton method contains also some second order information of the objective function in the form of approximate Hessian. Since the optimization problem arising in the hemivariational inequalities has a dominated quadratic part the second order method should be a good choice. The main question in the functioning of the methods is how remarkable is the advantage of the possible better convergence rate of bundle-Newton method when compared to the increased calculation demand.     

The sharp lower bound for the first positive eigenvalue of a sub-Laplacian on a pseudo-Hermitian manifold

This paper studies, using the Bochner technique, a sharp lower bound of the first eigenvalue of a subelliptic Laplace operator on a strongly pseudoconvex CR manifold in terms of its pseudo-Hermitian geometry. For dimensions greater than or equal to , the lower bound under a condition on the Ricci curvature and the torsion was obtained by Greenleaf. We give a proof for all dimensions greater than or equal to . For dimension , the sharp lower bound is proved under a condition which also involves a distinguished covariant derivative of the torsion.

     

From realistic to primitive models: a primitive model of methanol

An attempt to develop a methodology to construct a primitive model which descends directly from a parent realistic short-range model and reproduces its structural properties has been made. The realistic three-site OPLS model of methanol has been chosen as a test case. The primitive model copies the geometry of the OPLS model and thus pictures the methanol molecule as a hard heteronuclear dumbbell (representing oxygen and carbon atoms) with one embedded hydrogen site. All sites interact as hard spheres with the exception of the oxygen-hydrogen pair which may form a hydrogen bond mimicked by a square-well attraction. To determine parameters of the model two routes have been followed: (i) theoretical, based on an effective sphericalized site-site potential obtained from the parent potential, and (ii) semitheoretical which makes use of the knowledge of the structure of the dense parent fluid. Both sets of parameters provide similar results and reproduce the structure (site-site correlation functions, distribution of H-bonds and H-bond geometry) of the parent OPLS fluid reasonably well.