Curvature Conditions for Immersions of Submanifolds and Applications

Some curvature conditions about the geodesics emanating from a submanifold are obtained. These conditions are used to to study the topological and geometric properties of the ambient spaces which admit some minimal submanifolds.     

High energy physics in the atmosphere: phenomenology of cosmic ray air showers

The properties of cosmic rays with energies above 10⁶ GeV have to be deduced from the spacetime structure and particle content of the air showers which they initiate. In this review we summarize the phenomenology of these giant air showers. We describe the hadronic interaction models used to extrapolate results from collider data to ultra high energies, and discuss the prospects for insights into forward physics at the LHC. We also describe the main electromagnetic processes that govern the longitudinal shower evolution, as well as the lateral spread of particles. Armed with these two principal shower ingredients and motivation from the underlying physics, we provide an overview of some of the different methods proposed to distinguish primary species. The properties of neutrino interactions and the potential of forthcoming experiments to isolate deeply penetrating showers from baryonic cascades are also discussed. We finally venture into a terra incognita endowed with TeV-scale gravity and explore anomalous neutrino-induced showers.     

Mass‐lumping or not mass‐lumping for eigenvalue problems

In this article we analyze the effect of mass‐lumping in the linear triangular finite element approximation of second‐order elliptic eigenvalue problems. We prove that the eigenvalue obtained by using mass‐lumping is always below the one obtained with exact integration. For singular eigenfunctions, as those arising in non convex polygons, we prove that the eigenvalue obtained with mass‐lumping is above the exact eigenvalue when the mesh size is small enough. So, we conclude that the use of mass‐lumping is convenient in the singular case. When the eigenfunction is smooth several numerical experiments suggest that the eigenvalue computed with mass‐lumping is below the exact one if the mesh is not too coarse. © 2003 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 19: 653–664, 2003     

Optimally Stable Multivariate Bases

We show that the tensor product B-spline basis and the triangular Bernstein basis are in some sense best conditioned among all nonnegative bases for the spaces of tensor product splines and multivariate polynomials, respectively. We also introduce some new condition numbers which are analogs of component-wise condition numbers for linear systems introduced by Skeel.     

海洋激光雷达测量海中悬移质

研制了一套采用倍频YAG激光器的小型海洋激光雷达，用于测量海中悬移质浓度，2000年8月28日至9月5日，该系统安装于“东方红Ⅱ”号右舷下甲板，在渤海海区进行海中悬移质浓度现场测量，通过对18个站位的海洋激光雷达数据分析，获得的表层悬移质浓度与同步测量的海中悬移质浓度结果吻合较好。     

Volcanic monitoring for radon and chemical species in the soil and in spring water samples

Soil radon has been monitored at two fixed stations in the northern flank of Popocatepetl Volcano, a high risk volcano located 60 km SE from Mexico City. Water samples from three springs were also studied for radon as well as major and trace elements. Radon in the soil was recorded using track detectors. Radon in the water samples was evaluated using the liquid scintillation method and an Alphaguard. The major elements were determined through conventional chemical methods and trace elements using an ICP-MS equipment. Soil radon levels were low, indicating a moderate diffuse degassing through the flanks of the volcano. Groundwater radon had almost no relation with the eruptive stages. Water chemistry was stable in the reported time (2000–2002).     

Heuristic Rejection in Interval Global Optimization

Based on the investigation carried out in Ref. 1, this paper incorporates new studies about the properties of inclusion functions on subintervals while a branch-and-bound algorithm is solving global optimization problems. It is found that the relative place of the global minimum value within the inclusion function value of the objective function at the current interval indicates mostly whether the given interval is close to a minimizer point. This information is used in a heuristic interval rejection rule that can save a considerable amount of computation. Illustrative examples are discussed and an extended numerical study shows the advantages of the new approach.