arXiv subjects
Publications and source records attributed to Lei Cao.
We investigate convex polytopes of doubly stochastic matrices having special structures: symmetric, Hankel symmetric, centrosymmetric, and both symmetric and Hankel symmetric. We determine dimensions of these polytopes and classify their extreme points. We also determine a basis of the real vector spaces generated by permutation matrices with these special structures.
We present a new efficient algorithm to construct partitions of a special class of equiangular tight frames (ETFs) that satisfy the operator norm bound established by a theorem of Marcus, Spielman, and Srivastava (MSS), which they proved as a corollary yields a positive solution to the Kadison-Singer problem. In particular, we prove that certain diagonal partitions of complex ETFs generated by recursive skew-symmetric conference matrices yield a refinement of the MSS bound. Moreover, we prove that all partitions of ETFs whose largest subset has cardinality three or less also satisfy the MSS bound.
The use of building materials containing naturally occurring radionuclides,such as K-40, U-238 and Th-232 and their progeny, could lead to external exposures of the residents of such buildings. In this paper, a set of models are set up to calculate the specific effective dose rates(the effective dose rate per Bq/kg of K-40, U-238 series, and Th-232 series) imposed to residents by building materials with MCNPX code. Effect of chemical composition, position concerned in the room and thickness as well as density of material is analyzed. In order to facilitate more precise assessment of indoor external dose due to gamma emitting radionuclides in building materials, three regressive expressions are proposed and validated by measured data to calculate specific effective rate for K-40, U-238 series and Th-232 series, respectively.