The diagnonal multivariate natural exponential families and their classification

A natural exponential family (NEF)F in ? ⁿ ,n>1, is said to be diagonal if there existn functions,a ₁,...,a _n , on some intervals of ?, such that the covariance matrixV _F (m) ofF has diagonal (a ₁(m ₁),...,a _n (m _n )), for allm=(m ₁,...,m _n ) in the mean domain ofF. The familyF is also said to be irreducible if it is not the product of two independent NEFs in ? ^k and ? ^n-k , for somek=1,...,n?1. This paper shows that there are only six types of irreducible diagonal NEFs in ? ⁿ , that we call normal, Poisson, multinomial, negative multinomial, gamma, and hybrid. These types, with the exception of the latter two, correspond to distributions well established in the literature. This study is motivated by the following question: IfF is an NEF in ? ⁿ , under what conditions is its projectionp(F) in ? ^k , underp(x ₁,...,x _n )∶=(x ₁,...,x _k ),k=1,...,n?1, still an NEF in ? ^k ? The answer turns out to be rather predictable. It is the case if, and only if, the principalk×k submatrix ofV _F (m ₁,...,m _n ) does not depend on (m _k+1,...,m _n ).     

Comparison of the elastic and inelastic scatterings between152Sm+12C and148 Nd+16O

Angular distributions of elastic and inelastic scattering have been measured for¹⁵²Sm+¹²C at 63.2 MeV and¹⁴⁸Nd+¹⁶O at 90.9 MeV. An evident interference pattern in the inelastic scattering has been observed for the first time in a strong Coulomb coupling system.We are indebted to Dr. S. Pieper for supplying the Ptolemy Program. One of us (Chenglie Jiang) would like to acknowledge the Argonne National Laboratory for the opportunity given, to perform theoretical calculations with the code Ptolemy during his visit there. Thanks are also due to Mr. H. Folger (GSI, Germany) for supplying the targets. This work was supported in part by China National Nature Science Fundation.     

基于自校准技术的半球谐振陀螺正交误差的辨识补偿

在静电刚度校正技术的基础上,结合自校准算法,该文提出了一种实时辨识补偿正交误差的理论模型,并在两件套平面电极的半球谐振陀螺上进行了理论仿真和实验验证。结果表明,该方法不仅适用于半球谐振陀螺的力平衡和全角两种工作模式,还适用于虚拟进动的情况。此外,该文提出的补偿方法不会影响正交环路的控制精度,且对陀螺检测和驱动电路的增益和相位误差不敏感。