葛根提取物高效液相色谱分析方法的优化

针对葛根提取物的复杂体系,分别从色谱模式、流动相、添加剂以及梯度洗脱条件几个方面对其高效液相色谱分析 方法进行了优化。其中梯度洗脱条件的优化是根据各组分在5次线性梯度下的保留时间并借助于CSASS软件快速准确地计 算出各组分的液相色谱保留参数a,c值以及峰形参数σ和τ,在此基础上使用CSASS软件对葛根提取物的色谱分离情况进行 高精度仿真预测,从而优化了梯度洗脱条件。考察了优化条件下的分析方法的精密度和重现性,结果表明该方法稳定、可 靠、重现性好。     

Flocks and Partial Flocks of Hyperbolic Quadrics via Root Systems

We construct three infinite families of partial flocks of sizes 12, 24 and 60 of the hyperbolic quadric of PG(3, q), for q congruent to -1 modulo 12, 24, 60 respectively, from the root systems of type D ₄, F ₄, H ₄, respectively. The smallest member of each of these families is an exceptional flock. We then characterise these partial flocks in terms of the rectangle condition of Benz and by not being subflocks of linear flocks or of Thas flocks. We also give an alternative characterisation in terms of admitting a regular group fixing all the lines of one of the reguli of the hyperbolic quadric.     

Modified Lagrangian and Least Root Approaches for General Nonlinear Optimization Problems

Abstract In this paper we study nonlinear Lagrangian methods for optimization problems with side constraints.Nonlinear Lagrangian dual problems are introduced and their relations with the original problem are established.Moreover,a least root approach is investigated for these optimization problems.     

A Weighted Enumeration of Maximal Chains in the Bruhat Order

Given a finite Weyl group W with root system , assign the weight to each covering pair in the Bruhat order related by the reflection corresponding to . Extending this multiplicatively to chains, we prove that the sum of the weights of all maximal chains in the Bruhat order has an explicit product formula, and prove a similar result for a weighted sum over maximal chains in the Bruhat ordering of any parabolic quotient of W. Several variations and open problems are discussed.     

Stable iterations for the matrix square root

Any matrix with no nonpositive real eigenvalues has a unique square root for which every eigenvalue lies in the open right half-plane. A link between the matrix sign function and this square root is exploited to derive both old and new iterations for the square root from iterations for the sign function. One new iteration is a quadratically convergent Schulz iteration based entirely on matrix multiplication; it converges only locally, but can be used to compute the square root of any nonsingular M-matrix. A new Padé iteration well suited to parallel implementation is also derived and its properties explained. Iterative methods for the matrix square root are notorious for suffering from numerical instability. It is shown that apparently innocuous algorithmic modifications to the Padé iteration can lead to instability, and a perturbation analysis is given to provide some explanation. Numerical experiments are included and advice is offered on the choice of iterative method for computing the matrix square root.     

Synthesis of fixed-order compensators

In classical design, a low-order compensator is applied to a given plant. In this paper, we present an algebric construction of low (or fixed)-order compensators. Using the theory of root clustering, we achieve the following design requirements: closed-loop relative stability, relative stable compensators, and compensator's zero inclusion. In addition, we present a general robust analysis for real parameters. To reduce the computational difficulties, we suggest the use of low-order compensators.     

Proton magic even-even isotopes and giant halos of Ca isotopes with relativistic continuum Hartree-Bogoliubov theory

We study the proton magic O, Ca, Ni, Zr, Sn, and Pb isotope chains from the proton drip line to the neutron drip line with the relativistic continuum Hartree-Bogoliubov (RCHB) theory. Particulary, we study in detail the properties of even-even Ca isotopes due to the appearance of giant halos in neutron rich Ca nuclei near the neutron drip line. The RCHB theory is able to reproduce the experimental binding energiesE _b and two neutron separation energiesS _2n very well. The predicted neutron drip line nuclei are²⁸O,⁷²Ca,⁹⁸Ni,¹³⁶Zr,¹⁷⁶Sn, and²⁶⁶Pb. Halo and giant halo properties predicted in Ca isotopes withA>60 are investigated in detail through analysis of two neutron separation energies, nucleon density distributions, single particle energy levels, and the occupation probabilities of energy levels including continuum states. The spin-orbit splitting and the diffuseness of nuclear potential in these Ca isotopes, as well as the neighboring lighter isotopes in the drip line Ca region and find certain possibilities of giant halo nuclei in the Ne−Na−Mg drip line nuclei are also studied.     

Normalizing and variance stabilizing transformations of multivariate statistics under an elliptical population

Summary Normalizing and variance stabilizing transformations of a sample correlation, multiple correlation and canonical correlation coefficients are obtained under an elliptical population. It is shown that the Fisher'sz-transformation is efficient for these statistics. A normalizing transformation is also studied for a latent root of a sample covariance matrix in an elliptical sample.