多元统计分析中一类矩阵迹函数最小化问题的有效算法

研究来源于多元统计分析中的一类矩阵迹函数最小化问题$\min c+ tr(AX)+\sum\limits_{j=1}^{m}tr(B_j X C_jX^{T}),\ \ {\rm s. t.} \ X^TX=I_p,$其中$c$为常数, $A\in R^{p\times n}\ (n\geq p)$, $B_j\in R^{n\times n}, C_j\in R^{p\times p}$为给定系数矩阵. 数值实验表明已有的Majorization算法虽可行, 但收敛速度缓慢且精度不高. 本文从黎曼流形的角度重新研究该问题, 基于Stiefel流形的几何性质, 构造一类黎曼非单调共轭梯度迭代求解算法, 并给出算法收敛性分析.数值实验和数值比较验证所提出的算法对于问题模型是高效可行的.     

基于视觉辐条图案识别方法的蓝宝石引晶机制研究

工业生产蓝宝石晶体过程中,引晶步骤有着至关重要的地位。引晶必须在温度梯度较小,温度分布趋于稳定的条件下进行。目前,工业生产蓝宝石主要依靠人工经验操控籽晶杆实现引晶操作,但是人工引晶操作的准确性不高会导致成品品质不佳、资源浪费。为此,本文提出一种基于蓝宝石视觉辐条图案识别方法来检测蓝宝石熔体状态自由液面状态,从而实现一种高效率引晶的机制。此方法利用经典骨架化算法细化辐条图案,Harris算子实现特征信息的提取,提取的特征信息放入运动轨迹模型中判断熔体稳定性,分析液面温度分布稳定性从而实现引晶。结果表明,此算法具有有效性,蓝宝石晶体引晶效率大大提高,生产出的成品良率也有提升,可有效指导蓝宝石的工业生产。     

A rapid,spatially dispersive frequency comb spectrograph aimed at gas phase chemical reaction kinetics

This New Views article will highlight some recent advances in high sensitivity gas detection using direct infrared absorption frequency comb laser spectroscopy, with a focus on frequency comb use in chemical reaction kinetics and our own contribution to this field. Our recently implemented detection technique uses a combination of a 12.9?GHz free spectral range virtually imaged phased array and diffraction grating to spatially disperse the mid-infrared frequency comb onto a camera. Individual frequencies or ‘comb teeth’ of a 250?MHz repetition-rate frequency comb are able to be resolved. High molecular sensitivity is achieved by increasing the interaction path length using a Herriott multipass cell. High spectral resolution, broadband spectral coverage, and high molecular sensitivity are all achieved on an adjustable 1–50 µs timescale, making this frequency comb apparatus ideal for measuring chemical reaction kinetics where multiple absorbing species can be monitored simultaneously. This New Views article will also discuss some of the challenges and decisions that chemists might face in implementing this advanced physics technology in their own laboratory.

Spatially dispersed 250 MHz mid-infrared frequency comb laser, with absorption of some frequencies by a dilute sample of methane.     

Distinct effect of xenobiotics on the metal‐binding properties of protein molecules

The X‐ray standing‐wave method was applied to study the elemental composition and molecular organization of ordered protein films of alkaline phosphatase exposed to different xenobiotics (drug compounds, lead). Binding of metal ions from triply distilled water to protein molecules has been experimentally observed. Definite differences in the arrangement of impurity metal ions in the films have been established. The considerable enhancement of protein–metal interactions is attributed to partial rearrangement of the protein native structure, induced by xenobiotics.     

Homogeneous variable exponent Besov and Triebel–Lizorkin spaces

We introduce homogeneous Besov and Triebel–Lizorkin spaces with variable indexes. We show that their study reduces to the study of inhomogeneous variable exponent spaces and homogeneous constant exponent spaces. Corollaries include trace space characterizations and Sobolev embeddings.     

Explicit uniform bounds on integrals of Bessel functions and trace theorems for Fourier transforms

Explicit and partly sharp estimates are given of integrals over the square of Bessel functions with an integrable weight which can be singular at the origin. They are uniform with respect to the order of the Bessel functions and provide explicit bounds for some smoothing estimates as well as for the L² restrictions of Fourier transforms onto spheres in which are independent of the radius of the sphere. For more special weights these restrictions are shown to be Hölder continuous with a Hölder constant having this independence as well. To illustrate the use of these results a uniform resolvent estimate of the free Dirac operator with mass in dimensions is derived.     

Generalization of tangential trace spaces of H(curl,Ω) for curvilinear Lipschitz polyhedral domains Ω

For curvilinear Lipschitz polyhedral domains Ω, explicit characterizations of the tangential trace spaces of H ¹(Ω) are presented. These extend the original characterizations given by Buffa and Ciarlet that hold on Lipschitz polyhedral domains with plane faces. The tangential trace spaces of H ¹(Ω) are fundamental for the definition, analysis and intuitive understanding of the trace spaces of H ( curl ,Ω) and therefore, more general characterizations of the latter are obtained at the same time. Copyright © 2013 John Wiley & Sons, Ltd.     

微波消解-ICP-MS法测定药用明胶空心胶囊中微量重金属元素

采用微波消解技术,建立了一种电感耦合等离子体质谱法测定明胶空心胶囊中Cr,Co,Ni,Cu,Zn,As,Cd,Hg和Pb 9种微量重金属元素的方法。确定了微波消解仪和等离子体质谱仪的最佳操作参数,研究共存离子的干扰和消除方法,选择了各元素的测定同位素,以Ge,Rh和Tl为内标补偿基体效应,建立了样品测定方法。应用拟定的方法测定了不同生产厂家、不同批次的空心胶囊中微量重金属的含量。方法对试样中各元素测定的相对标准偏差为1.5%~14.1%,加标回收率在90.0%~102.0%。结果表明,方法简便、快速、灵敏,满足于空心胶囊中9种重金属元素的测定要求。     

A regularized trace formula and oscillation of eigenfunctions of a Sturm‐Liouville operator with retarded argument at 2 points of discontinuity

In this study, first, a formula for regularized sums of eigenvalues of a Sturm‐Liouville problem with retarded argument at 2 points of discontinuity which contains a spectral parameter in the boundary conditions is obtained. After that, oscillation properties of the related problem is investigated. Finally, under the condition that a subset of nodal points is dense in definition set, the potential function is determined.     

Difference Cochains and Reidemeister Traces

The authors consider the difference of Reidemeister traces and difference cochain of given two self-maps,and find out a relation involving these two invariants.As an application,an inductive formula of the Reidemeister traces for self-maps on a kind of CW-complex,including spherical manifolds is obtained.