A note on the necessary conditions for the algebraic Riccati equation

We derive some useful and easily computable necessary conditionsfor the existence of a positive semi-definite solution to thealgebraic Ricatti equation (ARE). A motivating example is givento highlight the usefulness of the conditions for controllerand observer designs for nonlinear systems. Further, an upperbound on the trace of the solution to the ARE is also derived.     

Spectral shift function and trace formula

The complete proofs of Krein’s theorem on the spectral shift function and the trace formula are given for a pair of self-adjoint operators such that either (i) their difference is trace-class or (ii) the difference of their resolvents is trace-class. The proofs, essentially due to Krein, is based on Herglotz’s theorem on the boundary value of the analytic functions whose imaginary part is non-negative on the upper half plane, and an almost optimal class of functions are obtained for which the trace formula is valid. Also an alternative method based on Weyl-von Neumann’s theorem for self-adjoint operators, avoiding the complex function theory and inspired by Voiculescu’s work, is given for the first case. Furthermore, some applications of the spectral shift function have been discussed.     

On the Positivity of the Coefficients of a Certain Polynomial Defined by Two Positive Definite Matrices

It is shown that the polynomialp(t) = Tr[(A+tB)^m]has positive coefficients when m = 6 and A and B are any two 3-by-3 complex Hermitian positive definite matrices. This case is the first that is not covered by prior, general results. This problem arises from a conjecture raised by Bessis, Moussa, and Villani in connection with a long-standing problem in theoretical physics. The full conjecture, as shown recently by Lieb and Seiringer, is equivalent to p(t) having positive coefficients for any m and any two n-by-n positive definite matrices. We show that, generally, the question in the real case reduces to that of singular A and B, and this is a key part of our proof.     

2+1维de-Sitter时空中光线的轨迹

通过求解2+1维de-Sitter时空中零测地线方程得到光线的轨迹方程,对轨迹方程进行分析发现其不存在封闭的轨迹解.     

燃煤锅炉粉煤灰中痕量元素赋存形态研究

本文运用改进的Tessier法对某燃煤电厂静电除尘器收集的三个电场的粉煤灰进行分级提取(SEE)实验研究.SEE实验将粉煤灰中的重金属分为五个存在形态进行分级提取:水溶态(pH=7),酸溶态(pH=5),氧化物结合态,难还原态及残渣态.试验结果表明,残渣态在ESP除尘器所收集的飞灰中含量占据绝大部分;在容易迁移的离子可交换态和酸溶态中,所研究的痕量重金属元素均呈现出FA1相似文献   

Unsupervised cell identification on multidimensional X‐ray fluorescence datasets

A novel approach to locate, identify and refine positions and whole areas of cell structures based on elemental contents measured by X‐ray fluorescence microscopy is introduced. It is shown that, by initializing with only a handful of prototypical cell regions, this approach can obtain consistent identification of whole cells, even when cells are overlapping, without training by explicit annotation. It is robust both to different measurements on the same sample and to different initializations. This effort provides a versatile framework to identify targeted cellular structures from datasets too complex for manual analysis, like most X‐ray fluorescence microscopy data. Possible future extensions are also discussed.     

Laser Based Techniques for Ultra Trace Isotope Production, Spectroscopy and Detection

A variety of research activities in the field of fundamental and applied nuclear physics has evolved in the last years using resonantly tuned radiation from powerful lasers. The technique of resonance ionization spectroscopy has delivered outstanding results and found broad acceptance in the last years as a particularly efficient and highly selective method for rare and exotic radioisotope studies. It is used for production, spectroscopy and detection of these species and provides complete isobaric, high isotopic and even some isomeric selection, which altogether is needed for on-line investigation of short lived species far off stability as well as for ultra trace determination. Good overall efficiency pushes the experimental limits of detection in elemental trace analysis down to below 10⁶ atoms per sample, and additionally isotopic selectivity as high as 3 × 10¹² has been demonstrated. The widespread potential of resonance ionization techniques is discussed, focusing on the experimental arrangements for applications in selective on-line isotope production, spectroscopy of rare radioisotopes and ultra trace determination of radiotoxic isotopes like ²³⁸Pu to ²⁴⁴Pu, ^135,137Cs, ^89,90Sr or ⁴¹Ca in environmental, technical and biomedical samples.     

傅立叶变换-主成份分析方法用于二维色谱数据的压缩和重构

结合傅立叶变换（ＦＴ）和主成份分析（ＰＣＡ）技术,实现了二维高效液相色谱数据的压缩和重构,并对不同信噪比的二维色谱测量数据进行了处理,即使对原始数据的压缩比高达２００倍,仍能很好地重构原始数据,当原始数据的信噪比较低时,阈值的选择受大振幅噪音的影响,使压缩比略有下降,但仍然能够保持信号基本不失真。     

微量元素与优生的关系

研究表明,微量元素与优先有着非常密切的关系。如果微量元素缺乏,就会导致各种疾病甚至先天残疾的产生。     

婴幼儿低发锌、铜、铁、钙与疾病的关系探讨

对846例低发锌、456例低发铜、488例低发铁以及595例低发钙婴幼儿与疾病的关系进行了探讨。结果显示,低发锌婴幼儿中反复呼吸道感染、食欲不振和异食癖的患病率分别为71.16%、57.57%和11.47％;低发铜和低发铁婴儿的贫血率分别为15.79%和73.16%,呼吸道感染的患病率分别为9.43%和35.66%：低发钙者中佝楼病的发病率为81.51%。