An unusual decomposition of a complete 7-partite graph of order 28

A decomposition of the complete 7-partite graph on 28 vertices where each set in the partition has four vertices is given. Several unusual properties of this decomposition are discussed, giving rise to several natural questions.     

On spectral radii of matrices governing some numerical estimating algorithms with incomplete data

Summary Many estimating procedures are carried out with incomplete data by means of different types of EM algorithms. They allow us to obtain maximum likelihood parameter estimates in classical inference and also estimates based on the posterior mode in Bayesian inference. This paper analyzes in detail the spectral radii of the Jacobian matrices algorithm as a possible way to evaluate convergence rates. The eigenvalues of such matrices are explicitly obtained in some cases and, in all of them, a geometric convergence rate is, at least, guaranteed near the optimum. Finally, a comparison between the leading eigenvalues of EM and direct and approximate EM-Bayes algorithms may suggest the efficiency of each case.     

An extension of Warnaar's matrix inversion

We present a necessary and sufficient condition for two matrices given by two bivariate functions to be inverse to each other with certainty in the cases of Krattenthaler formula and Warnaar's elliptic matrix inversion. Immediate consequences of our result are some known functions and a constructive approach to derive new matrix inversions from known ones.

     

Stability analysis for neural networks with inverse Lipschitzian neuron activations and impulses

In this paper, a new concept called α-inverse Lipschitz function is introduced. Based on the topological degree theory and Lyapunov functional method, we investigate global convergence for a novel class of neural networks with impulses where the neuron activations belong to the class of α-inverse Lipschitz functions. Some sufficient conditions are derived which ensure the existence, and global exponential stability of the equilibrium point of neural networks. Furthermore, we give two results which are used to check the stability of uncertain neural networks. Finally, two numerical examples are given to demonstrate the effectiveness of results obtained in this paper.     

电热原子吸收法测定人发中硒时不同改进剂的研究

对于生物体中硒的测定,国内外已有大量报道,所用方法也相当广泛。本文利用石墨炉原子吸收对人发中硒的测定进行了研究;对使用较多的两种硒的基体改进剂:铜与镍的作用与效果进行了研究,发现铜较镍在某些方面更为优越。当选用100 μg/mL的铜作改进剂时,硒的特征浓度为0.13 ng/1％abs,测定精度为3.4％～5.4％;线性范围达400 ng。     

Experimental realization of sustained simple kinetic regimes of release of particulate solutes subject to slow dissolution in the containing matrix

We examine the short-time and long-time limiting cases of the general equation commonly used to describe the kinetics of release of a particulate solute embedded in a planar solid matrix, complicated by slow dissolution of the particles in the matrix. The conditions under which the said limiting cases may be expected to yield sustained simple kinetic regimes of solute release in practice are determined. Finally an experimental illustration of the (simultaneous) occurrence of both simple regimes in a single system (consisting of strongly soluble and sparingly soluble salts embedded in an emulsified asphalt matrix) is given.     

矩阵方程X+A^{*}X^{-q}A=Q(q\geq 1)的Hermitian正定解

本文研究矩阵方程X A~*X~(-q)A=Q(q≥1)的Hermitian正定解,给出了存在正定解的充分条件和必要条件,构造了求解的迭代方法.最后还用数值例子验证了迭代方法的可行性和有效性.     

Matrix Effect of Alkali and Alkaline Earth Metal Halides on Fluorescence Quantum Yield of Indium in Laser‐Induced Fluorescence Flame Spectrometry

As interfered with by alkali and alkaline earth metal halides added as the matrix in an acetylene/air flame, the fluorescence quantum yield of In as the analyte in a laser‐induced fluorescence (LIF) flame spectrometry has been thoroughly characterized. The fluorescence quantum yield is determined by a ratio of F to A, where F is the measured fluorescence of In and A is the difference between the absorption signals recorded for the analyte and the blank solutions. The normalized fluorescence signal is treated to prevent deviations due to variations of the atomization efficiency under the conditions with and without the matrix added. The fluorescence quantum yield is measured to be almost independent of the matrix concentration up to 500 ppm (μg/mL) studied, under conditions of either optical unsaturation or saturation. By considering a quenching effect induced by electron‐atom collisions, the calculated fluorescence quantum yields are consistent with our observations.     

Investigation of the effects of 24 bio-matrices on the LC-MS/MS analysis of morinidazole

This study compares and evaluates the effect of various matrices on liquid chromatography (LC) coupled with tandem mass spectrometry (MS/MS) analysis. Permanent post-column infusion (PCI) was used to quantify matrix effects. In this way, the suppressed or enhanced signal of the target material resulting from different co-eluting matrix components could be assessed. Twenty-four biological samples from in vivo and in vitro experiments were selected for this study. In addition, 7 sample components were further analyzed after sample preparation by protein precipitation. Multiple regression analysis was used to investigate the collinear relationship between matrix effects and co-eluted components at different time intervals. We found that salt was the dominant factor which impacted changes in signal detection. In order to eliminate it, we used ammonium formate as a modifier of the mobile phase which resulted in charge-state redistribution profiles so that a homogeneous matrix formed. By employing pulse gradient chromatography in the presence of 5 mM ammonium formate, favorable improvements of enhanced signal intensity and reduced matrix effects were obtained. These experiments also indicated the feasibility of using analogue IS during bio-analysis which contributed to an overall faster assay that would be suitable for drug discovery and development purposes.     

Determination of polybrominated diphenyl ethers in fish tissues by matrix solid-phase dispersion and gas chromatography coupled to triple quadrupole mass spectrometry: Case study on European eel (Anguilla anguilla) from Mediterranean coastal lagoons

This paper describes the development and validation of an analytical methodology to determine 28 polybrominated diphenyl ethers (PBDEs) in European eel (Anguilla anguilla) tissues using matrix solid-phase dispersion (MSPD) and gas chromatography coupled to triple quadrupole mass spectrometry (GC-QQQ-MS/MS). A total of 28 PBDEs were targeted, including tri- to deca-brominated congeners.The robustness and effectiveness of the proposed sample preparation procedure was demonstrated in lipid-rich eel tissues. The use of batch MSPD with activated silica gel and H₂SO₄-impregnated silica gel, followed by H₂SO₄ digestion and multilayer cartridge clean-up allowed for complete lipid removal and eliminated matrix effects during GC-QQQ-MS/MS analysis. The average PBDE recoveries from eel muscle samples spiked with PBDEs at two levels were in the range 56.2-119.0%. Precision was satisfactory since relative standard deviations were lower than 19.6%, regardless of spike level, and method quantification limits ranged between 1 and 170 pg g⁻¹ (wet weight).The method demonstrated its successful application for the analysis of eel samples from two coastal lagoons located on the western French Mediterranean coast. All samples tested positive, but for tri- to hexa-brominated congeners only and total PBDE levels observed in this study were in the range 0.08-1.80 ng g⁻¹ wet weight.