Immanant positivity for Catalan-Stieltjes matrices

We give some sufficient conditions for the nonnegativity of immanants of square submatrices of Catalan-Stieltjes matrices and their corresponding Hankel matrices. To obtain these sufficient conditions, we construct new planar networks with a recursive nature for Catalan-Stieltjes matrices. As applications, we provide a unified way to produce inequalities for many combinatorial polynomials, such as the Eulerian polynomials, Schröder polynomials, and Narayana polynomials.     

Exact SOR convergence regions for a general class ofp-cyclic matrices

Linear systems whose associated block Jacobi iteration matrixB is weakly cyclic generated by the cyclic permutation = (₁,₂,..., _p ) in the spirit of Li and Varga are considered. Regions of convergence for the corresponding blockp-cyclic SOR method are derived and the exact convergence domains for real spectra, (B ^p ), of the same sign are obtained. Moreover, analytical expressions for two special cases forp = 5 are given and numerical results are presented confirming the theory developed. The tools used for this work are mainly from complex analysis and extensive use of (asteroidal) hypocycloids in the complex plane is made to produce our results.This work was supported in part by AFOSR grant F49620-92-J-0069 and NSF grant 9202536-CCR.     

On the extreme spectral properties of Toeplitz matrices generated byL 1 functions with several minima/maxima

In this paper we are concerned with the asymptotic behavior of the smallest eigenvalue ₁ ⁽ⁿ⁾ of symmetric (Hermitian)n ×n Toeplitz matricesT _n (f) generated by an integrable functionf defined in [–, ]. In [7, 8, 11] it is shown that ₁ ⁽ⁿ⁾ tends to essinff =m _f in the following way: ₁ ⁽ⁿ⁾ –m _f 1/n ^2k . These authors use three assumptions:A1)f –m _f has a zero inx =x ₀ of order 2k.A2)f is continuous and at leastC ^2k in a neighborhood ofx ₀.A3)x =x ₀ is the unique global minimum off in [–, ]. In [10] we have proved that the hypothesis of smoothnessA2 is not necessary and that the same result holds under the weaker assumption thatf L ¹[–, ]. In this paper we further extend this theory to the case of a functionf L ¹[–, ] having several global minima by suppressing the hypothesisA3 and by showing that the maximal order 2k of the zeros off –m _f is the only parameter which characterizes the rate of convergence of ₁ ⁽ⁿ⁾ tom _f .     

A “Multiplicative Coboundary” theorem for some sequences of random matrices

Schmidt(¹⁰) showed that if the family of distributions of the partial sums of a strictly stationary random sequence is tight, then that random sequence is a coboundary. Here an analog of that result is proved for some sequences of random matrices, with partial sums replaced by matrix products.     

Spectral-Null Codes and Null Spaces of Hadamard Submatrices

Codes of length 2 ^m over {1, -1} are defined as null spaces of certain submatrices of Hadamard matrices. It is shown that the codewords of all have an rth order spectral null at zero frequency. Establishing the connection between and the parity-check matrix of Reed-Muller codes, the minimum distance of is obtained along with upper bounds on the redundancy of . An efficient algorithm is presented for encoding unconstrained binary sequences into .     

Evaluation of the limit of performance of an analytical method based on a statistical calculation of its critical concentrations according to ISO standard 11843: Application to routine control of banned veterinary drug residues in food according to European Decision 657/2002/EC

Traceability of the measurement of analytical parameters capable of evaluating the performance of methods is an important concept for the assessment of quality for the routine control, especially for residue monitoring of non-authorized medicinal substances in food from animal origin. The European Decision no. 657/2002/EC recommends to calculate two statistical limits, CCα and CCβ, which allow to evaluate the critical concentrations above which the method reliably distinguish and quantify a substance taking into account the variability of the method and the statistical risk to take a wrong decision. The calculation, which can be derived from the ISO standard no. 11843 is applied on a routine basis. An example displays a very simple way for evaluating the performance of an LC-MSMS method which has been validated a few years ago and is qualified onto a Micromass Quattro LCZ tandem mass spectrometer to monitor and confirm the nitrofuran metabolite residues in food from animal origin. Community Reference Laboratory for Antimicrobial Veterinary Drug Residue Control in Food from Animal Origin     

高效除草剂快杀稗标准物质的制备及表征

从快杀稗工业品出发 ,经活性炭纯化、硅胶柱层析分离制得快杀稗标准物质 ,并进行熔点、高效液相色谱、紫外光谱、元素分析、红外光谱、质谱、核磁共振等方法的表征 ,以高效液相色谱法测得该标准品纯度在99%以上     

双波长K系数—标准加入吸光光度法同时测定锰和锌

研究应用双波长K系数—标准加入吸光光度法同时测定锰和锌二组分混合物.试验确定了锰和锌测定中K_(Mn)与K_(Zn)的回归方程.对合成试样、人发试样测定,结果满意.     

A new approach for the sequential injection spectrophotometric determination of the total antioxidant activity

A sequential injection system based on the ABTS (2,2′-azino-bis-(3-ethylbenzothiazoline-6-sulphonic-acid) methodology was developed. The proposed method, incorporating a mixing chamber in the side port of the selection valve, was evaluated to measure the total antioxidant activity of several beverages and foods.The ABTS⁺ is generated by oxidation of ABTS with potassium persulfate and is reduced in presence of hydrogen-donating antioxidants converting into a colourless product. The applicability of the developed method was tested by measurement of the antioxidant activity of pure compounds as well as by analysing complex food and beverage samples. The antioxidant activity was presented as l(+) ascorbic acid equivalence. The values obtained by this methodology were not significantly different from the results obtained by the original spectrophotometric ABTS assay. For most of the studied antioxidants, antioxidant activity varied with pH and dilution. The proposed SIA system is suitable for screening direct or diluted total antioxidant activity of pure compounds or food samples.     

Developing a sequential injection-square wave voltammetry (SI-SWV) method for determination of atrazine using a hanging mercury drop electrode

This paper describes the development of a sequential injection analysis method to automate the determination of atrazine by square wave voltammetry exploiting the concept of monosegmented flow analysis to perform in-line sample conditioning and standard addition. To perform these tasks, an 800 μL monosegment is formed, composed by 400 μL of sample and 400 μL of buffer/standard solution. To obtain an efficient homogenization, the sample solution is divided in five zones intercalated by four zones of the Britton-Robinson buffer (pH 2.0) in presence of appropriate concentration of NaNO₃ and varying atrazine standard concentrations. This mixture zone is isolated from the carrier solution by two 100 μL air bubbles. After homogenization in an auxiliary reaction coil the mixture zone is injected toward the flow cell, which is adapted to the capillary of a hanging drop mercury electrode, at a flow rate of 50 μL s⁻¹. After a suitable delay time, the potential is scanned from −0.5 to −1.2 V versus Ag/AgCl using a frequency of 300 Hz and pulse height of 25 mV. The linear dynamic range is observed for atrazine concentrations between 1.16 × 10⁻⁷ and 2.32 × 10⁻⁶ mol L⁻¹, obeying the linear equation i_p = (−6.91 ± 0.07) × 10⁸[atrazine] + (4 ± 8), with r² = 0.9996, for which the slope is given in nA L mol⁻¹. The detection and quantification limits of the method are 2.1 × 10⁻⁸ and 7.0 × 10⁻⁸ mol L⁻¹, respectively. The sampling frequency is 37 h⁻¹, when the standard addition protocol is followed. This frequency can be increased to 42 h⁻¹ if the protocol to obtain in-line calibration curve is used for quantification. The method was applied for determination of atrazine in spiked river water samples and its accuracy was evaluated by comparison with the batch standard addition approach, which revealed that there is no evidence of statistically significant differences between the two methods.