On the necessary and sufficient condition for the extended Wedderburn–Guttman theorem

Let A be a u by v matrix, and let M and N be u by p and v by q matrices, where p may not be equal to q or rank(M^′AN)<min(p,q). Recently, Galantai [A. Galantai, A note on the generalized rank reduction, Acta Math. Hungarica 116 (2007) 239–246] presented what he claimed to be the necessary and sufficient condition for rank(A-AN(M^′AN)^-M^′A)=rank(A)-rank(AN(M^′AN)^-M^′A) to hold. This rank subtractivity formula along with the condition under which it holds is called the extended Wedderburn–Guttman theorem. In this paper, we show that some of Galantai’s assertions are incorrect.     

The clique numbers of regular graphs of matrix algebras are finite

Let F be a field, char(F)≠2, and SGL_n(F), where n is a positive integer. In this paper we show that if for every distinct elements x,yS, x+y is singular, then S is finite. We conjecture that this result is true if one replaces field with a division ring.     

辫子群的全部二维不可约表示

通过直接解矩阵方程给出了Bn群的全部二维不可约表示．     

Selective Preparation of Phosphorus Mononitride (P≡N) from Phosphinoazide and Reversible Oxidation to Phosphinonitrene

The interstellar candidate phosphorus mononitride PN, a metastable species, was generated through high-vacuum flash pyrolysis of (o-phenyldioxyl)phosphinoazide in cryogenic matrices. Although the PN stretching band was not directly detected because of its low infrared intensity and possible overlaps with other strong bands, o-benzoquinone, carbon monoxide, and cyclopentadienone as additional fragmentation products were clearly identified. Moreover, an elusive o-benzoquinone-PN complex formed when (o-phenyldioxyl)phosphinoazide was exposed to UV irradiation at λ=254 nm. Its recombination to (o-phenyldioxyl)-λ⁵-phosphinonitrile was observed upon irradiation with the light at λ=523 nm, which demonstrates for the first time the reactivity of PN towards an organic molecule. Energy profile computations at the B3LYP/def2-TZVP density functional theory level reveal a concerted mechanism. To provide further evidence, UV/Vis spectra of the precursor and the irradiation products were recorded and agree well with time-dependent DFT computations.     

Application of ultra-high-pressure liquid chromatography–tandem mass spectrometry to the determination of multi-class pesticides in environmental and wastewater samples: Study of matrix effects

An ultra-high-pressure liquid chromatography–tandem mass spectrometry (UHPLC–MS/MS) method for the determination of 37 pesticides (herbicides, insecticides and fungicides) in environmental and wastewater has been developed. To efficiently combine UHPLC with MS/MS, a fast-acquisition triple quadrupole mass analyzer was used. This analyzer (minimum dwell time, 5 ms) allows acquiring up to three simultaneous transitions in the selected reaction monitoring mode for each compound assuring a reliable identification without resolution or sensitivity losses. A pre-concentration step based on solid-phase extraction using Waters Oasis HLB cartridges (0.2 g) was applied with a 100-fold pre-concentration factor along the whole analytical procedure. The method was validated based on European SANCO guidelines using surface, ground, drinking and treated water (from an urban solid residues treatment plant) spiked at two concentration levels (0.025 and 0.1 μg/L), the lowest having been established as the limit of quantification objective. The method showed excellent sensitivity, with instrumental limits of detection ranging from 0.1 to 7 pg. It was applied to environmental water samples (ground and surface water) as well as to samples of urban solid waste leachates (raw leachate and treated leachate after applying reversed osmosis) collected from a municipal treatment plant. Matrix effects have been studied in the different types of water samples analyzed, and several isotope-labelled internal standards have been evaluated as a way to compensate the signal suppression observed for most of the compounds studied, especially in wastewater samples. As a general remark, only those pesticides which response was corrected using their own isotope-labelled molecule, could be satisfactorily corrected in all type of samples, assuring in this way the accurate quantification in all matrix samples.     

Overcoming matrix effects using the dilution approach in multiresidue methods for fruits and vegetables

During recent years matrix effects in liquid chromatography coupled to tandem mass spectrometry (LC-MS/MS) have quickly become a major concern in food analysis. The phenomenon of ion suppression can lead to errors in the quantification of the analytes of interest, as well as can affect detection capability, precision, and accuracy of the method. Sample dilution is an easy and effective method to reduce interfering compounds, and so, to diminish matrix effects. In this work, matrix effects of 53 pesticides in three different matrices (orange, tomato and leek) were evaluated. Several dilutions of the matrix were tested in order to study the evolution of signal suppression. Dilution of the extracts led to a reduction of the signal suppression in most of the cases. A dilution factor of 15 demonstrated to be enough to eliminate most of the matrix effects, opening the possibility to perform quantification with solvent based standards in the majority of the cases. In those cases where signal suppression could not be reduced, a possible solution would be to use stable isotope-labelled internal standards for quantification of the problematic pesticides.     

A computational study of the chromatographic separation of racemic mixtures

Summary A model is devised using molecular mechanics to simulate chromatographic separations of enantiomers. Theoretical results derived from this model are compared with experimental findings obtained using supercritical fluid chromatography. The model is then developed to incorporate the effects of binding the stationary phase to a matrix. Computed results show that addition of the matrix into the model has significant effects on the ability of the stationary phase to separate racemic mixtures.     

Analogy between real irreducible tensor operator and molecular two-particle operator

. Molecular matrix elements of a physical operator are expanded in terms of polycentric matrix elements in the atomic basis by multiplying each by a geometrical factor. The number of terms in the expansion can be minimized by using molecular symmetry. We have shown that irreducible tensor operators can be used to imitate the actual physical operators. The matrix elements of irreducible tensor operators are easily computed by choosing rational irreducible tensor operators and irreducible bases. A set of geometrical factors generated from the expansion of the matrix elements of irreducible tensor operator can be transferred to the expansion of the matrix elements of the physical operator to compute the molecular matrix elements of the physical operator. Two scalar product operators are employed to simulate molecular two-particle operators. Thus two equivalent approaches to generating the geometrical factors are provided, where real irreducible tensor sets with real bases are used. Received: 3 September 1996 / Accepted: 19 December 1996     

Matrix Solid-phase Dispersion Extraction of Alkaloids from the Roots of Aconitum kusnezoffii Reichb

Matrix solid-phase dispersion(MSPD) was developed for the extraction of four alkaloids, including aconitine, mesaconitine, hypaconitine and deoxyaconitine, from the roots of Aconitum kusnezoffii Reichb. The determination of the analyte was carried out by high performance liquid chromatography with UV detection. The alkaline alumina was used as sorbent. The mixture of acetonitrile and water was used as elution solvent. Several extraction parameters, such as type of sorbent, the ratio of sample to solid suppo...     

α-腈基阿魏酸基体在MALDI-TOFMS测定中的应用研究

在基体辅助激光解吸电离飞行时间质谱（MALDI－TOFMS）测定中基体的作用举足轻重。有效或特效基体的发现和应用不仅可提高测试灵敏度和分辨率,加大分子量测定范围,还能扩增测试样品的种类,推动MALDI－TOFMS应用的发展。目前MALDI－TOFMS分析的常用基体^[1,2]测定多肽、蛋白质的α-腈基－4－羟基肉桂酸（4HCCA）和介子酸（SA）效果比较理想;而测定糖类物质的2,5－二羟基苯甲酸（DHB）则不能完全适用于在组成、结构、序列以及连接方式上存在多样性的碳水化合物的分子;测定DNA的3－羟基吡啶甲酸（3－HPA）使用时必须对样品、溶剂甚至基体本身进行严格纯化,较为烦琐,测定含百个碱基以上大分子量DNA的灵敏度和分辨率还不理想。本文考察研究α-腈基阿魏酸（CFA）旨在寻找MALDI－TOFMS测定的有效新基体,为MALDI－TOFMS测定提供更多的基体选择。