Solution of sparse quasi-square rectangular systems by Gaussian elimination

We present a general method for the linear least-squares solutionof overdetermined and underdetermined systems. The method isparticularly efficient when the coefficient matrix is quasi-square,that is when the number of rows and number of columns is almostthe same. The numerical methods for linear least-squares problemsand minimum-norm solutions do not generally take account ofthis special characteristic. The proposed method is based onLU factorization of the original quasi-square matrix A, assumingthat A has full rank. In the overdetermined case, the LU factorsare used to compute a basis for the null space of A^T. The right-handside vector b is then projected onto this subspace and the least-squaressolution is obtained from the solution of this reduced problem.In the case of underdetermined systems, the desired solutionis again obtained through the solution of a reduced system.The use of this method may lead to important savings in computationaltime for both dense and sparse matrices. It is also shown inthe paper that, even in cases where the matrices are quite small,sparse solvers perform better than dense solvers. Some practicalexamples that illustrate the use of the method are included.     

O-Heterocycles by the cyclization of side-chain bromomethoxylated 2′-acetoxychalcones

Summary The title chalcone derivatives react with aqueous sodium hydroxide of various concentrations to form aurones as the major product, together with small amounts of flavones. However, the introduction of 4-nitro or 4-chloro substituents resulted in the formation of flavones as the major product.

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O-Heterocyclen mittels Cyclisierung von an der Seitenkette brommethoxylierten 2-Acetoxychalconen

Zusammenfassung Die im Titel genannten Chalconderivate reagieren mit Natronlauge in verschiedenen Konzentrationen, wobei Aurone zusammen mit geringen Mengen an Flavonen entstehen. Die Einführung von 4-Nitro- oder 4-Chlor-Substituenten führte jedoch zur bevorzugten Bildung von Flavonen.

     

Perfluorocyclobutane aromatic ether polymers

Novel polymers containing alternating perfluorocyclobutane and aromatic ether subunits are prepared from aryl poly(trifluorovinyl ether) monomers via the thermal [2π + 2π] dimerization of the trifluorovinyl ether functionality. A model study is described, which probes the nature of the perfluorocyclobutane rings formed during the polymerization reaction. The bifunctional monomer 4,4′-bis(trifluorovinyloxy) biphenyl and the trifunctional monomer 1,1,1-tris(4-trifluorovinyloxyphenyl)ethane are prepared and polymerized to provide thermoplastic and thermoset polymers, respectively. Characterization of the mechanical and dielectric properties of these new polymers is presented. © 1993 John Wiley & Sons, Inc.     

Determination of deoxynivalenol (vomitoxin) by high-performance liquid chromatography with electrochemical detection

A rapid method for the analysis of deoxynivalenol (DON) was developed using high-performance liquid chromatography (HPLC) with reductive electrochemical detection (ED). Deoxynivalenol produced by Fusarium roseum growing on solid cornmeal and rice substrates and from naturally contaminated wheat was extracted and quantitated via ED. DON levels in wheat were verified by gas chromatography and structurally confirmed by mass spectrometry. DON was optimally resolved by HPLC employing a radially compressed octadecylsilane column and a mobile phase of deoxygenated methanol-40 mM borate buffer (35:65) at a flow-rate of 1.0 ml/min. Under these conditions DON exhibited an average retention time of 3.6 min. Reductive ED (-1.4 V) allowed a 12-fold increase in sensitivity and greater selectivity than classical UV absorption at 224 nm. A detection limit for DON of 25 pg/microliter was achieved under these conditions. The determination of DON in crude grain extracts was hindered by extractable interfering substances, whereas ED was more functional-group selective (i.e. reduction of the carbonyl moiety). ED permits a direct quantitation of DON from crude grain extracts and may facilitate the determination of this agent and associated metabolites in biological samples.     

Correlation between the structural disorder studied by EXAFS and the magnetic properties of intercalated MnPS3

Intercalation of various cations into layered MnPS₃ induces some disorder in the local structure of Mn(II) cations, observable by EXAFS at the manganese K edge. The amplitude of this disorder effect is correlated with the amplitude of the weak ferromagnetism also observed at low temperature in the intercalates.     

One‐Step Synthetic Access to Isosteric and Potent Anticancer Nitrogen Heterocycles with the Benzo[c]phenanthridine Scaffold

A versatile one‐step two‐component cyclization to build new tetracyclic nitrogen heterocycles is described. Ortho‐methylhetarenecarbonitrile components were condensed with aldehydes to access a large library of differently substituted ring systems. The heterocyclic core can be easily modified by variation of the position of the endocyclic nitrogen atom in the o‐methylhetarenecarbonitrile substrate. The manner of the nucleophilic attack that leads to the condensation can be triggered by different electron‐density distribution in the molecule induced by the position of the nitrogen atom. Taking this into account, there is an electronic preference that leads to either pyridophenanthrolines or the corresponding pyridoazacarbazoles as the main products. We demonstrate the high antitumor potential of some of our synthesized heterocycles, which is strongly dependent on the substitution pattern introduced through the aldehyde component. The position and number of endocyclic nitrogen atoms play an important role regarding cytotoxicity of the studied compounds.     

Measurement of radon concentration in groundwater in the Ashanti region of Ghana

Radon in groundwater and their annual effective dose in the Ashanti region of Ghana have been determined using the continuous grab sampling technique and an AB-5 detector. Mean levels of radon were in the range of 0.51–46.16 Bq L^?1. Effective annual doses ranged from 0.18–16.16, 0.13–12.08 and 0.09–8.31 μSv y^?1 for infants, children and adults, respectively. These values are significantly lower than the reference level of 0.1 mSv y^?1 recommended by the WHO and United Nations Scientific Committee on the Effects of Atomic Radiation for members of the public.