The Padé-Rayleigh-Ritz method for solving large hermitian eigenproblems

We make use of the Padé approximants and the Krylov sequencex, Ax,,...,A ^m–1 x in the projection methods to compute a few Ritz values of a large hermitian matrixA of ordern. This process consists in approaching the poles ofR _x()=((I–A)^–1 x,x), the mean value of the resolvant ofA, by those of [m–1/m]_Rx(), where [m–1/m]_Rx() is the Padé approximant of orderm of the functionR _x(). This is equivalent to approaching some eigenvalues ofA by the roots of the polynomial of degreem of the denominator of [m–1/m]_Rx(). This projection method, called the Padé-Rayleigh-Ritz (PRR) method, provides a simple way to determine the minimum polynomial ofx in the Krylov subspace methods for the symmetrical case. The numerical stability of the PRR method can be ensured if the projection subspacem is sufficiently small. The mainly expensive portion of this method is its projection phase, which is composed of the matrix-vector multiplications and, consequently, is well suited for parallel computing. This is also true when the matrices are sparse, as recently demonstrated, especially on massively parallel machines. This paper points out a relationship between the PRR and Lanczos methods and presents a theoretical comparison between them with regard to stability and parallelism. We then try to justify the use of this method under some assumptions.     

Elution order in gas chromatography

The retention behavior of a heterogeneous group of solutes has been examined on seven different stationary phases under isothermal and temperature-programmed conditions. Both ΔH_v (enthalpy of solute vaporization from the stationary phase) and ΔS_v (entropy of solute vaporization from the stationary phase) values were determined for each solute – stationary phase combination under isothermal conditions. Both program rate and carrier gas velocity were shown to affect solute elution order. Unless these and other experimental factors discussed are controlled, column equivalency studies based on solute elution order have dubious value.     

Simultaneous kinetic spectrophotometric determination of cyanide and thiocyanate using the partial least squares (PLS) regression

The partial least squares (PLS-1) calibration model based on spectrophotometric measurement, for the simultaneous determination of CN⁻ and SCN⁻ ions is described. The method is based on the difference in the rate of the reaction between CN⁻ and SCN⁻ ions with chloramine-T in a pH 4.0 buffer solution and at 30 °C. The produced cyanogen chloride (CNCl) reacts with pyridine and the product condenses with barbituric acid and forms a final colored product. The absorption kinetic profiles of the solutions were monitored by measuring absorbance at 578 nm in the time range 20-180 s after initiation of the reaction with 2 s intervals. The experimental calibration matrix for partial least squares (PLS-1) calibration was designed with 31 samples. The cross-validation method was used for selecting the number of factors. The results showed that simultaneous determination could be performed in the range 10.0-900.0 and 50.0-1200.0 ng mL⁻¹ for CN⁻ and SCN⁻ ions, respectively. The proposed method was successfully applied to the simultaneous determination of cyanide and thiocyanate in water samples.     

(N-Isocyanimino)triphenylphosphorane-Mediated,One-Pot,Efficient Synthesis of Sterically Congested 1,1,1-Trifluoro-2-(5-aryl-1,3,4-oxadiazol-2-yl)-2-propanol Derivatives via Intramolecular Aza-Wittig Reaction

Reactions of (N-isocyanimino)triphenylphosphorane with 1,1,1-trifluoroacetone in the presence of aromatic (or heteroaromatic) carboxylic acids (3-methylbenzoic acid, 1-naphthalenecarboxylic acid, 2-naphthalenecarboxylic acid, 2-furancarboxylic acid, and 2-thiophenecarboxylic acid) proceed smoothly at room temperature and in neutral conditions to afford sterically congested 1,1,1-trifluoro-2-(5-aryl-1,3,4-oxadiazol-2-yl)-2-propanol derivatives in high yields. The reaction proceeds smoothly and cleanly under mild conditions, and no side reactions were observed.

Supplemental materials are available for this article. Go to the publisher's online edition of Phosphorus, Sulfur, and Silicon and the Related Elements to view the free supplemental file.     

Ag3[PMo12O40]: An efficient and green catalyst for the synthesis of highly functionalized pyran‐annulated heterocycles via multicomponent reaction

A facile, efficient and eco‐friendly catalytic protocol was developed for the synthesis of medicinally important pyran‐annulated heterocycles via multicomponent reaction (MCR). Cyclocondensation of differently substituted aromatic aldehydes, malononitrile/ethyl cyanoacetate and various β‐dicarbonyl compounds in the presence of Ag₃[PMo₁₂O₄₀]?nH₂O as heterogeneous catalyst, in EtOH–H₂O, afforded diverse pyran‐fused chromene analogues. The merits observed for this approach were it being conducted via MCR, using commercially available or easily accessible starting materials in the presence of a green and easily separable heterogeneous and reusable catalyst, and affording high yields of desired products in very short reaction times with high purity in one‐pot fashion, thus providing a superior alternative approach for the synthesis of pyran‐annulated heterocycles.     

Aspartic-acid-loaded starch-functionalized Mn–Fe–Ca ferrite magnetic nanoparticles as novel green heterogeneous nanomagnetic catalyst for solvent-free synthesis of dihydropyrimidine derivatives as potent antibacterial agents

Research on Chemical Intermediates - Mn0.5Fe0.25Ca0.25Fe2O4@starch@aspartic acid magnetic nanoparticles (MNPs) as a new green nanocatalyst were designed and synthesized by a coprecipitation...     

One‐pot,four‐component synthesis of 1,3,4‐oxadiazole derivatives containing a ferrocene unit and their antimicrobial activity

A four‐component reaction between aromatic carboxylic acids, (N‐isocyanimino)triphenylphosphorane, ferrocenecarbaldehyde and dibenzylamine is reported. This approach is an efficient, simple and high‐yield procedure for the synthesis of 1,3,4‐oxadiazole derivatives containing a ferrocene unit. The antimicrobial activities of the products were investigated against Staphylococcus aureus and Pseudomonas aeruginosa in in vitro and in vivo assays. Copyright © 2015 John Wiley & Sons, Ltd.     

Synthesis of Heterocyclic Pentavalent Phosphorus Compounds from Phosphite Derivatives and Indane-1,2,3-Trione

Reaction of trialkylphosphite derivatives with indane-1,2,3-trione proceeds smoothly at room temperature to afford the corresponding heterocyclic pentavalent [P(V)] phosphorus compounds via an intermolecular [4+1] cycloaddition reaction in excellent yields under solvent-free conditions. We also used dimethylphosphite and diethylphosphite instead of trialkylphosphites in this reaction, but the corresponding pentavalent phosphorus compounds were not isolated, and in both cases phosphate derivatives were obtained. The structures of the products were deduced from their IR, ¹H NMR, ¹³C NMR, and ³¹P NMR spectra, and mass spectrometry.     

Thermoanalytical study of linkage isomerism in coordination compounds

The non-isothermal differential scanning calorimetry (DSC) experiments revealed that linkage isomerization of both pure trans-[Co(en)₂(ONO)₂]PF₆ (dinitrito isomer) and trans-[Co(en)₂(NO₂)₂]PF₆ (dinitro isomer) occurs in the solid state at elevated temperatures. The process was found to be exothermic for the dinitrito isomer and endothermic for dinitro isomer. The pure isomers could be considered to be in metastable states at ambient temperatures which would be converted to an equilibrium mixture of both isomers (stable state) upon heating. Since the isomerization of both isomers may be described as a two stages process, the corresponding DSC peaks have been resolved into two peaks by means of nonlinear curve fitting tools of PeakFit^® software. The resolution of the peaks helped us to determine enthalpy changes of stepwise isomerization of both isomers. A first-order initial rate and Kissinger methods have been employed to estimate kinetic parameters of the stepwise isomerization reactions. The Kissinger method provided more reliable kinetic results. The high activation energy and positive entropy changes of isomerization of both isomers are considered as indication of a dissociative mechanism in solid state.     

Identification of PET radiometabolites by cytochrome P450, UHPLC/Q-ToF-MS and fast radio-LC: applied to the PET radioligands [11C]flumazenil, [18F]FE-PE2I, and [11C]PBR28

A general method is presented for the identification of radiometabolites in plasma of human and monkey subjects after administration of positron emission tomography (PET) radioligands. The radiometabolites are first produced in vitro, using liver microsomes, subsequently separated using fast radio-liquid chromatography (radio-LC), and individually collected and identified by ultra high-performance liquid chromatography/quadrupole-time of flight-mass spectrometry in MS and MS^E mode. Fast radio-LC provided superior resolution compared to conventional radio-LC, resulting in separation of a greater number of metabolites. The radiometabolites produced in vivo are then compared to and identified based on the in vitro results. This approach was applied to three PET radioligands, [¹¹C]flumazenil, [¹⁸F]FE-PE2I, and [¹¹C]PBR28, resulting in the identification of five, two, and one radiometabolites, respectively. This procedure can easily be adopted to identify the radiometabolites produced in vivo from a variety of PET radioligands.