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.     

The use of hydrochloric acid in separating95Zr−95Nb activity from uranium fission products on silica gel

Dissolution of a neutron-irradiated uranium target in a medium of 6N HCl containing a few drops of very dilute HNO₃ yielded a matrix solution which on running on a silica gel column allowed the complete adsorption of the⁹⁵Zr−⁹⁵Nb activity formed in the fission process. The⁹⁵Zr−⁹⁵Nb activity is cleanly and totally eluted with 0.5% oxalic acid solution. None of the uranium or the activity of the other fission products was found to be adsorbed on the column.     

Stability-indicating methods for determination of pyritinol dihydrochloride in the presence of its precursor and degradation product by derivative spectrophotometry

A first-derivative spectrophotometric (1D) method and a derivative-ratio zero-crossing spectrophotometric (1DD) method were used to determine pyritinol dihydrochloride (I) in the presence of its precursor (II) and its degradation product (III) with 0.1N hydrochloric acid as a solvent. Linear relationships were obtained in the ranges of 6-22 microg/mL for the (1D) method and 6-20 microg/mL for the (1DD) method. By applying the proposed methods, it was possible to determine pyritinol dihydrochloride in its pure powdered form with an accuracy of 100.36 +/- 1.497% (n = 9) for the (1D) method and an accuracy of 99.92 +/- 1.172% (n = 8) for the (1DD) method. Laboratory-prepared mixtures containing different ratios of (I), (II), and (III) were analyzed, and the proposed methods were valid for concentrations of < or = 10% (II) and < or = 50% (III). The proposed methods were validated and found to be suitable as stability-indicating assay methods for pyritinol in pharmaceutical formulations.     

Mixed ligand complexes of diaquo (2,2′-bipyridine)palladium(II) with cyclobutane-1,1-dicarboxylic acid and DNA constituents

Complex formation equilibria involving [Pd(bpy)(H₂O)₂]²⁺ (bpy = 2,2-bipyridine) and the cyclobutanedicarboxylate ligand (cbdca), ethylenediamine and DNA have been investigated. Mixed ligand complexes of [Pd(bpy)(cbdca)] with inosine, inosine-5-monophosphate (5-IMP), uracil, uridine and adenine have been studied. The results show ring opening of the cbdca and monodentate chelation of the DNA components. Stoichiometries and stability constants for the complexes were determined at 25 °C and at constant 0.1 M ionic strength (adjusted using NaNO₃). The coordination sites were found to be pH-dependent. The [Pd(bpy)Cl₂], [Pd(bpy)(cbdca)] and [Pd(bpy)(inosine)](NO₃) complexes were isolated.     

Intramolecular charge-transfer interactions in pi-extended tetrathiafulvalene derivatives

New electron-donor (D)-electron-acceptor (A) TTF architectures are presented in which two electron-donating 1,3-dithiole moieties are connected by a pi bridge to the weak electron-accepting quinoxaline moiety (D-pi-A compounds 9a and 9b and also two 1,3-dithiole-2-ylidene moieties are connected by a pi bridge to the electron-accepting thieno[3,4-b]quinoxaline bridge (D-pi-A-pi-D compounds 12a-c). There are through-bond intramolecular charge-transfer (ICT) interactions, predicted in theoretical calculations, and confirmed by UV-vis spectroscopy and cyclic voltammetry measurements. This work constitutes the first use of quinoxalines as electron-accepting moieties in D-pi-A compounds.     

Thermodynamics of Ion-Association of NaClO4 in Aqueous-Methanol and Aqueous-Glycerol Using Conductance Measurements

The conductance of NaClO₄ at (25–45)°C in methanol-H₂O, and glycerol-H₂O mixtures in a concentration range up to 10^?2 M has been measured. The association constant, K_A, values have been determined, where the conductometric data were analysed by a M S X computer using the Fuoss-Aprano method. The K_A values for NaClO₄ in methanol-H₂O are higher than in glycerel-H₂O mixtures, Also K_A values increase as the proportional of methanol or glycerol increases in mixture. The thermodynamic parameters ΔH°, ΔG°, and ΔS° were also calculated. It is obvious that the entire process of the ionic association in those systems are endothermic ones. The Walden products, Λ_oη were calculated for all systems investigated.     

Mixed Polymer‐Coated Magnetic Nanoparticles as Forward Osmosis Draw Agents of Tuned Hydrophilicity

We recently reported a polymer‐coated magnetic nanoparticle (MNP) draw agent for the forward osmosis (FO) water desalination process. The water flux was found to increase when the polymer poly(sodium acrylate) (PSA) was anchored to the MNP surface as compared to the polymer (or polyelectrolyte solution) alone, due to the polymer chains being stretched out and most of the hydrophilic groups on the polymer contributing to water flux. We herein report the use of a secondary polymer poly(N‐isopropylacrylamide) PNIPAM to manipulate the PSA polymer conformation and influence inter‐ and intrachain interactions to enhance the efficiency of the FO draw agent. These PSA–PNIPAM‐coated MNPs generated a much higher water flux of ～11.66 LMH when compared to the 100 % PSA‐coated MNPs featuring a value of ～5.32 LMH under identical FO conditions. The osmotic pressure and water flux driven by the mixed polymer‐coated MNPs were found to be a strong function of the net polymer coverage on MNPs, that is, net available hydrophilic groups. Our new draw agent demonstrates potential for use in the water industry due to its improved efficiency and cost effectiveness as it uses only ～0.062 % (w/v) of the draw agent solution.     

Fatty amides synthesized from vegetable oil as extractant of molybdenum(VI)

In this study, fatty amides (FAs) synthesized from palm olein were used to extract and separate Mo(VI) from acidic media. Effects of various parameters upon the separation of Mo(VI) from Co(II), Ni(II), Al(III) and Mn(II), including extractant concentration, metal ion concentration, contact time, diluent, and acidity, were investigated. It was found that Mo(VI) was successfully separated from the above commonly associated metal ions by stripping from the loaded organic phase. Different acidic and alkaline solutions were used. Ammonium hydroxide solution was an optimal. Extraction of Mo(VI) into the organic phase involved the formation of 1:3 complexes. This work presents the development of a low-cost and environmentally friendly extractant to recycle and recover molybdenum.