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.     

Trends in lipase-catalyzed asymmetric access to enantiomerically pure/enriched compounds

Over the last few years, there has been a dramatic increase in the number of publications in the field of lipase-catalyzed reactions performed in common organic solvents, ionic liquids or even non-conventional solvents. A fairly large percentage of these publications have emerged from organic chemists who have recognized the potential of biocatalysis as a viable and popular technique in organic synthesis. Considerable research has shown that reactions catalyzed by enzymes are more selective and efficiently performed than many of their analogues in the organic chemistry laboratory. This review article focuses on some of the recent developments in the rapidly growing field of lipase-catalyzed asymmetric access to enantiomerically pure/enriched compounds. The literature search is dated back to the last five years and covers some comprehensive examples.     

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.     

Organotin polymers—I. Copolymerization parameters of tributyltin methacrylate with methyl methacrylate,propyl methacrylate and butyl methacrylate

The monomer reactivity ratios for radical copolymerizations of tributyltin methacrylate (monomer-1) with methyl methacrylate, propyl methacrylate and butyl methacrylate have been found as r₁ = 0.79 and r₂ = 1.0, r₁ = 0.58 and r₂ = 0.9, and r₁ = 0.65 and r₂ = 0.68 respectively.     

Rhodium(II)‐Catalyzed Inter‐ and Intramolecular Cyclopropanations with Diazo Compounds and Phenyliodonium Ylides: Synthesis and Chiral Analysis

Different classes of cyclopropanes derived from Meldrum's acid (=2,2‐dimethyl‐1,3‐dioxane‐4,6‐dione; 4 ), dimethyl malonate ( 5 ), 2‐diazo‐3‐(silyloxy)but‐3‐enoate 16 , 2‐diazo‐3,3,3‐trifluoropropanoate 18 , diazo(triethylsilyl)acetate 24a , and diazo(dimethylphenylsilyl)acetate 24b were prepared via dirhodium(II)‐catalyzed intermolecular cyclopropanation of a set of olefins 3 (Schemes 1 and 4–6). The reactions proceeded with either diazo‐free phenyliodonium ylides or diazo compounds affording the desired cyclopropane derivatives in either racemic or enantiomer‐enriched forms. The intramolecular cyclopropanation of allyl diazo(triethylsilyl)acetates 28, 30 , and 33 were carried out in the presence of the chiral dirhodium(II) catalyst [Rh₂{(S)‐nttl)₄}] ( 9 ) in toluene to afford the corresponding cyclopropane derivatives 29, 31 and 34 with up to 37% ee (Scheme 7). An efficient enantioselective chiral separation method based on enantioselective GC and HPLC was developed. The method provides information about the chemical yields of the cyclopropane derivatives, enantioselectivity, substrate specifity, and catalytic activity of the chiral catalysts used in the inter‐ and intramolecular cyclopropanation reactions and avoids time‐consuming workup procedures.     

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.     

Design,preparation and characterization of Cu/GA/Fe3O4@SiO2 nanoparticles as a catalyst for the synthesis of benzodiazepines and imidazoles

The synthesis and characterization of an efficient and reusable nanocatalyst, Cu/GA/Fe₃O₄@SiO₂, obtained by ultrasonic‐assisted grafting of guanidineacetic acid on modified Fe₃O₄@SiO₂ core–shell nanocomposite spheres and subsequent immobilization of Cu(II), are described. The catalyst was characterized by means of X‐ray diffraction, scanning and transmission electron microscopies, energy‐dispersive X‐ray spectroscopy, elemental analysis, thermogravimetric analysis, Fourier transform infrared spectroscopy, vibrating sample magnetometry and inductively coupled plasma optical emission spectrometry. The prepared nanocatalyst facilitated an efficient and straightforward friendly procedure for the synthesis of benzodiazepines and imidazoles in ethanol and under solvent‐free conditions, respectively. The nanocatalyst can be easily recovered using a magnet and reused several times without any significant loss of activity. Copyright © 2016 John Wiley & Sons, Ltd.