A self-dual variational approach to stochastic partial differential equations

Unlike many of their deterministic counterparts, stochastic partial differential equations are not amenable to the methods of calculus of variations à la Euler–Lagrange. In this paper, we show how self-dual variational calculus leads to variational solutions of various stochastic partial differential equations driven by monotone vector fields. We construct solutions as minima of suitable non-negative and self-dual energy functionals on Itô spaces of stochastic processes. We show how a stochastic version of Bolza's duality leads to solutions for equations with additive noise. We then use a Hamiltonian formulation to construct solutions for non-linear equations with non-additive noise such as the stochastic Navier–Stokes equations in dimension two.     

HPLC technique for quantitation of Chimassorb 944, and its evaluation in analysis of real and standard samples of polyolefins

A high performance liquid chromatography (HPLC) method is presented for the determination of Chimassorb 944 in polymeric matrix. A reversed phase column octadecyl silane (ODS) is used as a stationary phase. As a mobile phase, a mixture of THF:methanol:triethanol amine (90:10:1.5) (v:v:w) is used. The HPLC system was equipped with an UV detector and the absorbance of the analyte was recorded at 240 nm. In the case of polymers, 0.5 g of them along with 100 mg Irganox 1010 (for preventing oxidation of Chimassorb 944) were dissolved in boiling xylene, and then extracted with sulfuric acid 1 M four times. The extract was neutralized with sodium hydroxide solution and the analyte was re-extracted into carbon tetrachloride and then injected to the HPLC system. This method is an accurate and relatively fast technique for determination of Chimassorb 944 in polymers.     

Partitioning of Recombinant Pseudomonas putida POS-F84 Proline Dehydrogenase in Aqueous Two-Phase Systems: Optimization Using Response Surface Methodology

Applied Biochemistry and Biotechnology - Empirical modeling the partition behavior and recovery of a recombinant Pseudomonas putida POS-F84 proline dehydrogenase (ProDH) in aqueous two-phase...     

Cobalt supported on dendronized magnetic nanoparticles: A new highly efficient and recyclable catalyst for the Mizoroki–Heck cross‐coupling reaction

Polyamidoamine (PAMAM) is one of the most interesting types of hyperbranched polymers that carry a large number of amino groups on its surface. PAMAM has gained significant attention from synthetic organic chemists due to its structural characteristics, controllable structure, inner porosity, and ability to trap a wide range of ions and molecules. So, in this work, the PAMAM dendrimer was synthesized, grafted onto the surface of magnetite nanoparticles, and the resulting hybrid nanoparticles were then employed as suitable host for immobilizing cobalt nanoparticles. The newly developed catalyst was well characterized by Fourier transform‐infrared, X‐ray diffraction, thermogravimetric analysis, field emission‐scanning electron microscopy, transmission electron microscopy, atomic absorption spectroscopy, element mapping and energy‐dispersive X‐ray analysis. The efficiency of the as‐prepared nanocatalyst was evaluated for the Mizoroki–Heck cross‐coupling reactions. The MNP@PAMAM‐Co represented perfect catalytic efficiency and high selectivity for the Mizoroki–Heck cross‐coupling reaction compared with previously reported catalysts. The catalyst separation from the reaction mixture was easily achieved with the assistance of an external magnetic field, and its recycling was also investigated for five consecutive runs. Hot filtration confirmed no leaching of the active metal during the Heck coupling.     

Magnetic apple seed starch functionalized with 2,2′‐furil as a green host for cobalt nanoparticles: Highly active and reusable catalyst for Mizoroki–Heck and the Suzuki–Miyaura reactions

From the perspective of green chemistry, in catalytic systems, being low cost and eco‐friendly, in addition to high chemical and thermal stability, are requirements of support materials. In this regard, we used apple seed starch as an accessible, nontoxic, and cost‐effective support material. In order to take advantage of magnetic separation, the magnetite nanoparticles were chosen as an ideal pair for apple seed starch. Furthermore, during the Schiff base reaction, the magnetic apple seed starch was functionalized with 2,2′‐furil along with amine functionality to be used as a bio‐support for immobilization of cobalt. The introduction of cobalt had a significant effect on the greenness of the catalyst and reducing its price. FT‐IR, TGA, XRD, FE‐SEM, TEM, VSM, ninhydrin test, element mapping, AAS, and EDX analysis were applied to characterize the newly prepared catalyst. The effectiveness of this novel Schiff base supported catalyst was evaluated in the Mizoroki–Heck and the Suzuki–Miyaura coupling reactions. High reactivity and selectivity were among the most prominent characteristics of the catalyst as compared to previously reported catalysts. The longevity test and hot filtration showed the ability to use the catalyst at least 5 times and negligible cobalt leaching during the reaction, respectively. This work is the first report on the usage of apple seed starch as a supporting catalyst and 2,2′‐furil as a ligand in the catalyst modifications and catalytic activity. Accordingly, this can be the beginning of an attractive way in the design and synthesis of heterogeneous catalysts.     

The Importance of Ligand-Induced Backdonation in the Stabilization of Square Planar d10 Nickel π-Complexes

The electronic nature of Ni π-complexes is underexplored even though these complexes have been widely postulated as intermediates in organometallic chemistry. Herein, the geometric and electronic structure of a series of nickel π-complexes, Ni(dtbpe)(X) (dtbpe=1,2-bis(di-tert-butyl)phosphinoethane; X=alkene or carbonyl containing π-ligands), is probed using a combination of ³¹P NMR, Ni K-edge XAS, Ni K_β XES, and DFT calculations. These complexes are best described as square planar d¹⁰ complexes with π-backbonding acting as the dominant contributor to M−L bonding to the π-ligand. The degree of backbonding correlates with ²J_PP from NMR and the energy of the Ni 1s→4p_z pre-edge in the Ni K-edge XAS data, and is determined by the energy of the π*_ip ligand acceptor orbital. Thus, unactivated olefinic ligands tend to be poor π-acids whereas ketones, aldehydes, and esters allow for greater backbonding. However, backbonding is still significant even in cases in which metal contributions are minor. In such cases, backbonding is dominated by charge donation from the diphosphine, which allows for strong backdonation, although the metal centre retains a formal d¹⁰ electronic configuration. This ligand-induced backbonding can be formally described as a 3-centre-4-electron (3c-4e) interaction, in which the nickel centre mediates charge transfer from the phosphine σ-donors to the π*_ip ligand acceptor orbital. The implications of this bonding motif are described with respect to both structure and reactivity.     

Isoconversional analysis of thermal dissociation kinetics of hematite in air and inert atmospheres

Dissociation of hematite is an undesirable reaction for iron ore pelletizing process leading to severe deterioration in compressive cold strength and reducibility factors. It was shown that raising temperature in an induration machine would cause hematite’s dissociation, which is either present in the primary ore or formed by oxidation of magnetite in the feed. The oxidation reaction of magnetite is exothermic, which complicates temperature control within the non-isothermal area of preheating. Kinetics of the dissociation reaction is the temperature’s primary function, which controls the extent of the reaction. Pure hematite samples were subjected to several runs of thermal analysis carried out under both air and inert atmosphere, in order to achieve a comprehensive knowledge about the temperature dependencies of dissociation kinetics. Due to the observed uniformity, isoconversional methods were chosen in the present work over isothermal and non-isothermal for calculation of kinetic parameters of the reaction. Respectively, activation energy values of hematite dissociation were found to be 324 and 382 kJ mol^?1 in inert and air atmosphere. The high value of activation energy implies strong dependency of the single-step reaction rate on the temperature. It was also observed that the forward reaction had higher activation energy than the backward reaction; hence, an increase in temperature results in an overall acceleration of the dissociation reaction.     

The assignment of quantum numbers in the theoretical spectra of the H2 16O, H2 17O, and H2 18O molecules calculated by variational methods in the region 0–26000 cm−1

Quantum numbers have been assigned in the theoretical spectra of three isotopologues of the water molecule: H₂ ¹⁶O, H₂ ¹⁷O, and H₂ ¹⁸O. The spectra were calculated by variational methods in the region 0–26000 cm^?1 at a temperature of 296 K. For each molecule, the quantum numbers are assigned to more than 28000 levels. The quantum numbers are assigned to 216766, 210679, and 211073 spectral lines of the H₂ ¹⁶O, H₂ ¹⁷O, H₂ ¹⁸O molecules, respectively. The theoretical spectra with the assigned quantum numbers are available in the Internet.     

ZnS nanoparticles incorporated in polyaniline composite: Preparation and optical characterization

Hybrid polyaniline based composites incorporating zinc sulfide nanoparticles have been synthesized by using chemical oxidation technique. Morphological and optical properties of the nanocomposite were characterized by scanning electron microscopy, Fourier transform infrared and UV–Vis spectroscopy measurement. The results were compared with pure polyaniline. The characteristic FTIR peaks of polyaniline were found to shift to lower wave-number in nanocomposite. The band gap of nanocomposites increases and the refractive index of the nanocomposites decreases with increasing content of ZnS nanoparticles. These results showed the interaction between ZnS nanoparticles and polyaniline.