A Method for the Acetylation of Alcohols Catalyzed by Heteropolyoxometallates

Summary. Esterifications of acetic acid with some linear, secondary, tertiary, and benzylic alcohols mediated by catalytic amounts of Keggin, Wells–Dawson, and Preyssler type heteropolyacids were carried out under reflux at mild reaction conditions with good to excellent yields. Among the examined catalysts, H₃PW₁₂O₄₀ and H₁₄NaP₅W₃₀O₁₁₀ revealed better results than other heteropolyacids. This work was performed with the aim of simplifying the esterification process by omitting any solvents and mineral acid catalysts. Easy work-up, low cost, and acidic waste reduction, which are all important features from the environmental and economical points of view, are distinct aspects of this protocol. Heteropolyacid catalysts could be separated after a simple work-up and reused for several times.     

Spectral meshless radial point interpolation (SMRPI) method to two‐dimensional fractional telegraph equation

H. Ammari In this article, an innovative technique so‐called spectral meshless radial point interpolation (SMRPI) method is proposed and, as a test problem, is applied to a classical type of two‐dimensional time‐fractional telegraph equation defined by Caputo sense for (1 < α≤2). This new methods is based on meshless methods and benefits from spectral collocation ideas, but it does not belong to traditional meshless collocation methods. The point interpolation method with the help of radial basis functions is used to construct shape functions, which play as basis functions in the frame of SMRPI method. These basis functions have Kronecker delta function property. Evaluation of high‐order derivatives is not difficult by constructing operational matrices. In SMRPI method, it does not require any kind of integration locally or globally over small quadrature domains, which is essential of the finite element method (FEM) and those meshless methods based on Galerkin weak form. Also, it is not needed to determine strict value for the shape parameter, which plays an important role in collocation method based on the radial basis functions (Kansa's method). Therefore, computational costs of SMRPI method are less expensive. Two numerical examples are presented to show that SMRPI method has reliable rates of convergence. Copyright © 2015 John Wiley & Sons, Ltd.     

On The Existence of Multiple Solutions of a Class of Third-Order Nonlinear Two-Point Boundary Value Problems

A general approach is presented for proving existence of multiple solutions of the third-order nonlinear differential equation

$$Au^{\prime\prime\prime}(x) + u^{\prime\prime}(x)u^\prime(x) + u^\prime(x)f(u(x))=0,\quad x \in [0,1] ,$$

subject to given proper boundary conditions. The proof is constructive in nature, and could be used for numerical generation of the solution or closed-form analytical solution by introducing some special functions. The only restriction is about f(u), where it is supposed to be differentiable function with continuous derivative. It is proved the problem may admit no solution, may admit unique solution or may admit multiple solutions.

     

Error and stability analysis of numerical solution for the time fractional nonlinear Schrödinger equation on scattered data of general‐shaped domains

In present work, a kind of spectral meshless radial point interpolation (SMRPI) technique is applied to the time fractional nonlinear Schrödinger equation in regular and irregular domains. The applied approach is based on erudite combination of meshless methods and spectral collocation techniques. The point interpolation method with the help of radial basis functions is used to construct shape functions which play as basis functions in the frame of SMRPI. It is proved the scheme is unconditionally stable with respect to the time variable in and also convergent by the order of convergence , . In the current work, the thin plate spline are used as the basis functions and to eliminate the nonlinearity, a simple predictor‐corrector (P‐C) scheme is performed. It is shown that the SMRPI solution, as a complex function, is suitable one for the time fractional nonlinear Schrödinger equation. The results of numerical experiments are compared to analytical solutions to confirm the reliable treatment of these stable solutions. © 2016 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 33: 1043–1069, 2017     

Parametric inference for discrete observations of diffusion processes with mixed effects

Stochastic differential equations with mixed effects provide means to model intra-individual and inter-individual variability in repeated experiments leading to longitudinal data. We consider N i.i.d. stochastic processes defined by a stochastic differential equation with linear mixed effects which are discretely observed. We study a parametric framework with distributions leading to explicit approximate likelihood functions and investigate the asymptotic behavior of estimators under the asymptotic framework : the number N of individuals (trajectories) and the number n of observations per individual tend to infinity within a fixed time interval. The estimation method is assessed on simulated data for various models.     

Ni(II), Co(II), and Cu(II) complexes incorporating 2-pyrazinecarboxylic acid：Synthesis,characterization, electrochemical evaluation,and catalytic activity for the synthesis of 2H-indazolo[2,1-b]phthalazine-triones

Three complexes containing 2-pyrazinecarboxylate (pzca–), including [Ni(pzca)2(H2O)2], [Co(pzca)2(H2O)2], and [Cu(pzca)2(H2O)2], have been synthesized and characterized using physico-chemical and spectroscopic methods. Furthermore, the structure of each complex was determined by single-crystal X-ray diffraction. All three complexes have an octahedral geometry, where the metal ion chelated by two carboxylate oxygens, two nitrogen atoms belonging to pyrazinic acid molecules, and two oxygen atoms of two water molecules. The catalytic activities of these complex-es were also investigated in the green synthesis of 2H-indazolo[2,1-b]phthalazine-triones by the reaction of hydrazine hydrate with an arylaldehyde, phthalic anhydride, and dimedone in acetic acid.     

Synthesis and photophysical properties of some 6,6″-functionalized terpyridine derivatives

The synthesis and photophysical properties of several 6,6″ symmetrically substituted 4′-aryl-2,2′:6′,2″-terpyridine derivatives are reported herein. The UV-Vis spectra in acetonitrile as well as in dichloromethane show two intense bands in the UV areas 252–262 nm and 275–290 nm while the fluorescence emission spectra are only slightly influenced by chemical derivatization.     

Trypsin Inhibitor from Edible Mushroom Pleurotus floridanus Active against Proteases of Microbial Origin

Protease inhibitors can be versatile tools mainly in the fields of medicine, agriculture and food preservative applications. Fungi have been recognized as sources of protease inhibitors, although there are only few such reports on mushrooms. This work reports the purification and characterization of a trypsin inhibitor from the fruiting body of edible mushroom Pleurotus floridanus (PfTI) and its effect on the activity of microbial proteases. The protease inhibitor was purified up to 35-fold by DEAE-Sepharose ion exchange column, trypsin-Sepharose column and Sephadex G100 column. The isoelectric point of the inhibitor was 4.4, and its molecular mass was calculated as 37 kDa by SDS-PAGE and 38.3 kDa by MALDI-TOF. Inhibitory activity confirmation was by dot-blot analysis and zymographic activity staining. The specificity of the inhibitor toward trypsin was with Ki of 1.043?×?10^?10 M. The inhibitor was thermostable up to 90 °C with maximal stability at 30 °C, active over a pH range of 4–10 against proteases from Aspergillus oryzae, Bacillus licheniformis, Bacillus sp. and Bacillus amyloliquefaciens. Results indicate the possibility of utilization of protease inhibitor from P. floridanus against serine proteases.