A new scheme for solving nonlinear Stratonovich Volterra integral equations via Bernoulli’s approximation

In this paper, an efficient method for solving nonlinear Stratonovich Volterra integral equations is proposed. By using Bernoulli polynomials and their stochastic operational matrix of integration, these equations can be reduced to the system of nonlinear algebraic equations with unknown Bernoulli coefficient which can be solved by numerical methods such as Newton’s method. Also, an error analysis is valid under fairly restrictive conditions. Furthermore, in order to show the accuracy and reliability of the proposed method, the new approach is compared with the block pulse functions method by some examples. The obtained results reveal that the proposed method is more accurate and efficient than the block pulse functions method.     

Kinetic Study of Radical Polymerization v. Determination of Reactivity Ratio in Copolymerization of Acrylonitrile and Itaconic Acid by 1H‐NMR

Many reports exist in the literature about the application of ¹H and ¹³C‐NMR techniques to analyze the copolymer structure and composition and also determination of reactivity ratios. In this work, on‐line ¹H‐NMR spectroscopy has been applied to identify reactivity ratios of itaconic acid and acrylonitrile in the solution phase (DMSO as the solvent) and in the presence of AIBN as the radical initiator. All the peaks corresponding to the existing protons were assigned quietly. Therefore, the kinetics of the copolymerization reaction was investigated by studying the variation of integral of two characteristic peaks regarding each monomer. The obtained data were used to find the reactivity ratios of acrylonitrile and itaconic acid by linear least‐squares methods such as Finemann‐Ross, inverted Finemann‐Ross, Mayo‐Lewis, Kelen‐Tudos, extended Kelen‐Tudos and Mao‐Huglin. In addition, a non‐linear least‐square method (Tidwell‐ Mortimer) was used at low conversions. Extended Kelen‐ Tudos and Mao‐Huglin were applied to determine reactivity ratio values at high conversions as well.     

The role of hydrogen bonds in thermodynamic and structural properties in binary mixtures of morpholine + 2-methylcyclohexanol: a combined experimental and computational study

Structural Chemistry - Thermodynamic properties of binary mixtures of 2-methylcyclohexanol with morpholine are measured as a function of composition and temperature. The excess molar volumes were...     

Microwave-Assisted Aminomethylation of Electron-Rich Compounds Under Solvent-Free Condition

Electron-rich aromatic compounds react with formaldehyde and a secondary amine under solvent-free condition, in the presence of acidic alumina in a commercial microwave oven or at room temperature to produce aminomethylated products in good to excellent yields.     

One‐Step Synthesis of Aromatic Terminal Alkynes from Their Corresponding Ketones under Microwave Irradiation

One‐step microwave‐assisted synthesis of phenylacetylenes 2a–j from the corresponding ketones 1a–j in the presence of a new reagent, PCl₅–pyridine, is described. The reaction is carried out under a simple operational and experimental procedure, avoiding the use of the complicated and harsh multistep reaction.     

Molecular dynamics simulation of ferronanofluid behavior in a nanochannel in the presence of constant and time-dependent magnetic fields

Journal of Thermal Analysis and Calorimetry - For the first time, double phosphates(V) Zn3Cr4(PO4)6 and Mg3Cr4(PO4)6 were synthesized by non-waste solid-state reaction, performed in the temperature...     

Adsorption of Metanil Yellow Azoic Dye from Aqueous Solution onto Mg‐Fe‐NO3 Layered Double Hydroxide

We report the preparation and characterization of a layered double hydroxide (LDH) adsorbent for azoic dye, metanil yellow (yellow GX; YGX) removal. The nanoparticles of Mg‐Fe‐LDH‐NO₃ adsorbent were prepared with Mg/Fe molar ratio of 3:1 by a hydrothermal process and coprecipitation method at pH 9.5 and were characterized by X‐ray powder diffraction (XRPD), thermal gravimetric analysis (TGA), elemental analysis, and Fourier transform infrared spectroscopy (FT‐IR). The size and morphology of nanoparticles were examined by scanning electron microscopy (SEM). The XRD patterns indicate that the intercalation of YGX between the LDH layers has not occurred and surface adsorption has happened. In the adsorption experiments, the Gibbs free energy ΔG⁰ values, the enthalpy ΔH⁰, and entropy ΔS⁰ was determined. The isotherms showed that the adsorption of YGX by Mg‐Fe‐LDH‐NO₃ was both consistent with Langmuir and Freundlich equations.     

Four‐Component Cyclocondensation of Aminodiazines,Glyoxal, Formaldehyde,and Methanol to Imidazolidines

Four‐component reaction of aminodiazines (2‐aminopyrimidine and 2‐aminopyrazine), glyoxal, formaldehyde, and methanol yields trans‐4,5‐dimetoxy‐1,3‐bis(2‐pyrimidinyl)imidazolidine (5a) and trans‐4,5‐dimetoxy‐1,3‐bis(2‐pyrazinyl)imidazolidine (5b), respectively. Changing methanol to acetonitrile leads to the formation of the corresponding 1,3‐bis(2‐pyrimidinyl) and‐1,3‐bis(2‐pyrazinyl)‐ derivatives of trans‐4,5‐dihydroxyimidazolidine (6). Details of the proposed mechanism are discussed.     

A NONLINEAR MICROBEAM MODEL BASED ON STRAIN GRADIENT ELASTICITY THEORY

A micro scale nonlinear beam model based on strain gradient elasticity is developed.Governing equations of motion and boundary conditions are obtained in a variational framework.As an example,the nonlinear vibration of microbeams is analyzed.In a beam having a thickness to length parameter ratio close to unity,the strain gradient effect on increasing the natural frequency is predominant.By increasing the beam thickness,this effect decreases and geometric nonlinearity plays the main role on increasing the natural frequency.For some specific ratios,both geometric nonlinearity and size effects have a significant role on increasing the natural frequency.