On solvability of differential equations with the Riesz fractional derivative

We consider the solvability of fractional differential equations involving the Riesz fractional derivative. Our approach basically relies on the reduction of the problem considered to the equivalent nonlinear mixed Volterra and Cauchy-type singular integral equation and on the theory of fractional calculus. By establishing a compactness property of the Riemann–Liouville fractional integral operator on Lebesgue spaces and using the well-known Krasnoselskii's fixed point theorem, an existence of at least one solution is gleaned. An example is finally included to show the applicability of the theory.     

An approach to estimate the energy and strength of the intramolecular hydrogen bond in different conformers of 4‐methylamino‐3‐penten‐2‐one

The molecular structure and intramolecular hydrogen bond energy of 32 conformers of 4‐methylamino‐3‐penten‐2‐one were investigated at MP2 and B3LYP levels of theory using the standard 6–31G** basis set and AIM analyses. Furthermore, calculations for all the possible conformations of 4‐methylamino‐3‐penten‐2‐one in water solution were also carried out at B3LYP/6–31G** level of theory. The calculated geometrical parameters and conformational analyses in gas phase and water solution show that the ketoamine conformers of this compound are more stable than the other conformers (i.e., enolimine and ketoimine). This stability is mainly due to the formation of a strong N? H···O intramolecular hydrogen bond, which is assisted by π‐electrons resonance. Hydrogen bond energies for all conformers of 4‐methylamino‐3‐penten‐2‐one were obtained from the related rotamers method. The nature of intramolecular hydrogen bond existing within 4‐methylamino‐3‐penten‐2‐one has been investigated by means of the Bader theory of atoms in molecules, which is based on topological properties of the electron density. The results of these calculations support the results which obtained by related rotamers method. © 2007 Wiley Periodicals, Inc. Int J Quantum Chem, 2007     

Optimization using response surface methodology for fast removal of hazardous azo dye by γ-Fe<Subscript>2</Subscript>O<Subscript>3</Subscript>@CuO nanohybrid synthesized by sol–gel combustion

An efficient adsorption system was developed for removal of hazardous Direct Blue 71 as a sample azo dye. The γ-Fe₂O₃@CuO adsorption system was synthesized based on a sol–gel combustion route and characterized by energy-dispersive X-ray (EDX) analysis, X-ray diffraction (XRD) analysis, vibrating-sample magnetometry (VSM), and field-emission scanning electron microscopy (FESEM) techniques. The response surface methodology with Box–Behnken design was used to evaluate the effects of pH, shaking time, and adsorbent dose on dye adsorption. The results showed that solution pH was the parameter with greatest effect on dye adsorption. Adsorption equilibrium was reached quickly, within 8 min. Study of isotherms revealed adsorption capacity of 45.7 mg g^?1 according to the Freundlich model. Sorbent regeneration could be performed using methanol–NaOH (0.1 mol L^?1) solution.     

Polyhydroxyquinoline-carbon nanotube chelating resin for selective adsorption of lead ions: multivariate optimization,isothermic, and thermodynamic study

In this work a facile hydrothermal route has been employed to prepare a multiwall carbon nanotube wrapped in a chelating resin. 8-Hydroxyquinoline and p-formaldehyde were used as monomer and linker for polymer synthesis. The prepared composite was employed as an efficient adsorbent for lead adsorption and preconcentration from various matrices. Effective parameters on lead adsorption have been optimized by central composite design. Results showed that equilibrium adsorption was obtained at pH = 4, with a shacking time of 15 min and adsorbent dosage of 15 mg. Isotherm study showed that the sorbent has adsorbent capacity of 250 mg g^?1; moreover, the process followed a Langmuir isotherm model. Thermodynamic investigation confirmed that lead adsorption is spontaneous, as well as follows endothermic path.     

A Capillary Water-Retention Framework for the Effective Stress Parameter Considering Hydraulic Hysteresis

Transport in Porous Media - The establishment of the representative elementary volume (REV) in studies of porous media is crucial for linking microscopic structure and pore-scale fluid...     

Analytic study of sixth-order thin-film equation by tan(<Emphasis Type="BoldItalic">ϕ</Emphasis>/2)-expansion method

A improvement of the expansion methods, namely, the improved \(\tan (\phi (\xi )/2)\)-expansion method for solving the sixth-order thin-film equation is proposed. As a result, many new and more general exact traveling wave solutions are obtained including singular kink-type solutions. We obtained the further solutions comparing with other methods as Flitton and King (Eur J Appl Math 15:713–754, 2004) and Taha et al. (J King Saud Univ Sci 26:75–78, 2014). Recently this method is developed for searching exact traveling wave solutions of nonlinear partial differential equations. Abundant exact traveling wave solutions including kink and rational solutions have been found. These solutions might play important role in engineering and physics fields. Also the results demonstrate that the introduced method is powerful tools for solving the nonlinear partial differential equations.     

Reductive amination of aldehydes and ketones to their corresponding amines with N-methylpyrrolidine zinc borohydride

A simple and convenient procedure for reductive amination of aldehydes and ketones using N-methylpyrrolidine zinc borohydride (ZBHNMP) as a reducing agent is described. The reactions are carried out with 1 equiv of amine and 1 equiv of aldehyde or ketone using 1 equiv of ZBHNMP in methanol under neutral conditions at room temperature.     

On some new analytical solutions for the nonlinear long–short wave interaction system

This paper deals with exact soliton solutions of the nonlinear long–short wave interaction system, utilizing two analytical methods. The system of coupled long–short wave interaction equations is investigated with the help of two analytical methods, namely, the generalized \(\tan (\phi /2)\)-expansion method and He’s semi-inverse variational method. Moreover, in this paper we generalize two aforementioned methods which give new soliton wave solutions. As a consequence, solutions are including solitons, kink, periodic and rational solutions. Moreover, dark, bright and singular solition solutions of the coupled long–short wave interaction equations have been found. All solutions have been verified back into its corresponding equation with the aid of maple package program. We depicted the physical explanation of the extracted solutions with the free choice of the different parameters by plotting some 3D and 2D illustrations. Finally, we believe that the executed methods are robust and efficient than other methods and the obtained solutions in this paper can help us to understand the soliton waves in the fields of physics and mechanics.     

On the accuracy of bore reconstruction from input impedance measurements: application to bassoon crook measurements

The determination of a pipe bore from the measured reflection function is a technique that has reached a certain maturity. However, the measurement of the reflection function in the time domain (pulse reflectometry) requires equipment that is rather difficult to operate. On the other hand, the techniques for measuring the input impedance have reached an unquestionable maturity with respect to measurement setup and to calibration. It is thus likely that impedance measurements might be able to give the same information. By doing simulations, it is first shown that the reflection function deduced from the input impedance gives access to the bore with a precision comparable with that obtained with pulse reflectometry. It is then shown that the accuracy obtained with measurements is of the same order as that obtained from simulations. The technique is then used for the dimensional inspection of bassoon crooks.     

Preparation of PMMA/mesoporous diatomite nanocomposites by in situ SR&;NI ATRP

The catalytic effect of lead oxide nano- and microparticles (PbO) on the thermal behavior and decomposition kinetics of energetic formulations composed of nitrocellulose (NC), triethyleneglycol dinitrate (TEGDN) and diaminoglyoxime (DAG) was investigated by simultaneous thermogravimetric analysis and differential scanning calorimetry. The results show that lead oxide nano- and microparticles could significantly alter thermal pattern of the studied energetic compositions. The effect of lead oxide content on thermal behavior of energetic compositions was also studied, and the results revealed that addition of different amounts of lead oxide caused to shift in the DSC peaks. Moreover, the catalyst decreases activation energy of the decomposition stage of energetic composition at about 20–40 kJ mol^?1. However, the catalyst enhances decomposition temperature of TEGDN/NC/DAG energetic compositions. By the aid of DSC data resulted by non-isothermal methods, the thermokinetic parameters such as activation energy (E _a), frequency factor (A), the critical ignition temperature of thermal explosion, the self-accelerating decomposition temperature (T _SADT) and also thermodynamic parameters of the studied energetic compositions were calculated and compared.