Constructing rational and multi‐wave solutions to higher order NEEs via the Exp‐function method

In this paper, we present an application of some known generalizations of the Exp‐function method to the fifth‐order Burgers and to the seventh‐order Korteweg de Vries equations for the first time. The two examples show that the Exp‐function method can be an effective alternative tool for explicitly constructing rational and multi‐wave solutions with arbitrary parameters to higher order nonlinear evolution equations. Being straightforward and concise, as pointed out previously, this procedure does not require the bilinear representation of the equation considered. Copyright © 2011 John Wiley & Sons, Ltd.     

On Korovkin Type Theorem in the Space of Locally Integrable Functions

It is shown that a Korovkin type theorem for a sequence of linear positive operators acting in weighted space L _p,w (loc) does not hold in all this space and is satisfied only on some subspace.     

The effects of low dose leukotriene receptor antagonist therapy on airway remodeling and cysteinyl leukotriene expression in a mouse asthma model

Airway structural changes that occur in patients with asthma in response to persistent inflammation are termed airway remodeling. The cysteinyl leukotrienes (LTC(4), D(4) and E(4)) are known to play important roles in the pathobiology of asthma. To evaluate the effect of low dose montelukast (MK) on the development of airway remodeling using a chronic murine model of allergic airway inflammation with subepithelial fibrosis, BALB/c mice, after intraperitoneal ovalbumin (OVA) sensitization on days 0 and 14, received intranasal OVA periodically on days 14-75. MK treated mice received montelukast sodium intraperitoneally on days 26-75. The OVA sensitized/challenged mice developed an extensive eosinophil cell inflammatory response, goblet cell hyperplasia, mucus occlusion, and smooth muscle hypertrophy of the airways. In addition, in OVA sensitized/challenged mice, dense collagen deposition/fibrosis was seen throughout the lung interstitium surrounding the airways, blood vessels, and alveolar septae. The cysteinyl leukotriene 1 (CysLT1) receptor antagonist, MK significantly reduced the airway eosinophil infiltration, goblet cell hyperplasia, mucus occlusion, and lung fibrosis except airway smooth muscle hypertrophy in the OVA sensitized/challenged mice. The OVA sensitized/challenged mice had significantly increased epithelial desquamation compared with control mice. MK markedly reduced epithelial desquamation of airways in OVA/MK treated animals compared with OVA sensitized/challenged mice. MK treatment did not affect the levels of CysLT in lung tissue. Our results show that the important role of cysteinyl leukotrienes in the pathogenesis of asthma. Lower dose of CysLT1 receptor antagonism has a significant anti-inflammatory effect on allergen-induced lung inflammation and fibrosis but not airway smooth muscle hypertrophy in an animal model of asthma.     

Cosine expansion‐based differential quadrature algorithm for numerical solution of the RLW equation

The differential quadrature method based on cosine expansion is applied to obtain numerical solutions of the RLW equation. The propagation of single solitary wave is studied to validate the efficiency of the algorithm. Then, test problems including interaction of two and three solitary waves, undulation, and evolution of solitary waves are implemented. Solutions are compared with earlier results. Discrete conservation quantities are computed for test experiments. © 2009 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2009     

Incipient separation over wall irregularities in transonic flow

Incipient separation over wall irregularities in a steady two dimensional flow field of a perfect fluid which has transonic speed characteristics has been investigated considering viscous-inviscid interactions at high Reynolds number. The aim of this work is to investigate dependence of the critical hump height (when a well attached flow over rigid body surface turns into a separated one) on the Karman–Guderley parameter which characterizes of the local flow field. The analysis of the flow field starts with the so-called inspection analysis of the flow properties and then the interaction problem has been constructed using the asymptotic analysis of triple-deck structure of interaction region. Finally, a method based on a semi-direct solution of governing equations of the transonic interaction problem has been used to obtain the numerical solution of the problem.     

The Hadamard Inequality For Convex Function Via Fractional Integrals

In this paper, we establish several inequalities for some differantiable mappings that are connected with the Riemann-Liouville fractional integrals. The analysis used in the proofs is fairly elementary.     

Synthesis, Crystal Structure, Thermal Behavior and IR Characterization of Pentacarbonyl(4-methylpyridine)chromium(0) Complex

Abstract  Pentacarbonyl(4-methylpyridine)chromium(0) complex was isolated from n-hexane solution as yellow plate-like crystals and characterized by using X-ray crystallography. It crystallizes in the orthorhombic system with the space group Cmcm and Z = 4. The unit cell parameters are a = 11.737(1) ?, b = 12.857(2) ?, c = 8.465(1) ?. The single crystal X-ray structure of the complex shows that the coordination sphere around the chromium central atom is slightly distorted octahedron, involving the 4-methylpyridine (4-mp), ligand as a monodentate N-donor ligand and five carbonyl groups. The four equatorial CO groups in the complex, with the Cr–C2 distance of 1.886 Ǻ, are slightly bent away from the 4-methylpyridine ligand with the N–Cr–C2 angle of 91.69°. The pyridine ring plane makes an angle of 135.17° with the Cr–N–CO bond axis. The thermal analysis (differential thermal analysis and thermal gravimetry) and IR spectra of the complex indicated that the compound undergoes complete decomposition to form the Cr₂O₃ as the final decomposition product. Index Abstract  The crystal structure of pentacarbonyl(4-methylpyridine)chromium(0) complex has been determined and its thermal behavior has also been studied.      

Synthesis and characterization of epoxy resins containing imine group and their curing processes with aromatic diamine

The epoxy resins containing imine bonding were prepared from hydroxyl substituted Schiff base monomers in two steps. At the first step, hydroxyl substituted Schiff base monomers were synthesized via condensation reaction. At the second step, epoxy resins were synthesized from the reaction between Schiff base monomers and epichlorohydrine (EPC). Then curing processes of epoxy resins were achieved by p-phenylenediamine compound. The structures of resulting compounds were confirmed by FT-IR, UV-Vis and ¹H-NMR. TG-DTA and DSC measurements were performed for thermal characterizations of the compounds. Chemical resistances of the cured epoxy-amine systems were determined for coating applications in acidic, alkaline and organic solvents. HCl (10%, aqueous solution), NaOH (10%, aqueous solution), DMSO, DMF, N-methylpyrrolidone, ethanol, THF and acetone were used for corrosion tests. Chemical resistance data of the synthesized epoxy resins demonstrated that they have good chemical resistance against various acid, alkaline and common organic solvents. Surface morphologies of epoxy resin and the cured epoxy resin were determined with scanning electron microscopy (SEM) measurements. Also, optical band gap (E_g) values of Schiff base monomers and epoxy resins were calculated from UV-Vis measurements.     

Correction to: The effect of e/a ratio on thermodynamic parameters and surface morphology of Cu–Al–Fe–X shape memory alloys

Journal of Thermal Analysis and Calorimetry - In the original publication of the article, the second author’s family name was incorrectly published.