Some exact solutions of the oscillatory motion of a generalized second grade fluid in an annular region of two cylinders

The velocity field and the associated shear stress corresponding to the longitudinal oscillatory flow of a generalized second grade fluid, between two infinite coaxial circular cylinders, are determined by means of the Laplace and Hankel transforms. Initially, the fluid and cylinders are at rest and at t = 0＋ both cylinders suddenly begin to oscillate along their common axis with simple harmonic motions having angular frequencies Ω1 and Ω2. The solutions that have been obtained are presented under integral and series forms in terms of the generalized G and R functions and satisfy the governing differential equation and all imposed initial and boundary conditions. The respective solutions for the motion between the cylinders, when one of them is at rest, can be obtained from our general solutions. Furthermore, the corresponding solutions for the similar flow of ordinary second grade fluid and Newtonian fluid are also obtained as limiting cases of our general solutions. At the end, the effect of different parameters on the flow of ordinary second grade and generalized second grade fluid are investigated graphically by plotting velocity profiles.     

Some exact solutions for rotating flows of a generalized Burgers’ fluid in cylindrical domains

The velocity field and the adequate shear stress corresponding to the flow of a generalized Burgers’ fluid model, between two infinite co-axial cylinders, are determined by means of Laplace and finite Hankel transforms. The motion is due to the inner cylinder that applies a time dependent torsional shear to the fluid. The solutions that have been obtained, presented in series form in terms of usual Bessel functions J₁( ? ), J₂( ? ), Y₁( ? ) and Y₂( ? ), satisfy all imposed initial and boundary conditions. Moreover, the corresponding solutions for Burgers’, Oldroyd-B, Maxwell, second grade, Newtonian fluids and large-time transient solutions for generalized Burgers’ fluid are also obtained as special cases of the present general solutions. The effect of various parameters on large-time and transient solutions of generalized Burgers’ fluid is also discussed. Furthermore, for small values of the material parameters, λ₂ and λ₄ or λ₁, λ₂, λ₃ and λ₄, the general solutions corresponding to generalized Burgers’ fluids are going to those for Oldroyd-B and Newtonian fluids, respectively. Finally, the influence of the pertinent parameters on the fluid motion, as well as a comparison between models, is shown by graphical illustrations.     

Silver nanoclusters doped in zeolite to decontaminate water resources from the quinalphos pesticide

Ag (I) nanoclusters doped in mordenite zeolite were prepared and spectroscopically analyzed. Strong luminescence emission that is dependent on the excitation wavelength was observed. These variations in the emission modes are due to the site selective luminescence where various luminophores might be excited upon selecting the proper excitation wavelength. The selected material was found to have strong affinity to remove the quinalphos pesticide, which is widely used for the protection of several vegetable and fruit crops, from water bodies. HPLC and GC–MS techniques were used to follow the kinetic data and to identify the photodecomposition products, respectively. The photodecomposition of quinalphos in the presence of the silver doped mordenite catalyst gives different products compared to the irradiation of quinalphos without catalyst. The presence of the Ag-mordenite catalyst not only adsorbs the quinalphos from the solution but it also reduces its toxic effect as tested on the fruit fly (Drosophila melanogaster).     

Retraction Note to: N. Zamani “On graded distributive modules,”

Mathematical Notes - This article has been retracted at the request of the Editorial Board of the journal in accordance with the COPE guidelines. This article contains a significant amount of...     

Cofiniteness and finiteness of local cohomology modules over regular local rings

Let (R,m) be a commutative Noetherian regular local ring of dimension d and I be a proper ideal of R such that mAss _R (R/I) = Assh _R (_I). It is shown that the R- module H^ht(I) _I (R) is I-cofinite if and only if cd(I,R) = ht(I). Also we present a sufficient condition under which this condition the R-module H ⁱ _I (R) is finitely generated if and only if it vanishes.     

Elastic-plastic contact model for rough surfaces based on plastic asperity concept

A mathematical formulation for the contact of rough surfaces is presented. The derivation of the contact model is facilitated through the definition of plastic asperities that are assumed to be embedded at a critical depth within the actual surface asperities. The surface asperities are assumed to deform elastically whereas the plastic asperities experience only plastic deformation. The deformation of plastic asperities is made to obey the law of conservation of volume. It is believed that the proposed model is advantageous since (a) it provides a more accurate account of elastic-plastic behavior of surfaces in contact and (b) it is applicable to model formulations that involve asperity shoulder-to-shoulder contact. Comparison of numerical results for estimating true contact area and contact force using the proposed model and the earlier methods suggest that the proposed approach provides a more realistic prediction of elastic-plastic contact behavior.     

A review of calixarene applications in nuclear industries

Calixarenes has been subject to extensive research in development of many extractants, transporters, stationary phases, electrode ionophores and optical and electrochemical sensors over the past four decades. In this paper, the nuclear applications of calixarenes are summarized in six fields including complexation studies, solvent extraction, membrane transport, chromatography, luminescent and colorimetric applications, and electroanalytical applications. In the first to fourth sections, the extractability, extraction equilibria and extraction constants of lanthanide, actinide and other nuclear waste cations ions, which were subjected to solvent extraction by the macrocyclic ligands, are reviewed. In two last sections, the analytical applications of calixarene complexes towards nuclear waste cations, including spectroscopic and electroanalytic sensors, are discussed. The examples described in this review illustrate the potential of calixarene derivatives in the rapidly growing field of cations recognition in nuclear wastes.     

He-Ne laser-induced improvement in biochemical, physiological, growth and yield characteristics in sunflower (Helianthus annuus L.)

The water-soaked seeds of sunflower were exposed to low power continuous wave He-Ne laser irradiation of energies 0, 100, 300 and 500 mJ to evaluate the effect on various biochemical, physiological, growth and yield parameters of sunflower. The experiments which consisted of four replicates arranged in a completely randomized design (CRD) were carried out under the greenhouse conditions. The physiological attributes like, photosynthetic rate (A), transpiration rate (E), intrinsic CO(2) concentration (C(i) ), stomatal conductance (g(s)), chlorophyll a and b contents, relative membrane permeability and leaf water (ψ(w)), osmotic (ψ(s)) and turgor (ψ(p)) potentials, relative water contents and leaf area increased significantly as compared to control due to He-Ne treatment of seeds. The activities of superoxide dismutase, peroxidase and catalases and contents of total soluble proteins, malondialdehyde, proline and leaf total phenolic also increased due to laser treatment. Significant increase in growth parameters of sunflower like shoot fresh and dry masses, root fresh and dry masses, root and shoot lengths, number of leaves per plant and stem diameter has also been observed. The contents of K, Ca and Mg in shoot and root were also increased and an overall increase of up to 28.12% was observed due to laser treatment.     

Enhanced photocatalytic degradation of C.I. Basic Violet 2 using TiO2-SiO2 composite nanoparticles

In this report, TiO(2) -SiO(2) composite nanoparticles were prepared by the thermal hydrolysis method using titanium tetrachloride and tetraethylorthosilicate as TiO(2) and SiO(2) precursors, respectively. The prepared nanoparticles were characterized by X-ray powder diffraction (XRD), Fourier-transform infrared spectroscopy (FT-IR), scanning electron microscopy (SEM), energy dispersive X-ray spectroscopy (EDX), nitrogen adsorption/desorption and UV-Vis diffuse reflectance spectroscopy (DRS). The results indicated that, in comparison with pure TiO(2), TiO(2)-SiO(2) composite nanoparticles had a higher thermal stability, which prevents phase transformation from anatase to rutile. In addition, the TiO(2)-SiO(2) nanoparticles had a higher specific surface area, larger pore volume, greater band gap energy and smaller crystallite size. Thus, the surface area of TiO(2)-40% SiO(2) composite nanoparticles was about 17 times higher than that of pure TiO(2) nanoparticles. The photocatalytic activity of TiO(2)-SiO(2) composite nanoparticles in the photodegradation of C.I. Basic Violet 2 was investigated. The photodegradation rate of Basic Violet 2 using TiO(2)-40% SiO(2) nanoparticles calcined at 600°C was much faster than that using pure TiO(2) and Degussa P25 TiO(2) by 10.9 and 4.3 times, respectively. The higher photoactivity of the TiO(2)-SiO(2) composite nanoparticles was attributed to their higher surface area, larger pore volume, greater band-gap energy and smaller crystallite size compared with pure TiO(2).