An accurate mathematical study on the free vibration of stepped thickness circular/annular Mindlin functionally graded plates

An analytical solution based on a new exact closed form procedure is presented for free vibration analysis of stepped circular and annular FG plates via first order shear deformation plate theory of Mindlin. The material properties change continuously through the thickness of the plate, which can vary according to a power-law distribution of the volume fraction of the constituents, whereas Poisson’s ratio is set to be constant. Based on the domain decomposition technique, five highly coupled governing partial differential equations of motion for freely vibrating FG plates were exactly solved by introducing the new potential functions as well as using the method of separation of variables. Several comparison studies were presented by those reported in the literature and the FEM analysis, for various thickness values and combinations of stepped thickness variations of circular/annular FG plates to demonstrate highly stability and accuracy of present exact procedure. The effect of the geometrical and material plate parameters such as step thickness ratios, step locations and the power law index on the natural frequencies of FG plates is investigated.     

Surface effects on nonlinear free vibration of functionally graded nanobeams using nonlocal elasticity

In this paper, to consider all surface effects including surface elasticity, surface stress, and surface density, on the nonlinear free vibration analysis of simply-supported functionally graded Euler–Bernoulli nanobeams using nonlocal elasticity theory, the balance conditions between FG nanobeam bulk and its surfaces are considered to be satisfied assuming a cubic variation for the component of the normal stress through the FG nanobeam thickness. The nonlinear governing equation includes the von Kármán geometric nonlinearity and the material properties change continuously through the thickness of the FG nanobeam according to a power-law distribution of the volume fraction of the constituents. The multiple scale method is employed as an analytical solution for the nonlinear governing equation to obtain the nonlinear natural frequencies of FG nanobeams. The effect of the gradient index, the nanobeam length, thickness to length ratio, mode number, amplitude of deflection to radius of gyration ratio and nonlocal parameter on the frequency ratios of FG nanobeams is investigated.     

Topological Hypergroups in the Sense of Marty

In this paper, we introduce the concept of topological hypergroups as a generalization of topological groups. A topological hypergroup is a nonempty set endowed with two structures, that of a topological space and that of a hypergroup. Let (H, ○) be a hypergroup and (H, τ) be a topological space such that the mappings (x, y) → x ○ y and (x, y) → x/y from H × H to 𝒫*(H) are continuous. The main tool to obtain basic properties of hypergroups is the fundamental relation β*. So, by considering the quotient topology induced by the fundamental relation on a hypergroup (H, ○) we show that if every open subset of H is a complete part, then the fundamental group of H is a topological group.

It is important to mention that in this paper the topological hypergroups are different from topological hypergroups which was initiated by Dunkl and Jewett.     

Hydrodynamics of a bounded vertical film with nonlinear surface properties

The drainage of a thin liquid film with an insoluble monolayer down a vertical wall is studied. Lubrication theory is used to develop a model where the film is pinned at the top with a given thickness and the film drains into a bath at the bottom. A nonlinear equation of state is used for the surface tension and the surface viscosity is a nonlinear function of the surfactant concentration; these are appropriate for some aqueous systems. The three partial differential equations are solved via discretization in space and then the resulting differential algebraic system is solved. Results are described for a wide range of parameters, and the conditions under which the free surface is immobilized are discussed.     

Facile synthesis of α-hydroxy carboxylic acids from the corresponding α-amino acids

An effective and improved procedure is developed for the synthesis of α-hydroxy carboxylic acids by treatment of the corresponding protonated α-amino acid with tert-butyl nitrite in 1,4-dioxane–water. The amino moiety must be protonated and located α to a carboxylic acid function in order to undergo initial diazotization and successive hydroxylation, since neither β-amino acids nor acid derivatives such as esters and amides undergo hydroxylations. The method is successfully applied for the synthesis of 18 proteinogenic amino acids.     

pH-sensing properties of PbO<Subscript>2</Subscript> thin film electrodeposited on carbon ceramic electrode

In this paper, a new highly sensitive potentiometric pH electrode is proposed based on the solid-state PbO₂ film electrodeposited on carbon ceramic electrode (CCE). Two different crystal structures of PbO₂, α and β were examined and the similar results were obtained. Moreover, the experimental results obtained for the proposed pH sensor and a conventional glass pH electrode were in good agreement. The electromotive force (emf) signal between the pH-sensitive PbO₂-coated CCE and SCE reference electrode was linear over the pH range of 1.5–12.5. Near-Nernstian slopes of −64.82 and −57.85 mV/pH unit were obtained for α- and β-PbO₂ electrodes, respectively. The interferences of some mono-valence and multi-valence ions on potentiometric response of the sensor were studied. The proposed pH sensor displayed high ion selectivity with respect to K⁺, Na⁺, Ca²⁺, and Li⁺, with log values around −12 and has a working lifetime of about 30 days. Key parameters important for the pH sensor performance, including kind of PbO₂ film, selectivity, response time, stability, and reproducibility, have been characterized. The proposed electrode showed a good efficiency for direct pH-metry after calibration and pH-metric titrations without calibration step. The response time was about 1 s in acidic medium and less than 30 s in alkaline solutions. The pH values of complex matrix samples such as fruit juices measured by the proposed sensor and a conventional glass pH electrode were in good agreement.     

Preparation,Electrochemistry, and Electrocatalytic Activity of Lead Pentacyanonitrosylferrate Film Immobilized on Carbon Ceramic Electrode

Lead pentacyanonitrosylferrate (PbPCNF), a new Prussian blue analog, was immobilized on the surface of a carbon ceramic electrode (CCE) prepared by sol‐gel method. The immobilization process consists of adding a certain amount of metallic lead to the electrode matrix before gelation, and chemical derivatization of Pb on the electrode surface to a PbPCNF solid film by immersing the electrode in a solution of sodium pentacyanonitrosylferrate (PCNF). The composition of the synthesized PbPCNF was characterized by FTIR, scanning electron microscopy (SEM), and energy‐dispersive X‐ray (EDX) techniques. The resulting modified electrode showed electroactivity at two redox centers. The electrochemical behavior of the PbPCNF modified carbon ceramic electrode (PbPCNF|CCE) was studied by cyclic voltammetry. Under optimized conditions the peak‐to‐peak separation is only 39 mV, indicative of a surface reaction. Ion effects of the supporting electrolyte suggest that cations have a considerable effect on the electrochemical behavior of the modified electrode. The transfer coefficient (α) and the charge transfer rate constant at the modifying film|electrode interface (k_s) were calculated. The electrocatalytic activity of the modified electrode toward the electro‐reduction of peroxodisulfate was studied in details.     

Determination of brilliant green from fish pond water using carbon nanotube assisted pseudo-stir bar solid/liquid microextraction combined with UV-vis spectroscopy-diode array detection

This paper describes the development of a new design of hollow fiber solid/liquid phase microextraction (HF-SLPME) for determination of brilliant green (BG) residues in water fish ponds. This method consists of an aqueous donor phase and carbon nanotube reinforced organic solvent (acceptor phase) operated in direct immersion sampling mode. The multi-walled carbon nanotube dispersed in the organic solvent is held in the pores and lumen of a porous polypropylene hollow fiber. It is in contact directly with the aqueous donor phase. In this method the solid/liquid extractor phase is supported using a polypropylene hollow fiber membrane. Both ends of the hollow fiber segment are sealed with magnetic stoppers. This device is placed inside the donor solution and plays the rule of a pseudo-stir bar. It is disposable, so single use of the fiber reduces the risk of carry-over problems. Brilliant green (BG) after extraction from the aqueous samples with mentioned HF-SLPME device was determined by ultraviolet-visible spectroscopy with diode array detection (UV-vis/DAD). The absorption wavelength was set to 625 nm (λ(max)). The effect of different variables on the extraction was evaluated and optimized to enhance the sensitivity and extraction efficiency of the proposed method. The calibration curve was linear in the range of 1.00-10,000 μg L(-1) of BG in the initial solution with R(2)=0.979. Detection limit, based on three times the standard deviation of the blank, was 0.55 μg L(-1). All experiments were carried out at room temperature (25±0.5°C).     

Numerical solution of fractional differential equations via a Volterra integral equation approach

The main focus of this paper is to present a numerical method for the solution of fractional differential equations. In this method, the properties of the Caputo derivative are used to reduce the given fractional differential equation into a Volterra integral equation. The entire domain is divided into several small domains, and by collocating the integral equation at two adjacent points a system of two algebraic equations in two unknowns is obtained. The method is applied to solve linear and nonlinear fractional differential equations. Also the error analysis is presented. Some examples are given and the numerical simulations are also provided to illustrate the effectiveness of the new method.