Spectrophotometric determination of cadmium(II) using 2-(5-bromo-2-pyridylazo)-5-diethylaminophenol

The complex of cadmium with the reagent 2-(-5-bromo-2-pyridylazo)-5-diethylaminophenol (5-Br-PADAP) has been studied. The composition, stability constant, and free energy change of formation of the complex have been determined. A sensitive spectrophotometric method for the determination of cadmium has been developed and applied for a range of concentration of 0.4–4.0 μg/ml cadmium using the complex Cd-5-Br-PADAP. The optimum conditions for maximum sensitivity of determination such as standing time, pH, wavelength, and order of addition have been determined. The effect of foreign ions on this method has been also studied.     

Flow injection determination of cobalt after its sorption onto polyurethane foam loaded with 2-(2-thiazolylazo)-p-cresol (TAC)

An electrochemically stable monolayer of tris(2,2'-bipyridyl)ruthenium(II) was obtained for the first time. It was based on the electrostatic attachment of Ru(bpy)(3)(2+) to the benzene sulfonic acid monolayer film, which was covalently bound onto glassy carbon electrode by the electrochemical reduction of diazobenzene sulfonic acid. The surface-confined Ru(bpy)(3)(2+) underwent reversible surface process, and reacted with the coreactant, tripropylamine, to produce electrochemiluminescence. In view of the stability of the electrode, the results strongly suggested that light was emitted from the surface-confined Ru(bpy)(3)(2+), not from the detached Ru(bpy)(3)(2+). The Ru(bpy)(3)(2+) modified electrode was used to the determination of tripropylamine. It showed good linearity in the concentration range from 5 muM to 1 mM with a detection limit of 1 muM (S/N=4). The good stability of the Ru(bpy)(3)(2+) modified electrode also showed that the benzene sulfonic acid monolayer film prepared can be served as an excellent support to construct multilayers.     

Global Existence,Decay, and Blow up of Solutions of a Singular Nonlocal Viscoelastic Problem

In this work we consider a nonlinear hyperbolic one-dimensional viscoelastic nonlocal problem with a nonlocal boundary condition. We establish a blow up result for large initial data and a decay result for small enough initial data.     

A semiparametric test of independence in copula models for censored data

We propose a semiparametric test of independence in copula models for bivariate survival censored data. We give the limit laws of the estimate of the parameter and the proposed test statistic under the null hypothesis of independence.     

A residual-based a posteriori error estimator for a two-dimensional fluid–solid interaction problem

In this paper, we develop an a posteriori error analysis of a mixed finite element method for a fluid–solid interaction problem posed in the plane. The media are governed by the acoustic and elastodynamic equations in time-harmonic regime, respectively, and the transmission conditions are given by the equilibrium of forces and the equality of the normal displacements of the solid and the fluid. The coupling of primal and dual-mixed finite element methods is applied to compute both the pressure of the scattered wave in the linearized fluid and the elastic vibrations that take place in the elastic body. The finite element subspaces consider continuous piecewise linear elements for the pressure and a Lagrange multiplier defined on the interface, and PEERS for the stress and rotation in the solid domain. We derive a reliable and efficient residual-based a posteriori error estimator for this coupled problem. Suitable auxiliary problems, the continuous inf-sup conditions satisfied by the bilinear forms involved, a discrete Helmholtz decomposition, and the local approximation properties of the Clément interpolant and Raviart–Thomas operator are the main tools for proving the reliability of the estimator. Then, Helmholtz decomposition, inverse inequalities, and the localization technique based on triangle-bubble and edge-bubble functions are employed to show the efficiency. Finally, some numerical results confirming the reliability and efficiency of the estimator are reported.     

One-Parameter Homothetic Motions and Euler-Savary Formula in Generalized Complex Number Plane $${\mathbb{C}_{J}}$$

In this paper, we introduce one-parameter homothetic motions in the generalized complex number plane (\({\mathfrak{p}}\)-complex plane)

$$\mathbb{C}_{J}=\left\{x+Jy:\,\,\, x,y \in \mathbb{R},\quad J^2=\mathfrak{p},\quad \mathfrak{p} \in \{-1,0,1\} \right\} \subset \mathbb{C}_\mathfrak{p}$$

where

$$\mathbb{C}_\mathfrak{p}=\{x+Jy:\,\,\, x,y \in \mathbb{R}, \quad J^2=\mathfrak{p}\}$$

such that \({-\infty < \mathfrak{p} < \infty}\). The velocities, accelerations and pole points of the motion are analysed. Moreover, three generalized complex number planes, of which two are moving and the other one is fixed, are considered and a canonical relative system for one-parameter planar homothetic motion in \({\mathbb{C}_{J}}\) is defined. Euler-Savary formula, which gives the relationship between the curvatures of trajectory curves, during the one-parameter homothetic motions, is obtained with the aim of this canonical relative system.

     

A Blow-Up Result in a Nonlinear Wave Equation with Delay

In this paper, we consider a nonlinear wave equation with delay. We show that under suitable conditions on the initial data, the weights of the damping, the delay term and the nonlinear source, the energy of solutions blows up in a finite time.     

A primal-mixed formulation for the strong coupling of quasi-Newtonian fluids with porous media

In this work we analyze a primal-mixed finite element method for the coupling of quasi-Newtonian fluids with porous media in 2D and 3D. The flows are governed by a class of nonlinear Stokes and linear Darcy equations, respectively, and the transmission conditions on the interface between the fluid and the porous medium are given by mass conservation, balance of normal forces and the Beavers-Joseph-Saffman law. We apply a primal formulation in the Stokes domain and a mixed formulation in the Darcy formulation. The “strong coupling” concept means that the conservation of mass across the interface is introduced as an essential condition in the space where the velocity unknowns live. In this way, under some assumptions on the nonlinear kinematic viscosity, a generalization of the Babu?ka-Brezzi theory is utilized to show the well posedness of the primal-mixed formulation. Then, we introduce a Galerkin scheme in which the discrete conservation of mass is imposed approximately through an orthogonal projector. The unique solvability of this discrete system and its Strang-type error estimate follow from the generalized Babu?ka-Brezzi theory as well. In particular, the feasible finite element subspaces include Bernadi-Raugel elements for the Stokes flow, and either the Raviart-Thomas elements of lowest order or the Brezzi-Douglas-Marini elements of first order for the Darcy flow, which yield nonconforming and conforming Galerkin schemes, respectively. In turn, piecewise constant functions are employed to approximate in both cases the global pressure field in the Stokes and Darcy domain. Finally, several numerical results illustrating the good performance of both discrete methods and confirming the theoretical rates of convergence, are provided.     

Blow-up of positive-initial-energy solutions of a nonlinear viscoelastic hyperbolic equation

In this paper, we consider the nonlinear viscoelastic equation

with initial conditions and Dirichlet boundary conditions. For nonincreasing positive functions g and for p>m, we prove that there are solutions with positive initial energy that blow up in finite time.     

A dual-dual mixed formulation for nonlinear exterior transmission problems

We combine a dual-mixed finite element method with a Dirichlet-to-Neumann mapping (derived by the boundary integral equation method) to study the solvability and Galerkin approximations of a class of exterior nonlinear transmission problems in the plane. As a model problem, we consider a nonlinear elliptic equation in divergence form coupled with the Laplace equation in an unbounded region of the plane. Our combined approach leads to what we call a dual-dual mixed variational formulation since the main operator involved has itself a dual-type structure. We establish existence and uniqueness of solution for the continuous and discrete formulations, and provide the corresponding error analysis by using Raviart-Thomas elements. The main tool of our analysis is given by a generalization of the usual Babuska-Brezzi theory to a class of nonlinear variational problems with constraints.