On generalized Poisson–Nernst–Planck equations with inhomogeneous boundary conditions: a‐priori estimates and stability

In this paper, we consider the strongly nonlinear Nernst–Planck equations coupled with the quasi‐linear Poisson equation under inhomogeneous, moreover, nonlinear boundary conditions. This system describes joint multi‐component electrokinetics in a pore phase. The system is supplemented by the force balance and by the volume and positivity constraints. We establish well‐posedness of the problem in the variational setting. Namely, we prove the existence theorem supported by the energy and the entropy a‐priori estimates, and we provide the Lyapunov stability of the solution as well as its uniqueness in special cases. Copyright © 2016 John Wiley & Sons, Ltd.     

Exact boundary controllability for 1‐D quasilinear wave equations with dynamical boundary conditions

By equivalently replacing the dynamical boundary condition by a kind of nonlocal boundary conditions, and noting a hidden regularity of solution on the boundary with a dynamical boundary condition, a constructive method with modular structure is used to get the local exact boundary controllability for 1‐D quasilinear wave equations with dynamical boundary conditions. Copyright © 2016 John Wiley & Sons, Ltd.     

A free boundary problem arising from DCIS mathematical model

Ductal carcinoma in situ – a special cancer – is confined within the breast ductal only. We derive the mathematical ductal carcinoma in situ model in a form of a nonlinear parabolic equation with initial, boundary, and free boundary conditions. Existence, uniqueness, and stability of problem are proved. Algorithm and illustrative examples are included to demonstrate the validity and applicability of the technique in this paper. Copyright © 2016 John Wiley & Sons, Ltd.     

The direct and inverse problem for an inclusion within a heat-conducting layered medium

This paper is concerned with the problem of heat conduction from an inclusion in a heat transfer layered medium. Making use of the boundary integral equation method, the well-posedness of the forward problem is established by the Fredholm theory. Then an inverse boundary value problem, i.e. identifying the inclusion from the measurements of the temperature and heat flux on the accessible exterior boundary of the medium is considered in the framework of the linear sampling method. Based on a careful analysis of the Dirichlet-to-Neumann map, the mathematical fundamentals of the linear sampling method for reconstructing the inclusion are proved rigorously.     

Numerical solution of a singular integral equation arising in a cruciform crack problem

A singular integral equation arising in a cruciform crack problem is investigated in the present paper. Based on the convex technique, the piecewise Taylor-series expansion method is extended by introducing a weight parameter. An approximate solution of the singular integral equation is constructed and its convergence and error estimate are made. The variations of the approximate solutions associating with stress intensity factors are analyzed by considering internal pressures of power and sine functions, respectively. By comparing with the known methods, the observations reveal that a good approximation can be achieved using less derivative times, less discretization points, and a suitable weight parameter. The obtained results show that the crack growth is dependent on applied mechanical loadings.     

Visible‐Light‐Accelerated C−H Sulfinylation of Heteroarenes

Heteroaromatic sulfoxides are a frequent structural motif in natural products, drugs, catalysts, and materials. We report a metal‐free visible‐light‐accelerated synthesis of heteroaromatic sulfoxides from sulfinamides and peroxodisulfate. The reaction proceeds at room temperature with blue‐light irradiation and allows the C−H sulfinylation of electron‐rich heteroarenes, such as pyrroles and indoles. An electrophilic aromatic substitution mechanism is proposed based on the substrate scope, substitution selectivity, and competition experiments with different nucleophiles.     

Combining field‐amplified sample stacking with moving reaction boundary electrophoresis on a paper chip for the preconcentration and separation of metal ions

A common drawback of paper‐based separation devices is their poor detection limit. In this study, we combined field‐amplified sample stacking with moving reaction boundary electrophoresis on a paper chip with six array channels for the parallel separation and concentration of multiple samples. With a new hyphenated technique, the brown I₂ from the Fe³⁺/I⁻ oxidation–reduction reaction emerged near the boundary between the dilute ethylene diamine tetraacetic acid and potassium iodide and highly concentrated KCl solutions. For the separation and concentration of three components, Cr³⁺, Cu²⁺, and Fe³⁺, the Fe³⁺ detection limit was improved at least 266‐fold by comparing the hyphenated technique with moving reaction boundary electrophoresis. The detection limit of Fe³⁺ was found to be as low as 0.34 ng (20 μM) on the paper chip. We also demonstrated the analysis of a real sample of four metal ions, with detection limits as follows: 0.16 μg Cr³⁺, 1.5 μg Ni²⁺, 0.64 μg Cu²⁺, and 1.5 μg Co²⁺. The synergy of field‐amplified sample stacking and moving reaction boundary electrophoresis in the micron paper‐based array channels dramatically improved the detection limit and throughput of paper‐based electrophoresis.     

A new scheme for solving nonlinear Stratonovich Volterra integral equations via Bernoulli’s approximation

In this paper, an efficient method for solving nonlinear Stratonovich Volterra integral equations is proposed. By using Bernoulli polynomials and their stochastic operational matrix of integration, these equations can be reduced to the system of nonlinear algebraic equations with unknown Bernoulli coefficient which can be solved by numerical methods such as Newton’s method. Also, an error analysis is valid under fairly restrictive conditions. Furthermore, in order to show the accuracy and reliability of the proposed method, the new approach is compared with the block pulse functions method by some examples. The obtained results reveal that the proposed method is more accurate and efficient than the block pulse functions method.     

Study on convergence and error of a numerical method for solving systems of nonlinear Fredholm–Volterra integral equations of Hammerstein type

The aim of this paper is to present an efficient analytical and numerical procedure for solving systems of nonlinear Fredholm–Volterra integral equations of the Hammerstein type with the aid of fixed point techniques and the usual Schauder basis in an adequate Banach space.     

交错群A_5与二面体群D_6直积的整群环的挠单位

本文利用Luthar-Passi方法,研究了五次交错群A_5与六阶二面体群D_6直积的整群环的挠单位,得到了该群的Zassenhaus猜想成立.