Phase transition layers with boundary intersection for an inhomogeneous Allen–Cahn equation

We consider the nonlinear problem of inhomogeneous Allen–Cahn equation

${?}^2\mathrm{\Delta }u+V(y)u(1?u^2)=0\text{in}\mathrm{\Omega },\frac{?u}{?\nu }=0\text{on}?\mathrm{\Omega },$

where Ω is a bounded domain in ${\mathbb{R}}^2$ with smooth boundary, ? is a small positive parameter, ν denotes the unit outward normal of ?Ω, V is a positive smooth function on $\overline{\mathrm{\Omega }}$. Let Γ be a curve intersecting orthogonally with ?Ω at exactly two points and dividing Ω into two parts. Moreover, Γ satisfies stationary and non-degenerate conditions with respect to the functional ${\int }_{\mathrm{\Gamma }}{V}^{1/2}$. We can prove that there exists a solution $u_{?}$ such that: as $?\to 0$, $u_{?}$ approaches +1 in one part of Ω, while tends to ?1 in the other part, except a small neighborhood of Γ.     

Advancements in subsea riser analysis using quasi-rotations and the Newton–Raphson method

Beam structures undergoing finite deflections and rotations in space have extensive application in the subsea industry particularly for the analysis of holistic systems with larger numbers of mooring and riser components. In using the finite element analysis approach, there is an increasing requirement for large element sizes which preserve accuracy with regard to the coupling of axial, bending and torsion response.The authors outline a method for improving the current state of practice for the analysis of riser systems. The approach draws on the convected coordinates method, Euler–Bernoulli beam theory, the principle of virtual work and the finite element method. Two quasi-rotation measures are developed including a quasi-material rotation definition for rotational deformation relative to the convected axis of a beam and a quasi-space rotation definition to deal with the path dependent nature of rotations in three dimensions.The novel aspect of this work is to relate the rate of change of the quasi-material rotation vector along the beam axis to a linear transformation of the beam axis rate-of-rotation vector through utilising the convected coordinates axes system. In this way, incremental values of quasi-material rotation are directly linked to incremental values of nodal quasi-space rotation and a global Newton–Raphson solution technique for interconnecting beam elements is straightforward to assemble.Furthermore, this leads to accurate definitions of coupled axial, bending and torque response for beams with significant deflection. The approach has particular advantages in the analysis of subsea riser sections. Also, the accuracy of the solution is preserved for a fewer number of elements compared to alternative solutions for computationally sensitive load cases with highly non-linear loading regimes.     

Volatiles,color characteristics and other physico–chemical parameters of commercial Moroccan honeys

Seven commercial Moroccan honeys were considered for chemical characterisation. Volatile fraction, total polyphenols content, antioxidant and antiradical activities were evaluated by employing different analytical methodologies. Several physical parameters such as refractive index, pH, water content, solids content and colour were measured. Volatile fraction revealed an abundant presence of cis- and trans-linalool oxide in the seven studied samples. The presence of high levels of compounds related to the Maillard reaction, like furfural and hydroxymethylfurfural, could be the result of thermal treatments used to liquefy commercial honeys or of long storage times. The CIE L^*a^*b^*C_ab^*h_ab° chromatic coordinates confirmed the advanced stage of the Maillard reaction, showing L^* values lower than the common values found for honey of similar typologies.     

Local well-posedness for quasi-linear NLS with large Cauchy data on the circle

We prove local in time well-posedness for a large class of quasilinear Hamiltonian, or parity preserving, Schrödinger equations on the circle. After a paralinearization of the equation, we perform several paradifferential changes of coordinates in order to transform the system into a paradifferential one with symbols which, at the positive order, are constant and purely imaginary. This allows to obtain a priori energy estimates on the Sobolev norms of the solutions.     

Classical Backfitting for Smooth-Backfitting Additive Models

Smooth backfitting has been shown to have better theoretical properties than classical backfitting for fitting additive models based on local linear regression. In this article, we show that the smooth backfitting procedure in the local linear case can be alternatively performed as a classical backfitting procedure with a different type of smoother matrices. These smoother matrices are symmetric and shrinking and some established results in the literature are readily applicable. The connections allow the smooth backfitting algorithm to be implemented in a much simplified way, give new insights on the differences between the two approaches in the literature, and provide an extension to local polynomial regression. The connections also give rise to a new estimator at data points. Asymptotic properties of general local polynomial smooth backfitting estimates are investigated, allowing for different orders of local polynomials and different bandwidths. Cases of oracle efficiency are discussed. Computer-generated simulations are conducted to demonstrate finite sample behaviors of the methodology and a real data example is given for illustration. Supplementary materials for this article are available online.     

Oscillation theorems for symplectic difference systems

We consider symplectic difference systems involving a spectral parameter, together with the Dirichlet boundary conditions. The main result of the paper is a discrete version of the so-called oscillation theorem which relates the number of finite eigenvalues less than a given number to the number of focal points of the principal solution of the symplectic system. In two recent papers the same problem was treated and an essential ingredient was to establish the concept of the multiplicity of a focal point. But there was still a rather restrictive condition needed, which is eliminated here by using the concept of finite eigenvalues (or zeros) from the theory of matrix pencils.     

Plasmonic nanostructures for local field enhancement in the UV region

In this work we describe an ultraviolet subwavelength focusing in plasmonic nanostructures. A system which provides a 20–25 times local field enhancement at a wavelength of 350 nm is proposed. This system represents a metalized V-shaped groove in a surface of a dielectric medium. Subwavelength focusing is achieved by a plasmon wave propagation along the surface of metal film and by the transfer of electromagnetic field through the dielectric medium. The influence of system parameters on a local field enhancement is investigated. A simplified model that allows for determining the geometric parameters of an optimized resonator is proposed.     

Sufficient optimality conditions in nondifferentiable optimization ∗

The concept of local cone approximations, introduced in recent years by Ester and Thierfelder, is a powerful tool for establishing optimality conditions. In this paper we show how to use it for obtaining sufficient optimality conditions in nondifferentiable optimization     

Controllability of Nonsmooth Discrete Systems with Delay

This paper is concerned with a study of local controllability to discrete inclusions with delay. The sufficient conditions for relative and complete local controllability are obtained on the base of using Mordukhovich's nonsmooth constructions.     

带有二元连接函数的半参数模型

提出了一种新的带有二元连接函数的广义半参数模型,即二元连接模型(简称为BLM).使用轮廓似然方法估计模型的参数和非参数部分,并给出了计算算法.证明了所得的未知参数的估计量为n~(1/2)-相合,渐近正态且具有渐近最小方差,给出了实际数据分析和模拟研究,最终采用局部功效方法来检验非参数部分的线性性.