On duality for weakly minimized vector valued optimization problems

An ordering that accords with the definition of a weak minimum is used to establish quasiduality, duality and converse duality theorems for optimization problems where the objective function takes values in real normed spaces of any dimension.     

Remarks on a difficult test problem for quadratic boolean programming

We show that a “difficult” example is only difficult for special kinds of algorithms     

A numerical method for the viscous incompressible Oseen flow in shape reconstruction

This paper is concerned with the shape reconstruction of a bounded domain with a viscous incompressible fluid driven by the Oseen equations. For the approximate solution of the ill-posed and nonlinear problem we propose a regularized Gauss-Newton method. A theoretical foundation for the method is given by establishing the differentiability of the boundary value problem with respect to the boundary in the sense of the domain derivative. The results of several numerical experiments show that our theory is useful for practical purpose, and the proposed algorithm is feasible.     

On occupation times in the red of Lévy risk models

In this paper, we obtain analytical expression for the distribution of the occupation time in the red (below level 0) up to an (independent) exponential horizon for spectrally negative Lévy risk processes and refracted spectrally negative Lévy risk processes. This result improves the existing literature in which only the Laplace transforms are known. Due to the close connection between occupation time and many other quantities, we provide a few applications of our results including future drawdown, inverse occupation time, Parisian ruin with exponential delay, and the last time at running maximum.     

柔性PMMA反蛋白石结构薄膜的制备及表征

以粒径为270 nm的SiO_2微球胶体晶体作为模板,向其中填充过量单体MMA,热聚合后形成SiO_2/PMMA复合结构光子晶体,将此光子晶体浸泡入浓度为20%的HF溶液中,刻蚀半小时后得到脱离ITO玻璃基板的柔性PMMA反蛋白石结构薄膜.该薄膜为周期有序的三维多孔结构,孔径大小均一,约为210 nm,外观蓝紫色与测试得到的带隙位置相对应.分析其微观形貌可知,对模板的过量填充产生了一层附着于胶体晶体上表面的PMMA致密层,致密层与其下层PMMA反蛋白石结构骨架在热聚合过程中由于体积收缩产生一定的应力差,使反结构薄膜自发从原基板脱离,从而获得柔性反蛋白石结构光子晶体.该薄膜可用于柔性光子晶体器件的制备.     

Unique determination of sound speeds for coupled systems of semi-linear wave equations

We consider coupled systems of semi-linear wave equations with different sound speeds on a finite time interval $[0,T]$ and a bounded domain $\Omega$ in ${\mathbb{R}}^3$ with $C^1$ boundary $\partial \Omega$. We show the coupled systems are well posed for variable coefficient sound speeds and short times. Under the assumption of small initial data, we prove the source to solution map associated with the nonlinear problem is sufficient to determine the source to solution map for the linear problem. This result is a bit surprising because one does not expect, in general, for the interaction of the waves in the nonlinear problem to always behave in a tractable fashion. As a result, we can reconstruct the sound speeds in $\Omega$ for the coupled nonlinear wave equations under certain geometric assumptions. In the case of the full source to solution map in $\Omega \times [0,T]$ this reconstruction could also be accomplished under fewer geometric assumptions.     

Two-dimensional boundary shape reconstructions in rectangular and coaxial waveguides

We present a method for shape reconstruction of deformed metallic boundaries in rectangular and coaxial waveguides using microwave scattering. Our developed reconstruction method is a theoretical basis for a future on-line microwave-based monitoring system for power grid components. The bundle of winding conductors in the active part of a typical power grid component is modeled as a continuous metallic surface. Then, electromagnetic field perturbation theory in conjunction with inverse problem theory is used to reconstruct the shape parameters of this surface. We assume small perturbations of the boundaries, such that the scattering parameters of the waveguide in the first-order perturbation have linear dependencies of the continuous deformation function. Thus, the corresponding inverse problem can be linearized and we can employ direct inversion, without the need for optimization which requires a higher computational effort. Tikhonov regularization is used to regularize the arising ill-conditioned linear system. The reconstructions, performed with noisy synthetic measurement data, show a good agreement with the actual shapes of the studied two-dimensional localized shape deformations for both rectangular and coaxial waveguide boundaries.     

Detecting and classifying interfacial defects by inverse ultrasound scattering analysis

We formulate and solve a time-harmonic inverse scattering problem to estimate the interfacial stiffness distribution at an interface between two elastic solid half-spaces. We assume prior knowledge of the material properties of both solid half-spaces, as well as the ultrasound incident field. The interfacial stiffness distribution is then estimated from the reflected signal. We use the Quasi-Static-Approximation for the interface, where it is modelled by a set of tangential and normal springs, and allow the interfacial stiffness to depend upon the position along the interface. In addition, we use the Particle Swarm Optimization Technique to solve the formulated inverse problem. We validate our implementation and evaluate the presented method’s performance for noisy input data and different measurement scenarios with the aid of numerical simulations. From the obtained numerical results, we may say that the proposed method is robust to the presence of noise and has the potential to detect and classify interfacial defects.     

Wave Kernels with Bi-Inverse Square Potentials on Euclidean Plane

The Cauchy problemfor the wave equation with bi-inverse square potential on Euclidean plane is solved in terms of the two variables Appell F₂ hypergeometric functions. Our principal tools are the Hankel transforms and the special functions of mathematical physics.