A Least-Squares Mixed Finite Element for Quasi-Incompressible Elastodynamics

In the present work, a mixed finite element based on a modified least-squares formulation is proposed. Here, we consider the time-dependent equations for quasi-incompressible elastodynamics under small strain assumptions. The main goal is to obtain an accurate approximation of both displacements and stresses in particular for the lowest-order element. Basis for the element formulation is a weak form resulting from a least-squares method. The L₂-norm minimization of the time-discretized residuals of the given first-order system leads to a functional depending on approximations for displacements and stresses. By introducing a time-independent displacement test function, a weak form is derived. A numerical example concerning quasi-incompressible elasticity shows the performance of the approach for the lowest-order element RT₀P₁as. (© 2010 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Mathematical models for the elastic beam with structural damping

In this paper the existence, regularity and sharp estimates for the solutions of an abstract second order evolution equation are proved and applications to models of a (possibly non homogeneous) elastic beam with a frequency-proportional damping are given.     

Regularization of nonlinear illposed problems with closed operators

In this paper Tikhonov regularization for nonlinear illposed problems is investigated. The regularization term is characterized by a closed linear operator, permitting seminorm regularization in applications. Results for existence, stability, convergence and con- vergence rates of the solution of the regularized problem in terms of the noise level are given. An illustrating example involving parameter estimation for a one dimensional stationary heat equation is given.     

A Joint Tikhonov Regularization and Augmented Lagrange Approach for Ill-Posed State Constrained Control Problems with Sparse Controls

Abstract

We provide a modified augmented Lagrange method coupled with a Tikhonov regularization for solving ill-posed state constrained elliptic optimal control problems with sparse controls. We consider a linear quadratic optimal control problem without any additional L² regularization terms. The sparsity is guaranteed by an additional L¹ term. Here, the modification of the classical augmented Lagrange method guarantees us uniform boundedness of the multiplier that corresponds to the state constraints. We present a coupling between the regularization parameter introduced by the Tikhonov regularization and the penalty parameter from the augmented Lagrange method, which allows us to prove strong convergence of the controls and their corresponding states. Moreover, convergence results proving the weak convergence of the adjoint state and weak*-convergence of the multiplier are provided. Finally, we demonstrate our method in several numerical examples.     

A cooperative value in a multiplicative model

In this study, we consider positive cooperative TU games with finitely many players. We assume that all agents use the same scale. Furthermore, the worth that a coalition of players can achieve by cooperation is measured as a multiple of a defined standard base. In this multiplicative setting we characterise and analyse a solution concept which is related to the well known Shapley value. From a statistical point of view, the methodology allows computing relative importance of individual factors on the expected value. In particular, we present a specific application to general insurance pricing. As a result, the value may be used to analyse the business mix of an insurance portfolio by measuring exposure to risk factors. Similar applications refer to credit scoring and customer relationship management. In this sense, the modelling approach may be embedded as a risk analysis technique within a risk management framework.     

Optimal control of the bidomain system (II): uniqueness and regularity theorems for weak solutions

Motivated by the study of related optimal control problems, weak and strong solution concepts for the bidomain system together with two-variable ionic models are analyzed. A key ingredient for the analysis is the bidomain bilinear form. Global existence of weak and strong solutions as well as stability and uniqueness theorems is proven.     

Zinc Substitution of Cobalt in Vitamin B12: Zincobyric acid and Zincobalamin as Luminescent Structural B12‐Mimics

Replacing the central cobalt ion of vitamin B₁₂ by other metals has been a long‐held aspiration within the B₁₂‐field. Herein, we describe the synthesis from hydrogenobyric acid of zincobyric acid ( Znby ) and zincobalamin ( Znbl ), the Zn‐analogues of the natural cobalt‐corrins cobyric acid and vitamin B₁₂, respectively. The solution structures of Znby and Znbl were studied by NMR‐spectroscopy. Single crystals of Znby were produced, providing the first X‐ray crystallographic structure of a zinc corrin. The structures of Znby and of computationally generated Znbl were found to resemble the corresponding Co^II‐corrins, making such Zn‐corrins potentially useful for investigations of B₁₂‐dependent processes. The singlet excited state of Znby had a short life‐time, limited by rapid intersystem crossing to the triplet state. Znby allowed the unprecedented observation of a corrin triplet (E^T=190 kJ mol^?1) and was found to be an excellent photo‐sensitizer for ¹O₂ (Φ_Δ=0.70).