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Now showing items 21-23 of 23
Habilitation
Algorithmic Methods for Mixed Recurrence Equations, Zeros of Classical Orthogonal Polynomials and Classical Orthogonal Polynomial Solutions of Three-Term Recurrence Equations
(2019-07)
Using an algorithmic approach, we derive classes of mixed recurrence equations satisfied by classical orthogonal polynomials. Starting from certain structure relations satisfied by classical orthogonal polynomials or their connection formulae, we show that our mixed recurrence equations are structurally valid. However, they couldn't be easily obtained with classical methods and for this reason, our algorithmic approach is important. The main algorithmic tool used here is an extended version of Zeilberger's ...
Aufsatz
Numerical Solution of Viscoelastic Fluid-Structure-Diffusion Systems with Applications in Ophthalmology
(2019-09-04)
The research of fluid-structure interaction problems is a continuously growing field, especially regarding applications in medicine and biology. We present the coupling of a potentially viscoelastic fluid with multiple hyperelastic structures incorporating chemical processes in the arbitrary Lagrangian Eulerian framework. This monolithic formulation allows a robust numerical solution with Newton's method. The discretization is based on the backward Euler scheme for temporal discretization and the Galerkin finite ...
Aufsatz
Lenticular Imaging: A New Experimental and Quantitative Analysis of Capsular Dynamics, “Choi-Apple View”
(2019-05)
Purpose: Development of a means for quantitative estimation of lenticular and zonular dynamics by using real-time imaging of human autopsy eyes during implantation of different intraocular lens (IOL) models.
Methods: Isolated lenticular structures from human autopsy eyes were prepared in vitro. The following IOLs were implanted: a one-piece C-loop haptic IOL, a three-piece C-loop haptic IOL, and a one-piece plate-type IOL. The amount of deformation of lenticular structures during implantation was calculated and ...