Coffee break & Poster session

Existence of T-$\vec{p}(\cdot)$-solutions for some anisotropic quasilinear elliptic problem

Sarah Biesenbach
RWTH Aachen University, Germany

Optimal convergence rates for the Cahn-Hilliard equation on the line

We explain how to derive optimal algebraic-in-time rates for the decay to equilibrium under the assumption that the initial data has a finite (not small) distance to the limit state. The method exploits the gradient flow structure, Nash-type inequalities and a duality argument to establish sharp estimates. We present two examples. This is joint work with Felix Otto and Maria Westdickenberg.

Nonlinear Vibration analysis of hyperelastic plates

Nonlinear vibration of hyperelastic plates with physical and geometrical nonlinearities is elaborated. The hyperelastic and the initial deflection affects on the frequency and time responses are investigated. The Lagrange equations are used and nonlinear partial differential equations governing the motion are formulated. Various hyperelastic models are considered based on the multimodal analysis and the Garlekin procedure.The associated nonlinear differential system is obtained. The time response is computed for various geometrical and material parameters. The harmonic balance method is implemented and the nonlinear frequency-amplitude responses are analysed.

Oksana Chernova
Taras Shevchenko National University of Kyiv, Ukraine

Estimation in Cox proportional hazards model with measurement errors

I work on survival and event history analysis. Survival data often arise in medicine, engineering and insurance, where the outcome of interest is time to an event.
Statistical inference is usually complicated by the presence of incomplete observations.
For some subjects the event is not observed and only known that survival time exceeds some observed censoring time.
Since its introduction, the proportional hazards model proposed by Cox has become the workhorse of regression analysis for censored data.
I consider the case when covariates are observed with additive measurement errors and propose new approach for parameters estimation.

Noémie Combe
Max Planck Institute for Mathematics in the Sciences, Germany

Gauss Skizze operad & Frobenius manifolds

Consider a certain class of Frobenius manifolds: the space of complex polynomials of a fixed degree.
The existence of a decomposition, indexed by ``Gauss drawings'' (which are bi-colored graphs verifying properties) is shown.
Using this tool, and monodromy properties, we construct a (topological) operad: the Gauss skizze operad.

Rosa Antonia Kowalewski
University of Lübeck, Germany

Incorporating a Deformation Prior and Object Boundary Constraints for Multiple Shape Registration

Lise Maurin
Sorbonne Université, France

Robustness of the Adaptive Biasing Force method under a non-gradient perturbation

New Estimators Based on the Characteristics of Geometric Distribution and Aftershock Data Application

In this study, we have considered ratio and product exponential estimators of geometric distributed population in simple random sampling (SRS). The mean square error (MSE) equations of the proposed estimators are obtained and compared in application with the classical ratio estimator. In addition, theoretical findings are supported by an empirical study to show the superiority of the constructed estimators over others with aftershock data of Turkey.

Anne Pein
Technical University of Munich, Germany

Random Attractors for Stochastic Partly Dissipative Systems

Anna Schilling
Universität Heidelberg, Germany

Horofunction compactification of vector spaces

Any $n$-dimensional closed convex ball $B \subset \mathbb{R}^n$ containing the origin as an interior point defines a norm and therefore also a metric on $\mathbb{R}^n$ that has $B$ as its unit ball. The horofunction compactification, first defined by Gromov for any metric space, crucially depends on the metric of the space. Based on various examples we illustrate this construction and dependence and show that the horofunction compactification of $\mathbb{R}^n$ equipped with the norm defined by (some polyhedral) $B$ is homeomorphic to the dual unit ball $B^\circ$.

Caren Schinko
Universität Augsburg, Germany

Compact hyperkähler manifolds

An irreducible hyperkähler manifold is a compact Kähler manifold with a holomorphic symplectic form. One can see these manifolds as higher-dimensional analogues of K3 surfaces. The poster shows a brief overview of compact hyperkähler manifolds with focus on examples.

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