Shape optimization of a Timoshenko beam together with an elastic foundation

In this article we are going first to aim at the variational ormulation of the bending problem for the Timoshenko beam model. Afterwards we will extend this problem to the Timoshenko beam resting on the Winkler foundation, which is firmly connected with the beam. Hereafter a shape optimization for the aforementioned problems is presented. The state problem is here represented by the system of two ordinary differential equations of the second order. The optimization problem is given as a minimization of the so-called compliance functional on the set of all admissible design variables. For our purpose as the design variable we will select the beam thickness. Shape optimization problems have attracted the interest of many applied mathematicians and engineers. The objective of this article is to present a solution method for one of these problems and its demonstration by examples

Revisiting Resistance Speeds Up I/O-Efficient LTL Model Checking

Revisiting resistant graph algorithms are those that can tolerate re-exploration of edges without yielding incorrect results. Revisiting resistant I/O efficient graph algorithms exhibit considerable speed-up in practice in comparison to non-revisiting resistant algorithms. In the paper we present a new revisiting resistant I/O efficient LTL model checking algorithm. We analyze its theoretical I/O complexity and we experimentally compare its performance to already existing I/O efficient LTL model checking algorithms

Tests of additivity in mixed and fixed effect two-way ANOVA models with single sub-class numbers

In variety testing as well as in psychological assessment, the situation occurs that in a two-way ANOVA-type model with only one replication per cell, analysis is done under the assumption of no interaction between the two factors. Tests for this situation are known only for fixed factors and normally distributed outcomes. In the following we will present five additivity tests and apply them to fixed and mixed models and to quantitative as well as to Bernoulli distributed data. We consider their performance via simulation studies with respect to the type-I-risk and power. Furthermore, two new approaches will be presented, one being a modification of Tukey's test and the other being a new experimental design to test for interactions