Theory of differential inclusions and its application in mechanics

The following chapter deals with systems of differential equations with discontinuous right-hand sides. The key question is how to define the solutions of such systems. The most adequate approach is to treat discontinuous systems as systems with multivalued right-hand sides (differential inclusions). In this work three well-known definitions of solution of discontinuous system are considered. We will demonstrate the difference between these definitions and their application to different mechanical problems. Mathematical models of drilling systems with discontinuous friction torque characteristics are considered. Here, opposite to classical Coulomb symmetric friction law, the friction torque characteristic is asymmetrical. Problem of sudden load change is studied. Analytical methods of investigation of systems with such asymmetrical friction based on the use of Lyapunov functions are demonstrated. The Watt governor and Chua system are considered to show different aspects of computer modeling of discontinuous systems

Hippocampal-Dependent Spatial Memory in the Water Maze is Preserved in an Experimental Model of Temporal Lobe Epilepsy in Rats

Cognitive impairment is a major concern in temporal lobe epilepsy (TLE). While different experimental models have been used to characterize TLE-related cognitive deficits, little is known on whether a particular deficit is more associated with the underlying brain injuries than with the epileptic condition per se. Here, we look at the relationship between the pattern of brain damage and spatial memory deficits in two chronic models of TLE (lithium-pilocarpine, LIP and kainic acid, KA) from two different rat strains (Wistar and Sprague-Dawley) using the Morris water maze and the elevated plus maze in combination with MRI imaging and post-morten neuronal immunostaining. We found fundamental differences between LIP- and KA-treated epileptic rats regarding spatial memory deficits and anxiety. LIP-treated animals from both strains showed significant impairment in the acquisition and retention of spatial memory, and were unable to learn a cued version of the task. In contrast, KA-treated rats were differently affected. Sprague-Dawley KA-treated rats learned less efficiently than Wistar KA-treated animals, which performed similar to control rats in the acquisition and in a probe trial testing for spatial memory. Different anxiety levels and the extension of brain lesions affecting the hippocampus and the amydgala concur with spatial memory deficits observed in epileptic rats. Hence, our results suggest that hippocampal-dependent spatial memory is not necessarily affected in TLE and that comorbidity between spatial deficits and anxiety is more related with the underlying brain lesions than with the epileptic condition per se