276 research outputs found
Big and little Lipschitz one sets
Given a continuous function we denote the
so-called "big Lip" and "little lip" functions by and respectively}. In this paper we are interested in the
following question. Given a set is it possible to
find a continuous function such that or
?
For monotone continuous functions we provide the rather straightforward
answer.
For arbitrary continuous functions the answer is much more difficult to find.
We introduce the concept of uniform density type (UDT) and show that if is
and UDT then there exists a continuous function satisfying , that is, is a
set.
In the other direction we show that every set is
and weakly dense. We also show that the converse of this statement
is not true, namely that there exist weakly dense sets which are
not .
We say that a set is if there is
a continuous function such that . We
introduce the concept of strongly one-sided density and show that every
set is a strongly one-sided dense set.Comment: This is the final preprint version accepted to appear in European
Journal of Mathematic
Analysis and Control of Nonlinear Actuator Dynamics Based on the Sum of Squares Programming Method
Challenges and possibilities in variable geometry suspension systems
The variable-geometry suspension system is in the focus of the paper. The advantages of the variable-geometry system are the simple structure, low energy consumption and low cost. During maneuvers the variable-geometry system modifies the camber angle of the front wheels in order to improve road stability. The system affects both the chassis roll angle and the half-track change. Moreover, the tracking error of the reference yaw rate can also be reduced. In the paper the challenges and possibilities of the variable geometry suspension system are analyzed
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