We clarify the explici structure of the Hurwitz quaternion order, which is of fundamental importance in Riemann surface theory.

A stability test for time invariant linear systems can also be derived in the frequency domain. It is known as Nyquist stability criterion. It is based on the complex analysis result known as Cauchy's principle of argument. Note that the system transfer function is a complex function. By applying Cauchy's principle of argument to the open-loop system transfer function, we will get information a...

In this paper, we mainly study the robust stability of linear continuous systems with parameter uncertainties, a more general kind of uncertainties for system matrices is considered, i.e., entries of system matrices are rational functions of uncertain parameters which are varying in intervals. we present a method which can check the robust Hurwitz stability of such uncertain systems in finite s...

In this paper, using the approach of Hurwitz and the necessary conditions given in 4,6], we construct a third order linear diierential equation whose diierential Galois group is the primitive subgroup F SL3 36 S L(3; C) of order 108.

Magnetic Barkhausen technique has been used to parametrically image the effects of thermal exposure on the surface condition of industrial components. Wear and fatigue resistance of industrial components are primarily determined by the mechanical condition of the surface layer. Standard hardness measurement techniques cannot easily be used to assess the condition of components in service becaus...

This paper extends in a simple way the classical absolute stability Popov criterion to multivariable rational systems with time-varying memoryless nonlinearities subject to sector conditions. The proposed suucient conditions are expressed in terms of easy-to-check Linear Matrix Inequalities , or under a frequency-domain form well-suited for robustness issues, and lead to simple graphical interp...

We compute the stable reduction of some Galois covers of the projective line branched at three points. These covers are constructed using Hurwitz spaces parameterizing metacyclic covers. The reduction is determined by a certain hypergeometric differential equation. This generalizes the result of Deligne and Rapoport on the reduction of the modular curve X (p).