has a nonzero integer solution for every > 0. If some Qi is rational and is small enough then for x ∈ Zs the inequality |Qi(x)| < is equivalent to the equation Qi(x) = 0. Hence if all forms are rational then for sufficiently small the system (1.1) reduces to a system of equations. In this case W. Schmidt [10] proved the following result. Recall that the real pencil generated by the forms Q1, . ...

A class of continuous-time systems with periodic coefficients is analysed and controlled by robust linear controllers. Time varying parameters are considered as perturbations of a nominal timeinvariant linear system. The robust control synthesis is based on general solutions of Diophantine equations in the ring of proper and Hurwitz stable rational functions RPS and the Youla-Kučera parameteriz...

Heights are functions that measure the arithmetic complexity of an algebraically defined object. They have become a major tool in many branches of number theory such as Diophantine analysis, transcendental number theory, Diophantine approximation, arithmetic of dynamical systems, etc. Moreover, they have also some very subtle functorial and functional properties, making it worthwile to study th...

We show that a multiplicative form of Dirichlet’s theorem on simultaneous Diophantine approximation as formulated by Minkowski, cannot be improved for almost all points on any analytic curve on R which is not contained in a proper affine subspace. Such an investigation was initiated by Davenport and Schmidt in the late sixties. The Diophantine problem is then settled via showing that certain se...

MacMahon devoted a significant portion of Volume II of his famous book “Combinatory Analysis” to the introduction of Partition Analysis as a computational method for solving combinatorial problems in connection with systems of linear diophantine inequalities and equations. In a series of papers we have shown that MacMahon’s method turns into an extremely powerful tool when implemented in comput...