Let $L$ be a primitive Gaussian line, that is, line in the complex plane contains two, and hence infinitely many, coprime integers. We prove there exists an integer $G_L$ such for every $n\geq G_L$ are ma

This paper shows that coprime right factorizations exist for the input to state mapping of a continuous time nonlinear system provided that the smooth feedback stabilization problem be solvable for this system. In particular, it follows that feedback linearizable systems admit such factorizations. In order to establish the result a Lyapunov-theoretic definition is proposed for “bounded input bo...

In array processing, mutual coupling between sensors has an adverse effect on the estimation of parameters (e.g., DOA). While there are methods to counteract this through appropriate modeling and calibration, they are usually computationally expensive, and sensitive to model mismatch. On the other hand, sparse arrays, such as nested arrays, coprime arrays, and minimum redundancy arrays (MRAs), ...

Let k be an algebraically closed field of characteristic p > 0. Let B1/k and B2/k be two smooth proper connected curves, each endowed with an automorphism σi : Bi → Bi of order p. Let Y := B1 × B2, and let σ : Y → Y be the automorphism σ1 × σ2. We show that the graph of the resolution of the singularities of Y/ 〈σ〉 when B2 is an ordinary curve of positive genus is a star-shaped graph with three...

This paper deals with robust synchronization of directed and undirected multi-agent networks with uncertain agent dynamics. Given a network with identical nominal dynamics, we allow uncertainty in the form of coprime factor perturbations of the transfer matrix of the agent dynamics. These perturbations are assumed to be stable and have H∞norm that is bounded by an a priori given desired toleran...