Controllability properties for the Navier–Stokes system are closely related to observability properties for the adjoint Oseen–Stokes system; boundary observability inequalities are derived, for that adjoint system, that will be appropriate to deal with suitable constrained controls, like finite-dimensional controls supported in a given subset of the boundary. As an illustration, a new boundary ...

We provide sufficient conditions for the continuity of the free-boundary in a general class of finite-horizon optimal stopping problems arising for instance in finance and economics. The underlying process is a strong solution of one-dimensional, time-homogeneous stochastic differential equation (SDE). The proof relies on both analytic and probabilistic arguments and it is based on a contradict...

We consider a class of semi-linear dissipative hyperbolic equations in which the operator associated to the linear part has a nontrivial kernel. Under appropriate assumptions on the nonlinear term, we prove that all solutions decay to 0, as t → +∞, at least as fast as a suitable negative power of t. Moreover, we prove that this decay rate is optimal in the sense that there exists a nonempty ope...

A Hamilton cycle is a cycle containing every vertex of a graph. A graph is called Hamiltonian if it contains a Hamilton cycle. The Hamilton cycle problem is to find the sufficient and necessary condition that a graph is Hamiltonian. In this paper, we give out some new kind of definitions of the subgraphs and determine the Hamiltoncity of edges according to the existence of the subgraphs in a gr...

The feedback stabilization of the Burgers system to a nonstationary solution using finite-dimensional internal controls is considered. Estimates for the dimension of the controller are derived. In the particular case of no constraint in the support of the control a better estimate is derived and the possibility of getting an analogous estimate for the general case is discussed; some numerical e...

Unlimited access to a motorway network can, in overloaded conditions, cause a loss of capacity. Ramp metering (signals on slip roads to control access to the motorway) can help avoid this loss of capacity. The design of ramp metering strategies has several features in common with the design of access control mechanisms in communication networks. Inspired by models and rate control mechanisms de...

The Mathematics Subject Classification (MSC) is a widely used scheme for classifying documents in mathematics by subject. Its traditional, idiosyncratic conceptualization and representation makes the scheme hard to maintain and requires custom implementations of search, query and annotation support. This limits uptake e.g. in semantic web technologies in general and the creation and exploration...

A ringR is called generalized right Baer if for any non-empty subset S of R, the right annihilator rR(S ) is generated by an idempotent for some positive integer n. Generalized Baer rings are special cases of generalized PP rings and a generalization of Baer rings. In this paper, many properties of these rings are studied and some characterizations of von Neumann regular rings and PP rings are ...

We obtain an asymptotic upper bound for the smallest number of generators for a finite direct sum of matrix algebras with entries in a finite field. This produces an upper bound for a similar quantity for integer matrix rings. We also obtain an exact formula for the smallest number of generators for a finite direct sum of 2-by-2 matrix algebras with entries in a finite field and as a consequenc...

We model the influence of sharing large exogeneous losses to the reinsurance market by a bipartite graph. Using Pareto-tailed claims and multivariate regular variation we obtain asymptotic results for the Value-atRisk and the Conditional Tail Expectation. We show that the dependence on the network structure plays a fundamental role in their asymptotic behaviour. As is well-known in a non-networ...