We investigate the internal controllability of the wave equation with structural damping on the one dimensional torus. We assume that the control is acting on a moving point or on a moving small interval with a constant velocity. We prove that the null controllability holds in some suitable Sobolev space and after a fixed positive time independent of the initial conditions.

Nonhomeomorphic compact Hausdorff spaces X and Y and an isomorphism : C(X) -> C(Y) (onto) are constructed such that ||c/>|| \4>~ || = 2. Amir had asked if such a d> exists with || \\ ||cf> || < 3.

We study the complexity of randomized solution of initial value problems for systems of ordinary differential equations (ODE). The input data are assumed to be γ-smooth (γ = r+% : the r-th derivatives satisfy a %-Hölder condition). Recently, the following almost sharp estimate of the order of the n-th minimal error was given by Kacewicz (Almost optimal solution of initial-value problems by rand...

We present an Initial Value Representation for the semiclassical coherent state propagator based on complex trajectories. We map the complex phase space into a real phase space with twice as many dimensions and use a simple procedure to automatically eliminate non-contributing trajectories. The resulting semiclassical formulas do not show divergences due to caustics and provide accurate results.

The conformal method for constructing initial data for Einstein’s equations is presented in both the Hamiltonian and Lagrangian picture (extrinsic curvature decomposition and conformal thin sandwich formalism, respectively), and advantages due to the recent introduction of a weight-function in the extrinsic curvature decomposition are discussed. I then describe recent progress in numerical tech...

in Hilbert space and their realizations in function spaces as initial-boundary value problems for partial differential equations which may contain degenerate or singular coefficients. The Cauchy problem consists of solving (1.1) subject to the initial condition Jdu(0) = h. We are concerned with the case where the solution is given by an analytic semigroup; it is this sense in which the Canchy p...

We examine the participation of public and private firms in merger waves and productivity outcomes. We show that public firms participate more than private firms as buyers and sellers of assets and their participation is more cyclical. Public firms are affected more by credit spreads and aggregate market valuation. Public firm transactions are also impacted positively by their stock market valu...

This paper is devoted to the study of discrete fractional calculus; the particular goal is to define and solve well-defined discrete fractional difference equations. For this purpose we first carefully develop the commutativity properties of the fractional sum and the fractional difference operators. Then a ν-th (0 < ν ≤ 1) order fractional difference equation is defined. A nonlinear problem wi...