Characterisation of space debris has become a fundamental task to facilitate sustainable operations. Ground-based surveillance provides the means extract key attributes from spacecraft. However, signal inversion attempts are generally under-constrained, which is why an increase in measurement channels through multispectral observations expected benefit parameter estimation. The current approach...

We consider the numerical solution of an unsteady convection-diffusion equation using high order polynomial approximations both in space and time. General boundary conditions and initial conditions can be imposed. The method is fully implicit and enjoys exponential convergence in time and space for analytic solutions. This is confirmed by numerical experiments (in one space dimension) using a s...

We establish a general link between integrable systems in algebraic geometry (expressed as Jacobian flows on spectral curves) and soliton equations (expressed as evolution equations on flat connections). Our main result is a natural isomorphism between a moduli space of spectral data and a moduli space of differential data, each equipped with an infinite collection of commuting flows. The spect...

We establish a general link between integrable systems in algebraic geometry (expressed as Jacobian flows on spectral curves) and soliton equations (expressed as evolution equations on flat connections). Our main result is a natural isomorphism between a moduli space of spectral data and a moduli space of differential data, each equipped with an infinite collection of commuting flows. The spect...

We establish a general link between integrable systems in algebraic geometry (expressed as Jacobian flows on spectral curves) and soliton equations (expressed as evolution equations on flat connections). Our main result is a natural isomorphism between a moduli space of spectral data and a moduli space of differential data, each equipped with an infinite collection of commuting flows. The spect...

What Is Spectral Theory? By spectral theory we mean the theory of structure of certain bounded linear operators on a Hilbert space. In a broader sense, the history of spectral theory goes way back to the nineteenth century, when the objects of study used to be infinite systems of linear equations and integral equations. The subject was revolutionized in the late 1920s by von Neumann, when he de...

This paper proposes a new approach to construct high quality space-filling sample designs. First, we propose a novel technique to quantify the space-filling property and optimally trade-off uniformity and randomness in sample designs in arbitrary dimensions. Second, we connect the proposed metric (defined in the spatial domain) to the objective measure of the design performance (defined in the ...

We establish a general link between integrable systems in algebraic geometry (expressed as Jacobian flows on spectral curves) and soliton equations (expressed as evolution equations on flat connections). Our main result is a natural isomorphism between a moduli space of spectral data and a moduli space of differential data, each equipped with an infinite collection of commuting flows. The spect...