Given a closed (and non necessarily compact) basic semialgebraic set K ⊆ R, we solve the K-moment problem for continuous linear functionals. Namely, we introduce a weighted l1-norm lw on R[x], and show that the lw-closures of the preordering P and quadratic module Q (associated with the generators of K) is the cone Psd(K) of polynomials nonnegative on K. We also prove that P and Q solve the K-m...

Consider a Markov chain (ξv)v∈V ∈ [k] on the infinite b-ary tree T = (V,E) with irreducible edge transition matrix M , where b ≥ 2, k ≥ 2 and [k] = {1, . . . , k}. We denote by Ln the level-n vertices of T . Assume M has a real second-largest (in absolute value) eigenvalueλ with corresponding real eigenvector ν 6= 0. Letting σv = νξv , we consider the following root-state estimator, which was i...

Measurements of Rayleigh light scattering and Cotton-Mouton (CM) effect are carried out at room temperature for 100 mM NaCl solutions of apoferritin/ferritin loaded with 0, 90, 100, 500, 700, and 1500 Fe atoms/molecule. Because of the spherical shape, ferritin macromolecule should not manifest magnetic anisotropy; however, in solution it shows the induced magnetic birefringence (CM effect) and ...

A new closure for Grad’s 13 moment equations is presented that adds terms of SuperBurnett order to the balances of pressure deviator and heat flux vector. The additional terms are derived from equations for higher moments by means of the distribution function for 13 moments. The resulting system of equations contains the Burnett and Super-Burnett equations when expanded in a series in the Knuds...

The problem of proposing a framework for linear moment matching is tackled. It is possible to define five notions of moments, i.e., two from a complex ”s-domain” point of view and three from a time-domain point of view. Based on these notions, reduced order models that achieve moment matching are obtained. This paper sets the basis to develop the theory of model reduction by moment matching for...

This report describes how to optimize linear static control problems involving rst and second moments and yield objectives for Gaussian distributions. These problems can be cast as second-order cone programs, which is a class of convex optimization problems that can be solved very e ciently.

Abstract. We propose a positive-preserving moment closure for linear kinetic transport equations based on a filtered spherical harmonic (FPN ) expansion in the angular variable. The recently proposed FPN moment equations are known to suffer from the occurrence of (unphysical) negative particle concentrations. The origin of this problem is that the FPN approximation is not always positive at the...

This paper analyses moment and near-epoch dependence properties for the general class of models in which the conditional variance is a linear function of squared lags of the process. It is shown how the properties of these processes depend independently on the sum and rate of convergence of the lag coefficients, the former controlling the existence of moments, and the latter the memory of the v...