We study the problem of feedback control for skew-symmetric and skewHamiltonian transfer functions using skew-symmetric controllers. This extends work of Helmke, et al., who studied static symmetric feedback control of symmetric and Hamiltonian linear systems. We identify spaces of linear systems with symmetry as natural subvarieties of the moduli space of rational curves in a Grassmannian, giv...

This work extends to processes with finite moments or order p, 1 < P < 2 and to symmetric a-stable processes, 1 < a < 2, some of the basic linear theory known for processes with finite second moments (p=2) and for Gaussian processes (a=2). Here the IIcovariationll plays a role analogous to the covariance. Specifically, stochastic integrals of two types are introduced and studied for p-th order ...

In single-reference coupled-cluster (CC) methods, one has to solve a set of non-linear polynomial equations in order determine the so-called amplitudes which are then used compute energy and other properties. Although it is common practice converge (lowest-energy) ground-state solution, also possible, thanks tailored algorithms, access higher-energy roots these may or not correspond genuine exc...

In the present work, we focus on the cases of two-site (dimer) and three-site (trimer) configurations, i.e. oligomers, respecting the parity-time (PT) symmetry, i.e. with a spatially odd gain-loss profile. We examine different types of solutions of such configurations with linear and nonlinear gain/loss profiles. Solutions beyond the linear PT-symmetry critical point as well as solutions with a...

We show that if v is a symmetric regular Laguerre-Hahn linear form (functional), then the linear form u defined by u = −λx−2v + δ0 is also regular and symmetric LaguerreHahn linear form for every complex λ except for a discrete set of numbers depending on v. We explicitly give the coefficients of the second-order recurrence relation, the structure relation of the orthogonal sequence associated ...