Given a self-adjoint operator H0, a self-adjoint trace class operator V and a fixed Hilbert-Schmidt operator F with trivial kernel and co-kernel, using limiting absorption principle an explicit set of full Lebesgue measure Λ(H0, F) ⊂ R is defined, such that for all points of this set the wave and the scattering matrices can be defined unambiguously. Many well-known properties of the wave and sc...

Let V be a finite-dimensional vector space, either real or complex, and equipped with an inner product 〈· , ·〉. Let A : V → V be a linear operator. Recall that the adjoint of A is the linear operator A : V → V characterized by 〈Av, w〉 = 〈v, Aw〉 ∀v, w ∈ V (0.1) A is called self-adjoint (or Hermitian) when A = A. Spectral Theorem. If A is self-adjoint then there is an orthonormal basis (o.n.b.) o...

The observable algebra O of SOq(3)-symmetric quantum mechanics is generated by the coordinates Pi and Xi of momentum and position spaces (which are both isomorphic to the SOq(3)-covariant real quantum space IR 3 q). Their interrelations are determined with the quantum group covariant differential calculus. For a quantum mechanical representation of O on a Hilbert space essential self-adjointnes...

In this paper, we consider the band functions, Bloch functions and spectrum of self-adjoint differential operator L with periodic matrix coefficients. Conditions are found for coefficients under which number gaps in is finite.

This paper proposes a novel control scheme, named self-reflective model predictive control, which takes its own limitations in the presence of process noise and measurement errors into account. In contrast to existing output-feedback MPC and persistently exciting MPC controllers, the proposed self-reflective MPC controller does not only propagate a matrix-valued state forward in time in order t...

Complex matrices that are structured with respect to a possibly degenerate indefinite inner product are studied. Based on the theory of linear relations, the notion of an adjoint is introduced: the adjoint of a matrix is defined as a linear relation which is a matrix if and only if the inner product is nondegenerate. This notion is then used to give alternative definitions of selfadjoint and un...

A Jacobi matrix with matrix entries is a self-adjoint block tridiagonal matrix with invertible blocks on the off-diagonals. The Weyl surface describing the dependence of Green’s matrix on the boundary conditions is interpreted as the set of maximally isotropic subspace of a quadratic from given by the Wronskian. Analysis of the possibly degenerate limit quadratic form leads to the limit point/l...

Including tracer data into geostatistically based methods of inverse modeling is computationally very costly when all concentration measurements are used and the sensitivities of many observations are calculated by the direct di€erentiation approach. Harvey and Gorelick (Water Resour Res 1995;31(7):1615±26) have suggested the use of the ®rst temporal moment instead of the complete concentration...

This paper presents an accurate and efficient full-wave method, combined with iterative adjoint technique, for analyzing sensitivities of planar microwave circuits with respect to design parameters. Method of moments (MoM) in spatial domain is utilized, and generalized conjugate residual iterative scheme is applied to solve the linear matrix equations with fast convergence. Green’s functions fo...

We propose a new mechanism called " real CP violation " to originate spontaneous CP violation. Starting with a CP conserving theory with scalar fields in the adjoint representation of a global or local non-abelian symmetry, we show that even though the VEV's of such scalars are real they give rise to a spontaneous violation of CP. We provide an illustrative example of how this new mechanism of ...