We investigate the singular Weyl–Titchmarsh m-function of perturbed spherical Schrödinger operators (also known as Bessel operators) under the assumption that the perturbation q(x) satisfies xq(x) ∈ L(0, 1). We show existence plus detailed properties of a fundamental system of solutions which are entire with respect to the energy parameter. Based on this we show that the singular m-function bel...

The realization of a discrete-time, linear, time-invariant (LTI) filter from its impulse response provides insight into the role of linear algebra in the analysis of both dynamical systems and rational functions. For an LTI filter, a sequence of output data measured over some finite period of time may be expressed as the linear combination of the past input and the input measured over that same...

Finite element methods for a family of systems of singular perturbation problems of a saddle point structure are discussed. The system is approximately a linear Stokes problem when the perturbation parameter is large, while it degenerates to a mixed formulation of Poisson’s equation as the perturbation parameter tends to zero. It is established, basically by numerical experiments, that most of ...

The goal of this paper is to examine the possible extension of the singular perturbation differential equation to the concept of fractional order derivative. To achieve this, we presented a review of the concept of fractional calculus. We make use of the Laplace transform operator to derive exact solution of singular perturbation fractional linear differential equations. We make use of the meth...

The primitive equations are derived from the Boussinesq system of incompressible flow under the hydrostatic balance assumption, by taking the zero singular perturbation limit of the small aspect ratio. This singular perturbation limit of small aspect ratio can be rigorously justified, see, Azérad–Guillén [1] and Li–Titi [26]. The primitive equations play a fundamental role for weather predictio...

Abstract. This paper studies the problem of the computation of common infinity-norm Lyapunov functions. For a set of continuous-time LTI systems or discrete-time LTI systems whose system matrices are upper triangular form or lower triangular form, it is proved that there exist common infinity-norm Lyapunov functions for them. Then four algorithms of computing common infinity-norm Lyapunov funct...

Here and below, ‖A‖ always denotes the induced (by the Euclidean norm in Cn) operator norm of A, i. e. its maximal singular value. Entries of the matrices A and ∆ are complex, so we deal with complex structured singular value. The first equality above is the definition of μ, the second is a simple exercise in linear algebra. Note, that if in the definition of μ we take infimum over all matrices...

In chemical engineering, several processes are represented by singular boundary value problems. In general, classical numerical methods fail to produce good approximations for the singular boundary value problems. In this paper, Chebyshev finite difference (ChFD) method and DTM-Pad´e method, which is a combination of differential transform method (DTM) and Pad´e approximant, are applied for sol...

Ren-Cang Li University of Texas at Arlington 15.1 Eigenvalue Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15-1 15.2 Singular Value Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15-6 15.3 Polar Decomposition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15-7 15.4 Generalized Eigenvalue Problems . . . . . . . . . . . . . . . . . . . 15-...

This paper studies the transient and steady performance constraints on flexible joint manipulator system with exogenous disturbance, proposes a fixed-time prescribe tracking control method based singular perturbation model. For fast subsystem, subcontroller superior is proposed that guarantees suppression of vibration in fixed-time. The remaining slow subsystem can be linked rigid methods to ac...