The problems of swinging up an inverted pendulum on a cart and controlling it around the upright position have been traditionally treated as two separate problems. This paper proposes a strategy that is globally asymptotically stabilizing under actuator saturation and, in addition, locally exponentially stabilizing. The proposed methodology performs swing up and control simultaneously and uses ...

The Beverton-Holt and Ricker functions are two distinct ecological descriptions of the link between a parental population size and subsequent offspring that may survive to become part of the fish stock. This report presents a model consisting of a system of ordinary differential equations (ODEs), which couples a pre-recruit stage with several adult stages. Elements of slow-fast dynamics capture...

We consider an initial value problem for a class of evolution equations incorporating a memory term with a weakly singular kernel bounded by C(t − s)α−1, where 0 < α < 1. For the time discretization we apply the discontinuous Galerkin method using piecewise polynomials of degree at most q − 1, for q = 1 or 2. For the space discretization we use continuous piecewise-linear finite elements. The d...

A new method for implementing complex wavelet transform (CWT) based on analog sampled-data circuit and singular value decomposition (SVD) algorithm is presented. To begin with, the real and imaginary parts functions of the complex wavelet base are approximated by using SVD algorithm. As the main advantage of this approximation approach is its computational simplicity and general applicability. ...

We consider the approximation of a coupled system of two singularly perturbed reaction-diffusion equations by the finite element method. The solution to such problems contains boundary layers which overlap and interact, and the numerical approximation must take this into account in order for the resulting scheme to converge uniformly with respect to the singular perturbation parameters. We pres...

where F,G ∈ M(n × n;F), Yk ∈ M(n × 1;F) (i.e., the algebra of square matrices with elements in the field F), Xk ∈ M(m× 1;F), B ∈ M(n× l;F) and C ∈ M(m×n;F). For the sake of simplicity, we set Mn = M(n× n;F) and Mnm = M(n×m;F). We assume that the system (1) is singular, i.e. the matrix F is singular and that the input vector Vk changes only at equally space sampling instants. Many authors have s...

A robust and secure technique is required to protect multimedia data as it can be easily produced as illegal copies. Digital watermarking is used for Intellectual Property Rights protection and authentication. In this paper, a lossless watermarking scheme based on Integer wavelet transform (IWT) and singular value decomposition (SVD) is implemented. The watermark image is embedded on the elemen...

The piezoelectric boundary integral equation (BIE) formulation is applied to analyze thin piezoelectric solids, such as thin piezoelectric films and coatings, using the boundary element method (BEM). The nearly singular integrals existing in the piezoelectric BIE as applied to thin piezoelectric solids are addressed for the 2-D case. An efficient analytical method to deal with the nearly singul...

We consider the approximation of a weakly coupled system of two singularly perturbed reaction-diffusion equations, with the finite element method. The first differential equation contains a small parameter multiplying the highest derivative, while the second does not. As a result, the first component of the solution to the system will contain boundary layers and our goal is to construct and ana...

The ground impedance matrix elements of a multiconductor overhead transmission line do not have analytical inverse Fourier transforms in the time domain. Thus, in general, the ground transient resistance matrix elements are to be determined numerically. Using the low-frequency approximation analytical expressions are available for the ground transient resistance. These expressions present howev...