Quadrature of hyperbola. [I.]

GPR Objects Hyperbola Region Feature Extraction

The shape and feature extraction in Ground Penetrating Radar (GPR) data is the most addressed application in present underground object identification technique. The problem of automatically detecting the shape and feature in GPR data is in analysing and fitting the hyperbola features from GPR data objects. To address these, we propose a hyperbole fitting method to extract the shape and feature...

Eberlein Measure and Mechanical Quadrature Formulae. I: Basic Theory*

A uniform theory of numerical approximation of multiple integrals of arbitrary multiplicity is a long felt need of applied mathematics. In the absence of something better, the Monte Carlo method is the one most commonly used now (see [6] and [7]). For the integration of functions of one variable, for which purpose useful classical formulae exist, the error estimates are unsatisfactory inasmuch ...

TRANSITION BEHAVIOR OF k-SURFACE: FROM HYPERBOLA TO ELLIPSE

The transition behavior of the k-surface of a lossy anisotropic indefinite slab is investigated. It is found that, if the material loss is taken into account, the k-surface does not show a sudden change from hyperbola to the ellipse when one principle element of the permittivity tensor changes from negative to positive. In fact, after introducing a small material loss, the shape of the k-surfac...

Hyperbola of external debt: A Lesson from the Asian Crisis

The critical hyperbola for a Hamiltonian elliptic system with weights

In this paper we look for existence results for nontrivial solutions to the system, ⎧ ⎪⎪⎨ ⎪⎪⎩ − u = v p |x |α in , − v = u q |x |β in , with Dirichlet boundary conditions, u = v = 0 on ∂ and α, β < N . We find the existence of a critical hyperbola in the (p, q) plane (depending on α, β and N ) below which there exists nontrivial solutions. For the proof we use a variational argument (a linking ...