It is proved that a discrete delta function introduced by P. Smereka [10] gives a second-order accurate quadrature rule for surface integrals using values on a regular background grid. The delta function is found using a technique of A. Mayo [7]. It can be expressed naturally using a level set function.

We study second to fourth order numerical methods to a type of delta function integrals in one to three dimensions. These delta function integrals arise from recent efficient level set methods for computing the multivalued solutions of nonlinear PDEs. We show that the natural quadrature approach with usual discrete delta functions and support size formulas to the two dimensional delta function ...

Recently, it was shown that a large class of non-bandlimited signals that have a finite rate of innovation, such as streams of Diracs, non-uniform splines and piecewise polynomials, can be perfectly reconstructed from a uniform set of samples taken at the rate of innovation [1]. While this is true in the noiseless case, in the presence of noise the finite rate of innovation property is lost and...

Recent development in sampling theory now allows the sampling and reconstruction of certain non-bandlimited functions on the sphere, namely a sum of weighted Diracs. Because the signal acquired in diffusion Magnetic Resonance Imaging (dMRI) can be modeled as the convolution between a sampling kernel and two dimensional Diracs defined on the sphere, these advances have great potential in dMRI. I...

The Dirac delta function has solid roots in 19th century work in Fourier analysis by Cauchy and others, anticipating Dirac’s discovery by over a century.

a question of the existence of delta-convergent sequences that vanish at the support of the limit Dirac delta function and gave an example of sequences of this type. It is a sequence of even functions that don't have a compact support. Motivated by the question in this paper we develop some results concerning delta sequences and show more examples of delta sequences of the type with or without ...

Recently, a novel method for image scrambling (and unscrambling) has been proposed. This method is based on a linear transformation involving the Kroneker-delta function. However, while quite interesting, the way it was introduced, leaves some open issues concerning its actual usability for information hiding. Therefore, in this paper, we extend the original proposal and show how it can be used...

We consider a wave equation with damping coefficient ∂ 2 u ∂t 2 (x, t) = ∂ 2 u ∂x 2 (x, t) + p1(x) ∂u ∂t (x, t) + p2(x) ∂u ∂x (x, t), 0 < x < 1, −T < t < T , u(x, 0) = 0, ∂u ∂t (x, 0) = δ(x), 0 ≤ x ≤ 1, ∂u ∂x (0, t) = ∂u ∂x (1, t) = 0, −T ≤ t ≤ T where T ≥ 2, the complex-valued functions p1, p2 ∈ C 1 [0, 1] and δ(x) is the Dirac delta function. We discuss an inverse problem of determining simul...