Based on recent results for 2-D continuous-discrete systems, this paper develops 2-D Laplace-z transform, which can be used to analyze 2-D continuous-discrete signals and system in Laplace-z hybrid domain. Current 1-D Laplace transformation and z transform can be combined into the new 2-D s-z transform. However, 2-D s-z transformation is not a simple extension of 1D transform, in 2-D case, we n...

We propose a LT (Laplace transformation) method for solving the PIDE (partial integro-differential equation) arising from the financial mathematics. An option model under a jump-diffusion process is given by a PIDE, whose non-local integral term requires huge computational costs. In this work, the PIDE is transformed into a set of complex-valued elliptic problems by taking the Laplace transform...

Laplace barriers composed of full-posts or ridges have been previously reported as a mechanism for virtual fluid confinement, but with unstable displacement (capillary fingering or fluid trapping, respectively). A new platform of ‘partial-posts’ eliminates the disadvantages of full-posts or ridges, while providing 60–80% open channel area for rapid electrowetting fluid transport (>5 cm s ). The...

Linear canonical transform is an integral transform with four parameters and has been proved to be powerful tool for optics, radar system analysis, filter design etc. Fractional Fourier transform and Fresnel transform can be seen as a special case of linear canonical transform with real parameters. Further generalization of linear canonical transform with complex parameters is also developed an...

A dual-reciprocity boundary element method is presented for the numerical solution of a class of axisymmetric elastodynamic problems. The domain integrals that arise in the integrodifferential formulation are converted to line integrals by using the dual-reciprocity method together suitably constructed interpolating functions. The second order time derivatives of the displacement in the governi...

Laser-generated thermal wave diffraction theory is presented as a perturbative Born (or Rytav) approximation in a two-dimensional spatial domain for use with tomographic image reconstruction methodologies. The ranges of validity of the pertinent twodimensional spatial-frequencylthermal wavenumber domain complex plane contours are investigated in terms of the existence af inverse spatial Laplace...

In a series of papers, we discussed the solution of Laplace’s differential equation (DE) by using fractional calculus, operational calculus in the framework of distribution theory, and Laplace transform. The solutions of Kummer’s DE, which are expressed by the confluent hypergeometric functions, are obtained with the aid of the analytic continuation (AC) of Riemann–Liouville fractional derivati...

The Laplace-Beltrami operator of a smooth Riemannian manifold is determined by the Riemannian metric. Conversely, the heat kernel constructed from the eigenvalues and eigenfunctions of the Laplace-Beltrami operator determines the Riemannian metric. This work proves the analogy on Euclidean polyhedral surfaces (triangle meshes), that the discrete heat kernel and the discrete Riemannian metric (u...

In the highly interconnected realm of Internet of Things, exchange of sensitive information raises severe privacy concerns. The Laplace mechanism – adding Laplace-distributed artificial noise to sensitive data – is one of the widely used methods of providing privacy guarantees within the framework of differential privacy. In this work, we present Lipschitz privacy, a slightly tighter version of...