The paper supplies an alternative derivation of the exact boundary conditions needed for the solution of time-harmonic acoustic scattering problems modeled by the Helmholtz equation. The main idea is to consider the exterior domain problem as an initial value problem with initial data given on the boundary of a disc or sphere. The solution of the exterior domain problem is obtained via Laplace ...

Engineers and students in communications and mathematics are confronted with transformations such as the z-Transform, the Fourier transform, or the Laplace transform. Often it is quite hard to quickly find the appropriate transform in a book or the Internet, much less to have a comprehensive overview of transformation pairs and corresponding properties. In this document I compiled a handy colle...

A constraint logic programming system for the domain of complex functions is described. The intended users of the language are scientist and engineers who often reason/compute with constraints over complex functions, such as functional equalities, diierential equations, etc. Constraints are solved by iterating several solving methods such as Laplace transformation, non-linear equation solving, ...

It is proposed a new approach for solution of the boundary problems for wide class of partial differential equations of mathematical physics, which includes the Laplace, Poisson and Helmholtz equations and parabolic equations. The approach is based on the discovered by author Local Ray Property and leads to new General Ray (GR) Method that uses the explicit analytical formulas with inverse Rado...

The so-called ZOH discretization or step-invariant transformation is not one-to-one and hence one can not recover the continuous-time system from its discretized model without further information. Here we show that it is possible to reconstruct a continuous-time rational transfer function based on discretized models at several, suitably chosen, sampling rates. The results also relate to the pro...

We present a new approach to Ad-Hoc sensor network localization from pairwise received signal strength (RSSI). Localization problem is viewed as a classification problem. We map the output of Support Vector Machine (SVM) to probability and present various schemes for estimating nodes’ locations from it. We show that application of Laplace Eigenmaps followed by an appropriate Affine Transformati...

Methods for the numerical inversion of a Laplace transform F(s) which use a special bilinear transformation of s are particularly eeective in many cases and are widely used. The main purpose of this paper is to analyze the convergence and conditioning properties of a special class of such methods, characterized by the use of Lagrange interpolation. The results derived apply both to complex and ...

A new class of singular fractional linear systems and electrical circuits is introduced. Using the Caputo definition of the fractional derivative, the Weierstrass regular pencil decomposition and the Laplace transformation, the solution to the state equation of singular fractional linear systems is derived. It is shown that every electrical circuit is a singular fractional system if it contains...

A constraint logic programming system for the domain of complex functions is described. The intended users of the language are scientist and engineers who often reason/compute with constraints over complex functions, such as functional equalities, diierential equations, etc. Constraints are solved by iterating several solving methods such as Laplace transformation, non-linear equation solving, ...

We present a method for the calculation of the a3/2 heat kernel coefficient of the heat operator trace for a partial differential operator of Laplace type on a compact Riemannian manifold with oblique boundary conditions. Using special case evaluations, restrictions are put on the general form of the coefficients, which, supplemented by conformal transformation techniques, allows the entire sme...