In this paper we address the problem of determining and efficiently computing an approximation to the eigenvalues of the negative Laplacian −" on general domain Ω ⊂ R2 subject to homogeneous Dirichlet or Neumann boundary conditions. The basic idea is to look for eigenfunctions as the superposition of generalized eigenfunctions of the corresponding free space operator in the spirit of the classi...

An approach is proposed which, given a family of linearly independent functions, constructs the appropriate bi-orthogonal set so as to represent the orthogonal projector operator onto the corresponding subspace. The procedure evolves iteratively and it is endowed with the following properties: i) it yields the desired bi-orthogonal functions avoiding the need of inverse operations ii) it allows...

Recent research has shown that empathic virtual agents enable to improve human-machine interaction. Virtual agent’s expressions of empathy are generally fixed intuitively and are not evaluated. In this paper, we propose a novel approach for the expressions of empathy using complex facial expressions like superposition and masking. An evaluation study have been conducted in order to identify the...

Under certain conditions usually fulfilled in classical mechanics, the principle of conservation of linear momentum and the Newton’s third law are equivalent. However, the demonstration of such fact is usually incomplete in textbooks. We shall show here that to demonstrate the equivalence, we require the explicit use of the principle of superposition contained in the Newton’s second law. On the...

The Einstein equivalence principle (EEP) has a central role in the understanding of gravity and space-time. In its weak form, or weak equivalence principle (WEP), it directly implies equivalence between inertial and gravitational mass. Verifying this principle in a regime where the relevant properties of the test body must be described by quantum theory has profound implications. Here we report...

Cavity ring-down is becoming a widely used technique in gas phase spectroscopy. It holds promise for further important extensions, which will lead to even more frequent use. However, we have found widespread confusion in the literature about the nature of coherence effects, especially when the optical cavity constituting the ring-down cell is excited with a short coherence length laser source. ...

We “see” light only when some material detectors (dipoles) respond to the incident EM field. EM fields do not operate on each other to make themselves visible to us. Superposition of multiple fields becomes manifest only when the intrinsic properties of these dipoles allow them to respond to all the superposed fields simultaneously and thereby summing the effects of all the fields. Accordingly,...

Generating quasi-isospectral potentials by the methods of supersymmetric quantum mechanics (SUSYQM) is a simple and well-known mathematical technique [1]. Its relationships with intertwining, factorization, Darboux covariance, and inverse scattering procedures have been recently reviewed by the author [2]. Also, the author, either in collaboration or alone [3] dealt extensively with a SUSYQM pr...

A linear superposition principle of exponential traveling waves is analyzed for Hirota bilinear equations, with an aim to construct a specific sub-class of N-soliton solutions formed by linear combinations of exponential traveling waves. Applications are made for the 3 + 1 dimensional KP, Jimbo–Miwa and BKP equations, thereby presenting their particular N-wave solutions. An opposite question is...

A class of bilinear differential operators is introduced through assigning appropriate signs and used to create bilinear differential equations which generalize Hirota bilinear equations. The resulting bilinear differential equations are characterized by a special kind of Bell polynomials and the linear superposition principle is applied to the construction of their linear subspaces of solution...