− In the paper new methods of fault localisation and identification in linear electronic circuits (two-port or multiport type) based on bilinear transformations in multidimensional spaces are presented. The novelty of these methods lies in transferring family of identification loci from a plane to multidimensional spaces. It implies greater distances between the loci and, in consequence, better...

We show that the Painlevé equations PIII −PV I can be derived (in a unified way) from a periodic sequence of Darboux transformations for a Schrödinger problem with quadratic eigenvalue dependency. The general problem naturally divides into three different branches, each described by an infinite chain of equations. The Painlevé equations are obtained by closing the chain periodically at the lowe...

Time-frequency representations transform a one-dimensional function into a two-dimensional function in the phase-space of time and frequency. The transformation to accomplish is a nonlinear transformation and there are an infinite number of such transformations. We obtain the governing differential equation for any two-dimensional bilinear phase-space function for the case when the governing eq...

We show that eigenvalues of the family of Baxter Q-operators for supersymmetric integrable spin chains constructed with the gl(K|M)-invariant R-matrix obey the Hirota bilinear difference equation. The nested Bethe ansatz for super spin chains, with any choice of simple root system, is then treated as a discrete dynamical system for zeros of polynomial solutions to the Hirota equation. Our basic...

We have developed an algebraic framework for the study of recursion. For immediate linear recursion, a Horn clause is represented by a relational algebra operator. We show that the set of all such operators forms a closed semiring. In this formalism, query answering corresponds to solving a linear equation. For the first time, we are able to have the query answer expressed in an explicit algebr...

In this article, we give a complete characterization of all the unitary transformations that can be synthesized in a given time for a system of coupled spin-1/2 in presence of general time varying coupling tensor. Our treatment is quite general and our results help to characterize the reachable set at all times for a class of bilinear control systems with time varying drift and unbounded contro...

Let 800(1, n) denote the connected component of the group of linear transformations of IRn+l preserving the bilinear form Abstract Using techniques of Lie groups and ergodic theory, it can be shown that in a compact manifold of constant negative curvature, the closure of a totally geodesic, complete (immersed) submanifold of dimension atleast 2 is a totally geodesicimmersed submanifold. The mai...

Nonlinear input-affine systems in quasi-polynomial (QP) and Lotka-Volterra (LV) forms are investigated in this paper. It is shown that both the global stability analysis with an entropy-like Lyapunov function candidate and the local quadratic stability region determination can be performed by solving linear matrix inequalities (LMIs). The invariance transformations preserving the form of the de...

Novel atom-based molecular descriptors based on a bilinear map similar to use defined in linear algebra are presented. These molecular descriptors, called “local (atom, group and atom-type) and total (global) bilinear indices”, are proposed here as a new molecular parametrization easily calculated from the 2D molecular information. The proposed non-stochastic and stochastic molecular fingerprin...