After reviewing some basic properties of RT algebras, which appear to be the natural framework to deal with integrable systems in presence of an impurity, we show how any integrable system (including these possessing translation invariance) can be promoted to an integrable system with an impurity which can reflect and transmit particles. The technics allows bulk translation invariant S-matrices...

We prove that the focal set generated by the reflection of a point source off a translation invariant surface consists of two sets: a curve and a surface. The focal curve lies in the plane orthogonal to the symmetry direction containing the source, while the focal surface is translation invariant. This is done by constructing explicitly the focal set of the reflected line congruence (2-paramete...

Image copy detection is an important technology of copyright protection. This paper proposes efficient hashing method for image using 2D-2D (two-directional two-dimensional) PCA (Principal Component Analysis). The key the discovery translation invariance PCA. With property invariance, a novel model extracting rotation-invariant low-dimensional features designed by combining PCT (Polar Coordinat...

This paper concerns the problem of output consensus in nonlinear non-minimum phase systems. The main contribution of the paper is to guarantee achieving consensus in the presence of unstable zero dynamics. To achieve this goal, an output redefinition method is proposed. The new outputs of agents are functions of original outputs and internal states and defined such that the dynamics of agents a...

Image Indexing System or Invariant Associative Image Memory is an essential part of various multimedia, security and image processing systems. To create an Invariant Associative Image Memory two key problems occur: selection of effective invariant features and effective coding of the reference images. The paper gives the results of the development work related to design an Invariant Associative...

Two Lie algebraic forms of the 2-body Elliptic Calogero model are presented. Translation-invariant and dilatation-invariant discretizations of the model are obtained.

Symmetry reduces complexity. In physical systems realizing quantum computers, the highest degree of symmetry is therefore not the most desirable. A quantum computer needs to be sufficiently simple and robust to be controllable in an experiment yet complex enough to be universal. One may therefore ask the question, “how much symmetry does a quantum computer allow for?” In fact, a number of physi...

All continuous translation invariant complex-valued valuations on Lebesgue measurable functions are completely classified. And all rotation spherical also

We show how the variational principle for Gibbs States (which says that for the d{ dimensional cubic lattice, the set of translation invariant Gibbs States is the same as the set of translation invariant measures which maximize entropy minus energy and moreover that this quantity corresponds to the pressure) fails for nearest neighbor nite state statistical mechanical systems on the homogeneous...