We give a description of the duals linearized Reed–Solomon codes in terms obtained by taking residues Ore rational functions. Our construction shows particular that, under some assumptions on base field, class is stable duality. As byproduct our work, we develop theory setting, extending results [7].

A state-based peridynamic material model describes internal forces acting on a point in terms of the collective deformation of all the material within a neighborhood of the point. In this paper, the response of a state-based peridynamic material is investigated for a small deformation superposed on a large deformation. The appropriate notion of a small deformation restricts the relative displac...

The related fields of mobile robotics and ground vehicle localization lack a linearized theory of odometry error propagation. By contrast, the equivalent Schuler dynamics which apply to inertial guidance have been known and exploited for decades. In this paper, the general solution of linearized propagation dynamics of both systematic and random errors for vehicle odometry is developed and vali...

One of the most important problem in feature-based visual servoing is the slow sampling rate and the delay of the camera that can make the closed loop system oscillative or unstable easily. In this paper, a linearized observer that estimates the object velocity and updates the visual information with the joint sampling rate is proposed. Stability of the observer-based control system and effecti...

In this paper we consider the one-dimensional compressible Navier–Stokes system linearized about a constant steady state (Q0, 0) with Q0 > 0. We study the controllability and stabilizability of this linearized system. We establish that the linearized system is null controllable for regular initial data by an interior control acting everywhere in the velocity equation. We prove that this result ...

A three-blocks Burridge-Knopoff model is investigated. The dimension-less velocity-dependent friction force F (v) ∝ (1 + av) −1 is linearized around a = 0. In this way, the model is transformed into a six-dimensional mapping x(t n) → x(t n+1), where t n are time moments when a block starts to move or stops. Between these moments, the equations of motion are integrable. For a < 0.1, the motion i...