Can Computer Algebra be Liberated from its Algebraic Yoke ?

So far, the scope of computer algebra has been needlessly restricted to exact algebraic methods. Its possible extension to approximate analytical methods is discussed. The entangled roles of functional analysis and symbolic programming, especially the functional and transformational paradigms, are put forward. In the future, algebraic algorithms could constitute the core of extended symbolic manipulation systems including primitives for symbolic approximations.Comment: 8 pages, 2-column presentation, 2 figure

Computer algebra and operators

The symbolic computation of operator expansions is discussed. Some of the capabilities that prove useful when performing computer algebra computations involving operators are considered. These capabilities may be broadly divided into three areas: the algebraic manipulation of expressions from the algebra generated by operators; the algebraic manipulation of the actions of the operators upon other mathematical objects; and the development of appropriate normal forms and simplification algorithms for operators and their actions. Brief descriptions are given of the computer algebra computations that arise when working with various operators and their actions

BeamOptics: a Symbolic Platform for Modeling and the Solution of Beam Optics System

BeamOptics [1] is a Mathematica-based computing platform devoted to the following objectives; · Structured representation and manipulation of particle beam optics systems with symbolic capabilities, · Analytical and numerical modeling of beam optics system behaviors, · Solution to specific beam optical or general accelerator system problems, in algebraic form in certain cases, through customized algorithms. Taking advantage of and conforming to the highly formal and self-contained structure of Mathematica, BeamOptics provides a unique platform for developing accelerator design and analysis programs. The feature of symbolic computation and the ability to manipulate the beam optics system at the programming language level enable the user to solve or optimize his system with considerably more efficiency, rigour and insight than can be easily achieved with passive modeling or numerical simulation methods. BeamOptics is developed with continuous evolution in mind. New features and algorithms from diverse sources can be incorporated without major modification, due to its formal and generic structure. In this report, a survey is given of the basic structure and methodology of BeamOptics, as well as a demonstration of some of its more specialized applications, and possible direction of evolution

On Centroidal Dynamics and Integrability of Average Angular Velocity

In the literature on robotics and multibody dynamics, the concept of average angular velocity has received considerable attention in recent years. We address the question of whether the average angular velocity defines an orientation framethat depends only on the current robot configuration and provide a simple algebraic condition to check whether this holds. In the language of geometric mechanics, this condition corresponds to requiring the flatness of the mechanical connection associated to the robotic system. Here, however, we provide both a reinterpretation and a proof of this result accessible to readers with a background in rigid body kinematics and multibody dynamics but not necessarily acquainted with differential geometry, still providing precise links to the geometric mechanics literature. This should help spreading the algebraic condition beyond the scope of geometric mechanics,contributing to a proper utilization and understanding of the concept of average angular velocity.Comment: 8 pages, accepted for IEEE Robotics and Automation Letters (RA-L

Backpropagation training in adaptive quantum networks

We introduce a robust, error-tolerant adaptive training algorithm for generalized learning paradigms in high-dimensional superposed quantum networks, or \emph{adaptive quantum networks}. The formalized procedure applies standard backpropagation training across a coherent ensemble of discrete topological configurations of individual neural networks, each of which is formally merged into appropriate linear superposition within a predefined, decoherence-free subspace. Quantum parallelism facilitates simultaneous training and revision of the system within this coherent state space, resulting in accelerated convergence to a stable network attractor under consequent iteration of the implemented backpropagation algorithm. Parallel evolution of linear superposed networks incorporating backpropagation training provides quantitative, numerical indications for optimization of both single-neuron activation functions and optimal reconfiguration of whole-network quantum structure.Comment: Talk presented at "Quantum Structures - 2008", Gdansk, Polan

Optimal output feedback control of linear systems in presence of forcing and measurement noise

The problem of obtaining an optimal control law, which is constrained to be a linear feedback of the available measurements, for both continuous and discrete time linear systems subjected to additive white process noise and measurement noise was Necessary conditions are obtained for minimizing a quadratic performance function for both finite and infinite terminal time cases. The feedback gains are constrained to be time invariant for the infinite terminal time cases. For all the cases considered, algorithms are derived for generating sequences of feedback gain matrices which successively improve the performance function. A continuous time numerical example is included for the purpose of demonstration

Mini-Conference on Hamiltonian and Lagrangian Methods in Fluid and Plasma Physics

A mini-conference on Hamiltonian and Lagrangian methods in fluid and plasma physics was held on November 14, 2002, as part of the 44th meeting of the Division of Plasma Physics of the American Physical Society. This paper summarizes the material presented during the talks scheduled during the Mini-Conference, which was held to honor Allan Kaufman on the occasion of his 75th birthday.Comment: 14 pages, conference summar

Some numerical verification examples for plane stress elasto-viscoplasticity

This paper presents analytical, semi-analytical and numerical reference examples which can be employed for code verification of elasto-viscoplastic models under plane stress conditions. Mainly because of the overstress function the algorithms traditionally employed in elasto-plastic implementations must be rewritten to correctly impose the plane stress state along with the viscoplastic flow. The viscoplastic formulation presented here considers the strain-rate hardening effects by means of a hardening law that are assumed to have terms depending on the strain rate, which removed can represent a Voce type hardening. The proposed verification tests were employed for the numerical verification of an in-house implementation of the so-called stress-projected procedure inside the finite element method context. Although the focus of this paper is on the stressprojected algorithms the examples presented here can be employed for the verification of other algorithms intended to impose the plane stress state in viscoplasticit