This paper presents an example of an algebraic eigenvalue problem which can be used to motivate the study of numerical techniques for solving such problems. The problem consists of finding the axis and angle of rotation from a 3 x 3 rotation matrix and is referred to as the axis-angle problem. The problem is used to demonstrate the inverse power method for finding eigenvectors. The axis-angle p...

This paper presents a new approach for identifying and eliminating mislabeled instances in large or distributed datasets. We first partition a dataset into subsets, each of which is small enough to be processed by an induction algorithm at one time. We construct good rules from each subset, and use the good rules to evaluate the whole dataset. For a given instance Ik, two error count variables ...

In what follows by Ω we denote a bounded domain in R n with n ≥ 2, ∂Ω ∈ C 2,α and 0 < α < 1. We let Lu(x) = n i,k=1 a i,k (x) · u xix k (x) + n i=1 a i (x) · u xi (x) + a(x) · u(x) = f (x) to be a linear elliptic differential equation of second order with coefficients a ik , a i , a, f ∈ C 0,α (Ω) and a(x) ≤ 0 for all x ∈ Ω. The paper of J. Schauder " ¨ Uber lineare elliptische Differentialglei...

It is shown that smooth spatial paths for non-redundant serial robots can always be smoothly reparameterized in the vicinity of kinematic singularities with finite root multiplicity using a Puiseux series (i.e., fractional power series). This reparameterization, based on the algebraic structure of the manipulator kinematics, is formed using the -th root of the distance of the path parameter to ...

The problem of determining the inputs to the rotary axes of a 5–axis CNC machine is addressed, such that relative variations of orientation between the tool axis and surface normal are minimized subject to the constraint of maintaining a constant cutting speed with a ball-end tool. In the context of an orientable–spindle machine, the results of a prior study are directly applicable to the solut...

Qualitative spatial reasoning has seen little progress This paper attempts to explain why We provide a framework for qualitative kinematics (QK), qualitative spatial reasoning about motion We propose that no general-purpose, purely qualitative kinematics exists. We propose instead the MD/PV model of spatial reasoning, which combines the power of diagrams with qualitative representations Next we...

Knee osteoarthritis (OA) becomes a major public issue, but a strategy to prevent the disease has not established yet due to lack of an accurate method to measure an internal motion of the knee of individual patients. Therefore mechanical engineering model and a standard of evaluation of the disease is needed to improve the situation. Currently, there are a few studies to develop the model inclu...

Technische Universit at Dresden Herausgeber: Der Rektor A Generalized Inverse Iteration for Computing Simple Eigenvalues of Nonsymmetric Matrices Hubert Schwetlick and Ralf L osche IOKOMO-07-97 December 1997 Preprint-Reihe IOKOMO der DFG-Forschergruppe Identi kation und Optimierung komplexer Modelle auf der Basis analytischer Sensitivitatsberechnungen an der Technischen Universitat Dresden ...

This paper presents motion planning algorithms for underactuated systems evolving on rigid rotation and displacement groups. Motion planning is transcribed into (low-dimensional) combinatorial selection and inversekinematic problems. We present a catalog of solutions for all underactuated systems on SE(2), SO(3) and SE(2) × R classified according to their controllability properties.

We formulate the notion of parity for the periodic XXZ spin chain within the Quantum Inverse Scattering Method. We also propose an expression for the eigenvalues of the charge conjugation operator. We use these discrete symmetries to help classify low-lying Sz = 0 states in the critical regime, and we give a direct computation of the S matrix.