347 research outputs found
THE PRODUCTIVE NATURE OF SERVICE LABOUR-A CRITICISM ON THE CONTROVERSY CONCERNING PRODUCTIVE LABOUR-
The Influence of the Hebrew Infinitive on English Biblical Translations
Article人文科学論集 17: 115-127 (1983)departmental bulletin pape
The Influence of Hebrew Pronominal Usages on the English Bible
Article人文科学論集 18: 39-60 (1984)departmental bulletin pape
Pneumatic direct-drive stepping motor for robots
A new type of pneumatic stepping motor, named pneumatic nutation motor, was developed. This motor achieves stepping positioning of 720 steps/rotation without any electrical devices or sensors mounted on the servo mechanisms. This makes the motor possible to be used under hazardous conditions such as in water and in strong magnetic fields where conventional electromagnetic motors cannot be used. The motor torque is so big that the motor can be used as a direct motor. In this report, the driving principle and design of this motor are presented. Its characteristics are analyzed experimentally and theoretically. The motors were applied to a parallel linkage mechanism with six degrees of freedom. The mechanism shows that the pneumatic nutation motors can be used as a direct servo motor for robot mechanisms.</p
Koopman operators with intrinsic observables in rigged reproducing kernel Hilbert spaces
This paper presents a novel approach for estimating the Koopman operator
defined on a reproducing kernel Hilbert space (RKHS) and its spectra. We
propose an estimation method, what we call Jet Dynamic Mode Decomposition
(JetDMD), leveraging the intrinsic structure of RKHS and the geometric notion
known as jets to enhance the estimation of the Koopman operator. This method
refines the traditional Extended Dynamic Mode Decomposition (EDMD) in accuracy,
especially in the numerical estimation of eigenvalues. This paper proves
JetDMD's superiority through explicit error bounds and convergence rate for
special positive definite kernels, offering a solid theoretical foundation for
its performance. We also delve into the spectral analysis of the Koopman
operator, proposing the notion of extended Koopman operator within a framework
of rigged Hilbert space. This notion leads to a deeper understanding of
estimated Koopman eigenfunctions and capturing them outside the original
function space. Through the theory of rigged Hilbert space, our study provides
a principled methodology to analyze the estimated spectrum and eigenfunctions
of Koopman operators, and enables eigendecomposition within a rigged RKHS. We
also propose a new effective method for reconstructing the dynamical system
from temporally-sampled trajectory data of the dynamical system with solid
theoretical guarantee. We conduct several numerical simulations using the van
der Pol oscillator, the Duffing oscillator, the H\'enon map, and the Lorenz
attractor, and illustrate the performance of JetDMD with clear numerical
computations of eigenvalues and accurate predictions of the dynamical systems.Comment: We correct several typos. We have released the code for the numerical
simulation at https://github.com/1sa014kawa/JetDM
Deep Ridgelet Transform: Voice with Koopman Operator Proves Universality of Formal Deep Networks
We identify hidden layers inside a deep neural network (DNN) with group
actions on the data domain, and formulate a formal deep network as a dual voice
transform with respect to the Koopman operator, a linear representation of the
group action. Based on the group theoretic arguments, particularly by using
Schur's lemma, we show a simple proof of the universality of DNNs.Comment: NeurReps 202
Koopman spectral analysis of skew-product dynamics on Hilbert -modules
We introduce a linear operator on a Hilbert -module for analyzing
skew-product dynamical systems. The operator is defined by composition and
multiplication. We show that it admits a decomposition in the Hilbert
-module, called eigenoperator decomposition, that generalizes the concept
of the eigenvalue decomposition. This decomposition reconstructs the Koopman
operator of the system in a manner that represents the continuous spectrum
through eigenoperators. In addition, it is related to the notions of cocycle
and Oseledets subspaces and it is useful for characterizing coherent structures
under skew-product dynamics. We present numerical applications to simple
systems on two-dimensional domains
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