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 C∗C^*-modules

We introduce a linear operator on a Hilbert $C^*$-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 $C^*$-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