1,064 research outputs found
Equivariant Matlis and the local duality
Generalizing the known results on graded rings and modules, we formulate and
prove the equivariant version of the local duality on schemes with a group
action. We also prove an equivariant analogue of Matlis duality.Comment: 32pages, corrected a typ
Element Material Exposure Experiment by EFFU
The National Space Development Agency of Japan (NASDA) is planning to perform an 'Element Material Exposure Experiment' using the Exposed Facility Flyer Unit (EFFU). This paper presents an initial design of experiments proposed for this project by our company. The EFFU is installed on the Space Flyer Unit (SFU) as a partial model of the Space Station JEM exposed facility. The SFU is scheduled to be launched by H-2 rocket in January or February of 1994, then various tests will be performed for three months, on orbit of 500 km altitude, and it will be retrieved by the U.S. Space Shuttle and returned to the ground. The mission sequence is shown
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
Two Models for RHEED Specular Spot Intensity Recovery in Laser-triggered Chemical Beam Epitaxy GaP Growth
RHEED specular spot intensity (RSSI) has been observed while growing GaP by laser-triggered chemical beam epitaxy. The intensity decreases after each laser pulse, and then it recovers the original value. We present two models in order to explain the RSSI changes. The first model takes the chemisorption velocity of metalorganics as a limiting factor in RSSI recovery speed. On the other hand, the second model considers the reaction time of gallium with phosphorus as a limiting factor. The second model properly fits the experimental data and it allows a deeper understanding of chemical reactions on GaP surface during chemical beam epitaxial growth
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
PROGNOSTIC IMPLICATIONS OF TYPE 2 MYOCARDIAL INFARCTION IN VASOSPASTIC ANGINA: A HIGH-RISK SUBGROUP
summary:The Golomb space is the set of positive integers endowed with the topology generated by the base consisting of arithmetic progressions with coprime . We prove that the Golomb space has continuum many continuous self-maps, contains a countable disjoint family of infinite closed connected subsets, the set of prime numbers is a dense metrizable subspace of , and each homeomorphism of has the following properties: , , , and for all . Here and denotes the set of prime divisors of
Response of Insulin Secretion to Small Amount of Meal on Low Carbohydrate Diet (LCD)
Diabetic nutritional therapy has been changing from Calorie Restriction (CR) to a Low Carbohydrate diet (LCD). Authors et al. have developed LCD medically and socially through the Japan LCD promotion association (JLCDPA), and proposed meal tolerance test (MTT) using LCD breakfast. For our research protocol, healthy subjects (n=8, M/F=4/4, BMI 20.5kg/m2) received 75g oral glucose tolerance test (OGTT) and MTT, and changes in blood glucose and immunoreactive insulin (IRI) were measured. LCD meal included energy 307kcal, protein 13.8g, fat 23.9g, and carbohydrate 5.7g. The results from 0-30 min in average showed: i) 75gOGTT; 87.3-124.6mg/dL, 4.9-41.4μU/mL, ii) LCD; 90.3-84.3mg/dL, 5.4-12.2μU/mL, respectively. Decreased glucose may be from enough ability to secrete insulin to a glucose stimulus. These results would become reference data for future diabetic research
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