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Multiple Integration on Time Scales

2016
Let \({\mathbb {T}}_i\), \(i\in \{1,2,\ldots ,n\}\), be time scales. For \(i\in \{1,2,\ldots ,n\}\), let \(\sigma _i\), \(\rho _i\), and \(\varDelta _i\) denote the forward jump operator, the backward jump operator, and the delta differentiation, respectively, on \({\mathbb {T}}_i\).
Martin Bohner, Svetlin G. Georgiev
openaire   +1 more source

On Multiple Time Scales and Collapsibility

Lifetime Data Analysis
In this anniversary issue I briefly review some work on the notion of collapsibility and indicate some lingering questions.
openaire   +2 more sources

A multiple time scale minimum variance beamformer

IEEE International Conference on Acoustics Speech and Signal Processing, 1993
Expressions for mean output power and mean squared error are derived for the multiple time scale minimum variance beamformer in terms of adaptive degrees of freedom (DOF) and adaptation time scale when the same input data block is used to update weights and output.
George Henry Niezgoda, Jeffrey L. Krolik
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A multiple time scale modularized adaptive beamformer

IEEE Transactions on Signal Processing, 1994
This paper analyzes the cascaded equivalent form of the minimum variance distortionless response (MVDR) beamformer. A unique feature of the modularized MVDR (M/sup 2/VDR) beamformer is the ability to distribute adaptive degrees of freedom (DOF) among beamformer stages.
George Henry Niezgoda, Jeffrey L. Krolik
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Multiple Time Scale Systems, Time and Modeling

IFAC Proceedings Volumes, 1997
Abstract Time is analyzed from the point of view of time-varying dynamic systems and modeling. New time - light speed relationships are discovered. Comparisons with the Einstein principle and the Lorentz transformation are given. The new relationships appear inherent for time scaling of multiple time scale systems such as singularly perturbed systems.
openaire   +1 more source

Bayesian analysis of survival on multiple time scales

Statistics in Medicine, 1994
AbstractWe propose a Bayesian approach to the analysis of survival data on multiple time scales. Non‐parametric modelling of variation of rates with more than one time scale is achieved using priors which specifysmoothvariation. Computations are conveniently carried out using Gibbs sampling.
Berzuini, Carlo; id_orcid 0000-0001-6056-0489   +1 more
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Analysis of multiple time scales in a transistor amplifier

Physical Review E, 2005
It was shown previously in an experiment that when high frequency signals (on the order of 1 MHz) were injected into this low frequency amplifier, the nonlinearities of the pn junctions caused period doubling, chaos, and very low frequency oscillations (on the order of 1 Hz).
Douglas N, Armstead, Thomas L, Carroll
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On Nonlinear Control Systems with Multiple Time Scales

Journal of Dynamical and Control Systems, 2004
Consider the multiscale control system \[ \begin{aligned} \dot x_0 & =f_0 (x_0,x_1,\dots, x_n,u(t)),\\ \varepsilon_1\dot x_1 & =f_1(x_1,\dots,x_n, u(t)),\\ \dots \dots & \quad \dots \dots\\ \varepsilon_n\cdots\varepsilon_1\dot x_n & =f_n (x_n,u(t))\end{aligned} \] on the bounded time horizon \([0,1]\), where the control function \(u\) is measurable ...
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On balanced approximations for time integration of multiple time scale systems

Journal of Computational Physics, 2003
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Knoll, D. A.   +3 more
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Multiple time scales and subsystem embedding in the learning of juggling

Human Movement Science, 2004
To gain insight into the multiform dynamics and integration of remote yet pertinent subsystems into the performance of complex perceptual-motor skills, we recently conducted a series of longitudinal and cross-sectional experiments on the acquisition of 3-ball cascade juggling in which we measured, next to the ball trajectories, postural sway, eye and ...
Huys, R., Daffertshofer, A., Beek, P.J.
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