scholarly journals Pixel Approximation Errors in Common Watershed Algorithms

2009 ◽  
pp. 193-202 ◽  
Author(s):  
Hans Meine ◽  
Peer Stelldinger ◽  
Ullrich Köthe
Keyword(s):  
Approximation Errors

scholarly journals Two-stage segment linearization as part of the thermocouple measurement chain

2021 ◽  
Vol 54 (1-2) ◽  
pp. 141-151
Author(s):  
Dragan Živanović ◽  
Milan Simić
Keyword(s):  
Transfer Functions ◽  
Approximation Error ◽  
Linearization Method ◽  
Linear Segment ◽  
Virtual Instrumentation ◽  
Memory Consumption ◽  
Thermocouple Measurement ◽  
Two Stage ◽  
Approximation Errors ◽  
Input Range

An implementation of a two-stage piece-wise linearization method for reduction of the thermocouple approximation error is presented in the paper. First, the whole thermocouple measurement chain of a transducer is described, and possible error is analysed to define the required level of accuracy for linearization of the transfer characteristics. Evaluation of linearization functions and analysis of approximation errors are performed by the virtual instrumentation software package LabVIEW. The method is appropriate for thermocouples and other sensors where nonlinearity varies a lot over the range of input values. The basic principle of this method is to first transform the abscissa of the transfer function by a linear segment look-up table in such a way that significantly nonlinear parts of the input range are expanded before a standard piece-wise linearization. In this way, applying equal-segment linearization two times has a similar effect to non-equal-segment linearization. For a given examples of the thermocouple transfer functions, the suggested method provides significantly better reduction of the approximation error, than the standard segment linearization, with equal memory consumption for look-up tables. The simple software implementation of this two-stage linearization method allows it to be applied in low calculation power microcontroller measurement transducers, as a replacement of the standard piece-wise linear approximation method.

scholarly journals Measuring Multijet Structure of Hadronic Energy Flow or, What is a jet?

1997 ◽  
Vol 12 (30) ◽  
pp. 5411-5529 ◽  
Author(s):  
Fyodor V. Tkachov
Keyword(s):  
Energy Flow ◽  
Mass Spectra ◽  
Analytical Control ◽  
Final States ◽  
C Algebra ◽  
Approximation Errors ◽  
Basic Class ◽  
Jet Algorithms ◽  
Hadronic Energy ◽  
Optimal Recombination

Ambiguities of jet algorithms are reinterpreted as instability wrt small variations of input. Optimal stability occurs for observables possessing property of calorimetric continuity (C-continuity) predetermined by kinematical structure of calorimetric detectors. The so-called C-correlators form a basic class of such observables and fit naturally into QFT framework, allowing systematic theoretical studies. A few rules generate other C-continuous observables. The resulting C-algebra correctly quantifies any feature of multijet structure such as the "number of jets" and mass spectra of "multijet substates." The new observables are physically equivalent to traditional ones but can be computed from final states bypassing jet algorithms which reemerge as a tool of approximate computation of C-observables from data with all ambiguities under analytical control and an optimal recombination criterion minimizing approximation errors.

A Uniformly Stable Nonconforming FEM Based on Weighted Interior Penalties for Darcy-Stokes-Brinkman Equations

2017 ◽  
Vol 10 (1) ◽  
pp. 22-43 ◽  
Author(s):  
Peiqi Huang ◽  
Zhilin Li
Keyword(s):  
Finite Element ◽  
Mixed Finite Element ◽  
Discontinuous Coefficients ◽  
Brinkman Equation ◽  
Optimal Error Estimates ◽  
Discrete Problem ◽  
Brinkman Equations ◽  
Approximation Errors ◽  
Interior Penalties ◽  
Uniformly Stable

AbstractA nonconforming rectangular finite element method is proposed to solve a fluid structure interaction problem characterized by the Darcy-Stokes-Brinkman Equation with discontinuous coefficients across the interface of different structures. A uniformly stable mixed finite element together with Nitsche-type matching conditions that automatically adapt to the coupling of different sub-problem combinations are utilized in the discrete algorithm. Compared with other finite element methods in the literature, the new method has some distinguished advantages and features. The Boland-Nicolaides trick is used in proving the inf-sup condition for the multidomain discrete problem. Optimal error estimates are derived for the coupled problem by analyzing the approximation errors and the consistency errors. Numerical examples are also provided to confirm the theoretical results.

A New Approach to G1 Biarc Approximations for Making Smooth, Accurate, and Non-Gouged Profile Features Using CNC Contouring

2006 ◽  
Author(s):  
Zezhong C. Chen ◽  
Xujing Yang
Keyword(s):  
Manufacturing Industry ◽  
Cutting Tool ◽  
Minimum Size ◽  
Free Form ◽  
New Approach ◽  
B Spline ◽  
Tool Paths ◽  
The Past ◽  
Approximation Errors ◽  
The Individual

Extensive research on G1 biarcs fitting to free-form curves (i.e., Bezier, B-spline, and NURBS curves) has been conducted in the past decades for various purposes, including CNC contouring to make smooth, accurate profile features such as pockets, islands, and sides. However, all the proposed approaches only focused on the approximation errors and the biarc number, not on the radius of the individual fitting arc; so it could be smaller than the cutting tool, which would cause gouging during machining. This work, based on the tool radius pre-determined by the minimum size of the concavities of the design profile, proposes a new approach to approximating the profile with a G1 biarc curve in order to make smooth, accurate, and non-gouged profile features using CNC contouring. The significant new contribution of this work is a new mechanism that ensures all the concave arcs of the fitting curve are larger than the pre-determined tool and the fitting errors meet the specified tolerance. This approach can promote the use of G1 biarc tool paths in the manufacturing industry to make high precision profile features.

scholarly journals Approximation of positive operators by analytic vectors

2020 ◽  
Vol 12 (2) ◽  
pp. 412-418
Author(s):  
M.I. Dmytryshyn
Keyword(s):  
Banach Space ◽  
Positive Operator ◽  
Invariant Subspaces ◽  
Positive Operators ◽  
Interpolation Spaces ◽  
Jackson Type ◽  
Normalization Factor ◽  
Approximation Spaces ◽  
Similar Role ◽  
Approximation Errors

We give the estimates of approximation errors while approximating of a positive operator $A$ in a Banach space by analytic vectors. Our main results are formulated in the form of Bernstein and Jackson type inequalities with explicitly calculated constants. We consider the classes of invariant subspaces ${\mathcal E}_{q,p}^{\nu,\alpha}(A)$ of analytic vectors of $A$ and the special scale of approximation spaces $\mathcal {B}_{q,p,\tau}^{s,\alpha}(A)$ associated with the complex degrees of positive operator. The approximation spaces are determined by $E$-functional, that plays a similar role as the module of smoothness. We show that the approximation spaces can be considered as interpolation spaces generated by $K$-method of real interpolation. The constants in the Bernstein and Jackson type inequalities are expressed using the normalization factor.

scholarly journals Approximation errors in nonstationary inverse problems

2007 ◽  
Vol 1 (1) ◽  
pp. 77-93 ◽  
Author(s):  
Janne M.J. Huttunen ◽  
◽  
J. P. Kaipio ◽  
Keyword(s):  
Inverse Problems ◽  
Approximation Errors

A FAT-based adaptive controller for robot manipulators without regressor matrix: theory and experiments

Robotica ◽  
2005 ◽  
Vol 24 (2) ◽  
pp. 205-210 ◽  
Author(s):  
An-Chyau Huang ◽  
Shi-Chang Wu ◽  
Wen-Fa Ting
Keyword(s):  
Function Approximation ◽  
Matrix Theory ◽  
Robot Manipulator ◽  
Nonlinear Differential Equations ◽  
Lyapunov Stability Theory ◽  
Adaptive Controller ◽  
Approximation Technique ◽  
Control Scheme ◽  
Approximation Errors ◽  
Theory And Experiments

In this paper, an adaptive control scheme is proposed for an n-link rigid robot manipulator without using the regressor. The robot is firstly modeled as a set of second-order nonlinear differential equations with the assumption that all of the matrices in that model are unavailable. Since these matrices are time-varying and their variation bounds are not given, traditional adaptive or robust designs do not apply. The function approximation technique (FAT) is used here to represent uncertainties in some finite linear combinations of orthonormal basis. The dynamics of the output tracking can thus be proved to be a stable first order filter driven by function approximation errors. Using the Lyapunov stability theory, a set of update laws is derived to give closed loop stability with proper tracking performance. Experiments are also performed on a 2-D robot to test the efficacy of the proposed scheme.

Optimisation of a Polarisation Nephelometer

2021 ◽  
pp. 87-95
Author(s):  
Victor G. Oshlakov ◽  
Anatoly P. Shcherbakov
Keyword(s):  
Personal Computer ◽  
Position Control ◽  
Control Unit ◽  
Numerical Control ◽  
Radiation Beam ◽  
Drive Control ◽  
Control Units ◽  
Smooth Motion ◽  
Approximation Errors ◽  
Scattering Volume

An analysis of the influence caused by polarization nephelometer parameters on the scattering matrix measurement accuracy in a non-isotropic medium is presented. The approximation errors in the actual scattering volume and radiation beam by an elementary scattering volume and an elementary radiation beam are considered. A formula for calculating the nephelometer base is proposed. It is shown that requirements to an irradiation source of a polarizing nephelometer, i.e. mono-chromaticity and high radiation intensity and directivity in a wide spectral range can be satisfied by a set of high brightness LEDs with a radiating (self-luminous) small size body. A 5-wavelength monochromatic irradiation source, with an emission flux of (0.15–0.6) W required for a polarization nephelometer, is described. The design of small-sized polarizing phase control units is shown. An electronic circuit of a radiator control unit based on an AVR-Atmega 8-bit microcontroller with feedback and drive control realized by means of an incremental angular motion sensor and a software PID controller is presented. Precise and smooth motion of the radiator is ensured by standard servo-driven numerical control mathematics and the use of precision gears. The system allows both autonomous adjustment of the radiator’s reference positions and adjustment by means of commands from a personal computer. Both the computer and microcontroller programs were developed with the use of free software, making it possible to transfer the programs to Windows‑7(10), Linux and embedded Linux operating systems. Communication between the radiator’s position control system and the personal computer is realised by means of a standard noise immune USB-RS485 interface.

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