scholarly journals Super-Accuracy Calculation for the Half Width of a Voigt Profile

Mathematics ◽  
2022 ◽  
Vol 10 (2) ◽  
pp. 210
Author(s):  
Yihong Wang ◽  
Bin Zhou ◽  
Rong Zhao ◽  
Bubin Wang ◽  
Qi Liu ◽  
...  
Keyword(s):  
Approximation Scheme ◽  
Half Width ◽  
Simple Approximation ◽  
Quadruple Precision ◽  
Voigt Profile ◽  
Better Than

A simple approximation scheme to describe the half width of the Voigt profile as a function of the relative contributions of Gaussian and Lorentzian broadening is presented. The proposed approximation scheme is highly accurate and provides an accuracy better than 10−17 for arbitrary αL/αG ratios. In particular, the accuracy reaches an astonishing 10−34 (quadruple precision) in the domain 0 ≤ αL/αG ≤ 0.2371 ∪ αL/αG ≥ 33.8786.

scholarly journals Simple approximation scheme for the Anderson impurity Hamiltonian

1991 ◽  
Vol 83 (1) ◽  
pp. 153-153 ◽  
Author(s):  
G. Zwicknagl ◽  
V. Zevin ◽  
P. Fulde
Keyword(s):  
Approximation Scheme ◽  
Simple Approximation

Simple approximation scheme for the Anderson impurity Hamiltonian

1990 ◽  
Vol 79 (3) ◽  
pp. 365-375 ◽  
Author(s):  
G. Zwicknagl ◽  
V. Zevin ◽  
P. Fulde
Keyword(s):  
Approximation Scheme ◽  
Simple Approximation

An Examination of the Uniqueness of Gaussian and Lorentzian Profiles

1978 ◽  
Vol 32 (6) ◽  
pp. 563-566 ◽  
Author(s):  
A. Baruya ◽  
W. F. Maddams
Keyword(s):  
Curve Fitting ◽  
Half Width ◽  
Wide Range ◽  
Two Component ◽  
Lorentzian Profile ◽  
Experimental Errors ◽  
Overlapping Peaks ◽  
Practical Implications ◽  
Better Than

The conditions under which Gaussian and Lorentzian peaks may meaningfully be fitted in terms of two subcomponent bands have been examined. It is shown that good fits are possible for a wide range of relative intensities and half-widths, given that the separation of the two component peaks is limited. In the case of the Lorentzian profile, of particular interest because infrared and Raman bands approximate to this shape, fits significantly better than the limit imposed by experimental errors are obtained for separation less than about 40% of the half-width. The practical implications of these results for the curve fitting of overlapping peaks are considered; in most practical situations Gaussian and Lorentzian profiles are unique and curve fitting may be undertaken.

SIMPLE APPROXIMATION FOR QED O(α) CORRECTED FORWARD BACKWARD ASYMMETRY

1989 ◽  
Vol 04 (25) ◽  
pp. 2487-2491 ◽  
Author(s):  
TORD RIEMANN ◽  
ZBIGNIEW WAS
Keyword(s):  
Experimental Error ◽  
Analytical Formula ◽  
Photon Spectrum ◽  
Simple Approximation ◽  
Better Than

It is shown that the simple semi-analytical formula which involves a convolution of the Born asymmetry with the photon spectrum agrees to a precision better than LEP’s experimental error with exact O(α) result for the forward-backward asymmetry. The exact O(α) result differs from the convolution by 0.5×10−3 at the Z peak and by less than 3 ×10−3 close to Z peak. The result was obtained without kinematical cut-offs.

Constrained multispectrum analysis of CO2–Ar broadening at 6227 and 6348 cm–1 This article is part of a Special Issue on Spectroscopy at the University of New Brunswick in honour of Colan Linton and Ron Lees.

2009 ◽  
Vol 87 (5) ◽  
pp. 499-515 ◽  
Author(s):  
D. Chris Benner ◽  
C. E. Miller ◽  
V. Malathy Devi
Keyword(s):  
Nonlinear Least Squares ◽  
Solar Observatory ◽  
Half Width ◽  
Matrix Formalism ◽  
Line Shapes ◽  
National Solar Observatory ◽  
Voigt Profile ◽  
Line Mixing ◽  
Path Lengths ◽  
The University

We report the first extensive experimental measurements of Ar-broadened half-width and pressure-induced shift coefficients, speed dependence parameters, and line mixing coefficients for the 30013←00001 and 30012←00001 bands of 16O12C16O centered near 6227 and 6348 cm–1, respectively. These parameters were determined from 15 self-broadened and six Ar-broadened CO2 spectra recorded at room temperature with long absorption path lengths (25 to 121 m) using the McMath–Pierce Fourier transform spectrometer (FTS) at the National Solar Observatory. All 21 spectra were fit simultaneously using a multispectrum nonlinear least-squares technique. The line positions and line intensities were constrained to quantum mechanical expressions to obtain maximum accuracies in the retrieved parameters. Speed-dependent line shapes with line mixing (via the relaxation matrix formalism) were required to remove systematic errors in the fit residuals using only the Voigt profile. Remaining fit residuals were minimized by adjusting the half-width and pressure-induced shift coefficients of the overlapping 31113←01101 and 31112←01101 hot bands. We compare the Ar-broadening parameters with those recently determined for self- and air-broadening in the 30012←00001 and 30013←00001 bands and also with other Ar-broadening values from the literature, as appropriate.

scholarly journals A PTAS for Scheduling Unrelated Machines of Few Different Types

2018 ◽  
Vol 29 (04) ◽  
pp. 591-621 ◽  
Author(s):  
Jan Clemens Gehrke ◽  
Klaus Jansen ◽  
Stefan E. J. Kraft ◽  
Jakob Schikowski
Keyword(s):  
Optimization Problem ◽  
Approximation Scheme ◽  
Unrelated Machines ◽  
Polynomial Time Approximation Algorithm ◽  
Different Types ◽  
Number Formula ◽  
Maximum Completion Time ◽  
Scheduling Unrelated Machines ◽  
Better Than ◽  
Classical Optimization

Scheduling on Unrelated Machines is a classical optimization problem where [Formula: see text] jobs have to be distributed to [Formula: see text] machines. Each of the jobs [Formula: see text] has on machine [Formula: see text] a processing time [Formula: see text]. The goal is to minimize the makespan, i.e., the maximum completion time of the longest-running machine. Unless [Formula: see text], this problem does not allow for a polynomial-time approximation algorithm with a ratio better than [Formula: see text]. A natural scenario is however that many machines are of the same type, like a CPU and GPU cluster: for each of the [Formula: see text] machine types, the machines [Formula: see text] of the same type [Formula: see text] satisfy [Formula: see text] for all jobs [Formula: see text]. For the case where the number [Formula: see text] of machine types is constant, this paper presents an approximation scheme, i.e., an algorithm of approximation ratio [Formula: see text] for [Formula: see text], with an improved running time only single exponential in [Formula: see text].

Facility location with adjacent units: a simple approximation scheme

2013 ◽  
Vol 5 (3) ◽  
pp. 214
Author(s):  
Shailesh S. Kulkarni ◽  
Hakan Tarakci ◽  
Kwabena G. Boakye ◽  
Subramaniam Ponnaiyan ◽  
Matthew Lasuzzo
Keyword(s):  
Facility Location ◽  
Approximation Scheme ◽  
Simple Approximation

Time and Latitude in South Africa

1972 ◽  
Vol 1 ◽  
pp. 27-38
Author(s):  
J. Hers
Keyword(s):  
South Africa ◽  
Cape Town ◽  
Astronomical Observations ◽  
Royal Observatory ◽  
The Republic ◽  
Astronomical Determination ◽  
Limited Accuracy ◽  
Better Than

In South Africa the modern outlook towards time may be said to have started in 1948. Both the two major observatories, The Royal Observatory in Cape Town and the Union Observatory (now known as the Republic Observatory) in Johannesburg had, of course, been involved in the astronomical determination of time almost from their inception, and the Johannesburg Observatory has been responsible for the official time of South Africa since 1908. However the pendulum clocks then in use could not be relied on to provide an accuracy better than about 1/10 second, which was of the same order as that of the astronomical observations. It is doubtful if much use was made of even this limited accuracy outside the two observatories, and although there may – occasionally have been a demand for more accurate time, it was certainly not voiced.

Localization of immunolabels by electron microscopy and image averaging

1983 ◽  
Vol 41 ◽  
pp. 282-283
Author(s):  
J. Frank ◽  
P.-Y. Sizaret ◽  
A. Verschoor ◽  
J. Lamy
Keyword(s):  
Electron Microscopy ◽  
Single Particle ◽  
Attachment Site ◽  
Uranyl Acetate ◽  
Limulus Polyphemus ◽  
Resolution Limit ◽  
Electron Microscopic ◽  
Image Averaging ◽  
Top View ◽  
Better Than

The accuracy with which the attachment site of immunolabels bound to macromolecules may be localized in electron microscopic images can be considerably improved by using single particle averaging. The example studied in this work showed that the accuracy may be better than the resolution limit imposed by negative staining (∽2nm).The structure used for this demonstration was a halfmolecule of Limulus polyphemus (LP) hemocyanin, consisting of 24 subunits grouped into four hexamers. The top view of this structure was previously studied by image averaging and correspondence analysis. It was found to vary according to the flip or flop position of the molecule, and to the stain imbalance between diagonally opposed hexamers (“rocking effect”). These findings have recently been incorporated into a model of the full 8 × 6 molecule.LP hemocyanin contains eight different polypeptides, and antibodies specific for one, LP II, were used. Uranyl acetate was used as stain. A total of 58 molecule images (29 unlabelled, 29 labelled with antl-LPII Fab) showing the top view were digitized in the microdensitometer with a sampling distance of 50μ corresponding to 6.25nm.

Closing the GAP—A 5Å Scanning Microscope

1969 ◽  
Vol 27 ◽  
pp. 6-7
Author(s):  
A. V. Crewe
Keyword(s):  
Normal Form ◽  
The Other ◽  
Resolving Power ◽  
Scanning Microscope ◽  
Conventional Microscope ◽  
Other Hand ◽  
Closing The Gap ◽  
Thermal Sources ◽  
Better Than ◽  
Transmission Microscope

We have become accustomed to differentiating between the scanning microscope and the conventional transmission microscope according to the resolving power which the two instruments offer. The conventional microscope is capable of a point resolution of a few angstroms and line resolutions of periodic objects of about 1Å. On the other hand, the scanning microscope, in its normal form, is not ordinarily capable of a point resolution better than 100Å. Upon examining reasons for the 100Å limitation, it becomes clear that this is based more on tradition than reason, and in particular, it is a condition imposed upon the microscope by adherence to thermal sources of electrons.

Sign in / Sign up

Export Citation Format

Share Document