Least-square refinement of structure parameters from CBED integrated intensities: application to determination of temperature factors in Y BA2CU3O7

1992 ◽  
Vol 50 (2) ◽  
pp. 1456-1457
Author(s):  
Kjersti Gjønnes ◽  
Jon Gjønnes
Keyword(s):  
Least Square ◽  
Measured Intensity ◽  
Structure Information ◽  
Accurate Temperature ◽  
Least Square Fit ◽  
Case Application ◽  
Integrated Intensities ◽  
Temperature Factors ◽  
Narrow Bands

Electron diffraction intensities can be obtained at large scattering angles (sinθ/λ ≥ 2.0), and thus structure information can be collected in regions of reciprocal space that are not accessable with other diffraction methods. LACBED intensities in this range can be utilized for determination of accurate temperature factors or for refinement of coordinates. Such high index reflections can usually be treated kinematically or as a pertubed two-beam case. Application to Y Ba2Cu3O7 shows that a least square refinememt based on integrated intensities can determine temperature factors or coordinates.LACBED patterns taken in the (00l) systematic row show an easily recognisable pattern of narrow bands from reflections in the range 15 < l < 40 (figure 1). Integrated intensities obtained from measured intensity profiles after subtraction of inelastic background (figure 2) were used in the least square fit for determination of temperature factors and refinement of z-coordinates for the Ba- and Cu-atoms.

scholarly journals Atmospheric CO<sub>2</sub>, CH<sub>4</sub>, and CO with the CRDS technique at the Izaña Global GAW station: instrumental tests, developments, and first measurement results

2019 ◽  
Vol 12 (4) ◽  
pp. 2043-2066 ◽  
Author(s):  
Angel J. Gomez-Pelaez ◽  
Ramon Ramos ◽  
Emilio Cuevas ◽  
Vanessa Gomez-Trueba ◽  
Enrique Reyes
Keyword(s):  
Flow Rate ◽  
Random Noise ◽  
Least Square ◽  
Spatial Inhomogeneity ◽  
Inlet Pressure ◽  
Processing Scheme ◽  
Linear Relationships ◽  
Least Square Fit

Abstract. At the end of 2015, a CO2/CH4/CO cavity ring-down spectrometer (CRDS) was installed at the Izaña Global Atmosphere Watch (GAW) station (Tenerife, Spain) to improve the Izaña Greenhouse Gases GAW Measurement Programme, and to guarantee the renewal of the instrumentation and the long-term maintenance of this program. We present the results of the CRDS acceptance tests, the raw data processing scheme applied, and the response functions used. Also, the calibration results, the implemented water vapor correction, the target gas injection statistics, the ambient measurements performed from December 2015 to July 2017, and their comparison with other continuous in situ measurements are described. The agreement with other in situ continuous measurements is good most of the time for CO2 and CH4, but for CO it is just outside the GAW 2 ppb objective. It seems the disagreement is not produced by significant drifts in the CRDS CO World Meteorological Organization (WMO) tertiary standards. The more relevant contributions of the present article are (1) determination of linear relationships between flow rate, CRDS inlet pressure, and CRDS outlet valve aperture; (2) determination of a slight CO2 correction that takes into account changes in the inlet pressure/flow rate (as well as its stability over the years), and attributing it to the existence of a small spatial inhomogeneity in the pressure field inside the CRDS cavity due to the gas dynamics; (3) drift rate determination for the pressure and temperature sensors located inside the CRDS cavity from the CO2 and CH4 response function drift trends; (4) the determination of the H2O correction for CO has been performed using raw spectral peak data instead of the raw CO provided by the CRDS and using a running mean to smooth random noise in a long water-droplet test (12 h) before performing the least square fit; and (5) the existence of a small H2O dependence in the CRDS flow and of a small spatial inhomogeneity in the temperature field inside the CRDS cavity are pointed out and their origin discussed.

scholarly journals The Mie representation for Mercury’s magnetic field

2021 ◽  
Vol 73 (1) ◽  
Author(s):  
S. Toepfer ◽  
Y. Narita ◽  
K. -H. Glassmeier ◽  
D. Heyner ◽  
P. Kolhey ◽  
...  
Keyword(s):  
Magnetic Field ◽  
Field Data ◽  
Least Square ◽  
Simulation Code ◽  
Magnetic Field Data ◽  
Least Square Fit ◽  
High Precision Determination ◽  
The Magnetic Field ◽  
Magnetospheric Field

AbstractThe parameterization of the magnetospheric field contribution, generated by currents flowing in the magnetosphere is of major importance for the analysis of Mercury’s internal magnetic field. Using a combination of the Gauss and the Mie representation (toroidal–poloidal decomposition) for the parameterization of the magnetic field enables the analysis of magnetic field data measured in current carrying regions in the vicinity of Mercury. In view of the BepiColombo mission, the magnetic field resulting from the plasma interaction of Mercury with the solar wind is simulated with a hybrid simulation code and the internal Gauss coefficients for the dipole, quadrupole and octupole field are reconstructed from the data, evaluated along the prospective trajectories of the Mercury Planetary Orbiter (MPO) using Capon’s method. Especially, it turns out that a high-precision determination of Mercury’s octupole field is expectable from the future analysis of the magnetic field data measured by the magnetometer on board MPO. Furthermore, magnetic field data of the MESSENGER mission are analyzed and the reconstructed internal Gauss coefficients are in reasonable agreement with the results from more conventional methods such as the least-square fit.

LEAST SQUARES DETERMINATION OF THE VELOCITY FUNCTION V=V0+kz FOR ANY SET OF TIME DEPTH DATA

Geophysics ◽  
1943 ◽  
Vol 8 (4) ◽  
pp. 356-361 ◽  
Author(s):  
J. A. Legge ◽  
J. J. Rupnik
Keyword(s):  
Least Squares ◽  
Least Square ◽  
Actual Case ◽  
Velocity Function ◽  
Depth Data ◽  
Least Square Fit ◽  
Ray Path

A method is presented by means of which a least square fit of the circular ray path plotting function to time‐depth data is obtained. An example is worked out illustrating the application of the method to an actual case.

Direct phase determination in electron crystallography: small organic molecules

1992 ◽  
Vol 50 (2) ◽  
pp. 1166-1167
Author(s):  
Douglas L. Dorset
Keyword(s):  
Organic Molecules ◽  
Data Sets ◽  
Temperature Structure ◽  
3D Analysis ◽  
Intensity Data ◽  
Electron Crystallography ◽  
Phase Determination ◽  
Measured Intensity ◽  
3D Data

The quantitative use of electron diffraction intensity data for the determination of crystal structures represents the pioneering achievement in the electron crystallography of organic molecules, an effort largely begun by B. K. Vainshtein and his co-workers. However, despite numerous representative structure analyses yielding results consistent with X-ray determination, this entire effort was viewed with considerable mistrust by many crystallographers. This was no doubt due to the rather high crystallographic R-factors reported for some structures and, more importantly, the failure to convince many skeptics that the measured intensity data were adequate for ab initio structure determinations.We have recently demonstrated the utility of these data sets for structure analyses by direct phase determination based on the probabilistic estimate of three- and four-phase structure invariant sums. Examples include the structure of diketopiperazine using Vainshtein's 3D data, a similar 3D analysis of the room temperature structure of thiourea, and a zonal determination of the urea structure, the latter also based on data collected by the Moscow group.

Rapid determination of fractal structure of bacterial assemblages in wastewater treatment: implications to process optimisation

1998 ◽  
Vol 38 (2) ◽  
pp. 9-15 ◽  
Author(s):  
J. Guan ◽  
T. D. Waite ◽  
R. Amal ◽  
H. Bustamante ◽  
R. Wukasch
Keyword(s):  
Wastewater Treatment ◽  
Fractal Structure ◽  
Structural Information ◽  
Rapid Determination ◽  
Fractal Dimensions ◽  
Structure Information ◽  
Treatment Processes ◽  
On Line ◽  
Bacterial Aggregates

A rapid method of determining the structure of aggregated particles using small angle laser light scattering is applied here to assemblages of bacteria from wastewater treatment systems. The structure information so obtained is suggestive of fractal behaviour as found by other methods. Strong dependencies are shown to exist between the fractal structure of the bacterial aggregates and the behaviour of the biosolids in zone settling and dewatering by both pressure filtration and centrifugation methods. More rapid settling and significantly higher solids contents are achievable for “looser” flocs characterised by lower fractal dimensions. The rapidity of determination of structural information and the strong dependencies of the effectiveness of a number of wastewater treatment processes on aggregate structure suggests that this method may be particularly useful as an on-line control tool.

Determination of Pyridostigmine Bromide in Presence of its Related Impurities by Four Modified Classical Least Square Based Models: A Comparative Study

2020 ◽  
Vol 17 (1) ◽  
pp. 87-94
Author(s):  
Ibrahim A. Naguib ◽  
Fatma F. Abdallah ◽  
Aml A. Emam ◽  
Eglal A. Abdelaleem
Keyword(s):  
Comparative Study ◽  
Least Squares ◽  
Orthogonal Projection ◽  
Predictive Ability ◽  
Least Square ◽  
Projection To Latent Structures ◽  
Preprocessing Method ◽  
Spectral Residual ◽  
Latent Structures

: Quantitative determination of pyridostigmine bromide in the presence of its two related substances; impurity A and impurity B was considered as a case study to construct the comparison. Introduction: Novel manipulations of the well-known classical least squares multivariate calibration model were explained in detail as a comparative analytical study in this research work. In addition to the application of plain classical least squares model, two preprocessing steps were tried, where prior to modeling with classical least squares, first derivatization and orthogonal projection to latent structures were applied to produce two novel manipulations of the classical least square-based model. Moreover, spectral residual augmented classical least squares model is included in the present comparative study. Methods: 3 factor 4 level design was implemented constructing a training set of 16 mixtures with different concentrations of the studied components. To investigate the predictive ability of the studied models; a test set consisting of 9 mixtures was constructed. Results: The key performance indicator of this comparative study was the root mean square error of prediction for the independent test set mixtures, where it was found 1.367 when classical least squares applied with no preprocessing method, 1.352 when first derivative data was implemented, 0.2100 when orthogonal projection to latent structures preprocessing method was applied and 0.2747 when spectral residual augmented classical least squares was performed. Conclusion: Coupling of classical least squares model with orthogonal projection to latent structures preprocessing method produced significant improvement of the predictive ability of it.

Array design

1968 ◽  
Vol 58 (3) ◽  
pp. 977-991
Author(s):  
Richard A. Haubrich
Keyword(s):  
High Resolution ◽  
Data Processing ◽  
Least Square ◽  
Wave Number ◽  
Array Design ◽  
Least Square Fit ◽  
The Difference ◽  
Set Of Points ◽  
Array Output

abstract Arrays of detectors placed at discrete points are often used in problems requiring high resolution in wave number for a limited number of detectors. The resolution performance of an array depends on the positions of detectors as well as the data processing of the array output. The performance can be expressed in terms of the “spectrum window”. Spectrum windows may be designed by a general least-square fit procedure. An alternate approach is to design the array to obtain the largest uniformly spaced coarray, the set of points which includes all the difference spacings of the array. Some designs obtained from the two methods are given and compared.

A least squares method for earthquake mechanism determination using S-wave data

1964 ◽  
Vol 54 (6A) ◽  
pp. 2037-2047
Author(s):  
Agustin Udias
Keyword(s):  
Least Squares ◽  
Statistical Evaluation ◽  
Least Squares Method ◽  
Numerical Approach ◽  
Focal Mechanisms ◽  
Least Square ◽  
S Wave ◽  
Double Couple ◽  
Earthquake Mechanism

abstract In this paper a numerical approach to the determination of focal mechanisms based on the observation of the polarization of the S wave at N stations is presented. Least-square methods are developed for the determination of the orientation of the single and double couple sources. The methods allow a statistical evaluation of the data and of the accuracy of the solutions.

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