Fourth-order Polynomial Fitting Research Articles

Shortwave and longwave components of the surface radiation budget measured at the Thule High Arctic Atmospheric Observatory, Northern Greenland

Abstract. The Arctic climate is influenced by the interaction of shortwave (SW) and longwave (LW) radiation with the atmosphere and the surface. The comprehensive evolution of the Surface Radiative Fluxes (SRF) on different time scales is of paramount importance to understanding the complex mechanisms governing the Arctic climate. However, only a few sites located in the Arctic region provide long-term time series of SRF allowing for capturing of the seasonality of atmospheric and surface parameters and for carrying out validation of satellite products and/or reanalyses. This paper presents the daily and monthly SRF record collected at the Thule High Arctic Atmospheric Observatory (THAAO, 76.5∘ N, 68.8∘ W), in North-Western Greenland. The downwelling components of the SW (DSI) and the LW (DLI) irradiances have been measured at THAAO since 2009, whereas the collection of the upwelling SW (USI) and LW (ULI) irradiance was started in 2016, together with additional measurements, such as meteorological parameters and column water vapour. The datasets of DSI (Meloni et al., 2022a; https://doi.org/10.13127/thaao/dsi), USI (Meloni et al., 2022b; https://doi.org/10.13127/thaao/usi), DLI (Meloni et al., 2022c; https://doi.org/10.13127/thaao/dli), ULI (Meloni et al., 2022d; https://doi.org/10.13127/thaao/uli), and near-surface air temperature (Muscari et al., 2018; https://doi.org/10.13127/thaao/met), can be accessed through the THAAO web site (https://www.thuleatmos-it.it/data, last access: 16 January 2024). The DSI is absent (solar zenith angle ≥90∘) from 29 October to 13 February, assuming maxima in June (monthly mean of 277.0 Wm−2), when it is about half of the total incoming irradiance. The USI maximum occurs in May (132.4 Wm−2) owing to the combination of moderately high DSI values and high albedo. The shortwave surface albedo (A) assumes an average of 0.16 during summer, when the surface is free of snow. Differently, during months of snow-covered surface, when solar radiation allows A to be estimated, its values are greater than 0.6. A large interannual variability is observed in May and September, months characterized by rapidly changing surface conditions, having a link with air temperature anomalies. The DLI and ULI maxima occur in July and August, and the minima in February and March. ULI is always larger than DLI and shows a wider annual cycle. ULI is well described by a fourth-order polynomial fit to the air temperature (R2>0.99 for monthly data and R2>0.97 for daily data). The Surface Radiation Budget (SRB) is positive from April to August, when absorption of solar radiation exceeds the infrared net cooling, with a maximum value of 153.2 Wm−2 in June. From November to February, during the polar night, the LW net flux varies between −34.5 and −43.0 Wm−2. In March and September, the negative LW net flux overcomes the positive SW contribution, producing a negative SRB. The THAAO measurements show clear evidence of the influence of several regional weather/climate events, that appear strongly linked with SRF anomalies. These anomalies were found, for example, during summer 2012, when a large ice melting event took place over Greenland, and during winter 2019–2020, which was extraordinarily cold in the Arctic region.

Inverse algorithm for extraction of multiple parameters using analytical model of eddy current response

Eddy current (EC) technology is commonly used for detecting flaws, measuring geometric parameters, or determining properties of conducting materials. However, the measurement of a particular parameter can become more challenging if multiple influential parameters vary simultaneously. In particular, eddy current-based measurement of separation (gap) between a pressure tube (PT) and a calandria tube (CT) in the fuel channels of CANDU® reactors is made more difficult by variations in PT wall thickness, resistivity, and probe lift-off. An analytical model of the EC response to changes in PT–CT gap has been developed by approximating the geometry of the PT within the larger diameter CT as a pair of concentric tubes, where gap is varied by changing the CT radius. In this article, this model is used in combination with an error minimization algorithm to construct an inverse algorithm for the extraction of PT–CT gap, PT resistivity (ρ), and PT wall thickness (WT) from measured multi-frequency eddy current signals. Application of a linear regression tool in MATLAB, with fourth-order polynomial fitting of modeled data with varying ρ and WT as a function of PT–CT gap, is used to obtain coefficients that depend on ρ and WT. Output of multidimensional fitting of these coefficients is scaled and rotated to calibration data. Finally, implementation of an error minimization algorithm in MATLAB is used to produce estimates of multiple target parameters from experimental data. Simultaneous extraction of either one, two, or three parameters is examined, using experimental data obtained at frequencies used for in-reactor inspection of 4.2, 8, and 16 kHz, or just two frequencies of 4.2 and 8 kHz. Under full gap variation conditions, the inverse algorithm predicts gap to within 0.1 mm at gaps between 0 and 9 mm and to within 0.4 mm at gaps between 9 and 18 mm. PT resistivity is predicted to within 1 μΩ cm (2% relative error) and PT wall thickness within 0.03 mm (1% relative error) when each is the only extracted parameter. An excellent agreement between actual and predicted values of gap demonstrates the potential of the inverse algorithm for application to in-reactor gap measurement and simultaneous extraction of either PT wall thickness or resistivity when the other parameter is known. The extraction of PT resistivity may be particularly useful, as this parameter cannot otherwise currently be measured in-reactor.

Optical Simulation and Experimental Assessment with Time-Walk Correction of TOF-PET Detectors with Multi-Ended Readouts.

As a commonly used solution, the multi-ended readout can measure the depth-of-interaction (DOI) for positron emission tomography (PET) detectors. In the present study, the effects of the multi-ended readout design were investigated using the leading-edge discriminator (LED) triggers on the timing performance of time-of-flight (TOF) PET detectors. At the very first, the photon transmission model of the four detectors, namely, single-ended readout, dual-ended readout, side dual-ended readout, and triple-ended readout, was established in Tracepro. The optical simulation revealed that the light output of the multi-ended readout was higher. Meanwhile, the readout circuit could be triggered earlier. Especially, in the triple-ended readout, the light output at 0.5 ns was observed to be nearly twice that of the single-ended readout after the first scintillating photon was generated. Subsequently, a reference detector was applied to test the multi-ended readout detectors that were constructed from a 6 × 6 × 25 mm3 LYSO crystal. Each module is composed of a crystal coupled with multiple SiPMs. Accordingly, its timing performance was improved by approximately 10% after the compensation of fourth-order polynomial fitting. Finally, the compensated full-width-at-half-maximum (FWHM) coincidence timing resolutions (CTR) of the dual-ended readout, side dual-ended readout, and triple-ended readout were 216.9 ps, 231.0 ps, and 203.6 ps, respectively.

Shear test on damage evolution of brick masonry based on acoustic emission technique

Shear is the dominant mode of masonry structural failure. A shear test of brick masonry specimen based on acoustic emission (AE) monitoring was performed in this study to assess the damage state of masonry structure reliably. AE parameters and rate-process analysis were used to analyze the damage evolution of brick masonry in shear failure from qualitative and quantitative perspectives. Results showed that variation characteristics of different AE parameters of multiple channels are basically the same throughout the test process. The specimen enters the rapid failure stage when the relative stress reaches 80%. The fourth-order polynomial fitting model between the number of AE events and their corresponding was proposed in this study for quantitative assessment. Analysis of the AE rate-process based on the fourth-order polynomial demonstrated that AE probability density f(V) and damage index D can quantitatively reflect the damage degree of brick masonry in real time.

Artificial Intelligence Approaches to Estimate the Transport Energy Demand in Turkey

In this study, eight parameters are selected and their historical data are collected to predict the future of the energy demand of Turkey. The initial eight parameters were the gross domestic product (GDP) of Turkey, average annual US crude oil price (COP), inflation for Turkey in percentages (INF), the population of Turkey, total vehicle travel in kilometers for Turkey, total amount of goods transported on motorways, employment for Turkey, and trade of Turkey. However, after these eight parameters data are analyzed using Pearson and Spearman correlation methods, it is found out that five of these parameters are highly correlated. The remaining three parameters are the GDP of Turkey, COP, and INF for Turkey. Afterward, five separate scenarios are developed to forecast the future of the energy demand of Turkey. The first two scenarios involve the third- and fourth-order polynomial fitting, the third and fourth scenarios employ static and recurrent neural networks, and the fifth scenario utilizes autoregressive models to predict the future energy demand of Turkey. The efficient hybridization of the seagull optimization and very optimistic method of minimization metaheuristic algorithms is carried out to achieve the polynomial fitting of the data. The optimization performance of the hybrid algorithm is assessed by applying the algorithm on benchmark optimization problems and comparing the results with that of some other metaheuristic optimizers. Moreover, it is seen that the forecasts of the first scenario agree well with the Ministry of the Energy and Natural Resources estimates.

A Density Clustering Algorithm for Simultaneous Modulation Format Identification and OSNR Estimation

In this work, we propose a combined method to implement both modulation format identification (MFI) and optical signal-to-noise ratio (OSNR) estimation, a method based on density-based spatial clustering of applications with a noise (DBSCAN) algorithm. The proposed method can automatically extract the cluster number and density information of samples. The cluster number can be used for MFI and the density information combined with a fourth-order polynomial fitting can correctly estimate OSNR. We verify the feasibility of the method through simulation and conceptual proof experiments. The results show that the MFI can achieve 100% accuracy when the OSNR values are higher than the 7% forward error correction (FEC) thresholds for five commonly used modulation formats (MFs) like polarization division multiplexing (PDM)-QPSK, PDM-8PSK, PDM-16QAM, PDM-32QAM, and PDM-64QAM. Mean absolute OSNR estimation errors are not higher than 1 dB for different signals. There is no additional hardware required, so the proposed method has the ability to be integrated into existing optical performance monitoring systems without burden. Furthermore, the proposed method has the potential to be used in bit-error ratio (BER) calculation, linear, or nonlinear impairments monitoring. We believe that our multifunctional and simple method would be favorable to a future elastic optical network (EON).

Flow quantification dependency on background phase correction techniques in 4D-flow MRI.

To analyze the dependence of flow volume measurements on 3D cine phase-contrast MRI (4D-flow MRI) background phase correction. In 31 subjects scanned on a 1.5T MRI scanner, flow volume measurements at 4 vessels were made using phantom corrected 2D phase contrast and 4D flow with background phase correction performed by linear, second, third, and fourth-order polynomial fitting to static tissue. Variations in the amount and distribution of static tissue were made to investigate the influence on flow volume measurements. Bland Altman comparison of 2D phase-contrast and 4D-flow measurements showed low bias (2.3%-4.8%) and relatively large limits of agreement (13.5%-17.6%). Approximately half of this was attributable to sequence and physiological differences between the 2 scan sequences, demonstrated by smaller limits of agreement (5.3%-10.0%) when comparing 4D-flow measurements with differing background phase corrections. Using only 20% of available static tissue points for polynomial fitting resulted in only 1% difference in flow volume measurements. Using asymmetrically distributed static tissue or including nonstatic tissue for polynomial fitting yielded highly variable differences in flow volume measurements, which became more variable with increased polynomial order. Completely asymmetric static tissue selection resulted in high deviations in flow volume measurements (mean > 7%, max = 345%). Comparisons between 2D phase-contrast and 4D-flow volume measurements should consider influences from sequence and physiological differences. A subset of static tissue points may be used with low impact on flow measurements, but should avoid the inclusion of nonstatic tissue and avoid asymmetric distribution. Higher-order polynomial fits are more susceptible to inaccurate static tissue selection.

Programmable flow rate scanner for evaluating detector sensitivity regime

In order to expedite characterization of on-line detection systems, we have developed a flow rate scanner comprising a pump, an inexpensive single-board computer, and an associated Python program. The program controls the pump, triggers the detector, acquires raw data, filters/smooths the data, calculates the first derivative of the temporal signal trend, and determines the sensitivity regime threshold in real time. The slope of the curve relating the detector response with the sample flow rate is used to determine the sensitivity regime for a given analyte and a given detector. The key part of the data analysis is on-the-fly calculation of the first derivatives using a fourth-order polynomial fit to the raw data by the Savitzky-Golay algorithm. The device has been tested by determining the flow rate profiles for an ultraviolet absorption detector and a mass spectrometer operated with electrospray ionization, atmospheric pressure chemical ionization, and a dual ion source. The sensitivity regime thresholds for various test analytes have been determined automatically and robustly in time as short as a few minutes.

Performance analysis of 60-min to 1-min integration time rain rate conversion models in Malaysia

Utilizing the frequency band above 10 GHz is in focus nowadays as a result of the fast expansion of radio communication systems in Malaysia. However, rain fade is the critical factor in attenuation of signal propagation for frequencies above 10 GHz. Malaysia is located in a tropical and equatorial region with high rain intensity throughout the year, and this study will review rain distribution and evaluate the performance of 60-min to 1-min integration time rain rate conversion methods for Malaysia. Several conversion methods such as Segal, Chebil & Rahman, Burgeono, Emiliani, Lavergnat and Gole (LG), Simplified Moupfouma, Joo et al., fourth order polynomial fit and logarithmic model have been chosen to evaluate the performance to predict 1-min rain rate for 10 sites in Malaysia. After the completion of this research, the results show that Chebil & Rahman model, Lavergnat & Gole model, Fourth order polynomial fit and Logarithmic model have shown the best performances in 60-min to 1-min rain rate conversion over 10 sites. In conclusion, it is proven that there is no single model which can claim to perform the best across 10 sites. By averaging RMSE and SC-RMSE over 10 sites, Chebil and Rahman model is the best method.

Electrical determination of current injection and internal quantum efficiencies in AlGaN-based deep-ultraviolet light-emitting diodes.

We propose a method to determine the current injection efficiency (CIE) and internal quantum efficiency (IQE) of light-emitting diodes (LEDs) during current injection. The method is based on fourth-order polynomial fitting of a modified rate equation to electroluminescence data. Our method can extract the CIE at low injection current densities, unlike conventional methods that generally assume the CIE to be unity. We apply the method to AlGaN-based deep-ultraviolet LEDs. Results show that the CIE was only approximately 51% at low injection current densities and was almost independent of injection current density up to 100 A/cm2. The peak IQE was 77%.

Ultrasensitive Time-Resolved Fluoroimmunoassay for Saikosaponin a in Chaihu (Bupleuri Radix).

The aim of this study is to establish a time-resolved fluoroimmunoassay (TRFIA) system for quantitative analysis of saikosaponin a (SSa) in the crude drug of Chaihu (Bupleuri Radix). A 96-well microplate coated with rabbit anti-mouse IgG was incubated with the methanol extracts of Chaihu samples and a mouse anti-SSa monoclonal antibody, and a Eu3+-labeled SSa-human serum albumin conjugate was used as the tracer. The established competitive TRFIA showed a good fourth order polynomial fitting from 0.01 to 10.0 μg/mL for standard SSa sample with a detection limit of 0.006 μg/mL. The intra- and inter-assay coefficients of variation of the assay were 7.3% and 8.9%, respectively, and the average SSa recovery was 119.2%. For samples of Chaihu extract, the results of this assay showed a good correlation with those by enzyme-linked immunosorbent assay established previously. This TRFIA system is ultrasensitive for detecting SSa with a wide detection range and a good stability and represents the first attempt of using TRFIA for quality evaluation of the crude drug of Chaihu.

A High-Precision Calculation of Bond Length and Spectroscopic Constants of Hg2 Based on the Coupled-Cluster Theory with Spin—Orbit Coupling**Supported by the Start-Up Funds of Xi'an Polytechnic University under Grant No BS1211, and the Scientific Research Program Funded by Shaanxi Provincial Education Department under Grant No 2013JK0679.

Based on the two-component relativistic effective core potential and matched basis sets cc-pwcvnz-pp (n=Q, 5), combining the completed basis-set extrapolation of electronic correlation energy and the fourth-order polynomial fitting technique, the bond length and spectroscopic constants of Hg2 are studied by the coupled cluster theory with spin—orbit coupling. Spin—orbit coupling is included in the post Hartree—Fock procedure, i.e., in the coupled-cluster iteration, to obtain more reliable theoretical results. The results show that our theoretical values agree with the experimental values very well and will be helpful to understand the spectral character of Hg2.

Effect of Weld Residual Stress Fitting on Stress Intensity Factor for Circumferential Surface Cracks in Pipe

Recent studies have shown that the crack growth of primary water stress corrosion cracking (PWSCC) is mainly driven by the weld residual stress (WRS) within the dissimilar metal weld. The existing stress intensity factor (K) solutions for surface cracks in pipe typically require a fourth order polynomial stress distribution through the pipe wall thickness. However, it is not always possible to accurately represent the through thickness WRS with a fourth order polynomial fit and it is necessary to investigate the effect of the WRS fitting on the calculated Ks. In this paper, two different methods were used to calculate the K for a semi-elliptical circumferential surface crack in a pipe under a given set of simulated WRS. The first method is the universal weight function method (UWFM) where the through thickness WRS distribution is represented as a piece-wise monotonic cubic fit. In the second method, the through thickness WRS profiles are represented as a fourth order polynomial curve fit (both using the entire wall thickness data and only using data up to the crack-tip). In addition, three-dimensional finite element (FE) analyses (using the simulated weld residual stress) were conducted to provide a reference solution. The results of this study demonstrate the potential sensitivity of Ks to fourth order polynomial fitting artifacts. The piece-wise WRS representations used in the UWFM were not sensitive to these fitting artifacts and the UWFM solutions were in good agreement with the FE results. In addition, in certain cases, it was demonstrated that more accurate crack growth calculations of PWSCC are made when the UWFM is used.

Modeling the High Temperature Flow Behavior and Dynamic Recrystallization Kinetics of a Medium Carbon Microalloyed Steel

In this study, the hot deformation behavior of a medium carbon microalloyed steel was investigated. The hot compression test was conducted in the temperature range of 1000-1200 °C under strain rates of 0.01, 0.1 and 1 s−1. It has been observed that the flow stress increases with a decrease in temperature and/or an increase in strain rate. Furthermore, dynamic recrystallization (DRX) is found to be the main flow softening mechanism in almost all deformation conditions. Material parameters of the constitutive equations are found to be strain dependent. Their relationship with strain is identified by a fourth order polynomial fit. Then, a constitutive model is developed to predict the flow stress of the material incorporating the strain softening effect. The accuracy of the proposed model for the flow stress is evaluated by applying the absolute average error method. The result of 6.08% indicates a good agreement between predicted and experimental data. Moreover, the critical characteristics of DRX are extracted from the stress-strain curves at different deformation conditions. It is found that by increasing the strain rate at a constant temperature or decreasing deformation temperature under a constant strain rate, the recrystallization curve shifts to the higher strains. The kinetics of DRX increases with increasing deformation temperature or strain rate.

산업용 백금저항온도계를 위한 향상된 내삽식

We propose an improved interpolating equation to express temperature-resistance characteristics for modern industrial platinum resistance thermometers (PRTs). Callendar-van Dusen equation which has been widely used for platinum resistance thermometer fails to fully describe temperature characteristics of high quality PRTs and leaves systematic residual when the calibration point include temperatures above <TEX>$300^{\circ}C$</TEX>. Expanding Callendar-van Dusen to higher-order polynomial drastically improves the uncertainty of the fitting even with reduced degrees of freedom of the fitting. We found that in the fourth-order polynomial fitting, the third-order and fourth-order coefficients have a strong correlation. Using the correlation, we suggest an improved interpolating equation in the form of fourth-order polynomial, but with three fitting parameters. Applying this interpolating equation reduced the uncertainty of the fitting to 32 % of that resulted from the traditional Callendar-van Dusen. This improvement was better than that from a simple third-order polynomial despite that the degrees of the freedom of the fitting was the same.

Abstract 17144: Assessment of Tissue Heating During Cardiac Radiofrequency Ablation Using Referenceless MRI Thermography

Introduction: Imaging tissue heating during RF ablation may permit more accurate placement and titration of ablation lesions. Standard proton resonance frequency shift MRI thermography, however, is limited by sensitivity to physiologic motion and scanner phase drift between acquisition of ablation and reference pre-heating images. The aim of this study is to assess the feasibility of referenceless MRI thermography which addresses this limitation by eliminating need for a separate pre-heating image but has not yet been applied to cardiac ablation. Methods: An MRI compatible copper electrode catheter was inserted into the left ventricle in 6 dogs. Gradient recalled echo images were acquired while applying RF power in 3W increments until high impedance was reached. Gross pathology was obtained. The pre-heating image was estimated from the ablation image phase component (A) by unwrapping phase (B), masking the catheter tip region where heating was expected (C), and extrapolating phase from unmasked regions of the heart using a fourth order polynomial fit (D). Thermography images were then computed using standard methods (E). Thermography lesion extent was defined by tissue temperature above 50°C. Electrode artifact was defined by darkened myocardium adjacent to the catheter tip on the magnitude component of the ablation image. Results: Transmural lesion extent by referenceless MR thermography was within 20% of that obtained by pathology (inset F) in the four cases where the electrode artifact transmurality was less than 25%. However, thermography and pathology lesion extent differed by over 60% in the two cases where electrode artifact transmurality was greater than 40%. Conclusion: Referenceless MR thermography of cardiac RF ablation is possible and may permit more practical MR thermography monitoring of cardiac ablation. Reducing electrode artifact by using lower magnetic susceptibility materials appears required for more reliable temperature assessment.

An improved method for flat‐field correction of flat panel x‐ray detector

In this Technical Note, the effects of different flat-field techniques are examined for a cesium iodide flat panel detector, which exhibited a slightly nonlinear exposure response. The results indicate that the variable flat-field correction method with the appropriate polynomial fit provides excellent correction throughout the entire exposure range. The averaged normalized variation factor, used to assess the nonuniformity of the flat-field correction, decreased from 30.76 for the fixed correction method to 4.13 for the variable flat-field correction method with a fourth-order polynomial fit for the 60 kVp spectrum, and from 16.42 to 3.97 for the 95 kVp spectrum.

Analysis and Characterization of Device Variations in an LSI Chip Using an Integrated Device Matrix Array

For future large-scale integration design technology, the device matrix array (DMA), which precisely evaluates within-die variation in device parameters, has been developed. The DMA consists of a 14-by-14 array of common units. The unit size is 240 by 240 /spl mu/m, and each unit contains 148 measurement elements (52 transistors, 30 capacitors, 51 resistors, and 15 ring oscillators). The element selection and precise measurement are achieved with low parasitic resistance measurement buses and leakage-controlled switching circuits, which allow the measurement accuracy for a transistor, resistor, or capacitor of 90 pA, 11 m/spl Omega/, and 23 aF, respectively, in the 3/spl sigma/ range. The ability to obtain 29 008 samples from a chip enables statistical analysis of the variation in 148 elements of each chip with 240-/spl mu/m spatial resolution. This high resolution and large sample number allows us to precisely decompose the data into systematic and random variation parts with newly developed fourth-order polynomial fitting. Our methodology has been verified using a test chip fabricated by a 130-nm CMOS process with a 100-nm physical gate length and five Cu interconnect layers. In MOSFETs, the random part was dominant and indicated a certain /spl sigma/ value in every chip. In the case of the interconnect layers, the random and systematic parts of the resistance and the capacitance indicated variance fluctuations. By chip, by item, by size, by structure, random or systematic, the /spl sigma/ values of each variation show inconsistency which we believe is attributable to the Cu process. The correlation coefficients of systematic part between device element and ring oscillator frequency shown very high value (0.87-0.98), and those of a random part were low enough (-0.10-0.22) to prove the accuracy of decomposition.

High-resolution FTIR spectrum of Freon-13 at 1890 cm−1

High-resolution Fourier transform infrared spectra of natural CF3Cl (Freon-13) have been recorded in the region around 1890cm−1 with the purpose of analyzing the ν1+ν2 combination band. The K structure of the P(J) and R(J) manifolds was resolved and identified; the assignment of the rovibrational transitions was extended up to J=75, K=36 for CF335Cl and up to J=50, K=27 for CF337Cl. More than 1700 and 200 lines for CF335Cl and CF337Cl, respectively, were analyzed by a least-squares procedure and reliable spectroscopic parameters were determined for both the isotopomers. Additionally, for the CF335Cl species, the J clusters of the ν1+ν2+ν6−ν6 hot band have been observed and analyzed by a fourth-order polynomial fit.

Complete set of magnetic parameters in a novel nickel(II) chelate

A theoretical analysis of powder magnetic data based on the diagonalization of the spin Hamiltonian matrices is outlined. The first and second derivatives of the eigenvalues are determined from the fourth-order polynomial fit; they enter the van Vleck formula for the paramagnetic susceptibility. The procedure is capable of subtracting the complete set of magnetic parameters from powder susceptibility data. A five-member Ni(II) metallocycle ( S=1) was investigated by SQUID measurements down to 2 K and a substantial drop of the χT curve below 25 K was found. A reconstruction of the components of the magnetic susceptibility was done. An independent fitting procedure using four fundamental magnetic parameters gave Λ xx =42.8±0.1, Λ yy =49.9±0.1, Λ zz =26.6±0.1 au and zJ/ hc=−2.06±0.01 cm −1. These data reproduce the enlarged set of magnetic parameters well so that a selfconsistency of magnetic parameters is proven.