esa-sceva/satcom-chunk-collection huggingface dataset:
## 3 Results and Discussion  
### Effects of Grain Orientations  
Figure 16 shows a comparison of the micro-extrusion results between the two cases (EX1 and EX2) having the same grain sizes and grain boundaries, but having different grain orientations of the bottom grains. If all grains were oriented in the same direction (EX1), and the grain sizes and grain boundaries were symmetric along the extrusion direction, there should be no curvature at all. The results of EX1 demonstrated that the FE simulation was valid. The results of EX2 clearly showed that the bottom grain orientation that was rotated 75\({}^{\circ}\) with respect to the x-axis caused the micro-extrusion pin to bend (ECI = 4.45%). With no effects of grain sizes and grain boundaries under single-grain conditions, the change in grain orientation could cause the micro-extrusion pin to curve. Regarding the stress distributions, high stresses occurred at high deformation zones (reduction of billet diameter to the outlet diameter). These areas caused the grains to fragment, leading to smaller grain sizes and higher stress values. The simulation results provided effective stress (\(\sigma_{v}\)) values based on the following equation:  
\[\sigma_{v}=\sqrt{\frac{1}{2}[\left(\sigma_{1}-\sigma_{2}\right)^{2}+\left( \sigma_{2}-\sigma_{3}\right)^{2}+\left(\sigma_{1}-\sigma_{3}\right)^{2}]} \tag{3}\]  
where \(\sigma_{1}\), \(\sigma_{2}\), and \(\sigma_{3}\) are the principal stresses.  
Figure 15: The schematic and calculation of the Extrusion Curvature Index (_ECI_).
# Automatic Extraction of Material Defect Size by Infrared Image Sequence
## 4 Data Post-Processing
### Primary Detection of Defects
#### 4.2.3 Determination of ROI and Extraction of Defects  
ROI centers its corresponding blob and expands around it. For example, the blob is expanded twice its size in four directions i.e., up, down, left, and right, respectively. At the same time, ROI is restrained by the specimen boundary and its neighbor blobs.  
Figure 15 is a sketch of ROI based on blob and restrained by constraints, where the yellow area is a blob, and it expands the blue rectangle, but the red dotted portion is ROI due to the specimen boundary and neighbor blobs.  
The ROIs for each defect are determined as shown in Figure 16a,c, which are selected by the MSDSRM. After a median filter, defects #1 and #2 are respectively extracted by automatic threshold segmentation with the value of 4.6 and 3.6 determined by the Otsu method, as shown in Figure 16b,d. The relative errors are 2.08% and 2.91% for defects #1 and #2 respectively, as seen in Table 2. The value of threshold is important in image segmentations, which can influence the integrality and veracity of  
Figure 14: A suitable frame for each defect is determined by the maximum of standard deviation of sensitive region method (MSDSM) using single sensitive region.  
Figure 13: Single sensitive region on each defect is randomly selected.  
Figure 15: A sketch of the region of interest (ROI) based on the blob and restrained by constraints.  
the results. The Otsu method based on the maximum of between-cluster variance is always considered an optimal method of thresholds for automatic selection. It will divide the processing image into two categories, i.e., background and objectives. The optimal threshold is obtained by searching the maximum between-cluster variance. Comparing the data in Tables 1 and 2, the threshold changes very little from 0.47 to 0.46 for #1 and to 0.36 for #2, but the error of defect #1 decreases from 27.08% to 2.08%, and the error of defect #2 reduces to 2.91%, which is incomplete extraction after processing the full image, as shown in Figure 11b. At last, the two segmentation images are combined as a whole (see Figure 16e). The semicircular arc of the defect tip can be extracted accurately.
# Improving Polar-Coded SCMA System by Information Coupling and Parity Check
## 3 Design of Partially Information-Coupled Polar Code based on Parity Check
### Partially Information-Coupled PCCA-Polar Code
However, since the iterative system requires complete extrinsic messages, subsequent CBs' decoding cannot be terminated even if there is a CB decoding error for our decoding scheme. The CBs with feed-forward decoding failure were corrected only once by feed-back decoding.
# Creation, Analysis and Evaluation of AnnoMI, a Dataset of Expert-Annotated Counselling Dialogues +
## 3 Creating AnnoMI
### MI Demonstration Videos  
To balance privacy restrictions and the faithfulness of therapy, we leverage MI demonstrations on video-sharing websites (YouTube and Vimeo). We identified 346 videos that demonstrate high- and low-quality MI, using key phrases including \"good motivational interviewing\" and \"bad MI counselling\". According to the literature [2], high-quality MI is centred on the client and conducted with empathy, whereas low-quality MI is characterised by frequent instructions and suggestions.  
We label each video to be high-quality MI or low-quality using its title (e.g., \"Motivational Interviewing--Good Example\"/\"The Ineffective Physician: Non-Motivational Approach\"), as well as descriptions and narrator comments (e.g., \"Demonstration of the motivational interviewing approach in a brief medical encounter\"). We consider such labelling to be verified automatically, as the video uploaders are professional MI practitioners and organisations focused on healthcare and behaviour change. We also note that the definition of high- and low-quality MI is clear in the literature ([1,2], inter alia); therefore, the high/low MI quality divide is consistent across different institutions/therapists and different demonstrations.  
We gained explicit permission from the content owners (as well as the individuals appearing in the videos if applicable) for us to use their videos to create, analyse, and publicly release a transcript-based MI dialogue dataset. We eventually obtained permission to use 119 (42 overlapped with [13]) of these videos, which contain 133 complete conversations--a video may contain multiple dialogues. Moreover, 110 of the dialogues showcase high-quality MI, with 8839 utterances in total, and the other 23 dialogues illustrate low-quality MI, with 860 utterances in total. As shown in Figure 1, high-quality MI dialogues are generally longer than low-quality ones, with several surpassing 200 utterances in length, but most dialogues have less than 100 utterances. A pair of high- and low-quality MI session excerpts, both about smoking cessation/reduction, are presented in Table 1.  
Figure 1: Distribution of dialogue lengths (number of utterances per dialogue).  
The imbalance with respect to high- and low-quality MI dialogue volumes can be attributed to the following: (a) fewer low-quality MI video owners responded to our request or consented; (b) low-quality MI videos are relatively scarce on Youtube/Vimeo, possibly because MI adherence demonstrations are deemed more valuable as \"good examples\" and thus filmed and uploaded more.
## 4 Experimental Results
### Image Reconstruction Experiment of Abdomen Image
Figure 10: 48-views reconstruction results of abdomen image: (**a**) ground truth, (**b**) FBP, (**c**) OS-SART, (**d**) TV, (**e**) PICCS, (**f**) TVPI-G, and (**g**) NPICCS. The display window is \([-150\,250]\) HU. Figure 9: Abdomen image for the experiments: (**a**) the target image; (**b**) the prior image; and (**c**) the difference image between the prior image and the target image. Figure 11: 64-views reconstruction results of abdomen image: (**a**) ground truth, (**b**) FBP, (**c**) OS-SART, (**d**) TV, (**e**) PICCS, (**f**) TVPI-G, and (**g**) NPICCS. The display window is \([-150\;250]\) HU. Figure 12: 80-views reconstruction results of abdomen image: (**a**) ground truth, (**b**) FBP, (**c**) OS-SART, (**d**) TV, (**e**) PICCS, (**f**) TVPI-G, and (**g**) NPICCS. The display window is \([-150\;250]\) HU. As in the pelvic image reconstruction, we use the same method to select parameters, and the optimal parameters for reconstruction are the same at three angles; the relevant quantification curves are shown in Figure 16. The same conclusion can be drawn that the parameter values have an important impact on the image quality. When the parameters are too large or too small, the desired results are not achieved. \begin{table}
\begin{tabular}{l c c c c c c c c c} \hline \hline
**AlgorithmViews** & \multicolumn{2}{c}{**48**} & \multicolumn{2}{c}{**64**} & \multicolumn{2}{c}{**80**} \\ \cline{2-10}  & **RMSE** & **PSNR** & **SSIM** & **RMSE** & **PSNR** & **SSIM** & **RMSE** & **PSNR** & **SSIM** \\ \hline FBP & 0.0572 & 24.8531 & 0.3877 & 0.0532 & 25.4793 & 0.4416 & 0.0490 & 26.2008 & 0.4898 \\ OS-SART & 0.0194 & 32.2530 & 0.8487 & 0.0163 & 33.7509 & 0.8758 & 0.0140 & 35.1534 & 0.8987 \\ TV & 0.0149 & 35.0197 & 0.8911 & 0.0113 & 36.6015 & 0.9075 & 0.0108 & 37.8124 & 0.9103 \\ PICCS & 0.0102 & 38.0374 & 0.9158 & 0.0098 & 39.0875 & 0.9237 & 0.0082 & 40.2468 & 0.9304 \\ TVPI-G & 0.0091 & 39.4513 & 0.9276 & 0.0080 & 40.3687 & 0.9335 & 0.0068 & 41.8053 & 0.9489 \\ NPLCCS & **0.0078** & **40.5177** & **0.9383** & **0.0065** & **41.9674** & **0.9508** & **0.0050** & **43.0232** & **0.9612** \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Comparison of metric values by different algorithms. Figure 14: Line intensity distribution of CT images reconstructed from 80 projections at two areas: (**a**) red line; and (**b**) blue line. Figure 13: The ROIs from 48-views and 64-views reconstruction results. The first row is from 48-views ROI. The second row is from 64-views ROI. (**a**) ground truth, (**b**) FBP, (**c**) OS-SART, (**d**) TV, (**e**) PICCS, (**f**) TVPI-G, and (**g**) NPLCCS. The display window is \([-150\ 250]\) HU.
## 4 Results and Discussion
### Loaded Swelling Deformation
#### 4.2.2 Effect of Vertical Pressure  
As an impermeable material in engineering application, vertical swelling strain is an important factor for MB. The vertical swelling strain of MB represents the corresponding vertical load causing expansion to the same strain under the same load [43]. Hence, the relationship between vertical swelling strain of MB specimen and vertical pressure levels could express the constitutive relationship between vertical swelling strain and vertical swelling stress. Figure 10 demonstrates the final vertical swelling strain of MB specimens with different initial dry densities and the logarithm of vertical swelling pressures under saline water conditions. The final swelling strain decreased with the increase of vertical pressure for the MB specimens under all initial dry densities. With the increase of vertical pressure, the effective vertical stress on MB specimens increased, which could hinder water adsorption thereon and prevent the thickening of the water film on the surface of the soil particles. As a result, the swelling deformation of MB specimens was suppressed.  
Figure 10 shows the linear relationship between swelling strain (\(E_{P}\)) and the logarithm of swelling pressure (ln\(P\)). The relationship between the final swelling strain and vertical load can be expressed as Equation (9):  
\[\varepsilon_{P}=a-b\ln P\]  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Vertical Load (kPa)** & \(a\) & \(b\) \\ \hline
25 & 204.8 & 228.8 \\
50 & 174.8 & 199.3 \\
100 & 155.6 & 182.7 \\
150 & 144.7 & 175.5 \\
200 & 144.4 & 187.8 \\
300 & 143.1  
where \(\varepsilon_{\rm P}\) is the vertical swelling strain of an MB specimen under vertical pressure \(P\); \(P\) denotes the vertical pressure (kPa); and \(a\) and \(b\) are fitting parameters related to the initial dry density of the MB specimen and represent the swelling characteristics of MB.
# Experimental Investigation on Shear Behavior of Dune Sand Reinforced Concrete Deep Beams
## 2 Experimental Program  
### Materials  
The concrete mixtures were made with 42.5 grade ordinary Portland cement (OPC) and grade I fly ash, in accordance with GB 175-2007 standards [44]. The high water absorption of dune sand and the fine particle gradation lead to a reduction in concrete strength, and so the easily available fly ash was selected as one of the concrete mixtures, which is shown in Figure 1a. The chemical composition of the OPC and fly ash are presented in Table 1. The fine aggregate was river sand with a fineness modulus of 2.97 and an apparent density of 2487.5 kg/m\({}^{3}\), and the coarse aggregate was river gravel \(\leq\) 30 mm. The dune sand (DS)sample was collected from the Taklamakan Dune in the city of Korla, Xinjiang province of China, as shown in Figure 1b. The DS samples had an average particle size of 0.963 mm and a fineness modulus of 0.855. The chemical composition of the DS is presented in Table 2. To improve the workability of DS concrete, the Q8081 polycarbonate acid high-range water reducer (HRWR) agent with a water reduction rate of 37% was added. According to the suggestions of reference [15], DS replacement rate was chosen as one of the main variables in this paper and was set to 0, 30%, and 50%. Additionally, three sets of concrete of different strengths, each containing three cubic specimens (150 \(\times\) 150 \(\times\) 150 mm, and 150 \(\times\) 150 \(\times\) 300 mm), were cast from the concrete used in the specimens to measure the cubic concrete compressive strength and splitting tensile strength. The materials were thoroughly mixed in a standard rotating drum mixer before being poured into the mold. The specimens were demolded after one day and placed in a standard maintenance room at 20 \(\pm\) 2 \({}^{\circ}\)C and >95% relative humidity to cure for four weeks. Then, the specimens were removed for concrete strength testing. The mix proportions of concrete with different strengths and different DS replacement rates and the measured results are shown in Table 3.  
Smooth HPB300 bars with a nominal diameter of 6 mm were used as the stirrup, and ribbed HRB400 bars with nominal diameters of 12 mm and 16 mm were used as the longitudinal reinforcement. The joints between the longitudinal reinforcement and stirrup were protected with electrical tape and secured with plastic tape. The detailed mechanical properties of the reinforcing steel are reported in Table 4.
## 2 Field Monitoring
### Monitoring Instruments  
The meteorological parameters outside the burial chamber were monitored using a meteorological monitoring station.  
Tomb indoor environmental data were recorded using a temperature and humidity logger (model: TH10R), with a temperature measurement range of \(-40\)\({}^{\circ}\)C to \(80\)\({}^{\circ}\)C, a humidity measurement range of 0-100% relative humidity (RH), a temperature measurement accuracy of \(\pm 0.5\)\({}^{\circ}\)C and a humidity measurement accuracy of \(\pm 5\)% RH.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Density** **(g/cm\({}^{3}\))**} & **Isothermal** & **Water Vapor** & **Liquid Water** & **Thermal** & **Specific Heat** \\  & **Hygroscopic** & **Permeability Coefficient** & **Diffusion Coefficient** & **(m/s\({}^{2}\))** & **(W/(m K))** & **(J/(kg K))** \\ \hline
2.42 & \(\mathrm{u}=\mathrm{e}^{-4.81+0.053\varphi}\) & \(2.33\times 10^{-7}\) & \(4.49\times 10^{-6}\) & 2.54 & 863 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Thermo-hygroscopic parameters of the sandstone from [PERSON]’s tomb.  
Figure 2: Plan of [PERSON]’s tomb and location of the meteorological stations outside and inside the chamber: (**a**) outside the chamber; (**b**) inside the chamber.
## 4 Results and Analysis
### Simulation Results and Analysis
#### 4.1.2 Transient Response and Decoupling Effectiveness  
Figure 13 illustrates transient responses of the gird current applying the proposed ADRC controller for increasing current reference to 1.0 p.u. from 0.5 and then decreasing to 0.5 p.u. from 1.0, respectively.  
The Grid-tie inverter with improved ADRC in the outer loop can bring the d-axis current component to a steady state within 0.03 s. In contrast, the traditional ADRC has a d-axis current regulation time of approximately 0.05 s.
## 4 Proposed Approach
A particular weight coefficient may be adjusted relatively to the others to obtain an optimal result for a particular network configuration. For example, in a low density environment, the residual energy should be favored. In case of a dense network, the connectivity should be favored. Whereas, in a noisy environment, the communication link quality needs to be considered. However, the proposed scheme is designed to work under a typical network with various configurations to cover different use-case scenarios. Therefore, in this experiment, all the weight coefficients are considered equal. In DC2 HC, the clustering is completely distributed where each node has only a partial view of the network which consists of its two-hop neighbors knowledge. The algorithm is designed by a set of rules of the form [If _condition_ then _action_], where the _condition_ is a predicate defined over the node partial information. If the predicate is true, then the node is said to be enabled to make a move (execute an action). This algorithm structure is inspired from the self-stabilization algorithms that are considered as advantageous approaches for tolerating transient faults in a network [54], which is desirable in an environment with a dynamic topology. We assume that each node \(i\) has a unique identifier and maintains a set of variables that constitute the Local State Values of the node (\(LSV\)): node identifier (\(ID_{i}\)), its weight \(W_{i}\), \(Mych_{i}\) (the relative CH of the current node), \(CH_{weight}\) (the weight of the relative CH), \(Dist(i,Mych_{i})\) that indicates the distance to \(Mych\) (in term of hops), \(Deg(i)\), and its parent \(P_{i}\) in the shortest data aggregation path. The structure of \(LSV\) is illustrated in Figure 3. Each node has a clustering record list \(CRL\) that contains a set of neighbors information required by the clustering process. Nodes store the received clustering information (\(LSV\) beacons) in this list. Table 3 summarizes various notations used in the proposed approach. DC2 HC is composed of three phases: the initialization phase, cluster heads election phase, and maintenance phase. Figure 3: Example of Local State Values (\(LSV\)) structure.
## 3 Simulation Results  
Simulations were performed to evaluate the performance of our proposed method using MATLAB/Simulink as shown in Figure 4a. The PM stepper motor model consisting of SimScape model and PWM drivers as shown in Figure 4b was used. The parameters of the PM stepper motor are listed in Table 1. The PM stepper motor's parameters listed in Catalog (PK266-01A) [26] were used in the simulations. The nominal and actual parameters may be different, thus, the simulations were tested with the parameter uncertainties, at least, 10 %. The control gains listed in Table 2 were used. \(L(s)\) and \(Q(s)\) were designed such that \(Q(s)\approx 1\), \(L(s)\approx P^{-1}(s)\) for the frequency period (0-100 rad/s). The desired position and velocity shown in Figure 5 were used. To validate the performance of our proposed method, three  
steady-state response, the average position and velocity tracking errors of the peak of the desired position were \(\pm\)0.002 rad and \(\pm\)0.275 rad/s after only one iteration.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Parameter** & **Value** & **Parameter** & **Value** \\ \hline \(L\) & 40 mH & \(R\) & 14.8 \(\Omega\) \\ \(J\) & \(5\times 10^{-5}\) kg\(\cdot\)m\({}^{2}\) & \(K_{m}\) & 0.51 N\(\cdot\)m/A \\ \(N_{r}\) & 50 & \(B\) & \(5\times 10^{-3}\) N\(\cdot\)m\(\cdot\)s/rad \\ \hline \hline \end{tabular}
\end{table}
Table 1: Parameters of the PM stepper motor.  
Figure 4: Simulation structure.  
Figure 5: Desired position and velocity.  
Figure 6: Past error-based ILC.  
Figure 8: Performance of Case 2 (PI controller with past error-based ILC).  
Figure 7: Performance of Case 1 (proportional–integral (PI) controller).
## 3 The Test Results
### Carrying Capacity Analysis
\begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline \multirow{2}{*}{**Specimen Number**} & \multirow{2}{*}{\(N_{t}\) (kN)} & \multicolumn{2}{c}{**EC4(2004)**} & \multicolumn{2}{c}{**A1 SC360-10**} & \multicolumn{2}{c}{**GB50936-2014**} & \multirow{2}{*}{\(N_{k}\) (kN)} \\ \cline{3-4} \cline{6-9}  & & **Calculated Value (kN)** & & & **Calculated Value (kN)** & & **Ratio** & **Calculated Value (kN)** \\ \hline PT300-1 & 810.6 & 766.6 & 94.57\% & 754.3 & 93.05\% & 798.5 & 98.51\% & 437.6 \\ BZ300-1 & 823.4 & 782.9 & 95.08\% & 761.6 & 92.49\% & 798.9 & 97.02\% & 441.2 \\ PT300-2 & 1141.7 & 1107.4 & 97.00\% & 1067.6 & 93.51\% & 1138.7 & 99.74\% & 601.6 \\ QZ300-1 & 1150.5 & 1103.2 & 95.89\% & 1059.8 & 92.12\% & 1120.3 & 97.38\% & 612.6 \\ BZ300-2 & 1089.9 & 1060.6 & 97.31\% & 1006.5 & 92.35\% & 1082.9 & 99.36\% & 574.8 \\ QZ300-2 & 1107.3 & 1075.0 & 97.08\% & 1020.5 & 92.16\% & 1083.9 & 97.89\% & 585.8 \\ BZ300-3 & 1528.4 & 1484.4 & 97.12\% & 1405.9 & 91.99\% & 1490.0 & 97.49\% & 805.4 \\ QZ300-3 & 1539.1 & 1490.5 & 96.84\% & 1413.0 & 91.81\% & 1507.3 & 97.93\% & 810.5 \\ PT400-1 & 792.9 & 769.7 & 97.07\% & 726.5 & 91.63\% & 826.7 & 104.26\% & 437.6 \\ BZ400-1 & 799.7 & 780.5 & 97.60\% & 731.3 & 91.45\% & 796.2 & 99.56\% & 441.2 \\ PT400-2 & 1091.4 & 1068.7 & 97.92\% & 996.0 & 91.26\% & 1107.2 & 101.45\% & 601.6 \\ QZ400-1 & 1110.0 & 1086.6 & 97.89\% & 1011.0 & 91.08\% & 1093.0 & 98.47\% & 612.6 \\ BZ400-2 & 1075.8 & 1055.2 & 98.09\% & 977.9 & 90.90\% & 1074.3 & 99.86\% & 574.8 \\ QZ400-2 & 1094.5 & 1073.2 & 98.05\% & 992.9 & 90.72\% & 1096.4 & 100.17\% & 585.8 \\ BZ400-3 & 1528.2 & 1494.6 & 97.80\% & 1383.6 & 90.54\% & 1499.4 & 98.12\% & 805.4 \\ QZ400-3 & 1537.1 & 1504.0 & 97.85\% & 1388.9 & 90.36\% & 1529.6 & 99.51\% & 810.5 \\ PT500-1 & 723.0 & 695.7 & 96.22\% & 652.0 & 90.18\% & 713.8 & 98.73\% & 437.6 \\ BZ500-1 & 716.4 & 685.4 & 95.67\% & 644.1 & 89.91\% & 712.4 & 99.44\% & 441.2 \\ PT500-2 & 1001.1 & 965.3 & 96.42\% & 899.0 & 89.80\% & 977.6 & 97.65\% & 601.6 \\ QZ500-1 & 995.7 & 920.7 & 92.47\% & 893.1 & 89.70\% & 986.1 & 99.04\% & 612.6 \\ BZ500-2 & 946.5 & 924.7 & 97.70\% & 848.0 & 89.59\% & 940.3 & 99.34\% & 574.8 \\ QZ500-2 & 961.4 & 948.0 & 98.61\% & 860.3 & 89.48\% & 935.5 & 97.31\% & 585.8 \\ BZ500-3 & 1279.4 & 1217.7 & 95.18\% & 1143.5 & 89.38\% & 1262.6 & 98.69\% & 805.4 \\ QZ500-3 & 1323.3 & 1208.9 & 91.35\% & 1181.3 & 89.27\% & 1295.6 & 97.91\% & 810.5 \\ PT600-1 & 556.2 & 547.8 & 98.49\% & 495.9 & 89.16\% & 548.5 & 98.62\% & 437.6 \\ BZ600-1 & 531.8 & 538.3 & 101.22\% & 473.6 & 89.06\% & 515.0 & 96.84\% & 411.2 \\ PT600-2 & 771.4 & 757.6 & 98.21\% & 686.2 & 88.96\% & 757.6 & 98.21\% & 601.6 \\ QZ600-1 & 759.3 & 759.1 & 99.97\% & 674.6 & 88.84\% &
# Parameter Estimation for Some Probability Distributions Used in Hydrology
## 2 Probability Distributions
### Weibull Distribution (W3)  
The distribution represents a particular case of the GEV distribution when the shape parameter is negative. It is also known as the Type II extreme value distribution, [11; 15; 16].  
\[f(x)=\frac{\alpha}{\beta}\cdot\left(\frac{x-\gamma}{\beta}\right)^{\alpha-1} \cdot e^{-\left(\frac{x-\gamma}{\beta}\right)^{\alpha}}=\frac{\alpha}{\beta} \cdot dweight\left(\frac{x-\gamma}{\beta},\alpha\right) \tag{8}\]  
\[F(x)=e^{-\left(\frac{x-\gamma}{\beta}\right)^{\alpha}}=1-pweibull\left(\frac{ x-\gamma}{\beta},\alpha\right) \tag{9}\]  
\[x(p)=\gamma+\beta\cdot(-\ln(p))^{1/\alpha}=\gamma+\beta\cdot qweibull(1-p,\alpha) \tag{10}\]  
where \(\alpha,\beta,\gamma\) are the shape, the scale and the position parameters; \(\alpha,\beta>0,x\geq\gamma\).