esa-sceva/satcom-chunk-collection huggingface dataset:
## 5 Conclusions  
These results indicate that it is feasible to optimize a system for monitoring and capturing a pest insect such as SWD. The use of a microencapsulated attractant (WVM) in delta-type traps allowed for the capture of a significantly higher number of females compared to males. This is advantageous because capturing females and preventing their mating can reduce infestation levels in ripe fruits, which are preferred by gravid females for oviposition. Additionally, measuring the release rate of the attractant enabled us to estimate its durability under specific weather conditions for a given area. Future research should focus on (1) determining the electrophysiological response of SWD to volatiles from WVM bait, (2) evaluating this monitoring system in commercial cherry orchards, (3) assessing its efficacy in other SWD host plants, and (4) evaluating the capture efficiency of SWD in traps baited with encapsulated WVM versus WVM in liquid format. This information will help to better understand the behavior of SWD in our country, particularly in generating SWD flight curves in areas where it is already established, which is a critical component of an effective integrated pest management (IPM) program for this economically significant dipteran.  
**Author Contributions:** M.L.: conceptualization, investigation, methodology, and writing--original draft preparation. F.M.A.-S.: validation and writing--review and editing. L.M.N.-G.: validation and writing--review and editing. D.M.-C.: methodology, investigation, and writing--original draft preparation. C.M.: methodology, investigation, and writing--original draft preparation. R.R.: validation and writing--original draft preparation. M.C.-F.: software, formal analysis, and writing--review and editing. L.B.: conceptualization, writing--review and editing, and supervision. All authors have read and agreed to the published version of the manuscript.  
**Funding:** This research was supported by Programa de Doctorado en Ciencias Agroalimentarias y Medioambiente de la Universidad de La Frontera (Temuco-Chile) and by Programa de Doctorado en Ciencia e Ingenieria Agroalimentaria y de Biosistemas de la Universidad de Valladolid (Valladolid-Espana). The authors also thank the Laboratorio de Entomologia Aplicada and Laboratorio de Quimica Ecologica, both of Universidad de La Frontera (Temuco-Chile).  
**Data Availability Statement:** The data presented in this study are available upon request from the corresponding author.  
**Conflicts of Interest:** The authors declare no conflicts of interest.
# Six Sigma-Based Frequency Response Analysis for Power Transformer Winding Deformation
## 3 Results--Verify Phase
### Case 3
#### 3.3.1 Case 3: Analysis of 10-1000 Frequency Range (Hz)  
The low-frequency band (10-1000 Hz) is dominated by core-related influences, including core deformation, magnetostriction effects, and core movement (Table 7). These phenomena manifest due to changes in the magnetic flux distribution within the core laminations, which in turn affect the inductive coupling between windings.  
In Figure 17a, the FRA response shows a progressive downward deviation from the baseline, with the \(X_{latest}\) curve consistently below the lower control limit (LCL) in the range of 200 Hz to 600 Hz. This indicates a mechanical displacement of the core structure, potentially caused by core clamping pressure loss or transportation-induced stress.  
Figure 16: Case 3, transformer fingerprint.  
The Six Sigma process capability indices, \(C_{p}\) and \(C_{pk}\), seen in Figure 17b, decline toward 1.0, signifying marginal stability (Table 4). The range chart further highlights increasing variability, suggesting that the core movement is not uniform but fluctuating under different operational states.  
Figure 17: Case 3, 10–1000 frequency range (Hz). (**a**) Six Sigma control chart and process capability. (**b**) Six Sigma range variation and upper control limits.  
Remarks: It should be noted that the transformer exhibits early-stage core movement or looseness. This could lead to increased magnetostriction-induced vibrations, potentially escalating into severe acoustic noise or overheating issues if not addressed.
## 2 Research Methodology
### Probing Fiducials with the On-Machine Measurement System  
In this study, a five-axis ultra-precision machine tool incorporated with the developed on-machine measurement system as shown in Figure 1, is used to evaluate the working volumetric error with the fiducial-aided artefact. The positions of fiducials in the artefact are provided by using the probing system for each re-localization of the artefact. A total of 30 points in a 6 mm \(\times\) 6 mm area are sampled uniformly on one standard sphere to guarantee its center position using the least square method. The calibrated diameter of the spherical fiducial was 9.997 mm. Figure 3 illustrates the probing directions.  
In order to reduce the error source caused by the integrated on-machine measurement system, the probe error should be identified before the measuring tasks. The repeatability of measurement of the integrated probing system is evaluated by probing a standard sphere three times. The Cartesian repeatability ranges contributed by the pooled standard deviation are 0.36 \(\upmu\)m, 0.41 \(\upmu\)m and 0.25 \(\upmu\)m [18], respectively. In addition, the best fitted standard deviations of the sphere center coordinates are 0.18 \(\upmu\)m, 0.21 \(\upmu\)m and 0.24 \(\upmu\)m, respectively. As for other measurement errors, for instance, the errors of the linear axes and rotary axes, which could affect the measurement results, these are treated as errors caused by the machine tool itself.  
Figure 3: Probing points on the standard sphere (left: \(z\) view; Right: \(y\) view).
## 3 Results and Discussion
### Optical Properties by UV-vis Spectroscopy
According to this, we can conclude that the sample synthesized via the in situ approach has smaller MoS\({}_{2}\) particles than the sample synthesized via the ex situ method, with some level of particle stacking observed in the last case (as HRTEM imaged in Figures 2 and 3). Figure 5: UV–vis spectra of TiO\({}_{2}\) anatase nanosheet (n-sh) pretreated at 873 K (black line), of pure bulk MoS\({}_{2}\) used as a reference material (grey line), of in situ MoS\({}_{2}\)/TiO\({}_{2}\) n-sh (red line), and of ex situ MoS\({}_{2}\)/TiO\({}_{2}\) n-sh (blue line). The grey dotted lines indicate the positions of the typical MoS\({}_{2}\) A and B excitonic transitions. All spectra were recorded in the diffuse reflectance mode and converted to equivalent absorption Kubelka–Munk units. The reflectance responses are reported vs. wavenumber (bottom axis) and vs. wavelength (top axis).
# From Trees to Barcodes and Back Again: Theoretical and Statistical Perspectives
## 2 Mathematical Background
### Barcodes  
A persistence _barcode_ is a finite multi-set \(B=\{(b_{i},d_{i})\}_{i=0,...,n}\) of open intervals, called _bars_, in the real line, \(\mathbb{R}\). We call \(b_{i}\) the _birth time_ and \(d_{i}\) the _death time_ of the \(i\)th interval. For barcodes of geometric trees, generated with the TMD algorithm (cf. Section 2.3), the birth time \(b_{i}\) is the distance from the first bifurcation of branch \(i\) to the root, while the death time \(d_{i}\) is the distance from the branch termination to the root. Let \(\mathcal{B}\) denote the set of all barcodes.  
A persistence barcode can equivalently be represented as a multi-set of points in \(\mathbb{R}^{2}\), called a _persistence diagram_, where a bar \((b_{i},d_{i})\) corresponds to a point in \(\mathbb{R}^{2}\) with \(x\)-coordinate \(d_{i}\) and \(y\)-coordinate \(b_{i}\) (The inversion of the coordinates that we apply here is motivated by the TMD algorithm (cf. Section 2.3), which decomposes a geometric tree into bars, starting at the leaves and progressing down to the root.). If \(B\) is a barcode, we let \(\mathrm{PD}(B)\) denote the associated persistence diagram. Note that, under this correspondence, the points of \(\mathrm{PD}(B)\) lie below the diagonal, since \(b_{i}\) is less than \(d_{i}\) for every \(i\).  
We say that a barcode \(B=\{(b_{i},d_{i})\}_{i=0,...,n}\) is _strict_ if the first bar \((b_{0},d_{0})\) properly contains all the others, i.e., \(b_{0}<b_{i}\) and \(d_{i}<d_{0}\) for all \(i\), and no bars are born or die at the same time, i.e., \(b_{i}\
eq b_{j}\) and \(d_{i}\
eq d_{j}\) for all \(i\
eq j\). The birth times of a strict barcode admit a total ordering. Without loss of generality, we assume that the bars are ordered by birth value that is \(b_{0}<b_{1}<\cdots<b_{n}\). Let \(\mathcal{B}^{\mathrm{st}}\) denote the set of strict barcodes, and let \(\mathcal{B}^{\mathrm{st}}_{n}\) denote the subset of those strict barcodes with \(n+1\) bars.  
We say that two strict barcodes \(B=\{(b_{i},d_{i})\}_{i=0,...,n}\) and \(B^{\prime}=\{(b^{\prime}_{i},d^{\prime}_{i})\}_{i=0,...,n}\) with the same number of bars _are equivalent_, denoted \(B\underset{\mathrm{bar}}{\sim}B^{\prime}\), if their deaths occur in the same order \((d_{i}>d_{j}\Leftrightarrow d^{\prime}_{i}>d^{\prime}_{j})\), which clearly defines an equivalence relation on \(\mathcal{B}^{\mathrm{st}}_{n}\). There is a bijection from the set of equivalence classes of strict barcodes with \(n+1\) bars to the symmetric group \(\mathfrak{S}_{n}\) on \(n\) letters, taking the equivalence class of a barcode \(B=\{(b_{i},d_{i})\}_{i=0,...,n}\) to the permutation \(\sigma_{B}:\{1,...,n\}\to\{1,...,n\}\), where \(\sigma_{B}(i)=\#\{j\mid d_{j}\leq d_{i}\}\).  
We denote the equivalence class containing a strict barcode \(B=\{(b_{i},d_{i})\}_{i=0,...,n}\) by \((i_{1}...i_{n})\), where \(d_{i_{k}}>d_{i_{k+1}}\) for all \(1\leq k<n\). For example, \((2134)\) corresponds to the barcode with five bars shown in Figure 2.
## 3 CFSFDP Algorithm  
The CFSFDP algorithm, proposed by [PERSON] and [PERSON], forms the basis of a clustering procedure in which the number of clusters arises intuitively, and outliers are automatically spotted and excluded from the analysis. Clusters are recognized regardless of their shape and the dimensionality of the space in which they are embedded. The nodes with higher local density and larger distance will be chosen as cluster heads.  
For each data point \(x_{i}\), two variables: local density \(\rho_{i}\) and distance \(\delta_{i}\) will be obtained through CFSFDP. The local density can be calculated by two ways [10]. One is by cut-off kernel:  
\[\rho_{i}=\sum_{j\in I\backslash\{i\}}\chi(d_{ij}-d_{c}) \tag{1}\]  
\[\chi(a)=\left\{\begin{array}{ll}1&a<0\\ 0&a\geq 0\end{array}\right. \tag{2}\]  
where \(I=(1,2,...,N)\) represents the set of indices of data points. \(N\) is the number of data  
The other important variable is distance which is based on the local density. Sort all the \(\rho_{i}(i=1,2,...,N)\) in descending order, then the distance \(\delta_{i}\) of the point with highest local density \(\rho_{\max}\) is set to the maximum value of distance \(d_{\max}\). The distance of other points are set to the minimum distance between the point \(i\) and any other points with higher density. The expression of distance is defined as Equation (4) [10]:  
\[\delta_{i}=\left\{\begin{array}{cc}\max\left(d_{ij}\right)&if\rho_{i}=\rho_ {\max}\\ \min\limits_{j:\rho_{j}>\rho_{i}}\left(d_{ij}\right)&if\rho_{i}\
eq\rho_{ \max}\end{array}\right. \tag{4}\]  
As mentioned above, the data points with high distance \(\delta\) and relatively high local density \(\rho\) are regarded as the cluster centers. In order to determine the number of cluster centers accurately, [PERSON] set \(\gamma\) to represent the product of local density and distance [10]:  
\[\gamma_{i}=\rho_{i}\delta_{i}\quad i\in I \tag{5}\]  
The data point with \(\gamma_{i}\) which is higher than the threshold \(\eta\) will be selected as cluster center. After the cluster centers have been found, each remaining point is allocated to the same cluster as its nearest neighbor with higher density.  
CFSFDP, which needs less parameters and no iteration, is highly efficient and effective for clustering non-spherical and unbalanced data and the clustering process is performed in a single step. Due to these advantages, we applied it to a WSN to get a better clustering division and cluster heads selection.
# Optimal Robust LQI Controller Design for Z-Source Inverters
## 3 Robust LQI Controller Design
Usually, the weighting matrices are adjusted using a trial and error approach, which makes the design procedure a long and laborious task. Hence, this paper utilizes the BA to find the optimal values for the weighting matrices by minimizing an objective function. To this end, there exist multiple performance indices such as integral of absolute error (IAE), the integral of squared error (ISE) or integral of time-weighted-squared-error (ITSE), each of which has its advantages and disadvantages. This paper utilizes the ITSE performance index for tuning the weighting matrices, as given by (24). \[V(x)=x^{T}\mathbf{\Theta}x>0\ \ \ \forall x\
eq 0 \tag{16}\]1  
In this regard, weighting matrices are considered as \(\mathcal{R}=r\) and \(\mathcal{Q}=diag[q_{11},q_{22},q_{33},q_{44}]\), in which each microbat codes the \(q_{ii}\) and \(r\). Furthermore, as shown in Figure 3b, to provide zero steady-state error and regulated output, the LQR control is equipped with a simple integral action leading to the LQI control.
### Technological Context and Related Research
Thus, by capturing images from different angles and positions of the object or scene to be modeled, an extremely realistic virtual recreation can be achieved. Applying the NeRF technique in an industrial context within a metaverse opens up opportunities for more accurate representation of models than traditional meshing methods, for machinery, products, and manufacturing processes in a shared virtual space. One of the key features that sets this technique apart from traditional ones is its ability to capture reflections on materials. However, it is important to note that using NeRFs can be computationally intensive, resulting in significant processing overhead and requiring powerful hardware. Several studies aim to enhance NeRF's capabilities in different areas. For example, in [13], efforts are made to improve the NeRF technique to capture scenes in motion, while, in [14], the goal is to achieve high-quality results in less time than the traditional NeRF method. As the NeRF technique is a developing technology, it remains a work in progress, implying that its effectiveness and applicability may improve over time. This leads to ongoing monitoring and adaptation as its limitations are investigated and addressed, with the potential emergence of new, similarly performing techniques in the near future. The current literature highlights the increasing use of virtual environments in industrial settings, but it underscores the necessity for more advanced 3D modeling techniques to accurately represent complex objects and scenarios. While traditional methods have limitations in capturing reflections and intricate details, the emergence of Neural Radiance Fields (NeRFs) offers a promising solution.
## 3 Results
### Postural Stability and Proprioception Assessment  
#### 3.1.1 Double-Stance Test  
The mean PI value measured during the double-stance test for males and females was significantly higher with respect to the reference values, both in the OA and CE trials (Table 2).  
\begin{table}
\begin{tabular}{c c c c c} \hline  & & **Mean** & **SD** & \(p\) **Value** \\ \hline Age & F & 66.8 & 7.6 & 0.60 \\  & M & 69.3 & 3.9 & 0.60 \\  & all & 67.9 & 6.3 & \\  & F & 30.6 & 5.1 & 0.11 \\ BMI & M & 27.9 & 3.1 & 0.11 \\  & all & 29.4 & 4.4 & \\ Kellgren– & F & 3.6 & 0.5 & \\ Lawrence & M & 3.7 & 0.4 & 0.52 \\  & all & 3.6 & 0.5 & \\ KSS-Clinical & F & 57.1 & 19.0 & 0.69 \\  & all & 54.8 & 16.5 & 0.69 \\  & all & 56.1 & 17.7 & \\ KSS-Functional & F & 55.2 & 12.5 & \\  & M & 68.5 & 14.3 & 0.004 \\  & all & 61.1 & 14.7 & \\  & F & 6.5 & 2.5 & 0.001 \\ SPPB & M & 9.3 & 2.0 & 0.001 \\ all & 7.7 & 2.6 & \\ \hline \end{tabular} SD = standard deviation; ANOVA = analysis of variance; F = females; M = males; all = all patients; BMI = body mass index; KSS = Knee Society Score; SPPB = Short Physical Performance Battery.  
\end{table}
Table 1: General data of the patients.  
\begin{table}
\begin{tabular}{c c c c c} \hline  & & **Mean** & **SD** & \(n\) & \(p\) **Value** \\ \hline PI-OE & F & 0.63 & 0.23 & 21 & <0.0001 \\  & M & 0.66 & 0.20 & 17 & <0.0001 \\  & all & 0.63 & 0.22 & 38 & \\ PI-CE & F & 0.84 & 0.27 & 21 & <0.0001 \\  & M & 0.82 & 0.21 & 17 & <0.0001 \\  & all & 0.83 & 0.23 & 38 & \\ Reference & F & 0.45 & 0.14 & 117 & \\ data OE 1  & M & 0.46 & 0.13 & 119 \\  & all & n.a. & n.a. & - \\ Reference & F & 0.58 & 0.17 & 117 \\ data CE 1  & M & 0.65 & 0.19 & 119 \\  & all & n.a. & n.a. & - \\  & all & n.a. & n.a. & - \\ \hline \end{tabular} SD = standard deviation; \(n\) = number of patients; F = females; M = males; all = all patients; n.a. = not available; PI-OE = Postural Instability open eyes. PI-CE = Postural Instability closed eyes; OE = open eyes; CE = closed Eyes. \({}^{\mathrm{a}}\) Reference data from [PERSON] et al. [21] on a sample of patients ranging in age from 65 to 74 years.  
\end{table}
Table 2: Double limb stance test.
## 5 Cross-Layer Cluster-Based Energy-Efficient Protocol
### Steady Transmission Phase
In order to send neighbor information to all possible CH candidates in the direction of the sink, the CH will broadcast the next CH's signals. Furthermore, the CHs create a route towards the sink and select a final CH for relaying information to the sink. The \"Final CH\" is the CH node that has the next hop as the sink node. Forwarding packets through this route can reduce energy consumption compared to the direct transmission of messages from all CHs to the sink. During the creation of the route for inter-cluster routing, the CHs carry out their duties while transforming into the following three modes while relying on different roles. * Initial mode: When the inter-cluster routing phase starts, all CHs are assigned with initial values during the initialization process. * Route broadcasting mode: This is the mode where the signals are broadcast to establish an inter-cluster route. * Route establishing mode: In this mode, routes are established from their own routes and those of their neighbors. In this paper, we compare the CCBE algorithm with the LEACH [4] and HEED algorithm in terms of the network lifetime and throughput. \begin{table}
\begin{tabular}{l l} \hline Aggregation Level 0 & \(2<=E_{res}<1.8\) \\ Aggregation Level 1 & \(1.8<=E_{res}<1.6\) \\ Aggregation Level 2 & \(1.6<=E_{res}<1.4\) \\ Aggregation Level 3 & \(1.4<=E_{res}<1.2\) \\ Aggregation Level 4 & \(1.2<=E_{res}<1.0\) \\ Aggregation Level 5 & \(1.0<=E_{res}<0.8\) \\ Aggregation Level 6 & \(0.8<=E_{res}<0.6\) \\ Aggregation Level 7 & \(0.6<=E_{res}<0.4\) \\ Aggregation Level 8 & \(0.4<=E_{res}<0.2\) \\ Aggregation Level 9 & \(0.2<=E_{res}=>0\) \\ \hline \end{tabular}
\end{table} 
Table 1: Aggregation levels based on the residual energy of the CH.
# Voxel-Based Digital Twin Framework for Earthwork Construction
## 3 Methodology
### Earthwork Virtual Model Construction
#### 3.3.1 Surface and Geotechnical Model  
The original ground model digitally represents the terrain topography, slopes, design zones, and their properties. Several representations were reviewed to select the ground model type. The ground model provides a static environment for equipment mobility and is not directly manipulated by the equipment. Hence, a simplified and accurate TIN-based surface modeling approach was used to represent the ground conditions. TIN constructs a mesh model of irregular triangles from drone surveys or LIDAR scans to represent complex and large-scale geographical conditions (Figure 4a).  
The geotechnical model represents the variation in geological profiles, along with characteristics such as earthwork materials, bearing strength, and moisture content. Investigation reports and borehole data were used to generate a subsurface model. B-rep was used to represent the subsurface volumetric information by defining the geometries using the boundary surfaces. Before modeling, the borehole coordinates were transferred from the local to the standard Universal Transverse Mercator (UTM) to obtain georeferenced data. The borehole coordinates were then transferred using a transformation equation.  
For a borehole point p = [x, y, z]\({}^{\top}\) in the local coordinate system, its transformed position is  
\[P_{unified\ coordinate}=R.P_{local\ coordinate}+t \tag{1}\]  
where R is a rotational matrix and t is a translational vector.  
R = Rx. Ry. Rz  
\[R_{x}=\begin{bmatrix}1&0&0\\ 0&\cos\theta x&-sin\ \theta x\\ 0&sin\ \theta x&\cos\theta x\end{bmatrix} \tag{2}\]\[R_{y}=\begin{bmatrix}cos\ \theta y&0&sin\ \theta y\\ 0&1&-sin\ \theta x\\ -sin\ \theta y&0&cos\ \theta y\end{bmatrix} \tag{3}\]  
\[R_{z}=\begin{bmatrix}cos\ \theta z&-sin\ \theta z&0\\ sin\ \theta z&cos\ \theta z&0\\ 0&0&1\end{bmatrix} \tag{4}\]  
Assuming the boreholes are created vertically, their coordinates are determined through the following equation:  
\[P_{unified\ coordinate}=t \tag{5}\]  
\[t_{x}\]  
where \(t=[t_{y}]\), and t\({}_{x}\), t\({}_{y}\), and t\({}_{z}\) are translations in the x-, y-, and z-directions, respectively.  
\[t_{z}\]  
After determining the coordinate values for each borehole, they were integrated with the ground surface and modeled. First, boreholes were created from the point data at different depths obtained through a geotechnical investigation (Figure 4b). Layers were created at each depth to obtain surface information for each material type (Figure 4c,d). The top and bottom layers of each material were used to develop the volumetric B-rep model (Figure 4e,f). A detailed method for creating the geotechnical model can be found in our previous article [24].
## 2 Nonlinear Finite-Element Modeling
### Material Model
#### 2.5.1 CDP Model  
The concrete damaged plastic (CDP) model [19; 20; 21] assumed compressive and tensile failure as two failure mechanisms. The yield surfaces and deviatoric plane of the CDP model are shown in Figure 3. The yield function of the CDP model is depicted as [19] follows:  
\[F=\frac{1}{1-\alpha}[\overline{q}-3\alpha\overline{p}+\beta(\tilde{\varepsilon }_{t}^{pl},\tilde{\varepsilon}_{c}^{pl})(\hat{\sigma}_{\max})-\gamma(-\hat{ \sigma}_{\max})]-\overline{\sigma}_{c}(\tilde{\varepsilon}_{c}^{pl}) \tag{11}\]  
\[\overline{p}=-\frac{1}{3}\text{tr}(\mathbf{\sigma}) \tag{12}\]  
\[\overline{q}=\sqrt{\frac{3}{2}\|\text{dev}(\mathbf{\sigma})\|} \tag{13}\]  
with  
\[\alpha=\frac{(\sigma_{b0}/\sigma_{c0})-1}{2(\sigma_{b0}/\sigma_{c0})-1}; \quad\quad 0\leq\ \alpha\leq 0.5 \tag{14}\]  
\[\beta=\frac{\overline{\sigma}_{c}(\tilde{\varepsilon}_{c}^{pl})}{\overline{ \sigma}_{t}(\tilde{\varepsilon}_{t}^{pl})}(1-\alpha)-(1+\alpha) \tag{15}\]  
\[\gamma=\frac{3(1-K_{c})}{2K_{c}-1} \tag{16}\]  
where \(\overline{p}\) and \(\overline{q}\) are the hydrostatic stress and the von [PERSON] equivalent stress, respectively; \(\tilde{\varepsilon}_{t}^{pl}\) and \(\tilde{\varepsilon}_{c}^{pl}\) are the plastic strain in tension and compression, respectively; \(\hat{\sigma}_{\max}\) is the max principal effective stress; \(\mathbf{\sigma}\) denotes the stress tensors; \(\sigma_{b0}\)/\(\sigma_{c0}\) is the initial equi-biaxial compressive yield stress to initial uniaxial compressive yield stress, which was taken as 1.16 in this study. \(\overline{\sigma}_{c}(\tilde{\varepsilon}_{c}^{pl})\) and \(\overline{\sigma}_{t}(\tilde{\varepsilon}_{t}^{pl})\) are cohesion values in tension and compression, assumed to depend on the compressive and tensile equivalent plastic strains, \(\tilde{\varepsilon}_{c}^{pl}\) and \(\tilde{\varepsilon}_{t}^{pl}\), respectively.  
As shown in Figure 3, \(K_{c}\) is the ratio of the second stress invariant on the tensile meridian to that on the compressive meridian, which directly controls the shape of the yield surfaces in the deviatoric plane. According to the work of [PERSON] [20], \(K_{c}\) was taken as 2/3 in this study.