esa-sceva/satcom-chunk-collection huggingface dataset:
## 2 The Proposed Method
### Weight Initialization  
CNNs have three primary layers: convolutional, pooling, and fully connected. The convolutional layer extracts spatial features by convolving multiple filters of different sizes with the input data. Proper initialization of the weights and biases is critical to obtaining meaningful features. However, during training, problems like vanishing or exploding gradients may occur due to the different hyperparameter settings, such as the learning rate. Researchers have explored various hyperparameter configurations to fine-tune the model weights and optimize performance.  
Figure 2: Diagram of the internal structure of the autoencoder, which is the basic building block of the proposed model.  
There are three types of weight initialization methods. The first method uses a constant set of weights for network initialization, which can prevent the learning algorithm from updating the network weights. The second method uses distribution-based initialization, such as uniform or Gaussian distribution, to assign random values to the distribution matrices. However, setting appropriate parameters for the network, such as the standard deviation and mean of the distribution, is challenging. This can impact the model's training and result in vanishing gradient problems. The third approach utilizes random initialization based on prior knowledge.  
The traditional CNN models use the backpropagation error approach to fine-tune parameters, resulting in slow convergence and a prolonged search for local minima, which needs longer training times. To address this issue, neural networks that leverage random weight initialization have been proposed in the literature. Currently, deep learning approaches have demonstrated promising results across a range of domains. However, these models also present challenges such as higher computation costs, specific task-oriented parameter tuning, and low convergence rates.  
Heuristic approaches randomly initialize the layer weights and activation functions to cope with these issues. Heuristic strategies involve problem-solving without the use of an optimal solution method. This type of randomization allocates the normal distribution variance based on the input shape, which reduces the problem of vanishing or exploding gradients. As a result, the model achieves faster convergence and mitigates the oscillation of minima.
# The Firmware Design and Implementation Scheme for C Form-Factor Pluggable Optical Transceiver +
## 3 CFP Firmware Design Scheme
### MCU Design
#### 3.3.2. DDM Function  
The DDM function monitors the state of the CFP optical component read from the external ADC chip and the hardware status read by the MCU internal sensor. The values read through the external ADC are the transmit/receive optical power, transmit bias current, and transmit optical component temperature for each channel. The internal MCU sensor values are temperature and voltage. The MCU updates the monitored values from the ADC in the corresponding memory and converts the values  
Figure 7: MCU Function Block Diagram.  
into unit values defined in the standard document. In particular, to increase the accuracy of the transmitted and received optical power of the DDM without deviating from the standard error range, the MCU is designed to calculate the DDM value using a higher-order polynomial. The Equation (1) is DDM equation representing the received optic power.  
\[RXPWR=\sum\limits_{n=1}^{m}C_{n}A^{n}+Offset(i)+TempCal(i) \tag{1}\]  
Here is the received optical power DDM value for channel \(i\) and is the \(n\)th-order coefficient value, and calculations are performed up to the mth order. The maximum value of \(m\) is 4. \(A\) is the value monitored from the ADC, \(C\) is the value of coefficient of each term and _Offset_ represents the offset of each channel. All coefficient values and offsets can be assigned to the CFP VENDOR PRIVATE memory, and the coefficients and offsets of each order can be set to values in floating point format (IEEE 754). In addition, the DDM value is corrected using a look-up table (LUT) to reduce the DDM error caused by the ambient temperature. The LUT value is stored in the MCU's flash memory. Values stored in flash memory are copied to the CFP VENDOR PRIVATE memory during the optical transceiver initialization. The optical component for CFP transceiver requires a DDM calibration procedure according to temperature, as the properties of optical component vary slightly depending on the environmental temperature. The proposed method is to store the temperature-dependent calibration values in the LUT and reflect them in the final DDM value. _TempCal(i)_ is the temperature calibration value of channel \(i\) according to the temperature. _TempCal_ is obtained from LUT. For receiver, the final received optical power DDM value is obtained by adding the calibration value to _RXPWR_. The transmitter optical power DDM vaule also used the same DDM method.  
Detecting the property change of the optical component by aging in the firmware itself is difficult. Therefore, DDM-related parameters are determined by sufficient age testing and precise measurements.
## 2 Fundamentals of SAR for Antenna Sizing and Transmitting Power Consideration
### Selection of Operating Frequency
In this study, one of the fixed parameters of the analyzed SAR system is selected as the X-band, in line with recent examples presented in Table 1.
# Study on Drone Handover Methods Suitable for Multipath Interference Due to Obstacles
## 3 How to Evaluate Flying Drones
### Evaluation Results of Conventional Methods  
The developed simulator was used to evaluate a conventional handover sequence, as shown in Figure 7. The simulation model of the conventional method was evaluated using STA flight paths on the map shown in Figure 12. The map was obtained using the GSI map data download service [41]. In this map, the drone at the mobile station is designated as an STA and repeats the handover while passing along the red-dotted path from AP1 to AP4 of the base station. The service model assumes that the STA uploads video images captured while flying to the AP on the ground and continuously sends UDP data from the STA to the AP.  
Table 1 lists the parameters used for the evaluation. The communication method used was the IEEE802.11g standard [42], frequency band 2.4 GHz, and transmission power 0.2 mW. The STA and AP were at the same height of 5 m above the ground, and the flight speed of the STA was 5 km/h.  
The simulation results for the evaluation model are presented in Figure 13. Figure 13 shows time [s] on the horizontal axis and throughput [Mbps] on the vertical axis. Handover occurs between AP1 and AP4; however, after connecting to AP2, a period of low throughput is followed by a connection to AP4 without connecting to AP3 because no beacon reception  
Figure 12: Simulation model and flight path.  
failure occurs after handover to AP2; therefore, the decision to initiate handover is not made, and the connection to AP2 with low reception power is maintained, resulting in a situation where handover to AP3 with high reception power cannot be performed. These results confirm that the handover to the optimal AP is not performed unless a beacon failure occurs in the conventional method.
## 3 Analysis of Results  
As mentioned above, the particularity of the granite wastes from gang saws used in this test (GCW-GS) is that they contain higher percentages of CaO (4.5%) and Fe\({}_{2}\)O\({}_{3}\) (14.6%) than the granite cutting waste from diamond saws (GCW-D) [14]. Therefore, the results obtained will be related, in some way, to the presence of these compounds in the manufactured concrete. Both CaO and Fe\({}_{2}\)O\({}_{3}\) are occasionally used as additives in the form of nanoparticles to change the properties of mortars and concretes. For this reason, to facilitate the analysis of results, the percentage increase of Fe\({}_{2}\)O\({}_{3}\) and CaO with respect to the amount of cement used in the different mixtures was calculated (Table 5). The use of GCW-GS in substitutions of 35%, 70%, and 100% is equivalent to the addition of 1.43%, 2.88%, and 4.1% of Fe\({}_{2}\)O\({}_{3}\), and of 0.44%, 0.88%, and 1.26% of CaO, respectively, in relation to the amount of cement in the mix.  
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{2}{*}{**Properties**} & \multicolumn{2}{c}{**Control**} & \multicolumn{2}{c}{**35\% GCW-GS**} & \multicolumn{2}{c}{**70\% GCW-GS**} & \multicolumn{2}{c}{**100\% GCW-GS**} \\ \cline{2-9}  & **Value** & **Variation** & **Value** & **Variation** & **Value** & **Variation** & **Value** & **Variation** \\ \hline Slump (cm) & 25 & & 23 & & 20 & & 21 & \\ Density (kg/m\({}^{3}\)) & 2410 & \(\pm\)35 & 2420 & \(\pm\)44 & 2470 & \(\pm\)35 & 2500 & \(\pm\)14 \\ Compressive strength (MPa) & 117 & \(\pm\)2.9 & 127 & \(\pm\)6.5 & 134 & \(\pm\)4.6 & 129 & \(\pm\)6.5 \\ Modulus of elasticity (GPa) & 45 & \(\pm\)1.0 & 43.4 & \(\pm\)1.2 & 42 & \(\pm\)1.6 & 41 & \(\pm\)0.1 \\ Flexural strength (MPa) & 23 & \(\pm\)0.8 & 25.7 & \(\pm\)0.3 & 19 & \(\pm\)1.6 & 22 & \(\pm\)3.4 \\ Tensile strength (MPa) & 8.7 & \(\pm\)0.6 & 11.8 & \(\pm\)0.1 & 6.8 & \(\pm\)1.2 & 8.8 & \(\pm\)0.8 \\ \hline \hline \end{tabular}
\end{table}
Table 4: Average results of UHPFRC.  
Figure 4: Modulus of elasticity and flexural strength tests.  
Iron oxide (Fe\({}_{2}\)O\({}_{3}\)) is often used as an additive in mortar and concrete in percentages of up to 5% of the amount of cement because the pozzolanic reactions it causes improve the mechanical strength [28; 29; 30; 31].  
Calcium oxide (CaO) is also used as an additive in mortars and concretes in percentages of up to 5% to reduce shrinkage without adverse effects on the compressive strength in high-performance concrete. This is due to its pozzolanic effect when used in combination with silica fume [32].
## 2 Related Work
### Feature Fusion  
Feature fusion refers to the fusion of information from different feature sources into a unified feature vector to improve the performance and robustness of a model in various tasks. It includes feature-level fusion, modality-level fusion and feature correction. For example, in image recognition tasks, features such as different scales and colors can be extracted from the original image and then fused to form a new feature vector. [PERSON] et al. [32] proposed a deep residual structure to fuse different levels of features across scales, and [PERSON] et al. [11] proposed a model using a deep Boltzmann machine for training features from visual, text and speech data from different modalities for cross-modal learning and feature fusion, and [PERSON] et al. [33] proposed a convolutional neural network based image retrieval method that integrates feature correction mechanisms such as local voting and pooling in the network structure, which is used to improve retrieval robustness and accuracy. Regardless, feature enhancement is a not an indispensable part of feature fusion, which refers to the reconstruction or expansion of existing features, such as data enhancement [10], transformation of features from different sources [11], gradient selection [9] and feature reconstruction [34]. We borrowed the feature fusion ideas from the above papers and proposed the use of attention mechanism and global average residual structure to fuse long and short interest features, and proved the effectiveness of our method in the final feature fusion comparison experiments.
# Vibration Fatigue Life Reliability Cable Trough Assessment by Using Weibull Distribution
## 4 Numerical Application
### Weibull Stress Random Analysis  
Since the determination of the fatigue is based on the random behavior of the \(\sigma_{2}\) stress value, here the random behavior of the \(\sigma_{1}\) and \(\sigma_{2}\) are calculated by Equations (19) and (20). Then, by using the \(\beta_{s}\) and the \(Y_{i}\) values in Equation (18), the basic Weibull elements [20]\(t_{0i}\) for each \(Y_{i}\) are obtained. Whereas using the \(\eta_{s}\) and \(\sigma_{1}\) values in Equation (21), the Weibull \(t_{01}\) value from the \(\sigma_{1}\) and \(\sigma_{2}\) stresses values are reproduced, it is calculated as,  
\[t_{01}=\frac{626.13}{1188}=0.52705\]  
Additionally, by using the value \(\beta_{s}\) in Equation (22), the \(Y_{1}\) value that belongs to the \(t_{01}\) value is determined as,  
\[Y_{1}=\ln(0.52705)*1.7087=-1.09438\]  
Next, by substituting the \(Y_{1}\) value in the Equation (23), the reliability \(R(t)\) that belongs to the \(t_{01}\) element is,  
\[R(t)=\exp\{-\exp\{-1.09438\}\}=0.716\]  
The previous results shown in this section are included in Table 4. Here, it is important to mention that the reliability obtained \(R(t)\) = 0.716 does not represent the reliability of the design component. The minimal reliability of the component is obtained when the \(Y_{1}\) value that belongs to the \(S_{y}\) value is used in Equation (23). The steps to have the reliability of the design component when the \(S_{y}\) value is used as \(\sigma_{1}\) in Equation (21) are, the \(t_{Sy}\) element that belongs to the \(S_{y}\) value is, \(t_{sy}=\frac{626.13}{4350}=0.14394\). From Equation (22) the corresponding \(Y_{Sy}\) value is, \(Y_{sy}=\ln(0.14394)*1.7087=-3.31213\). The reliability index for the \(Y_{sy}\) value is calculated by using Equation (23), \(R(t)=\exp\{-\exp\{-3.31213\}\}=0.964\). Thus, we conclude that the reliability of the design component is \(R(t)=0.964\).  
The reliability \(R(t)\)  calculated so far is with the condition provided that the component is subjected to constant stress, however, the random vibration that induces the stress, is variant stress. Therefore, for variant stress, the following is stated.
## 2 Materials and Methods
### Characterization Techniques  
The X-ray Diffraction (XRD) measurements were performed on a Rigaku SmartLab [Cu K] radiation (1.54 A) source. The morphology of as-synthesized electrode material and EDS (energy-dispersive X-ray spectroscopy) were investigated using the JEOL/ISM-7800F field emission scanning electron microscopy instrument. The FTIR spectra for electrode material on NF substrate were acquired using an FT-IR microscope, the Hyperion 2000. Electrochemical studies on a fabricated two-terminal supercapacitor device were carried out using an IVIUM Technologies Compactstat.h electrochemical workstation. On NF, the mass loadings on INS and INSC are 1.8 and 2.2 mg/cm\({}^{2}\), respectively. The electrochemical performance of prepared, direct-grown electrode samples was investigated using cyclic voltammetry (CV), galvanostatic charge-discharge (GCD), and electrochemical impedance spectroscopy (EIS) techniques.  
The following equation can be used to determine the specific capacitance (Cs) of electrode samples based on CV curves [7].  
\[C_{S}\ =\ \frac{1}{ms(V_{2}-V_{1})}\int_{V_{1}}^{V_{2}}I(V)dv \tag{1}\]  
where \"m\" denotes the mass of electrode material deposited on the substrate as determined by the mass difference method, \"s\" denotes the scan rate, \"I(V)\" denotes the response current, and \"(V\({}_{2}-V_{1}\))\" denotes the measurement potential window.  
The specific capacitance can be determined from the GCD study.  
\[C_{S}\ =\ Q/\left(\Delta V\times m\right)\ =\ \left(I\times\Delta t\right)/ \left(\Delta V\times m\right) \tag{2}\]  
I, \(\Delta\)t, \(\Delta\)V, and m denote the utilized current, discharge time, accepted potential window of the GCD curve, and active mass deposited on the substrate.  
The following formulae are utilized to calculate both parameters, energy density and power density, from GCD curves.  
\[E\ =\ 1/2\left(C_{S}\times V_{max}^{2}\right) \tag{3}\]  
\[P\ =\ \left(E\times 3600\right)/\Delta t \tag{4}\]  
\(V_{max}\), E, and P are used to denote the maximum voltage, energy density, and power density, respectively.
## 2 Theory and Model
### The Separate Model of Multiple Low-Rank Constraints
\right\| _{F}^{2}\right\}=\underset{l_{i}}{arg}\left\{\frac{\lambda_{i}}{\mu_{k}}\|L_{i} \|_{s}+\frac{1}{2}\|l_{i}-T_{i,k}\|_{F}^{2}\right\} \tag{8}\]  
\[N_{k+1}^{s}=\underset{n}{arg}\left\{\frac{\beta}{\mu_{k}}kur(N)+\frac{1}{2} \right\|x-\sum\limits_{j=1}^{q}l_{j,k}-N+\frac{1}{\mu_{k}}Y_{k}\bigg{\|}_{F}^{ 2}\right\} \tag{9}\]  
The suboptimization problem of Equation (8) can be solved by singular value decomposition (SVD) and soft threshold operations:  
\[[U_{i},S_{i},V_{i}]=\text{SVD}(w(T_{i,k},o_{i},p_{i})) \tag{10}\]  
\[l_{i;k+1}=\text{reshape}\Big{(}U_{i}S_{\lambda_{i}/\mu_{k}}[S_{i}]V_{i}^{T},1,o_{i}\times p_{i}\Big{)} \tag{11}\]  
where \(\text{SVD}()\) is the singular value decomposition operator, and \(S_{\lambda_{i}/\mu_{k}}[\)\(]\) is the soft threshold shrinkage operator for the positive parameter \(\lambda_{i}/\mu_{k}\). For the suboptimization problem in Equation (9), the penalty term \(\left\|x-\sum\limits_{j=1}^{q}l_{j,k}-N+\frac{1}{\mu_{k}}Y_{k}\right\|_{F}^{2}\) can be transformed into \(x+\frac{1}{\mu_{k}}Y_{k}=\sum\limits_{j=1}^{n}l_{j,k}+N\) to obtain the equivalent optimization subproblem, as follows:  
\[\underset{n}{minkur(N),s.t.}\ x+\frac{1}{\mu_{k}}Y_{k}=\sum\limits_{j=1}^{n}l _{j,k}+N \tag{12}\]  
The problem of Equation (12) can also be solved by singular value decomposition and soft threshold operations, as follows:  
\[[U_{N},S_{N},V_{N}]=\text{SVD}\bigg{(}w\bigg{(}x+\frac{1}{\mu_{k}}Y_{k},o_{1},p_{1}\bigg{)}\bigg{)} \tag{13}\]  
\[\text{N}_{k+1}=N_{k}-\text{reshape}\Big{(}U_{N}S_{\beta}[S_{N}]V_{N}{}^{T},1,o_{i}\times p_{i}\Big{)} \tag{14}\]  
where \(S_{\beta}[\)\(]\) is the soft threshold shrinkage operator of the positive parameter \(\beta\). Equations (10), (11), (13), and (14) can be used to solve Equations (8) and (9) by updating \(l_{i,k+1}\). The Lagrange operator \(Y_{k+1}\) and threshold \(\alpha_{k+1}\) need to be updated by:  
\[Y_{k+1}=Y_{k}+\alpha_{k}\bigg{(}x-\sum\limits_{i=1}^{q}l_{i,k+1}-n_{k+1}\bigg{)} \tag{15}\]  
\[\alpha_{k+1}=\rho\alpha_{k},\ \rho=1.5 \tag{16}\]
# A Data-Driven Model for the Energy and Economic Assessment of Building Renovations
## 3 Results
### Feature Importance Analysis by Random Forest
Based on this comparative evaluation, random forest was selected as the primary model for subsequent analyses, offering both technical robustness and operational value in the context of data-driven energy renovation planning. To assess the importance of each feature, permutation importance, a model-agnostic method that evaluates how shuffling the values of each variable affects prediction accuracy, has been employed. This approach provided a reliable, unbiased ranking of the most influential variables. The model achieved an R\({}^{2}\) score of 0.91 on the test set, indicating excellent predictive performance. To enhance interpretability, the resulting importance scores were normalized, offering a clear comparative view of feature impacts. Figure 3 presents the feature importance analysis results, illustrating the relative contribution of each building characteristic to energy consumption prediction. The horizontal  
bar chart clearly demonstrates that envelope components--particularly wall U-values (28%), glass U-values (18%), and glass surface percentage (12%)--have the most substantial impact on energy performance. This visualization quantifies the relative influence of each parameter, showing that the top three factors alone account for approximately 60% of the model's predictive power. Notably, occupancy-related parameters contribute minimally (5% combined), suggesting that physical building characteristics offer significantly greater leverage for energy efficiency improvements. The color-coded categorization further enhances interpretability by grouping similar architectural elements, enabling stakeholders to identify which building systems present the most promising retrofit opportunities. This visualization serves as a critical decision-support tool, allowing building owners and policy makers to direct limited resources toward modifications with the highest potential impact. The ranking of feature importance in Figure 3 guided the identification of a digital representative building and the selection of retrofit strategies in the subsequent sections. The results of the analysis revealed that wall insulation performance (wall U-value), the percentage of glass surface, and year of construction were the most critical predictors of total energy consumption. These findings are consistent with physical building energy simulation models and reinforce the significance of envelope design in determining energy efficiency. By statistically quantifying the influence of each parameter, this methodology provides a concrete basis for prioritizing retrofit measures. Instead of applying generic solutions, stakeholders can now identify and target the most impactful areas for intervention. For building owners, designers, and policymakers, this analysis offers a valuable tool for maximizing energy savings and return on investment, particularly in the context of constrained renovation budgets and evolving energy performance regulations.
# Hybrid NOMA Protocol with Relay Adaptive AF/DF Collaboration and Its Modeling Analysis in NB-IoT
## 3 Performance Modeling Analysis of H-NOMA Protocol
### Relay-Based Adaptive Collaboration and H-NOMA Signal Transmission Process
#### 3.1.2 Collaboration Stage
\begin{array}{ll}&\mathrm{Let}\ y-\frac{\tau}{\rho_{P}\bar{\beta}_{1}-\tau \rho_{P}\bar{\beta}_{2}}=t.\ \mathrm{Then,}\ \mathrm{the,}\ \mathrm{above}\ \mathrm{equation}\ \mathrm{is:}\\ &P^{A}_{RU_{1}}=1-\int_{0}^{\infty}\frac{1}{\lambda_{\bar{\beta}1}}\exp(- \frac{t+\frac{\tau}{\rho_{P}\bar{\beta}_{1}-\tau\rho_{P}\bar{\beta}_{2}}}{ \lambda_{\bar{\beta}1}\lambda_{\bar{\beta}1}\rho_{P}\bar{\beta}_{1}(\bar{\beta }_{1}-\bar{\beta}_{2})})\cdot\exp(-\frac{\tau\rho_{P}(t+\frac{\tau}{\rho_{P} \bar{\beta}_{1}-\tau\rho_{P}\bar{\beta}_{2}})+\tau}{\lambda_{\bar{\beta}1} \rho_{P}\bar{\beta}_{1}(\bar{\beta}_{1}-\bar{\beta}_{2})})\mathrm{d}t\\ &=1-\frac{1}{\lambda_{\bar{\beta}1}}\exp(-\frac{\lambda_{\bar{\beta}1}\tau \rho_{P}+\lambda_{\bar{\beta}1}\tau\rho_{P}}{\lambda_{\bar{\beta}1}\lambda_{ \bar{\beta}1}\lambda_{\bar{\beta}1}\rho_{P}\bar{\beta}_{1}(\bar{\beta}_{1}- \bar{\beta}_{2})})\sqrt{\frac{\lambda_{\bar{\beta}1}\tau\bar{\beta}_{P}+ \lambda_{\bar{\beta}1}\tau\rho_{P}(\bar{\beta}_{1}-\bar{\beta}_{2})}{ \lambda_{\bar{\beta}1}\lambda_{\bar{\beta}1}\rho_{P}(\bar{\beta}_{1}-\tau \rho_{P}\bar{\beta}_{2})^{2}}}K_{1}\left(2\sqrt{\frac{\tau^{2}\rho_{P}+\tau \rho_{P}(\bar{\beta}_{1}-\bar{\beta}_{2})}{\lambda_{\bar{\beta}1}\lambda_{ \bar{\beta}1}\rho_{P}(\bar{\beta}_{1}-\tau\rho_{P}\bar{\beta}_{2})^{2}}} \right).\end{array} \] (23)

\(\bullet\) Calculation of outage probability for R to user \(U_{2}\).The solution is the same as Equation (20):

\[ \begin{array}{ll}P^{A}_{RU_{2}}&=Pr(\log_{2}(1+\gamma^{A}_{RU_{2}})<R_{th}) =Pr(|g_{2}|^{2}<\frac{\tau}{\rho_{P}\bar{\beta}_{2}})+Pr(|h_{r}|^{2}<\frac{ \tau\rho_{P}|g_{2}|^{2}+\tau}{\rho_{P}\rho_{P}|g_{2}|^{2}-\tau\rho_{s}},|g_{2} |^{2}>\frac{\tau}{\rho_{P}\bar{\beta}_{2}})\\ &=Pr(|g_{2}|^{2}<\frac{\tau}{\rho_{P}\bar{\beta}_{2}})+\int_{\frac{\tau\rho_{P} \bar{\beta}_{2}}{\bar{\beta}_{2}}}^{\infty}\frac{1}{\lambda_{\bar{\beta}2}}\exp \left(-\frac{y}{\lambda_{\bar{\beta}2}}\right)\int_{0}^{\frac{\tau\rho_{P}\bar {\beta}_{2}}{\rho_{P}\bar{\beta}_{2}}{\rho_{P}\bar{\beta}_{2}}{\rho_{P}\bar{ \beta}_{2}}{\rho_{P}\bar{\beta}_{2}}}\frac{1}{\lambda_{\bar{\beta}2}}\exp\left(- \frac{y}{\lambda_{\bar{\beta}2}}\right)\mathrm{d}x\mathrm{d}y\\ &=1-\int_{\frac{\tau}{\rho_{P}\bar{\beta}_{2}}}^{\infty}\frac{1}{\lambda_{ \bar{\beta}2}}\exp\left(-\frac{y}{\lambda_{\bar{\beta}2}}\right)\cdot\exp\left(- \frac{\tau\rho_{P}y+\tau}{\lambda_{\bar{\beta}1}\mu\rho_{s}(\rho_{P}\bar{\beta}_ {2}-\tau)}\right)\mathrm{d}y.\end{array} \] (24)

Let \(y-\frac{\tau}{\rho_{P}\bar{\beta}_{2}}=t\).