esa-sceva/satcom-chunk-collection huggingface dataset:
## 3 Methodology
### Local Blur Transformation (LBT)
#### 3.2.2 Parameter Generator Network (PGN)  
Once the local region is determined, it enters the PGN. Then, PGN generates the weight of a filter matrix for blur transformation. The parameters, four transformation weights \(W_{1},\ldots,W_{4}\), form the following \(3\times 3\) filter matrix.  
\[S_{1}=\left(\begin{array}{ccc}0&W_{1}&0\\ W_{2}&0&W_{4}\\ 0&W_{3}&0\end{array}\right). \tag{1}\]  
The detailed structure of PGN is shown in Table 1. It contains convolutional, pooling, and fully connected layers. In particular, MP donates a max pooling layer, and BN stands for batch normalization. Note that the kernel size, stride, and padding size are, respectively, 3, 1, and 1. At the end, FC layer outputs four parameters, which contribute to another filter matrix.  
As shown in Figure 3, we used a filter matrix with the original sample to synthesize the augmented blur image; see Section 3.2.3 for more details. To produce the four augmented samples, the other three filter matrices \(S_{2}\), \(S_{3}\), and \(S_{4}\) must be created. By rotating the positions of the weight parameters clockwise, we obtain the following filter matrices.  
\[S_{2}=\left(\begin{array}{ccc}0&W_{2}&0\\ W_{3}&0&W_{1}\\ 0&W_{4}&0\end{array}\right),S_{3}=\left(\begin{array}{ccc}0&W_{3}&0\\ W_{4}&0&W_{2}\\ 0&W_{1}&0\end{array}\right),S_{4}=\left(\begin{array}{ccc}0&W_{4}&0\\ W_{1}&0&W_{3}\\ 0&W_{2}&0\end{array}\right). \tag{2}\]  
Finally, we utilize the four filter matrices \(S_{1},\ldots,S_{4}\) with original sample \(x\) to transform four augmented samples \(x_{1},\ldots,x_{4}\). The four augmented samples are made by LBT. Our  
\begin{table}
\begin{tabular}{c c} \hline \hline
**Description** & **Dimension** \\ \hline Original & \(1\times h\times w\) \\ Con16, Relu, MP & \(16\times 16\times 50\) \\ Con64, Relu, MP & \(64\times 8\times 25\) \\ Con128, BN, [PERSON] & \(128\times 8\times 25\) \\ [PERSON], [PERSON], MP & \(128\times 4\times 12\) \\ [PERSON], [PERSON], [PERSON] & \(64\times 4\times 12\) \\ [PERSON], [PERSON], [PERSON], MP & \(16\times 2\times 6\) \\ [PERSON] & \(4\) \\ \hline \hline \end{tabular}
\end{table}
Table 1: Structure of PGN. **BN** means batch normalization and **MP** represents \(2\times 2\) max pooling. The inputted \(1\times h\times w\) image size is generated by LRS.  
innovation lies in the generation of transformation parameters by using a neural network, which greatly improves the efficiency of the framework.
## 3 Single Linear System
### Stability of Autonomous System
: _Compared with Lemma 2 in [42], there are more adjustable parameters in the conditions of Theorem 1, and therefore, the conditions of Theorem 1 are more flexible._  
When the parameter in Theorem 1 \(\vartheta(t)=\pi(t)=\theta(t)=0\), the following corollary can be easily obtained. **Corollary 1**. : _The constants are \(T,\rho\), \(\alpha>0\) with \(\rho\alpha<1\), and vector-value function \(\eta(t)\succ 0\). If there exists a vector-valued function \(v(t)\succ 0\) such that_ \begin{tabular}{l l} _(1)_ & \(v^{\rm T}(t)+v^{\rm T}(t)A(t)\prec 0\)_,_ \\ _(2)_ & \(v^{\rm T}(t)H(t)-\rho_{\rm v}^{\rm T}(t)\preceq 0\)_, and_ \\ _(3)_ & \(\eta^{\rm T}(t)C(t)-\alpha v^{\rm T}(t)\preceq 0\)_,_ \\ \end{tabular}  _hold, then system (6) is positive and there is IO-FTS w.r.t. \((\omega_{1},\eta(\cdot),T)\), where \(A(t)\) is a Metzler matrix-valued function, \(H(t)\succeq 0\), \(C(t)\succeq 0\), \(x(t_{0})=0\), \(v(\cdot)\in\omega_{1}\), and \(t\in[t_{0},T]\)._  
**Theorem 2**: _The constants are \(T,\rho,\lambda,\alpha>0\) with \(\rho\alpha<1\), and vector-value function \(\eta(t)\succ 0\). If there exist vector-valued functions \(v(t),\theta(t),\pi(t):\mathbb{R}_{+}\to\mathbb{R}_{+}^{n}\) and \(\theta(t):\mathbb{R}_{+}\to\mathbb{R}^{n}\), such that_  
_(1)_ \(\hat{v}^{\mathsf{T}}(t)+v^{\mathsf{T}}(t)A(t)+\pi^{\mathsf{T}}(t)+\theta^{ \mathsf{T}}(t)\prec 0\)_,_  
_(2)_ \(v^{\mathsf{T}}(t)H(t)+\theta^{\mathsf{T}}(t)-\rho\xi^{\mathsf{T}}(t)\preceq 0\)_,_  
_(3)_ \(\lambda\pi^{\mathsf{T}}(t)+\hat{\theta}^{\mathsf{T}}(t)+\theta^{\mathsf{T}}(t) A(t)+\lambda\theta^{\mathsf{T}}(t)\succeq 0\)_,_  
_(4)_ \(\lambda\theta^{\mathsf{T}}(t)+\theta^{\mathsf{T}}(t)H(t)\succeq 0\)_, and_  
_(5)_ \(\tilde{\eta}^{\mathsf{T}}(t)C(t)-\alpha v^{\mathsf{T}}(t)\preceq 0\)_,_  
_hold, then system (6) is positive and there is IO-FTS w.r.t. \((\omega_{\infty},\eta(\cdot),T)\), where \(A(t)\) is a Metzler matrix-valued function, \(H(t)\succeq 0\), \(C(t)\succeq 0\), \(\tilde{\eta}(t)=(t-t_{0})\eta(t)\), \(x(t_{0})=0\), \(v(\cdot)\in\omega_{\infty}\), and \(t\in[t_{0},T]\)._  
When \(A(t)\) is a Metzler matrix-valued function and \(H(t)\succ 0\), system (6) is positive by Lemma 1. Choose  
\[V(t,x(t))=v^{\mathsf{T}}(t)x(t)+\int_{t_{0}}^{t}e^{-\lambda(t-s)}\pi^{\mathsf{ T}}(s)x(s)ds+\int_{t_{0}}^{t}e^{-\lambda(t-s)}\hat{\sigma}^{\mathsf{T}}(s)v(s)ds.\]  
According to the proof process of Theorem 1, for any \(t\in[t_{0},T]\), \(x(t_{0})=0\), and \(v(\cdot)\in\omega_{\infty}\), we can obtain  
\[V(t,x(t))\leq\int_{t_{0}}^{t}\xi^{\mathsf{T}}(\tau)v(\tau)dt<\rho(t-t_{0}).\]  
From condition (5) of Theorem 2,  
\[\tilde{\eta}^{\mathsf{T}}y(t)=\tilde{\eta}^{\mathsf{T}}C(t)x(t)\leq\alpha v^{ \mathsf{T}}x\leq\alpha V(t,x(t))<t-t_{0},\]  
then  
\[\eta^{\mathsf{T}}(t)y(t)=\frac{1}{t-t_{0}}\tilde{\eta}^{\mathsf{T}}y(t)<1.\]  
Thus system (6) is positive and there is IO-FTS w.r.t. \((\omega_{\infty},\eta(\cdot),T)\) in the sense of Definitions 4 and 5.
# Recent Advances in Photodetectors Based on Two-Dimensional Material/Si Heterojunctions
## 2 Figures of Merit for Photodetectors
### Response Time  
The response time is a critical parameter that characterizes the performance of photodetectors. Typically, this parameter is represented by the rise time and decay time of a photodetector. The rise time and decay time are defined as the time required for the photocurrent to rise from 10% to 90% of its static value and vice versa, respectively, as shown in Figure 1e. The response time of a photoconductor is influenced by the lifetime of the photogenerated carriers and their mobility. In the case of diode-like photodetectors, the response time is determined by the diffusion time of carriers out of the depletion region, the drift time within the depleted region and the capacitance of the junction [51].
## 3 Methods
### Evaluation Methods  
The accuracy of the segmentation was then evaluated with three quality factors: \(Q_{\text{seg}}\), \(S_{r}\), and an error factor \(E_{s}\). The factor \(Q_{\text{seg}}\) is based on both kernels and background regions, and ranges from zero to unity. \(Q_{\text{seg}}\) reflects the consistency of all the image pixels, including the leaf part and the remaining part, and \(Q_{\text{seg}}=1\) represents a perfect outcome. Conversely, the factor \(S_{r}\) reflects the consistency of only the leaf parts. From the perspective of an image, it reflects the completeness of the segmentation results. Furthermore, \(E_{s}\) indicates the portion of misclassified leaf pixels relative to true total leaf pixels. These evaluation indicators are calculated as follows:  
\[Q_{\text{seg}}=\frac{\sum\limits_{\begin{array}{c}i,j=a,b\\ i,j=0\end{array}}\left[M(\delta)_{i,j}\cap N(\delta)_{i,j}\right]}{\sum\limits_ {\begin{array}{c}i,j=a,b\\ i,j=0\end{array}}\left[M(\delta)_{i,j}\cup N(\delta)_{i,j}\right]}, \tag{10}\]  
\[S_{r}=\frac{\sum\limits_{\begin{array}{c}i,j=a,b\\ i,j=0\end{array}}\left[M(\delta)_{i,j}\cap N(\delta)_{i,j}\right]}{\sum\limits_ {\begin{array}{c}i,j=a,b\\ i,j=0\end{array}}\left[N(\delta)_{i,j}\right]}, \tag{11}\]\[E_{s}=\frac{\sum\limits_{\begin{array}{c}i,j=a,b\\ i,j=0\end{array}}\begin{bmatrix}M(\delta)_{i,j}\cap N(i\delta)_{i,j}\end{bmatrix}}{ \sum\limits_{\begin{array}{c}i,j=a,b\\ i,j=0\end{array}}\begin{bmatrix}N(\delta)_{i,j}\end{bmatrix}}, \tag{12}\]  
where \(M\) is the set of leaf pixels (\(\delta=1\)) or pixels for other parts (\(\delta=0\)) separated by the segmentation method, \(N\) is the ground truth for these two parts, i; j are the row and column coordinates of an image, respectively, and a, b are the width and height of the image, respectively. Furthermore, \"\(\cap\)\" is a logical \"and\", \"\(\cup\)\" is a logical \"or\", and \"\(\cup\)\" is a logical \"not\". The accuracy of the segmentation can be measured by comparing \(M\) and \(N\) on a pixel-by-pixel basis. In addition, the mean intersection-over-union (mIOU) serves to determine the processing precision for the validation sets. It generates two boxes called the \"predicted bounding box\" and the \"ground-truth bounding box,\" and then compares the overlap rate between them. The schematic diagram and formula are given by  
\[mIOU=\text{mean}\bigg{(}\frac{\text{Detection Leaf Area}\cap\text{ Ground Truth}}{\text{Detection Leaf Area}\cup\text{Ground Truth}}\bigg{)}. \tag{13}\]  
Our goal is to take the training images plus the bounding boxes, construct an object detector, and then evaluate its performance on the testing set. The mIOU varies within the range [0, 1], and mIOU \(>\) 0.5 is normally considered a \"good\" prediction.
# Breath Analysis: A Promising Tool for Disease Diagnosis--The Role of Sensors
## 4 Differential Diagnosis and Disease Phenotyping and Staging in Breath Analysis
### Liver, Renal, and Intestinal Diseases  
Liver cirrhosis, chronic hepatitis [244], CKD [113], and inflammatory bowel diseases (IBD) comprise common liver, kidney, and intestinal diseases, respectively. As far as CKD is concerned, it is characterized by gradual loss of kidney function within months or years, while different treatment is demanded depending on disease stage (stages I-V) [113]. Similarly, in the case of chronic liver disease (CLD), disease staging is of great importance; following CLD diagnosis, using invasive biopsy, liver function assessment is conducted biochemically [244]. On the other hand, early stage and precise IBD and IBS diagnosis, as well as the invasive diagnostic methods followed for IBD, comprise challenging issues [111]. Consequently, precise diagnosis and staging of liver, kidney and intestinal diseases are particularly important and have been attempted using breath analysis with sensing devices. [PERSON] et al. for instance used BIONOTE e-nose to successfully differentiate not only liver cirrhosis and CLD from non-cirrhotic CLD (chronic hepatitis) but also liver cirrhosis stages by taking into account smoking habits and potential comorbidities (e.g., diabetes, lung, and heart diseases) [244]. Concerning renal diseases, [PERSON]'s group achieved CKD staging using organically functionalized Au NPs-based chemeirsistors and SVM [113]. The classification of CKD stage IV in relation to stage V was permitted by 2 or 3 sensors with an accuracy of 85%, a sensitivity of 75% and specificity of 92% while only one sensor allowed for the discrimination of early and advanced stages with 76% accuracy, 75% sensitivity, and 77% specificity [113]. The discrimination of CKD from other diseases has been also attempted. Specifically, discrimination of CKD, diabetes, and HC with high or low creatinine has been attempted with success using an array of commercial (MQ) sensors along with different classification methods, with SVM and PCA leading to good group classification [245]. Remarkably, pre-concentration or dehumidification were not needed for clear classification to be accomplished [245]. The effective discrimination between the intestinal diseases IBD and IBS has been also reported along with further differentiation of the IBD into ulcerative colitis (UC) and [PERSON]'s disease (CD), using not only artificial but also real-breath samples and a MCNPs-based chemeirsistor (Table 4) [111]. The higher accuracy values observed when using artificial samples is expected and attributed to the standard concentration of VOCs, contrary to the variable concentration of VOCs in breath [111].
## 2 Study Area and Method
### Model Parameters and Input Data
#### 2.3.4 Soil Data  
Soil data with 1 km resolution for Zhejiang province was derived from the Harmonized World Soil Database (HWSD1.2), including silt and clay fraction, depth of soil layer, and soil effective water holding capacity. Soil bulk density was calculated by the silt and clay fraction with the Brooks-Corey model of Saxton [44]. The wilt point was calculated by the silt and clay fraction [45].
## 3 Experimental Results and Specim Behavior
### Strengthened Columns
It was found that the steel tubes had some buckling in the outward direction and small cracks in the fill concrete. Cracks were located around the corners of the RC column in the radial direction, as shown in Figure 12a. No cracks were detected in the core RC column. Dissimilar to the crushing failure of plain RC columns, shown in Figure 6a,b, the concrete in strengthened columns can keep its integrity because of the confinement pressure produced by the steel jacket [21]. Therefore, the strengthened column can keep a great part of its load-bearing capacities following the failure of the basic RC column. The confinement of the steel jacket to the fill concrete and onto the RC column is fairly even over the entire height of the specimen, and the entire section of the concrete core is efficiently confined. The embedded bearing plate on top of specimen B23 is shown in Figure 12b. Figure 11: Typical axial force versus deformation curves for strengthened columns. All strengthened column models after finished testing are presented alongside in Figure 13. Failure of the composite column models was a combination of outward buckling of the steel jacket and concrete crushing due to excess of its compressive strength. Ultimate load forces of strengthened columns registered during experimental testing are listed in Table 1. It was found that the bearing capacity of strengthened columns increases with the increase of the fill concrete compressive strength.
###### Abstract  
By introducing the arrayed waveguide router (AWGR) optical true time-delay (OTTD) architecture in bent-pipe satellite optical inter-link to optically assist the RF phased array in Low-earth orbit satellites will extend the multi-hop bent-pipe satellite beam-hopping protocol proposed in DVB-S2X. It solves the challenge of beam steering with the support of precise, broadband, and wide-range scanning. This architecture utilizes a subarray to combine the advantages of AWGR and a high-precision RF phase shifter to realize the beam pointing without an oblique view. Unlike the traditional digital and analog phased array architecture, the introduction of OTTD can solve the problem of beam squint and also ensure the high-precision scanning of the beam.  
LEO satellite constellation; bent-pipe satellite; beamforming; beam-hopping; optical true time delay +
Footnote †: journal: Medical Imaging  
**Citation:** [PERSON]; [PERSON]; [PERSON]; [PERSON]; [PERSON]; [PERSON]; [PERSON]; [PERSON] Large Scale Optical Assisted Mm-Wave Beam-Hopping System for Multi-Hop Bent-Pipe LEO Satellite Networks. _Appl. Sci._**2023**, 13, 3480. [[https://doi.org/10.3390/appl3063480](https://doi.org/10.3390/appl3063480)]([https://doi.org/10.3390/appl3063480](https://doi.org/10.3390/appl3063480))
## 5 Case Study  
CPS represents an innovative era of manufacturing systems that facilitate the seamless integration of organizational functions, encompassing entire supply chains and distribution channels.  
CPS has a profound impact on the entire manufacturing value chain, spanning from suppliers to customers. Through facilitating instantaneous data exchange, CPS enhances visibility and transparency within the supply chain, empowering manufacturers to swiftly adapt to demand fluctuations, monitor inventory levels, and streamline logistics operations.  
Moreover, CPS fosters more efficient collaboration between manufacturers, suppliers, and customers. This collaboration involves the sharing of data and insights, leading to enhanced overall supply chain performance. Real-time data exchange and tracking capabilities enable manufacturers to optimize logistics processes, resulting in reduced transportation costs and improved delivery times. Additionally, CPS empowers manufacturers to tailor their products and services to precisely meet the unique needs of their customers. This means that CPS and its application allow us to obtain and implement computing paradigms related to Manufacturing-as-a-Service (MaaS) and Resource-as-a-Service (RaaS).  
Scanning techniques/technologies such as RFID, QR-Codes, or Bar-Codes can be used to scan and track goods, but complementary information can be collected if vehicle tracking is also used. Scanning products allows us to know where they were at a specific timestamp in the past; however, unless the timestamp is very recent, it does not provide information about where the products are now, or, for example, adjust delivery estimation date and time. If we can link the goods to the transportation vehicles, then we only need to track the vehicle to track the products, which is a common practice in logistics applications and used by big logistics companies such as Tao Bao and Jin Dong.  
In the case study, two types of tracking devices were installed in vehicles, and their location was tracked every 10 s. One of these devices was a custom-tailored device that can use either NBIoT (Narrow Bant IoT) or LTE-M (Long-Term Evolution--Machine Type Communication) for data communications, and the other was an off-the-shelf device, which uses 4G communications. Despite both device types using TCP/IP communications, the cellular network technologies that they use have different constraints related to coverage, data rate, and delivery delay. Also, these two devices use different Application-Level protocols and data PDU (Protocol Data Unit) formats.  
Even though these two CPS devices have different specifications and features, the objective was to present the logistics management applications and a homogeneous view of the devices. Therefore, the architecture that was chosen to support this application was based on that presented by the authors in [52]. Using this architecture, as presented in Figure 1, it is possible to perform the integration of these devices and send their data in real time as required.
## 2 Experimental Evaluation
### Shaking Table Test Setup  
The experimental configuration for the shaking table test is illustrated in Figure 3. To connect the specimen to the shaking table, the masonry wall was mounted on top of a 2300 \(\times\) 300 \(\times\) 1500 mm concrete slab and fixed using bolts. A 1750 \(\times\) 370 \(\times\) 540 mm concrete block was placed on top of the masonry wall to apply vertical loading and generate inertial forces during the shaking table test. Steel brackets were installed at the bottom 880 mm and top 440 mm of the wall. This restraint configuration was intentionally designed to prevent premature failure at both ends of the wall and to guide damage initiation toward the center. This setup ensured that the failure occurred within the retrofitted region, allowing for clearer observation of the strengthening effects across specimen types. Although this configuration may differ from real boundary conditions in building walls, it enabled controlled crack development and reproducible comparison between experimental and numerical results. The seismic load was applied in the out-of-plane direction using El Centro earthquake records, as shown in Figure 4. The El Centro ground motion was selected due to its historical significance and well-characterized frequency content (1-2 Hz), which overlaps with the natural frequency range of typical unreinforced masonry structures [32; 33]. The load was first applied with a peak ground acceleration (PGA) of 0.1 g and then increased by 0.1 g increments until the specimen failed.  
Figure 1: Masonry wall specimen for shaking table test: (**a**) front view; (**b**) side view (unit. mm).  
Figure 2: Shaking table test specimen type: (**a**) MWN type; (**b**) MWP2 type; (**c**) MWP5 type.
## 3 Proposed Method  
In the proposed depth estimation network, the inputs captured by MR glasses are RGB images and low-resolution low-quality (LRLQ) depth maps. The RGB image and the corresponding LRLQ depth map are fed into the feature extractors to extract their high- and low-level features separately. Those encoded features of image and depth are fused as multilevel dense depth features in a multilevel shared decoder. The multilevel shared decoder then decodes these dense features at different levels as the inputs of an adaptive bin estimator, as Figure 1 shows. The adaptive bins estimator conducts the prediction of bin divisions, which can delineate the depth distributions of current scenes. As a result, each high-resolution depth can be resulted from the linear combination of centers of divided bins with the bins probabilities. In our proposed network, the division of bins is hereafter named the bin-division vector, which contains the consecutive bins where a bin records the granularity (range) of a depth fragment.
## 2 Development of Beam Element-Based Simulation
### Model Description
#### 2.1.2 Multipoint Constraints
\[\epsilon_{u}\bigg{(}x,-\frac{h}{2},t\bigg{)}-\bigg{(}\epsilon_{l}\bigg{(}x, \frac{h}{2},t\bigg{)}-\epsilon_{l}\bigg{(}x,\frac{h}{2},\mu_{u}^{act}\bigg{)} \bigg{)}=0 \tag{10}\]  
Substituting Equation (9) into Equation (10) offers the required strain compatibility Equation (11) at the bead interface in terms of element displacements in a form suitable for inclusion in a displacement-based finite element analysis,  
\[B_{u}\bigg{(}x,-\frac{h}{2}\bigg{)}U_{u}^{el}(t)-B_{l}\bigg{(}x,\frac{h}{2} \bigg{)}U_{l}^{el}(t)+B_{l}\bigg{(}x,\frac{h}{2}\bigg{)}U_{l}^{el}\big{(}t_{u }^{act}\big{)}=0. \tag{11}\]  
For the structure as a whole, the multipoint constraints required to ensure strain compatibility at the interfaces of all beads are expressed in the form given in Equation (12),  
\[G^{T}U=C, \tag{12}\]  
where \(G^{T}\) is a matrix of constraint coefficients, \(U\) is a vector of global nodal displacements and rotations, and \(C\) is a vector of constraint constants. Equation (11), which applies within a single element, is a function of local element displacements that are easily transformed to global nodal displacements using standard techniques. As discussed in Section 2.1.1, elements have an initial displacement \(U^{0}\), which does not cause strain, that is defined when the element is activated and must be subtracted from the total nodal displacements as shown in Equation (13) to obtain the strain producing displacement \(U^{el}\),  
\[U^{el}=U-U^{0}. \tag{13}\]  
Because the total longitudinal strain due to both bending and axial force within a single element vary linearly along the length of the element at any depth, the strain compatibility must be enforced at two locations within each pair of bonded elements to ensure strain compatibility along the full length in contact. For simplicity, the end nodes of the elements are chosen. Once activated, a constraint is present in every subsequent time step. Substituting Equation (13) into Equation (11), recognizing that the constants in \(G^{T}\) are terms in \(B_{u}\) and \(B_{l}\) at the element ends, and isolating the unknowns offers the final constraint equations for a single element pair, shown in Equations (14) and (15),  
\[G_{u}(0)U_{u}(t)-G_{l}(0)U_{l}(t)=G_{u}(0)U_{u}\big{(}t_{u}^{act}\big{)}-G_{l} (0)U_{l}\big{(}t_{u}^{act}\big{)} \tag{14}\]  
\[G_{u}(L)U_{u}(t)-G_{l}(L)U_{l}(t)=G_{u}(L)U_{u}\big{(}t_{u}^{act}\big{)}-G_{l} (L)U_{l}\big{(}t_{u}^{act}\big{)}, \tag{15}\]  
where vectors \(G_{l}\) and \(G_{u}\) are given below in Equations (16)-(19). \[G_{l}(0)=\bigg{[}-\frac{1}{L}-\frac{3h}{L^{2}}-\frac{2h}{L}\ \frac{1}{L}\ \frac{3h}{L^{2}}-\frac{h}{L}\bigg{]}, \tag{16}\]  
\[G_{u}(0)=\bigg{[}-\frac{1}{L}\ \frac{3h}{L^{2}}\ \frac{2h}{L}\ \frac{1}{L}\ \frac{ -3h}{L^{2}}\ \frac{h}{L}\bigg{]}, \tag{17}\]  
Figure 4:0  
Figure 4:1