esa-sceva/satcom-chunk-collection huggingface dataset:
## 4 Bearing with Longitudinal Microgrooves
### Ideal Air Flow Pattern without circumferential Crossflows
#### 4.4.1 Non-Crossflowing Model for Small Eccentricities  
In the absence of crossflows, the differential equation of Problem (8) takes the form  
\[\frac{d^{2}\Delta\Psi}{dZ^{2}}=0.\]  
Figure 7: Dependencies of the load capacity \(W\) of the end zones on their length \(L_{1}\) for different eccentricities \(\varepsilon\).  
Taking this and (13) into account, the solution to the problem is the function of small pressure deviation  
\[\Delta P(Z)=\Delta P_{k}\left\{\begin{array}{cc}\frac{P_{k0}(L_{1}-Z)}{P_{0}(Z) L_{1}},&Z\leq L_{1},\\ 1,&Z\leq L_{2}.\end{array}\right. \tag{68}\]  
Substituting (68) into (14), we obtain  
\[\Delta W=A_{w}\Delta P_{k}, \tag{69}\]  
where  
\[A_{w}=L_{2}+\frac{P_{k0}}{L_{1}}\int\limits_{0}^{L_{1}}\frac{(L_{1}-Z)}{P_{0}( Z)}dZ.\]  
The formula for the flow rate in the bearing gap near the pressurization line has the form  
\[\Delta Q_{h}=A_{qp}\Delta P_{k}-A_{qp}\Delta\varepsilon, \tag{70}\]  
where \(A_{qp}=\frac{2P_{k0}}{L_{1}}\) corresponds to (30). Formulas (39) and (40) remain unchanged.  
Substituting the obtained simplified Formulas (69) and (70) into (43), we obtain the formula for bearing compliance without circumferential air flows in the bearing gap for small deviations of functions from the central equilibrium position of the shaft.  
Figure 8 shows the dependences of the compliance \(K_{e}\) on the length \(L\) at various values of the injection pressure \(P_{s}\) for \(\lambda_{1}=0.2\), \(\chi=0.45\), and \(\varsigma=0.15\). The solid lines show the characteristics of a conventional bearing, and the dashed lines show the bearing with longitudinal microgrooves (\(n_{g}\geq 12\)). It can be seen that at \(L>0.5\), the use of microgrooves contributes to a significant decrease in bearing compliance. Thus, at \(P_{s}=3\) and \(L=1.5\), the compliance decreases by \(65\%\), and at \(L=2\), the compliance is halved. For \(L>2\), the difference will be even greater. A similar difference is observed at \(P_{s}=5\).
# A Long-Distance WiFi Network as a Tool to Promote Social Inclusion in Southern Vercarruz, Mexico
## 2 Theoretical Framework
### WiFi Antennas
The goal is to showcase the potential advantages offered by DRAs, such as improved bandwidth and gain, as well as the development of active DRAs using ferrite materials. Additionally, efforts have been made to create compact and low-profile antennas. As part of this research, linear and planar arrays of DRAs have been designed and manufactured, with a strong emphasis on practical implementation to demonstrate the feasibility of using DRAs in an array setup [42; 45; 46]. DRAs possess several appealing characteristics that make them highly desirable for various wireless communication applications: 1. High radiation efficiency: DRAs exhibit a high radiation efficiency of approximately 95. 2. Size and bandwidth control: DRAs offer a wide range of control over their size and bandwidth, allowing for tailored designs based on specific application requirements. 3. Design flexibility: Various shapes of resonators, such as rectangular, cylindrical, or hemispherical, can be employed in DRAs, providing design flexibility to meet different needs. 4. Integration with existing technologies: DRAs can be seamlessly integrated with different existing technologies by utilizing a variety of feeding mechanisms, including probes, slots, microstrip lines, dielectric image guides, and co-planar lines. 5. Radiation patterns: DRAs are capable of radiating broadside or conical-shaped patterns, allowing for versatility in meeting diverse coverage requirements. 6. Tolerance error resistance: DRAs are less susceptible to tolerance errors compared to microstrip antennas, particularly at higher frequencies. These features make DRAs highly versatile elements that can be adapted to numerous wireless communication (WiFi) applications through careful selection and adjustment of the design parameters. In this project, dielectric resonator-type antennas with cylindrical geometry are used. Four designs have been developed for use in applications working in different WiFi bands. To achieve the optimal antenna designs, matching, radiation pattern, and transmit and receive power were analyzed. The theoretical parameters were calculated analytically and then adjusted through different simulations. In these simulations, the effects of varying the dimensions of the cylinder such as radius, and height, as well as the effect of varying the position and dimensions of the antenna feed, are seen. Additionally, manufacturing materials with different characteristics, limitations, and costs are considered. Finally, a prototype of a cylindrical dielectric resonator-type antenna is constructed. Recycled (low-cost) materials were used for this purpose. The resulting antenna has good matching and radiation pattern characteristics, resulting in an antenna of reduced size and cost, which is a good candidate for wireless communications [47].
## 4 Discussion
### The Essential Elements and IoT Architecture Framework to Implement an IAQ Monitoring Study
#### 4.1.3 Communication Protocol  
The users must consider the suitability of different communication protocols for the specific task at the designated site. The factors that determine whether a device is suitable are: (i) the coverage where different wireless protocols can communicate at differing distances, (ii) the power consumption of the sensing device, and (iii) the required dedicated gateway hardware. Figure 5 illustrates the communication protocols utilized in our study, which highlight the sensor and IoT cloud platform multiple communication protocols. Users must be aware that the device manufacturers have a set protocol for the hardware that is not easily interchangeable. Furthermore, to communicate sensors' data to the IoT cloud platform, each sensor required, at a minimum, a 4G gateway to connect the device to a wider network, and in some cases, they required further specific hardware. An example of such a consideration is a LoRaWAN-based device that requires a compatible gateway in order to access the LoRaWAN network server. The server is needed to handle the connection between the sensor device and the Internet via compatible protocols.  
It is important to note that in any environmental monitoring scenario, it is likely that multiple sensing devices will be utilized based on the number of measured IAQ parameters. It then falls on the users to integrate multiple devices, with possibly varying communication protocols, and independent cloud platforms. It is highly recommended that the selected sensors support either open standards or provide APIs for streaming the data out. This would enable the creation of a system architecture that builds into a centralized location for data storage as shown in Figure 5.
## 4 Discussion
### Spatial and Temporal Dynamic and Distribution of CUE and WUE in NMR
The variations in CUE across different vegetation types were relatively minor, with areas where CUE exceeded 0.5 comprising 50.11% of the study region. Shrubland exhibited the highest average CUE (0.570), whereas forest displayed the lowest (0.440), resulting in a difference of 0.130. The reduced CUE observed in forests can be explained by a combination of factors. Irregular seasonal rainfall in the region increases physiological stress on vegetation during the dry season, which reduces its carbon fixation capacity [49]. The complex structure of forest stands may lead to the uneven distribution of light and resources, further impacting the CUE of certain vegetation [50]. Moreover, studies indicate that human activities in South China, such as deforestation and afforestation, have led to frequent land use changes, which can disrupt the balance of existing ecosystems and influence vegetation CUE [51]. The geographic distribution of vegetation WUE typically shows greater values in the southeast and smaller values in the northwest. WUE showed substantial variation among different vegetation types, underscoring significant differences in water resource utilization across vegetation categories. Forested regions demonstrated the highest WUE at 0.831 g C\(\cdot\)m\({}^{-2}\cdot\)mm\({}^{-1}\), while shrubland exhibited the lowest WUE at 0.624 g C\(\cdot\)m\({}^{-2}\cdot\)mm\({}^{-1}\), resulting in a notable difference of 0.207 g C\(\cdot\)m\({}^{-2}\cdot\)mm\({}^{-1}\) between the two extremes. This disparity can be attributed to several factors. On the one hand, forest ecosystems tend to have dense canopies, which enhance photosynthetic efficiency [52]. Additionally, the well-developed root systems of forest vegetation contribute to better water retention. On the other hand, the long-term execution of the \"Grain for Green\" initiative within the study region has improved vegetation conditions, thereby enhancing water conservation functions [53]. In contrast, the lower WUE in croplands may be due to poorer soil texture, which affects soil permeability and water retention capacity, thereby reducing WUE [54].
## Appendix A Position and Orientation Matrix Derivation  
The relationship between the design parameters and the force and moment generated can be summarized as follows:  
The propeller's position can be described with rotation about the body frame \(Z_{b}\) axis by angle \(\theta\) as shown in Equation (3) in Section 2. The generalized position matrix \(x\) of the assumed Hexarotor UAV preliminary configuration shown is defined as:  
\[x=\begin{bmatrix}0&0&\mathrm{s}(\theta)&-\mathrm{s}(\theta)&\mathrm{s}(\theta )&-\mathrm{s}(\theta)\\ \mathrm{c}\theta&-\mathrm{c}\theta&-\mathrm{c}(\theta)&\mathrm{c}(\theta)& \mathrm{c}(\theta)&-\mathrm{c}(\theta)\\ 0&0&0&0&0\end{bmatrix}\]  
Referring from Section 5, for optimization purposes, the orientation matrix was modified with offsetting angle \(\beta\) as:  
\[\hat{x} =\begin{bmatrix}0&0&\mathrm{s}(\theta-\beta)&-\mathrm{s}(\theta- \beta)&\mathrm{s}(\theta-\beta)&-\mathrm{s}(\theta-\beta)\\ \mathrm{c}(\theta-\beta)&-\mathrm{c}(\theta-\beta)&-\mathrm{c}(\theta-\beta) &\mathrm{c}(\theta-\beta)&-\mathrm{c}(\theta-\beta)\\ 0&0&0&0&0\end{bmatrix}\]The orientation of each propeller can be computed as the successive rotation of the arm with an angle \(\theta\) about the body frame \(Z_{b}\) axis and about propellers coordinate axis \(y_{p}\) and \(x_{p}\) with angles \(\alpha_{y}\) and \(\alpha_{x}\), respectively.  
\[R_{Z_{b}}(\theta)=\begin{bmatrix}c_{\theta}&s_{\theta}&0\\ -s_{\theta}&c_{\theta}&0\\ 0&0&1\end{bmatrix}\]  
\[R_{y_{p}}(\alpha_{y})=\begin{bmatrix}c_{\alpha_{y}}&0&-s_{\alpha_{y}}\\ 0&1&0\\ s_{\alpha_{y}}&0&c_{\alpha_{y}}\end{bmatrix}\]  
\[R_{x_{p}}(\alpha_{x})=\begin{bmatrix}1&0&0\\ 0&c_{\alpha_{x}}&s_{\alpha_{x}}\\ 0&-s_{\alpha_{x}}&c_{\alpha_{x}}\end{bmatrix}\]  
From Equation (4), the generalized propellers orientation matrix is given as:  
\[q=\begin{bmatrix}\text{s}(\alpha_{1})&-\text{s}\alpha_{2}&-\text{s}(\theta) \text{s}\alpha_{3}&-\text{s}(\theta)\text{s}\alpha_{4}&-\text{s}(\theta)\text{ s}\alpha_{5}&-\text{s}(\theta)\text{s}\alpha_{6}\\ 0&0&-\text{c}(\theta)\text{s}\alpha_{3}&-\text{c}(\theta)\text{s}\alpha_{4}& -\text{c}(\theta)\text{s}\alpha_{5}&-\text{c}(\theta)\text{s}\alpha_{6}\\ \text{c}\alpha_{1}&\text{c}\alpha_{2}&\text{c}\alpha_{3}&\text{c}\alpha_{4}& \text{c}\alpha_{5}&\text{c}\alpha_{6}\end{bmatrix}\]  
Recalling from Section 2 for opmization purposes, the orientation matrix can be modified with offseting angle \(\beta\) as:  
\[\hat{q}=\begin{bmatrix}\text{s}\alpha_{1}&-\text{s}\alpha_{2}&-\text{s}( \theta-\beta)\text{s}\alpha_{3}&-\text{s}(\theta-\beta)\text{s}\alpha_{4}&- \text{s}(\theta-\beta)\text{s}\alpha_{5}&-\text{s}(\theta-\beta)\text{s}\alpha _{6}\\ 0&0&-\text{c}(\theta-\beta)\text{s}\alpha_{3}&-\text{c}(\theta-\beta)\text{s} \alpha_{4}&-\text{c}(\theta-\beta)\text{s}\alpha_{5}&-\text{c}(\theta-\beta) \text{s}\alpha_{6}\\ \text{c}\alpha_{1}&\text{c}\alpha_{2}&\text{c}\alpha_{3}&\text{c}\alpha_{4}& \text{c}\alpha_{5}&\text{c}\alpha_{6}\end{bmatrix}\]
## 3 Upper Bounds on the Number of Channels
### Background Results  
By constructing the conflict graph for a link set, and representing each channel by a different color, we found that the requirement that no two conflicting links share the same channel is equivalent to the constraint that no two adjacent vertices share the same color in graph coloring. Therefore, the problem of channel assignment on a link set can be converted to the classical vertex coloring problem (in graph theory, the vertex coloring problem is a way of assigning \"labels\"--colors--to vertices of a graph such that no two adjacent vertices share the same color) on the conflict graph. The vertex coloring problem, as one of the most fundamental problems in graph theory, is known to be NP-hard even in the very restricted classes of planar graphs [25]. A coloring is regarded as valid if no two adjacent vertices use the same color.  
The minimum number for a valid coloring of vertices in a graph \(G\) is denoted by a _chromatic_ number, \(\chi(G)\). There are two well-known results on the upper bound of \(\chi(G)\), which will be used to derive our results.  
**Lemma 1**: _[_26_]_ _If \(\Delta(G)\) denotes the largest degree among \(G\)'s vertices, i.e., \(\Delta(G)=\max_{v\in G}Degree(v)\), then we have_  
\[\chi(G)\leq\Delta(G)+1\]  
**Lemma 2**: _[_27_]_ _If \(G\) contains a subgraph \(H\) in which each node has a degree at least \(d>0\), we define such degree as \(LD(H)=\min_{v\in H}Degree(v)\). We have_  
\[\chi(G)\leq\delta(G)+1\]  
_where the maximum degree among all the \(LD(H)\) is denoted by \(\delta(G)=\max_{H\subseteq G}LD(H)\)._
# Underwater Object Detection Method Based on Improved Faster RCNN
## 4 Experiments
### Comparative Experiments of Backbone Network Selection  
In this paper, the Res2 Net101 network module is selected as the feature extraction structure of the improved Faster RCNN in order to optimize its backbone network for better performance in the underwater object detection. In this section, many comparison experiments are conducted for the Faster RCNN (VGG16), the Faster RCNN (ResNet50), the Faster RCNN (ResNet101) and the Faster RCNN (Res2 Net101), respectively.  
The 3500 underwater environment images are divided into training data samples, validation data samples and test data samples, with a ratio of 7:2:1. After 300 epochs of iterative training and learning, the learning rate drops to 0.0001 and the parameters of the underwater object detection model converge. The improved Faster RCNN improves the performance in the underwater object detection by combining different feature extraction modules. The results of the comparative experiments are shown in Table 1.  
Figure 4: Mosaic data enhancement, (**a**) four randomly entered pictures (from left to right, they are respectively a starfish, water plants, a scallop, a sea cucumber), (**b**) data augmentation results.  
It can be known from Table 1 that the ResNet network with residual units has stable performance in underwater object detection. With the deepening of the network layers, the Faster RCNN (ResNet101) has better accuracy in underwater object detection than the original Faster RCNN. The recently appeared Res2 Net network, which establishes a multi-level residual network connection inside the original residual module, can describe the multi-scale feature information in a finer area. The experimental result of the improved Faster RCNN (Res2 Net101) is the best, with [EMAIL_ADDRESS] reaching 69.1%. Therefore, it can be known from Table 1 that the improved operation of the Faster RCNN backbone network is effective, and the improved Faster RCNN algorithm is more conducive to underwater object detection.
# A Compact Quad-Element UWB-MIMO Antenna System with Parasitic Decoupling Mechanism
## 3 Isolation Mechanisms  
Two distinct techniques are employed to achieve isolation for side-by-side and across antenna arrangements. A horizontal parasitic decoupling strip is designed and placed in the middle of the rear-side for isolating antennas placed across and diagonally. Isolation among side-by-side antennas is achieved through a dumbbell shaped stub attached to the ground plane. The same structure is also produced on the top layer between antennas. The fabricated UWB-MIMO antenna design is shown in Figure 3.
## 3 The CPN Model
### The CPN Formalism
#### 3.1.1 Data Extensions
If we consider two tokens \(\tau_{1},\tau_{2}\) as a set of elements or values in the form \(\{\tau_{1}\_Value1,\tau_{1}\_Value2,\ldots\tau_{1}\_ValueN\}\) and \(\{\tau_{2}\_Value1,\tau_{2}\_Value2,\ldots\tau_{2}\_ValueN\}\) then the new token is the union of the two sets:  
\[\tau_{12} =\{\tau_{1}\_Value1,\tau_{1}\_Value2,\ldots\tau_{1}\_ValueN\} \cup\{\tau_{2}\_Value1,\tau_{2}\_Value2,\ldots\tau_{2}\_ValueN\}\] \[=\{\tau_{1}\_Value1,\tau_{1}\_Value2,\ldots\tau_{1}\_ValueN,\tau_ {2}\_Value1,\tau_{2}\_Value2,\ldots\tau_{2}\_ValueN\}.\]  
In Figure 3, notice the new token \(\tau_{12}\) in place \(p_{4}\). It is the union of the set of values of \(\tau_{1}\) and \(\tau_{2}\). Its color is red-black, to denote this union in a pictorial manner. Now, \(t_{2}\) and \(t_{3}\) are also enabled. When \(t_{2}\) is also enabled. When it fires, the token \(\tau_{12}\) is split again and its red part only moves to \(p_{3}\) as a new token \(\tau_{3}\) (recall that \(p_{3}\) accommodates only red tokens) while its black part only moves to \(p_{4}\) as a new token \(\tau_{4}\) (recall that \(p_{4}\) accommodates only black tokens). Now, we can typically define a CPN network. It is composed of 4 elements:  
1. A set of places \(P\)
2. A set of transitions \(T\)
3. An input function \(I\)
4. An output function \(O\)  
Figure 3: Example of an Enabled Transition in a Colored Petri Nets (CPN). The input and output function relate places to transitions. An input function \(I\) is a mapping from a set of places to a transition \(t_{i}\). It is denoted by \(I(t_{i})\) and the set of places is called _input places_ for the transition. As mentioned in our example, \(I_{t_{1}}=\{p_{1},p_{2}\}\). The output function \(O\) is a mapping from a transition to a set of places. It is denoted by \(O(t_{i})\) and the set of places is called _output places_ for the transition. As mentioned in our example, \(O_{t_{1}}=\{p_{4}\}\). The tokens \(\tau_{i}\) are distinguished according to the CPN formalism, as described above. Then, a Colored Petri Net \(C\) is typically defined as a quadruple of the form \(C=\{P,\ T,\ I,\ O\}\), where:  
\(P=\{p_{1},\ p_{2},\ \ldots,p_{n},\ \}\) is a finite set of places, \(n\geq 0\)  
\(T=\{t_{1},\ t_{2},\ \ldots,t_{n},\ \}\) is a finite set of transitions, \(n\geq 0\)  
\(R\to T\) is an input function from a subset of places \(R\) to a transition of set \(T\), and  
\(T\to R\) is an output function from a transition of set \(T\) to a subset of places \(R\). Finally, we define the _marking_ of a network \(C\) as the number and type of all the tokens residing in all the places at a certain time. An initial marking is necessary when we start the simulation engine. This initial marking defines the initial system conditions.
# Digital Twins in Solar Farms: An Approach through Time Series and Deep Learning
## 2 Background
### Deep Learning
#### 2.2.1 Recurrent and Convolutional Networks  
A convolutional neural network is a neural network in which a convolution operation is used instead of matrix multiplication operations in at least one of its layers [7]. These networks, by combining convolutional layers, pooling layers and dense layers, can correctly capture the spatial-temporal interdependencies of the provided samples.  
A brief description of the main layers of a CNN is as follows:  
* Convolutional Layer: In this layer, a convolution operation is applied to its input by means of a kernel to extract a map of characteristics. It can be denoted as \(s(t)=\sum_{\alpha=-\infty}^{\infty}x(\alpha)w(t-\alpha)\) where \(x\) is the input and \(w\) the kernel, and the output can be referred to as a feature map. It presents as main parameters the number of filters to apply and the size of the kernel.
* Pooling layer: A pooling function is applied by replacing the network output at a certain location with a statistical summary of nearby points. This operation helps to make the representation invariant to small variations in the input.
* Dense or fully connected layer: This layer operates on a flattened input, where each input is connected to all neurons. They are usually used at the end of the convolutional architecture and are used with the aim of optimizing the score of the classes.  
Proposed by [PERSON] and [PERSON] [9], LSTMs avoid gradient fading by including a so-called \"state cell\", the information of which is carefully regulated by structures called gates. The gates can be denoted as \(\Gamma=\sigma(W_{x^{t}}+U_{a^{t-1}}+b)\), where \(W,~{}U,~{}b\) are specific coefficients of the gate and \(\alpha\) is the sigmoid function.  
The dependencies between the state \(c^{t}=\Gamma_{u}~{}\vec{c}^{t}+\Gamma_{f}~{}\vec{c}^{t-1}\) are such that the vector with the new values of the state cell \(\vec{c}^{t}=\tanh(W_{c}[\Gamma_{r}~{}a^{t-1},x^{t}]+~{}\mathrm{b}_{c}\) and activation \(a^{t}\), where \(\Gamma_{u}\) is the update gate, \(\Gamma_{r}\) is the relevance gate, \(\Gamma_{f}\) is the forgetting gate, \(\Gamma_{o}\) is the exit gate and \(W_{c},~{}b_{c}\) are coefficients of the state cell.