esa-sceva/satcom-chunk-collection huggingface dataset:
# On the Existence of Solutions of Nonlinear Fredholm Integral Equations from Kantorovich's Technique
## 3 Existence and Uniqueness of a Solution  
Following [PERSON]'s technique, the convergence of sequence \(\{x_{n}\}\) in \(\Omega\) is then guaranteed from the convergence of sequence \(\{t_{n}\}\), since \(\{t_{n}\}\) majorizes \(\{x_{n}\}\), which allows us to draw conclusions on the location of a solution of equation (1). After locating a solution of Equation (1), we establish the uniqueness of a solution. For this, from now on, we denote \(\overline{B(x,\varrho)}=\{y\in\mathcal{C}[a,b]:\|y-x\|\leq\varrho\}\) and \(B(x,\varrho)=\{y\in\mathcal{C}[a,b]:\|y-x\|<\varrho\}\).  
Theorem 4: _Let \(x_{0}\in\Omega\) be such that condition (6) is satisfied and \(\phi(t)\) the function defined in (8). If \(\phi(\sigma)\leq 0\), where \(\sigma=\min\{t>0:\phi^{\prime}(t)\geq 0\}\), and \(B(x_{0},r)\subset\Proof.: From \((i)\) and \((ii)\), it is clear that \(\|x_{1}-x_{0}\|\leq t_{1}<r\) and \(x_{1}\in B(x_{0},r)\subset\Omega\). If we now suppose that \(x_{j}\in B(x_{0},r)\subset\Omega\), for \(j=1,2,\ldots,n-1\), it follows, from Theorem 3, that the operator \([\mathfrak{F}^{\prime}(x_{n-1})]^{-1}\) exists with \(\|[\mathfrak{F}^{\prime}(x_{n-1})]^{-1}\|\leq-\frac{1}{\mathfrak{F}^{\prime}( \frac{1}{n-1})}\), \(\|\mathfrak{F}^{(i)}(x_{n-1})\|\leq\phi^{(i)}(t_{n-1})\), for \(i=2,3,\ldots,k-1\), \(\|\mathfrak{F}(x_{n-1})\|\leq\phi(t_{n-1})\) and \(\|x_{n}-x_{n-1}\|\leq t_{n}-t_{n-1}\), so that  
\[\|x_{n}-x_{0}\|\leq\sum_{i=0}^{n-1}\|x_{i+1}-x_{i}\|\leq\sum_{i=0}^{n-1}(t_{i +1}-t_{i})=t_{n}<r\]  
and therefore \(x_{n}\in B(x_{0},r)\) and \(x_{n}\) are well defined.  
After that, it follows that \(\{x_{n}\}\) is a Cauchy sequence; as a consequence, \(\{t_{n}\}\) is a Cauchy sequence and \(\lim_{n}t_{n}=r\), since, from Theorem 2, the sequence \(\{t_{n}\}\) is increasing and bounded above by \(r\). Thus, \(\{x_{n}\}\) is convergent, \(\lim_{n}x_{n}=x^{*}\) and  
\[\|x^{*}-x_{n}\|\leq r-t_{n},\quad n\geq 0. \tag{9}\]  
In addition, the combination of this and \((iii)\) yields \(\mathfrak{F}(x^{*})=0\), where \(\mathfrak{F}\) is defined in (2).  
Next, from Section 2.1, we have  
\[\|\mathfrak{F}^{\prime\prime}(x)\|\leq|\alpha|p(p-1)S\left(\|x_{0}\|+t-t_{0} \right)^{p-2},\]  
provided that \(\|x-x_{0}\|\leq t-t_{0}\). Now, as \(t_{0}=0\), it is clear that \(\|\mathfrak{F}^{\prime\prime}(x)\|\leq\phi^{\prime\prime}(t)\), for \(\|x-x_{0}\|\leq t\), and, as a consequence of this, the uniqueness of a solution \(x^{*}(s)\) follows exactly that given for Theorem 11 in [18].
## 2 Material and Methods
### Trace Element Determination  
The analysis of trace elements was carried out by atomic absorption spectroscopy. For Fe (\(\lambda\) = 248.3 nm) and Zn (\(\lambda\) = 213.9 nm), flame absorption atomic spectroscopy was used (FAAS) (Varian Spectra AA-50B model, Palo Alto, CA, USA), equipped with a standard air-acetylene flame and single-element hollow cathode lamps. For the following elements studied (Co, Cr, Cu, and Ni), we used electrothermal atomic absorption spectroscopy (ET-AAS) (Agilent Technologies model 240Z, Santa Clara, CA, USA). The instrumental conditions for the analysis of these elements are shown in Table 1.  
Finally, Se content in samples was determined by atomic fluorescence spectroscopy (AFS) (\(\lambda\) = 196.0 nm) (Millennium Excalibur Instrument, PSA Analytical, Kent, Orpington, UK). The formation of the Se hydride was carried out by pumping 0.7% \(w/v\) NaBH\({}_{4}\) (in 0.1 M NaOH) and 4.5 M HCl with a flow rate set at 10 mL/min. A gas-liquid separator and Argon gas (300 mL/min) were used to transport the selenium hydride.  
Standard solutions for quantifying Co, Cr, Cu, Fe, Ni, Se, and Zn were prepared prior to usage. These solutions were created by diluting with deionized water 1000 mg/L  
\begin{table}
\begin{tabular}{c c c c c c c c c} \hline  & \multicolumn{2}{c}{**Co**} & \multicolumn{2}{c}{**Cr**} & \multicolumn{2}{c}{**Cu**} & \multicolumn{2}{c}{**Ni**} & \\  & **(\(\lambda\) = 240.7 nm)** & **(\(\lambda\) = 357.9 nm)** & **(\(\lambda\) = 324.8 nm)** & **(\(\lambda\) = 232.0 nm)** & & \\ \hline \hline
**Step** & **T** (°C) & **t** (s) & **T** (°C) & **t** (s) & **T** (°C) & **t** (s) & **T** (°C) & **t** (s) & **Argon Flow** (L/min)** \\ \hline Drying & 85 & 5 & 85 & 5 & 85 & 5 & 85 & 5 & 0.3 \\  & 95 & 40 & 95 & 40 & 95 & 40 & 95 & 40 & 0.3 \\  & 120 & 8 & 120 & 20 & 120 & 10 & 120 & 10 & 0.3 \\ Pyrolysis & 750 & 5 & 1000 & 5 & 800 & 5 & 800 & 5 & 0.3 \\  & 750 & 3 & 1000 & 3 & 800 & 3 & 800 & 3 & 0 \\ Atomization & 2300 & 2.8 & 2600 & 2.8 & 2300 & 2.8 & 2400 & 2.8 & 0 \\ Cleaning & 2300 & 2 & 2600 & 2 & 2300 & 2 & 2400 & 2 & 0.3 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Instrumental conditions for Co, Cr, Cu, and Ni analysis by ET—AAS.  
standard solutions obtained from Certipur, Merck (Darmstadt, Germany). Samples were analyzed in duplicate.
## 4 Experiments and Results
### Evaluation Metrics  
To measure the performance of the proposed method and other methods for comparison, we used the peak signal-to-noise ratio (PSNR) and structural similarity index measure (SSIM) [33] as evaluation metrics.
## 4 Results and Discussion
### Comparison with Other Algorithms
Moreover, LSTM is rather more complicated compared to our proposed RDSCNN algorithm, so we can predict that our algorithm will be faster in the authentication process. In [PERSON] et al. [25], the features were extracted from fiducial, non-fiducial, and its fusion. There were two different classifiers used, i.e., an artificial neural network (ANN) for MIT-BIH and a support vector machine (SVM) for ECG-ID. Only 30 out of 48 subjects in the MIT-BIH database were tested, while all 90 subjects in the ECG-ID database were tested. In summary, the algorithm in [25] has three stages, including beat segmentation, feature extraction, and different classifiers for different databases. In contrast, our proposed algorithm has only two (faster) stages, including beat segmentation and an RDSCNN classifier, which can be applied for both databases. [PERSON] et al. [9] used [PERSON]'s method for ECG beat detection and segmentation starting from 0.24 s and 0.4 s before and after \(R_{peak}\), respectively. The QRST feature was extracted after the beats were decomposed using the discrete wavelet transform (DWT). They used a CNN model that functions like PCA, called PCA-Net, to extract ECG features from the results of DWT decomposition. For classification and authentication, SVM was used. The algorithm is rather complicated (higher computational time) and the accuracy for the ECG-ID database is only 97.75%. As shown in Table 6, our proposed algorithm using residual depthwise separable convolution neural network outperforms other algorithms, in which it can achieve 100% accuracy for both the ECG-ID and MIT-BIH databases. Furthermore, using [PERSON]'s method for automatic beat segmentation, it requires around 100 us (see Section 4.4). The classification process for eight consecutive ECG beats required around 560 us. Therefore, our proposed algorithms required around 660 us for the authentication process, i.e., automatic beat segmentation and classification. For a further comprehensive evaluation, other ECG databases could be used as highlighted in [30], including six public domain databases and twelve private databases.
## 4 Field Application and Results
### Artificial Neural Network (ANN)  
The RBFN model is trained with an expected outcome, such as porosity using well-log and seismic data to create an appropriate range of weights between nodes. As training wells, X-3, X-4, X-5, and X-6 wells are used, while X-7, X-8, and XD-2 wells are retained to validate the predicted results. In the RBFN model, the sigma value is 0.1 for estimating porosity with a different time window of each well. The time windows are 1000-1650 ms at X-3, 1000-1250 ms at X-4, 1000-1650 ms at X-5, and 1000-1490 ms at X-6, which is considered for the study of training error. For validation error analysis, the time windows are 1000-1320 ms at XD-2, 1000-1600 ms at X-7, and 1000-1620 ms at X-8. The training dataset is used for modelling, while the validation dataset determines its prediction error.  
Figure 22: (**a**) Averaged SQp data horizon slice within an interval between Top H and H60 horizons; (**b**) Averaged SQs data horizon slice within an interval between Top H and H60 horizons.  
Figure 23 demonstrates the training error analysis window for X-3, X-4, X-5, and X-6 wells, while the validation error analysis window for porosity prediction is shown in Figure 24 for XD-2, X-7, and X-8 wells.  
The trained-porosity from ANN demonstrates a 0.03 training error and a 0.83 correlation between the true and trained-porosity (Figure 23). The predicted porosity is validated  
Figure 23: The error analysis window for ANN training demonstrates a 0.03 training error and a 0.83 correlation between the true and estimated porosity.  
Figure 24: The error analysis window for ANN validation demonstrates a 0.04 validation error and 0.81 correlation between the true and estimated porosity.  
with a correlation of 0.81 and an error of 0.04 of the RBFN model (Figure 24). The predicted porosity consistently correlates with the values obtained from the log, equally in well locations for training and validation.  
Furthermore, to generate a 3D volume of porosity, the validated RBFN porosity model was applied to the 3D seismic data. The RBFN porosity-derived volume ranges from 23% to 76%, as shown in Figure 25.  
Figure 26 shows the spatial changes of porosity data within the zone of interest (between Top H and H60 horizons). The area of interest (dotted line in Figure 26) responded as a high porosity value, indicating the HPHT reservoir with possible hydrocarbon fluids.  
Figure 25: ANN predicted porosity crossline section containing Top H, H60, and H160 horizons and XD-2 well.
## 5 Evaluation of Bubble Size Correlation with CFD Code
### Grid Sensitivity Test  
The fully developed forced convective bubbly flow in the vertical pipe was axisymmetric along the azimuthal direction; hence, we employed a quasi-2D cylindrical geometry for the simulation. This geometry is a narrow cylindrical sector with a central angle of \(10^{\circ}\), which has symmetry boundary conditions on the side faces. The grid was divided into equal intervals along the axial direction. The flow domain and cross-sectional view of the grid are shown in Figure 3. The size in the axial direction was fixed at 5 mm, and the grid sensitivity test was conducted by changing the number of grids along the radial direction. The grid test was carried out with four meshes. Furthermore, we performed a grid geometry study with the full and half circular shapes for the simulation; however, there was no substantial difference in the calculation results. Here, the physical models introduced in Section 3 were used. Figure 4 compares the results obtained with different meshes in the Hibiki experiments. For the Hibiki experiment, \(25\times 612\) meshes revealed good independence on mesh and were, therefore, selected for the following calculation. A similar grid test was also performed for other experiments. The grids utilized in each of the calculations are summarized in Table 5.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Experiment**} & \multicolumn{2}{c}{**Superficial Gas**} & \multicolumn{2}{c}{**Superficial Liquid**} & \multirow{2}{*}{**Void Fraction (\(-\))**} & \multicolumn{2}{c}{**Absolute Pressure**} \\  & & **Velocity (m/s)** & & **Velocity (m/s)** & & **at the Outlet (Bar)** \\ \hline DEDALE & 1103 & 0.1851 & 0.877 & 0.152 & 1.0 \\ \hline \multirow{4}{*}{Hibiki} & Case 1 & 0.321 & 0.986 & 0.231 & \multirow{4}{*}{1.0} \\  & Case 2 & 0.518 & 5 & 0.106 & \\  & Case 3 & 0.624 & 2.01 & 0.228 & \\  & Case 4 & 0.471 & 2.01 & 0.183 & \\ \hline \multirow{4}{*}{Kalkach-Navarro} & Case 1 & 0.081 & 0.5 & 0.109 & \multirow{4}{*}{3.5} \\  & Case 2 & 0.114 & 0.5 & 0.142 & \\  & Case 3 & 0.135 & 0.5 & 0.169 & \\ \cline{1-1}  & Case 4 & 0.148 & 0.5 & 0.211 & \\ \cline{1-1}  & Case 5 & 0.1 & 1.0 & 0.077 & \\ \cline{1-1}  & Case 6 & 0.191 & 1.0 & 0.138 & \\ \cline{1-1}  & Case 7 & 0.27 & 1.0 & 0.195 & \\ \cline{1-1}  & Case 8 & 0.4 & 1.0 & 0.241 & \\ \hline \multirow{4}{*}{VAWL} & V01 & 0.05 & 0.5 & 0.063 & 1.0 \\ \cline{1-1}  & V03 & 0.16 & 0.5 & 0.161 & 1.0 \\ \cline{1-1}  & V10 & 0.27 & 1 & 0.163 & 1.0 \\ \cline{1-1}  & V19 & 0.12 & 2 & 0.073 & 2.0 \\ \cline{1-1}  & V25 & 0.17 & 2.85 & 0.063 & 1.0 \\ \hline \hline \end{tabular}
\end{table}
Table 4: Experimental conditions of each experiment used to simulation.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Experiment** & **Inner Diameter (mm)** & **Height (m)** & **Measurement Location (z/D)** \\ \hline DEDALE [44] & 38.1 & 6 & 55 \\ Hibiki [45] & 50.8 & 3.06 & 53.5 \\ Kalkach-Navarro [46] & 60 & 3.5 & 50 \\ VAWL [48] & 80 & 10 & 42.2 \\ \hline \hline \end{tabular}
\end{table}
Table 3: Air-water bubbly flow experiments used to evaluate the bubble size correlation.
## 4 Results  
### Electrical Resistivity Models  
Two inversion methods have been used for the P1 to P7 ERT cross-sections: smoothing-constrained and robust. In all cases, the results of the mathematical inversion process have been satisfactory, as the convergence criterion used (root mean square or RMS) has values always below 5%. However, after comparing the two sections obtained in each case, the smooth method was chosen for interpreting ERT results and for modeling. The smoothing-constrained method has shown a more consistent geological interpretation and better definition of the geometry of the identified lithological units, especially the contact between the aquifer and the basement.  
The electrical resistivity values obtained from the inversion of the 17 ERT cross-sections mainly ranged between 13 and 5000 \(\Omega\)-m. From geoelectrical records, three layers can be distinguished according to their electrical resistivity values. The shallowest layer is characterized by resistivity values higher than 600 \(\Omega\)-m and can be identified at the upper part of geoelectrical cross-sections. The level is interpreted as gravels and sands from the shallow aquifer above the water table and has a thickness always identified below 15 m. At this layer, there were important lateral variations in the resistivity values. These variations reflect lateral changes in the facies, which are usually transitions to fine-grained sediments.  
Below, the ERT cross-sections show a unit of variable thickness from 3 to 45 m thickness characterized by 20-600 \(\Omega\)-m resistivity values. These electrical resistivity values are interpreted as fine particles or saturated sediments from the shallow aquifer.  
The third unit is characterized by high resistivity values in the 600-2500 \(\Omega\cdot\)m range and corresponds to the schists of the basement and their top limit has been used to infer the aquifer/aquiclude contact. The contact is identified as a long amplitude irregular surface in most of the cases, but in particular, some sections show a stepped morphology as can be identified in Figure 5.
# FPGA Implementation of a BPSK 1D-CNN Demodulator
## 1 Introduction
A time-delay network for convolutional calculation and a structure for piecewise approximation of the activation function were designed, to further simplify calculation and shorten latency. The rest of this paper is organized as follows: Section 2 introduces the basic principle of 1D-CNN demodulation. Section 3 describes the FPGA implementation of a 1D-CNN demodulator. In Section 4, the training and test process of the 1D-CNN demodulator are introduced, and their results are analyzed. Finally, Section 5 summarizes this paper.
## 4 Case Study and Results
### Event Log and Process Discovery
\begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline  & **WtExc1** & **WtExc2** & _LdExc1_ & _LdExc2_ & _Haul_ & _Wt2 Dmp_ & _Dump_ & _Wt2 Ret_ & _Return_ \\ \hline _WtExc1_ & \# & \(\mid\mid\) & \(\rightarrow\) & \# & \# & \# & \# & \# \\ \hline _WtExc2_ & \(\mid\mid\) & \# & \# & \(\rightarrow\) & \# & \# & \# & \# \\ \hline _LdExc1_ & \# & \# & \# & \(\mid\mid\) & \(\rightarrow\) & \# & \# & \# & \# \\ \hline _LdExc2_ & \# & \# & \(\mid\mid\) & \(\rightarrow\) & \# & \# & \# & \# \\ \hline _Haul_ & \# & \# & \# & \# & \(\rightarrow\) & \(\rightarrow\) & \# & \# \\ \hline _Wt2 Dmp_ & \# & \# & \# & \# & \# & \(\rightarrow\) & \# & \# \\ \hline _Dump_ & \# & \# & \# & \# & \# & \# & \(\rightarrow\) & \(\rightarrow\) \\ \hline _Wt2 Ret_ & \# & \# & \# & \# & \# & \# & \# & \(\rightarrow\) \\ \hline _Return_ & \(\rightarrow\) & \(\rightarrow\) & \# & \# & \# & \# & \# & \# \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Footprint of the event log showing the relationship between activities. The operation starts with the trucks waiting for either excavator 1 or 2 and they are loaded with soil. Then the soil-filled truck hauls to the dump zone. Sometimes, due to queues, the trucks had to wait to get into the dump area. The trucks then dump the earth and sometimes wait to get out from the dump area due to queues. Finally, the trucks return to the load area and wait to be loaded again. Heuristic miner was also used to generate the direct succession graph and dependency graph demonstrating inter-class dependencies between the event classes as shown in Figure 10. The direct succession graph shows how many times each activity was followed by another. For example, the _Haul_ activity was followed by the _Dump_ activity 28 times, and the _Wt2 Dmp_ activity 4 times. The dependency measures were calculated using the following equation. Figure 10: Process discovery using heuristic miner. Figure 9: Discovered Petri net using \(\alpha\)-algorithm. If \(|a\ \Rightarrow b|\) is the value of the dependency relation between \(a\) and \(b\),  
\[|a\ \Rightarrow b|=\left\{ \begin{array}{cc}\frac{|a>b|-|b>a|}{|a>b|+|b>a|+1},&a \
eq b\\ \\ \frac{|a|a|}{|a>a|+1},&x\geq 0\end{array} \right. \tag{4}\]  
In the dependency graph the dependency value of \(|Haul|\Rightarrow|Dump|\) is 0.966. As _Haul_ was followed by _Dump_ 28 times, and _Dump_ was never followed by _Haul_, according to Equation (4), the dependency value is 28/29 or 0.966.
###### Abstract
However, the actual use of these models by practitioners is very limited as there is a lack of guidelines that will provide the required steps to the final user regarding the appropriate occupant behaviour modelling technique [16]. In addition, as occupants' interaction with building systems significantly influences the total energy use of buildings [27], this has attracted the interest of social scientists to research the area of user behaviour, attitudes, consumption patterns, etc. [6; 30]. Conversely, the engagement of social scientists into energy research has resulted in more awareness of the role of occupants in buildings [27]. Taking the above under consideration, this paper is in agreement with the suggestion of [PERSON] et al. [16] that there are two possible solutions to confront occupants' behaviour interaction on a building's energy performance: improving performance predictions and changing the way occupants behave. It should also be mentioned here that this study takes the latter path; our intention is not to simulate human behaviour but, instead, to attempt to track and communicate and create awareness of the occupants' behaviour at the moment of its occurrence. Our key premise here is that awareness is the first step towards behavioural change. Hence, this paper presents a methodology, relatively easily applicable, that will track, in real-time, and identify instances--events as we call them--of problematic occupant behaviour, assess their energy impact and communicate them both, event and impact, to building users. These users may be either facility managers having an overview of how the building performs or even simple building users, provided they are somehow associated with the poor behaviour tracked and may, therefore, be meaningful recipients of the event/impact information.
# A Process-Oriented Method for Tracking Rainstorms with a Time-Series of Raster Datasets
###### Abstract  
Extreme rainstorms have important socioeconomic consequences, but understanding their fine spatial structures and temporal evolution still remains challenging. In order to achieve this, in view of an evolutionary property of rainstorms, this paper designs a process-oriented algorithm for identifying and tracking rainstorms, named PoAIR. PoAIR uses time-series of raster datasets and consists of three steps. The first step combines an accumulated rainfall time-series and spatial connectivity to identify rainstorm objects at each time snapshot. Secondly, PoAIR adopts the geometrical features of eccentricity, rectangularity, roundness, and shape index, as well as the thematic feature of the mean rainstorm intensity, to match the same rainstorm objects in successive snapshots, and then tracks the same rainstorm objects during a rainstorm evolution sequence. In the third step, an evolutionary property of a rainstorm sequence is used to extrapolate its spatial location and geometrical features at the next time snapshot and reconstructs a rainstorm process by linking rainstorm sequences with an area-overlapping threshold. Experiments on simulated datasets demonstrate that PoAIR performs better than the Thunderstorm Identification, Tracking, Analysis and Nowcasting algorithm (TITAN) in both rainfall tracking and identifying the splitting, merging, and merging-splitting of rainstorm objects. Additionally, applications of PoAIR to Integrated Multi-satellite Retrievals for Global Precipitation Mission (GPM/IMERG) final products covering mainland China show that PoAIR can effectively track rainstorm objects.  
process-oriented tracking; rainstorm object; evolution sequence; raster datasets +
Footnote †: journal: Applied Sciences