esa-sceva/satcom-chunk-collection huggingface dataset:
## 2 Background and Related Work
However, it is important to note that this is meant to complement, rather than replace, classical test track certification. Combining multiple methods, as depicted in Figure 2, represents a prevalent practice within numerous assessment initiatives [10, 15, 17], with a sequential flow of activities in scenario-based evaluations of ADS, starting with a scenario catalogue. The efficacy and efficiency of the assessment process are heavily contingent upon the data in the scenario catalogue. Safety-performance indicators (SPIs) are tools for monitoring the validity of safety claims throughout the design, simulation, testing, and deployment stages [15]. The effective use of SPIs lies in their ability to prompt timely improvements by linking specific metrics to safety claims, ensuring a direct connection between the observed data and overall safety objectives. One limitation is that NATM is still in the proposal stage and has not been widely adopted or implemented. As a result, limited data are available to assess its effectiveness and suitability [18] for different Automated Driving Systems. Since NATM is technology-neutral, it may be difficult for assessors to apply the framework consistently and effectively across different ADS applications. Another difficulty is the dynamic nature of automated systems and the rapid pace of technological advancements. Safety assessments must keep up with the evolving technology, requiring continuous updates and adaptations to assessment frameworks and standards. The emergence of new sensor technologies, AI algorithms, and connectivity features further complicates the assessment process. The authors argue that the method of using the assessment templates proposed in this paper can help mitigate these limitations. An assessment template can add general scenarios to the scenario catalogue that cover conditions in the ODD by examining scenarios linked to road users' behaviour, environmental conditions, driver behaviour, and technology reliance, and provides some consistency of evaluation across applications.
## 5 Simulation Results and Analysis
### A Case Study for the Best Classical and RL Algorithms
From a practical standpoint, maintaining a constant speed during the entire mission may be more energy-efficient than repeatedly accelerating and decelerating. Such behavior may be attributed to the limitations of classical PID controllers. Alternative low-level control strategies, such as Model Predictive Control (MPC), sliding mode control (SMC), or fuzzy logic controllers, could potentially provide smoother and more robust behavior, especially during aggressive maneuvers. In the context of DRL, it is also possible to bypass the traditional controller layer entirely. The agent can instead directly output actuator-level commands, such as thruster RPMs or force vectors. This approach enables the learning algorithm to handle nonlinear dynamics and time-varying environmental conditions better. Figure 6: Trajectory comparison within test episode. Figure 7: Comparison of the AUV’s heading over time in the selected episode.
## 4 Discussion
This is especially beneficial for runners who wish to increase training intensity while minimizing injury risk. The issue of muscle activity patterns while running on an anti-gravity treadmill has been thoroughly discussed in many studies. The variations in muscle activity with different levels of unweighting are complex and not consistent across various muscle groups [24; 33; 34]. Earlier studies have shown that, in healthy runners, there is a general reduction in muscle activity of the biceps femoris, rectus femoris, tibialis anterior, and gastrocnemius with progressive unloading. Additionally, muscle activity is higher at speeds of 115-125% of the preferred running speed, regardless of the level of unweighting. Surface electromyography (sEMG) measurements of lower extremity muscles (gastrocnemius medialis and lateralis, tibialis anterior, and vastus medialis and lateralis) during running with body weight support (BWS) reveal that preactivation levels do not change with unweighting. This consistency is believed to be due to maintained muscle preactivation, which counteracts the anticipated impact from a longer flight time. Other researchers have reported nearly linear reductions in the activity of the rectus femoris, vastus medialis and lateralis, gastrocnemius, and soleus muscles with 20% increases in BWS [35]. However, during the braking and push-off phases, the muscle activity of the soleus and gastrocnemius (both medial and lateral) decreased by 10-20% as BWS increased. Moreover, increasing the cadence by 10% from the preferred habitual value boosts the muscle activity of the rectus femoris, biceps femoris, and tibialis anterior, regardless of the BWS level. Therefore, manipulating cadence may be an effective strategy to preserve more natural muscle activation patterns during rehabilitation with unweighting. In accordance with the literature, the zero-crossing rate (ZCR) and amplitude of muscle tension (AMT) can quantitatively assess muscle fatigue from EMG signals [36]. However, in this study, muscle fatigue parameters were not used as evaluation criteria because the test protocol, both in terms of exercise volume and intensity, was designed to ensure that the athletes did not experience muscle fatigue. Future studies should involve higher training intensity and volume, and the analysis should include additional measurements of fatigue using signal frequency analysis, supplemented by isometric conditions.
## 3 Results and Discussion  
### Main Characteristics of Residual Sludge  
The main physicochemical indexes of residual sludge are shown in Table 1.  
\begin{table}
\begin{tabular}{c c c c c} \hline
**pH** & **Moisture Content (\%)** & **Loss on Ignition (\%)** & **Ash Content** & **Percentage of Contraction (\%)** \\  & & & **Wet\(\rightarrow\)Dry** & **Dry\(\rightarrow\)Product** \\ \hline
6.78 \(\pm\) 0.12 & 76.7 \(\pm\) 1.4 & 25.7 \(\pm\) 0.9 & 74.3 \(\pm\) 0.9 & 50.7 \(\pm\) 0.5 & 2.5–11.3 \(\pm\) 0.2 \\ \hline \end{tabular} Note: The value is the average of 10 samples.  
\end{table}
Table 1: The main physicochemical characteristics of residual sludge.  
As can be seen from Table 1, the pH of the residual sludge is close to neutral, the burning loss is low, and the ash content is high, which indicates that the content of organic matter in the sludge is relatively small, which will lead to the low porosity of the ceramics obtained after calcining and the low content of available biochar, thus affecting its adsorption effect. However, the high content of inorganic substances increased the compressive strength of ceramics.  
The content of major metal elements in the residual sludge is shown in Table 2.  
As illustrated in Table 2, the content of Al and Fe is high in the residual sludge, among which, Al is mainly from the flocculant used in sewage treatment, Fe may come from soil minerals, while the content of Cr is significantly higher than other heavy metals.
# Dynamic Prediction Model for Progressive Surface Subsidence Based on MMF Time Function
## 2 Models and Methods
### The Final State Prediction Method  
In China, the most popular final state prediction method is the probability integral method (PIM), which is based on the stochastic medium theory [4]. Consider horizontal or gently inclined coal seam mining, if it is a rectangular working panel, the subsidence prediction model based on coordinate transformation can be constructed along the strike or inclined main section of the working panel, as shown in Equation (24):  
\[\left\{\begin{array}{l}W^{0}(x)=\frac{W_{0}}{2}\Big{\{}erf\Big{[}\frac{\sqrt {\pi}}{\tau}(x-s_{3})\Big{]}-erf\Big{[}\frac{\sqrt{\pi}}{\tau}(x-D_{3}+s_{4}) \Big{]}\Big{\}}\\ W^{0}(y)=\frac{W_{0}}{2}\Big{\{}erf\Big{[}\frac{\sqrt{\pi}}{\tau_{1}}(y+H_{1} \cos\theta_{0}-s_{1}\cos\alpha)\Big{]}-erf\Big{[}\frac{\sqrt{\pi}}{\tau_{2}}(y- (D_{1}-s_{2})\cos\alpha+H_{2}\cot\theta_{0})\Big{]}\Big{\}}\end{array}\right. \tag{24}\]  
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Name of** & **Mining Height** & \begin{tabular}{c} **Average Mining** \\ **Depth** \\ **\(H_{0}\), \(m\)** \\ \end{tabular} & \begin{tabular}{c} **Thickness of** \\ **Loose Layer** \\ \(h_{m}\) \\ \end{tabular} & \begin{tabular}{c} **Advance Velocity** \\ **\(h_{m}\)** \\ \end{tabular} & \begin{tabular}{c} **Subsidence** \\ **\(v\), \(m\)/d** \\ \end{tabular} & \
\begin{tabular}{c} **In \(a\)** \\ **\(q\)** \\ \end{tabular} &
\begin{tabular}{c} **b** \\ **\(q\)** \\ \end{tabular} \\ \hline RL7222 & 2.2 & 390 & 285 & 1.64 & 1.08 & 18.02 & 3.83 \\ BZ1203 & 2.3 & 255 & 42.5 & 7.19 & 1.1 & 19.25 & 5.24 \\ BZ4303 & 4.6 & 217 & 52.4 & 2.30 & 0.91 & 23.61 & 5.87 \\ BZ4410 & 5.78 & 314 & 50 & 5.06 & 0.81 & 32.31 & 8.40 \\ LI1203 & 4.19 & 327 & 45 & 2.30 & 0.77 & 19.74 & 4.57 \\ I2201 & 3.  
where \(W^{0}(x)\) and \(W^{0}(y)\) are the final subsidence of strike main section and inclined main section, respectively. \(W_{0}\) is the maximum surface subsidence, \(W_{0}=Mq\)cos \(\alpha\), \(M\) is the mining thickness, \(q\) is the subsidence coefficient, or the ratio of maximum surface subsidence value to mining thickness under critical mining conditions and \(\alpha\) is the coal seam dip angle. \(H_{1}\) and \(H_{2}\) are the mining depth in downhill and uphill directions, respectively; \(r\), \(r_{1}\) and \(r_{2}\) are the main influence radius of strike, downhill and uphill directions, respectively; \(s_{3}\), \(s_{4}\), \(s_{1}\) and \(s_{2}\) are the inflection point offsets of strike left, right, downhill and uphill directions, respectively. \(D_{1}\) and \(D_{3}\) are mining lengths along the strike and inclined directions, respectively; \(\theta_{0}\) is the mining influence propagation angle.  
The coordinate system used in the construction of the mathematical model is shown in Figure 8a,b.
# Demodulation Technique Based on Laser Interference for Weak Photo-Acoustic Signals on Water Surface
## 3 Results
### Frequency Measurement Results  
Taking the interference signals of 3 kHz and 1 kHz underwater acoustic sources as an example, the spectrograms are shown in Figure 7. It can be seen from this figure that the low-frequency band caused by the natural water surface fluctuations is about 1 kHz in width. The 1 kHz underwater acoustic source signals experienced aliasing with low-frequency bands in Figure 6b, which coincides with theoretical analysis.  
Based on the previously mentioned demodulation theory, we first grouped the detected signals in the interference signal spectrum into high-frequency and low-frequency categories. Low-frequency signals are handled with improved PGC demodulation technique. The phase demodulation signals have exactly the same frequency as the signal generator. For high-frequency signals, the central points of the high-frequency components were extracted for frequency measurement, as shown in Figure 8.  
Figure 6: (**a**) Optical dark chamber; (**b**) interference optical path; (**c**) test water pool (height 100 cm, diameter 80 cm); (**d**) signal amplifier, power amplifier, and laser controller; (**e**) PC measurement screen.  
Figure 7: Spectrum aliasing phenomenon: (**a**) spectrum of 3 kHz source; (**b**) spectrum of 1 kHz source.  
With the central frequency extraction method, detection tests were performed on underwater acoustic sources in the frequency range between 2 kHz and 10 kHz. For each frequency, the measurement was repeated five times. It can be seen from the results given in the above table that for signals above 2 kHz, the frequency measurements were generally accurate and repeatable, with a measurement error and a standard deviation not exceeding 1 Hz.
## 4 Hierarchical Cooperative MIMO Clustering
### Clustering
#### 4.2.1 Information Exchange  
Initially, when sensor nodes are placed, the network is not clustered. When a node wakes up and finds that its not a part of any cluster it triggers clustering algorithm. When the algorithm starts, nodes contend for the channel using carrier sense multiple access collision avoidance (CSMA/CA) scheme. Each node sends its neighbor node a HELLO message. The HELLO message is broadcast at a low power level. Aim of using low power is to send the message to only one hop neighbors which are in close geographic vicinity and to save power. The HELLO message consists of node ID, its remaining energy and a list of its neighbors. Every node calculates its weight on the basis of neighborhood information. Weight is the sum of the normalized values of clustering parameters. For implementation simplicity, we assume that a node's weight is equal to its own residual energy (_i.e._, the highest weight is assigned to residual energy of the nodes). Unlike LEACH algorithm [12] which assumes that each clusterhead has a radio powerful enough to directly reach the base station, in this work our focus is on sensor nodes spread over a large area where all nodes/clusterheads cannot communicate with CCS directly. In LEACH the clusterheads rotate after a given time and each node resumes the job of a clusterhead with probability p. In our work we designate the power of CH to the most suitable node and CH changes when the energy level drops below a certain level. This level is an arbitrary parameter and can be varied. Nodes continue to exchange this information for a finite number of rounds.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Parameter** & **Meaning** & **Value** \\ \hline \(R_{b}\) & Bit Rate & 1 Mbps \\ \(P_{DAC}\) & Digital-to-Analog converter & 15 mW \\ \(P_{ADC}\) & Analog-to-Digital converter & 15 mW \\ \(P_{mix}\) & Mixer & 30.3 mW \\ \(P_{filt}\) & Active filters at transmitter & 2.5 mW \\ \(P_{filt}\) & Active filters at receiver & 2.5 mW \\ \(P_{syn}\) & Frequency synthesizer & 50 mW \\ \(P_{LNA}\) & Low noise amplifier & 20 mW \\ \(P_{IFA}\) & Intermediate frequency amplifier & 2 mW \\ \(B\) & Bandwidth & 10 KHz \\ \(N_{0}\) & PSD & \(-171\) dBm/Hz \\ \(M_{l},N_{f}\) & Link margin, Receiver noise figure & 10 dB \\ \hline \hline \end{tabular}
\end{table}
Table 1: System Parameters.
# Comparison of the Observation Errors of Augmented and Spatial Reality Systems
## 3 Results
### Consistency  
The results of the horizontal measurements in the SP, which were re-measured after 2 weeks, confirmed no reliability issues (ICC > 0.78). From the Bland-Altman analysis, 14 out of 14 raters obtained results within the confidence interval for the Model, 12 out of 14 for HMD, and 13 out of 14 for SRD. Table 2 shows the results of the ICC. Figure 12 shows the results of the Bland-Altman analysis.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline  & **Posture** & **Direction** & **Mean** & **SD** \\ \hline \multirow{4}{*}{Model} & \multirow{2}{*}{SP} & Horizontal & 42.77 & 0.38 \\ \cline{3-5}  & & Depth & 42.52 & 0.40 \\ \cline{2-5}  & & Horizontal & 43.46 & 0.33 \\ \cline{2-5}  & & Depth & 43.29 & 0.37 \\ \hline \multirow{4}{*}{HMD} & \multirow{2}{*}{SP} & Horizontal *.\({}^{\dagger}\)* & 44.70 & 0.78 \\ \cline{3-5}  & & Depth & 42.82 & 1.55 \\ \cline{2-5}  & & Horizontal & 45.16 & 0.61 \\ \cline{2-5}  & & Depth & 43.66 & 1.00 \\ \hline \multirow{4}{*}{SRD} & \multirow{2}{*}{SP} & Horizontal & 42.80 & 0.32 \\ \cline{3-5}  & & Depth & 42.11 & 0.77 \\ \cline{1-1} \cline{2-5}  & & Horizontal & 42.87 & 0.37 \\ \cline{1-1} \cline{2-5}  & & Depth & 43.27 & 0.63 \\ \hline \hline \end{tabular} Model, control model; HMD, head-mounted display; SRD, spatial reality display; SP, sitting posture; SRP, standing posture; SD, standard deviation. Wilcoxon signed-rank test (\(\alpha\) = 0.01). *; HMD + SP + Horizontal vs. Model + SP + Horizontal (T = 6 \(p\) = 0.0035). *: HMD + SP + Horizontal vs. SRD + SP + Horizontal (T = 5 \(p\) = 0.0028). *: HMD + StP + Horizontal vs. Model + StP + Horizontal (T = 7 \(p\) = 0.0042). *: HMD + StP + Horizontal vs. SRD + StP + Horizontal (T = 0 \(p\) = 0.00098).  
\end{table}
Table 1: Aggregation of measurement results.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline  & & \multicolumn{4}{c}{**Intra-Rater Reliability**} \\ \cline{3-5}  & & **ICC** & **95\% Confidence Interval** & \(p\) \\ \hline \multirow{3}{*}{SP + Horizontal} & Model & 0.79 & 0.55 to 0.92 & 0.00 * \\ \cline{2-5}  & HMD & 0.79 & 0.56 to 0.92 & 0.00 * \\ \cline{2-5}  & SRD & 0.78 & 0.54 to 0.92 & 0.00 * \\ \hline \hline \end{tabular} ICC, intra-class correlation. * \(p\)-value \(<\) 0.01.  
\end{table}
Table 2: Intra-rater reliability of 14 raters.
## 2 Preliminaries
### Notation  
The 2-norm of a vector or a matrix is provided by \(\|\cdot\|\). \(\lambda_{\max}(\text{Z})\) and \(\lambda_{\min}(\text{Z})\) represent the maximal and minimum eigenvalue of the matrix Z, respectively. Moreover, the operator \(\boldsymbol{S(\cdot)}\) denotes a vector \(\kappa=\left[\begin{array}{cc}\kappa_{1}&\kappa_{2}&\kappa_{3}\end{array} \right]^{T}\) to a skew symmetric matrix as  
\[\boldsymbol{S(\kappa)}=\left[\begin{array}{ccc}0&-\kappa_{3}&\kappa_{2}\\ \kappa_{3}&0&-\kappa_{1}\\ -\kappa_{2}&\kappa_{1}&0\end{array}\right] \tag{1}\]  
The sign function is given as  
\[sign(\kappa)=\left\{\begin{array}{cc}\frac{\kappa}{|\kappa|},&|\kappa|\
eq 0 \\ 0,&|\kappa|=0\end{array}\right. \tag{2}\]
# Shaping 1,2,4-Triazolium Fluorinated Ionic Liquid Crystals
## 2 Materials and Methods
### Synthesis of Trifluoromethanesulfonate Triazolium Salts  
To a solution of neutral triazole (0.25 g, 0.26 mmol) in toluene (10 mL), 0.4 mL (15 eq.) of CF\({}_{3}\)SO\({}_{3}\)CH\({}_{3}\) was added in a sealed tube. The mixture was stirred and heated at 110 \({}^{\circ}\)C for 24 h. The reaction mixture was dried under a vacuum, and the compounds [Ph-Tri-(n)\({}_{2}\)][OTf] were isolated by chromatography, using petroleum ether/ethyl acetate 20:1 and 3:1 as elevents.  
**5-(3,5-bis(decyloxy)phenyl)-1,4-dimethyl-3-(perfluoroheptyl)-1H-1,2,4-triazoleol-4-ium trifluoromethanesulfonate [Ph-Tri-(10)2][OTf]**: white solid. Yield = 30% \({}^{1}\)H NMR (300 MHz, CD\({}_{3}\)OD) 8, ppm: 0.93 (t, J = 6 Hz, 6H), 1.32 (m, 28H), 1.83 (m, 4H), 3.95 (s, 3H), 4.01 (t, J = 6 Hz, 4H), 4.13 (s, 3H), 6.91 (d, J = 3 Hz, 2H), 6.95 (d, 1H). ESI-MS analysis for [C\({}_{37}\)H\({}_{51}\)F\({}_{15}\)N\({}_{3}\)O\({}_{2}\)\({}^{+}\)]: Calc.: 854.3736 g mol\({}^{-1}\), exp.: 854.3794 g mol\({}^{-1}\).  
**5-(3,5-bis(dodecyloxy)phenyl)-1,4-dimethyl-3-(perfluoroheptyl)-1H-1,2,4-triazoleol-4-ium trifluoromethanesulfonate [Ph-Tri-(12)2][OTf]**: white solid. Yield = 32% \({}^{1}\)H NMR (300 MHz, CD\({}_{3}\)CN) 8, ppm: 0.88 (t, J = 6 Hz, 6H), 1.28 (m, 32H), 1.45 (m, 4H), 1.77 (m, 4H), 3.81 (s, 3H), 4.01 (m, 4H), 4.04 (m, 3H), 6.73 (m, 2H), 6.86 (s, 1H). ESI-MS analysis for [C\({}_{41}\)H\({}_{59}\)F\({}_{15}\)N\({}_{3}\)O\({}_{2}\)\({}^{+}\)]: Calc.: 910.4368 g mol\({}^{-1}\), exp.: 910.4394 g mol\({}^{-1}\).  
**5-(3,5-bis(tetradecyloxy)phenyl)-1,4-dimethyl-3-(perfluoroheptyl)-1H-1,2,4-triazoleol-4-ium trifluoromethanesulfonate [Ph-Tri-(14)2][OTf]**: white solid. Yield = 41% \({}^{1}\)H NMR (300 MHz, CD\({}_{3}\)) 8, ppm: 0.87 (t, J = 6 Hz, 6H), 1.25 (m, 40H), 1.44 (m, 4H), 1.78 (m, 4H), 3.92 (s, 3H), 4.02 (t, J = 6 Hz, 4H), 4.11 (s, 3H), 6.77 (m, 1H), 6.95 (d, 2H). ESI-MS analysis for [C\({}_{45}\)H\({}_{67}\)F\({}_{15}\)N\({}_{3}\)O\({}_{2}\)\({}^{+}\)]: Calc.: 966.4950 g mol\({}^{-1}\), exp.: 966.4989 g mol\({}^{-1}\).  
**5-(3,5-bis(hexadecyloxy)phenyl)-1,4-dimethyl-3-(perfluoroheptyl)-1H-1,2,4-triazoleol-4-ium trifluoromethanesulfonate [Ph-Tri-(16)2][OTf]**: white solid. Yield = 30% \({}^{1}\)H NMR (300 MHz, CD\({}_{3}\)) 8, ppm: 0.87 (t, J = 6 Hz, 6H), 1.25 (m, 48H), 1.44 (m, 4H), 1.78 (m, 4H), 3.92 (s, 3H), 4.01 (t, J = 6 Hz, 4H), 4.10 (s, 3H), 6.77 (s, 1H), 6.94 (s, 2H). ESI-MS analysis for [C\({}_{49}\)H\({}_{75}\)F\({}_{15}\)N\({}_{3}\)O\({}_{2}\)\({}^{+}\)]: Calc.: 1022.5614 g mol\({}^{-1}\), exp.: 1022.5787 g mol\({}^{-1}\).
# Electromagnetic Assessment of UHF-RFID Devices in Healthcare Environment
## 3 Results
### Hospital Universitario de Canarias (HUC)--Tenerife (Measurement-Based Assessment)
#### 3.1.2 EMF Exposure near the AS-RFID Reader  
The distance was measured from the rear panel of the cabinet, where the RF emitting antennas are located, to the center of the antenna. The measurements at 135\({}^{\circ}\) and 180\({}^{\circ}\) have been made at angles of 45\({}^{\circ}\) and 90\({}^{\circ}\) angles, for the rear wall of the cabinet. The heights were measured from the floor to the center of the antenna. Figure 5 presents the map where the measurement points are marked.  
At 1.0 m, 1.3 m and 1.7 m heights, the average of the recorded E-field strength values was 0.056 V/m, 0.059 V/m and 0.061 V/m, respectively.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline  & & \multicolumn{4}{c}{**E-Field Peak Value [V/m]**} \\ \hline \multirow{2}{*}{**Distance (m)**} & \multicolumn{4}{c}{**Angle (\({}^{\circ}\))**} \\ \cline{2-6}  & **0** & **45** & **90** & **135** & **180** \\ \hline
0.25 & 0.117 & 0.117 & 0.117 & 0.118 & 0.118 \\
0.50 & 0.118 & 0.118 & 0.118 & 0.118 & 0.119 \\
1.00 & 0.119 & 0.119 & 0.112 & 0.109 & 0.105 \\
2.00 & 0.099 & 0.070 & 0.06 Along with the distance increase, there the E-Field decrease was recorded, that was more specific and more clearly observable as the measuring angle was getting narrower, the foregoing can be up to almost 10 dB/m at 4.0 m for zero angles. However, at 180\({}^{\circ}\) we can observe more constant values.  
The test was also carried out for the same 866 MHz frequency value, inside the cabinet at different heights of from 0.61 and 1.65 m, above the cabinet floor. Measures were also carried out at 0.075 m from the rear panel, where the emitting equipment was located, and at 0\({}^{\circ}\) angle. The field levels remained at approximately 0.270 V/m for all heights applied for the purpose of the test. The results obtained are presented as the Radiation Diagram in Figure 7 and the results presented on a 2D contour maps are accurately depicted in Section 3.5. later on.
## 3 Results and Discussion
### Recommendations for the Optimal Orientation in Ecuador  
The available literature indicates that countries located in the northern hemisphere should orient their solar panels or modules towards the southern hemisphere, and vice versa for the countries located in the southern hemisphere. This is not the case for countries situated in the equator, where some works, such as Reference [36], suggest that the inclination should be \(0^{\circ}\). However, other works suggests that the inclination angle should not be less than \(5^{\circ}\) to avoid dirtiness on the PV panels. Moreover, other works demonstrated that, in Quintorland Latacunga, an angle higher than \(30^{\circ}\) will result in significant losses [37; 38].  
Similarly, the authors of Reference [39] analyzed various inclination angles in Cuenca (from \(0^{\circ}\) to \(30^{\circ}\)) and evidenced that the losses become significant close to \(30^{\circ}\).  
The authors of Reference [40] establish that the PV system site has a higher annual generation as it faces east with a slope close to the horizontal, but without significant differences with respect to the rest of the orientations with similar slopes. This indicates that, in equatorial latitudes, the inclination and orientation is not an important limitation in the production of energy based on solar systems, as it happens in higher latitudes, such as those of Europe, the United States, Argentina, or Australia.  
Thus, each author has it own criteria to select the optimal orientation and inclination angles. In this work, the optimal angles of the most populated cities were obtained based on the presented models.