esa-sceva/satcom-chunk-collection huggingface dataset:
## 3 Special-Function Solvability
### Double-Well Dynamical Regime with \(D>0\)  
In the double-well regime with positive \(d=\
u^{2}>0\) the presence of the square-root branch-point of Equation (25) at \(x=\
u^{2}\), i.e., _inside_ the interval of physical coordinates would make the direct use of the asymptotically correct closed-form solutions (28) slightly uncomfortable. The key new technicality is that one must keep the choice of the proper branch of the coordinate function \(x=x(z)=d\pm\sqrt{z}\) under explicit control.  
For this reason we recommend the use of an alternative bound-state construction in which one recalls the \(\mathcal{P}\)-symmetry of our Schrodinger Equation (1) and employs a variant of the so called shooting method. In the language of mathematics this means that one simply separates the spatially even wave functions (for which we set \(\psi(0)=1\) and \(\psi^{\prime}(0)=0\) as an initial boundary condition) from the spatially odd solutions (for which we have \(\psi(0)=0\) and \(\psi^{\prime}(0)=1\))--this is to be compared with Equations (30) and (31), respectively. In each of these two subcases one arrives again at the Kummer's Equation (25) which is now defined in an extended and partially doubly covered interval of \(z\in(0,\infty)\) and \(z\in(0,\
u^{4})\).  
In contrast to preceding subsection we will now solve the initial-value _alias_ Cauchy problem knowing that we know its general solution in confluent-hypergeometric form  
\[\psi(x)=\psi(x,E)=C_{1}\,w_{(even)}[z(x)]+C_{2}\,w_{(odd)}[z(x)]\,. \tag{32}\]  
In the next stage of development we fix the ratio of the coefficients \(C_{j}\) via the above-mentioned initial conditions imposed upon the both-sided limits of \(\psi(x)\) and \(\psi^{\prime}(x)\) at \(x=0\) (i.e., at \(z=\
u^{4}\) when taken below its square-root branch). The subsequent necessary control of the choice of the branch of function (27) (i.e., of the analytic-function component \(w_{(odd)}[z(x)]\) of our solution (32) at \(z=0\)) is not difficult because we have \(b=1/2\) (i.e., a square-root branch) in definition (27).  
In the last step we may finally recall the standard oscillation theorems [38] which  
* relate the quantum number \(n=0,1,\dots\) of a bound-state energy \(E_{n}\) to the number \(Z_{n}=n\) of the finite nodal zeros \(x_{j}\in(-\infty,\infty)\) of \(\psi_{n}(x)\);
* enable us to perturb \(E_{n}\to E_{n}^{(+)}=E_{n}+\delta^{2}\), localize the related maximal real (and, say, positive) finite nodal zero \(x_{(max)}^{(+)}>0\) and find the one-to-one correspondence between the exact-bound-state-energy limits of \(\delta\to 0\) and of \(x_{(max)}^{(+)}\to\infty\).  
The latter correspondence enables us to localize, numerically, the exact energy, with arbitrary preselected precision, via a trial-and-error choice of \(E_{n}^{(\pm)}\), to be iteratively amended by a tentative, smaller and smaller decrease (whenever the maximal real node \(x_{(max)}^{(+)}\) keeps growing) or increase (whenever the maximal node happens to leave the real line and become complex).
## 2 Materials and Methods
### Landmark Configuration  
On the extracted 3D surfaces, obtained after segmentation of the skull from CT-scans, 41 landmarks (biologically homologous points) were placed over the cranial vault and face using Avizo 9.0 (FEI visualisation) (Figure 1). A list of the landmarks and their anatomical definitions can be found in Appendix B. The final landmark point in the landmark configuration was located on the most deviated point of the nasal septum and was found using the \"orthoslice\" function in Avizo 9.0 to gain a series of coronal CT images of each specimen. This method allowed clear visualisation of the nasal septum, which enabled placement of the landmark on the most lateral point from a cranial midsagittal plane by scrolling antero-posteriorly through the coronal slices [19]. This can be seen in Figure 2. To estimate the level of nasal septum deviation (calculated in mm), for each specimen, a virtual midsagittal plane was built in R software [20]. The midsagittal plane was estimated by finding the least squares plane that best fits the midsagittal cranial landmarks, namely the points bregma, lambda, and the anterior point along the cribriform plate. These landmarks were used in building a midsagittal plane for estimating nasal septum deviations and were not included in measuring facial asymmetry nor in the Generalised Procrustes Analysis (GPA) [21] of the facial morphology. Then, the linear distance between the deviation landmark and the midsagittal plane was measured using R software. To account for cranial size differences, the septal deviation was recorded using landmark configurations after GPA. In this way, the linear distance was scaled to the unit size of the cranium. The deviation landmark was only used to estimate septal deviation and was not included in measuring facial asymmetry nor in the GPA of the facial morphology.  
Figure 1: Three-dimensional landmark configuration displayed on one of the male skulls: Frontal view top left, lateral view top right, posterior view bottom left, inferior view bottom right. The landmark numbers refer to the definitions in Appendix B. Image created using Avizo 9.0 (FEI visualisation).
## 4 Sample Failure Characteristics  
### Brittleness Index  
In order to study the brittleness characteristics of the samples during failure, [PERSON] et al. [33] proposed the brittleness index as the evaluation criteria, as shown in Equation (1):  
\[I=q_{\max}/q_{0.1}-1 \tag{1}\]  
where \(q_{\max}\) and \(q_{0.1}\) represent the peak stress and stress at 10% axial strain, respectively, and \(I\) represents the brittleness index. The brittleness index of PCS samples can be obtained by substituting the relevant data in Figure 2 into Equation (1), as shown in Figure 10. The figure indicates that:  
1. When the fiber mass content is fixed, with the increase in confining pressure, the brittleness index of PCS samples decreases and the ductility increases. Under a confining pressure of 100 kPa, the brittleness index is the highest and the brittle failure is obvious. The brittleness index reaches its lowest value when the confining pressure is 400 kPa, which suggest the best mitigation effect of brittle failure.  
2. Under the same confining pressure, with the increase in fiber mass content, the brittleness index of PCS samples first decreases and then increases. When the fiber mass content is 6%, the brittleness index reaches the minimum. Compared with 0% PCS sample, the brittleness index decreases from 52% to 79% with the increase in confining pressure, indicating that the incorporation of fiber can improve the brittle failure of the sample, and the modification effect is enhanced with the increase in confining pressure.  
The main reason is that, with the change of confining pressure, there will be an interfacial interaction force between the fiber and the soil particles. When the PCS sample is subjected to an external force, the fiber will bear a part of the external force through the interfacial interaction, whereby improving the brittle failure of the sample.
## 1 Introduction
[14] proposed a precise control method based on fuzzy PID for the supporting force of a shield-type temporary support robot and verified the stability of the control system through experiments to ensure the safe and stable support of the surrounding rock during the pushing movement. In summary, the existing temporary support equipment can only address excavation issues in roadways with widths below 5 m, and there is a high risk of damaging the roof during the support process. There are few reports on temporary support equipment for a short-wall working face with a length of 15-40 m required for the face section coal pillar excavation and mining system. Therefore, aiming at the needs of the face section coal pillar excavation and mining system, this paper designs a self-propelled temporary support robot (TSR). The working principle of TSR driving under pressure is analyzed, and mechanical models of TSR for stable support and dynamic models for driving under pressure are constructed. The stable support state, the boundary conditions of driving under pressure, and the process of driving under pressure are simulated and analyzed to solve the support and driving problems of excavation equipment in short-wall working face tunnels. This paper is organized as follows: Section 1 designs a self-moving TSR and clarifies its working principle. Section 2 constructs a mechanical model of the TSR during stable support. Section 3 constructs a dynamic model of the TSR when driving under pressure. Section 4 establishes a criterion system for the boundary condition of the dynamic model, and clarifies the mechanism of interaction between the TSR and the surrounding rock under the driving under pressure condition. Section 5 conducts a finite element analysis on the TSR and the floor and simulates the critical value of the boundary condition of the dynamic model for driving under pressure, as well as the process of driving under pressure.
## 3 Formulation  
In this section, we formulate a mathematical model to design the operational plan for additional trains in peak periods. The parameters in the model are listed in Table 3, and decision variables are listed in Table 4. First, some assumptions are listed to simplify the problem.  
\begin{table}
\begin{tabular}{c c} \hline
**Notions** & **Definitions** \\ \hline \(S=\{1,\ 2,\cdots,|S|\}\) & Set of stations \\ \(T_{s}\) & The set of traveling time of segments. \\ \(K_{1}=\{1,\ 2,\cdots,\ |K_{1}|\}\) & The set of existing trains \\ \(K_{2}=\{1,\ 2,\cdots,\ |K_{2}|\}\) & The set of expected additional trains \\ \([1,\ \ T]\) & The time window of additional train arrives at its \\  & terminal station \\ \(i,j\) & The index of station, \(i,\,j\in S\). \\ \((i,j)\) & The index of OD pair, \(i,j\in S\). \\ \((i,i+1)\) & The index of segment on the railway corridor, \\  & \(i\in S/\{|S|\}\) \\ \(t_{ij+1}\) & The traveling time of train on the segment \((i,i+1)\) \\ \(L_{i}\) & The distance from station \(i\) to station 1 \\ \(k\) & The index of train, \(k\in\ K_{1}\cup K_{2}\) \\ \(h_{min}\) & The minimum headway of trains \\ \(d_{min}\) & The minimum dwelling time \\ \(d_{max}\) & The maximum dwelling time \\ \(D^{e}_{i,k}\) & The departure time of existing train \(k\) at station \\  & \(i,\ k\in K_{1},\ s\in S\). \\ \(A^{e}_{i,k}\) & The arrival time of existing train \(k\) at station \\  & \(i,\ k\in K_{1},s\in S\). \\  & Indicator for station \(i\in\ S\) as origin station of existing \\ \(z^{el}_{ki}\) & train \(k\in K_{1}\) for:= 1 if train \(k\) select station \(i\) as its \\  & origin station, =0 otherwise. \\  & Indicator for station \(i\in\ S\) as terminal station for \\ \(z^{elT}_{ki}\) & existing train \(k\in K_{1}\):= 1 if train \(k\) select station \(i\) as its \\  & origin station, =0 otherwise. \\  & origin station, =0 otherwise. \\ \(y^{e}_{ki}\) & Indicator for existing train \(k\in K_{1}\) stopping at station \\ \(i\in S\):= 1 if train \(k\) stop at station \(i\), =0 otherwise. \\ \(C_{k}\) & The maximum loading capacity of train \(k\) \\ \(y_{min}\) & The required minimum number of boarding and \\  & alighting passengers for train stopping. \\ \(Q_{ij}\) & Passenger demand for OD pair \((i,j)\) \\ \(Q_{max}\) & The total outbound passenger demand along the \\  & whole railway corridor \\ \(N_{K_{1}}\) & The number of existing trains \\ \(N^{e}_{K_{2}}\) & The expected number of additional trains \\ \(N^{e}_{K_{2}}\) & The number of additional trains \\ \hline \end{tabular}
\end{table}
Table 3: Parameters.  
1. The traveling time of each segment is fixed.
2. The capacity of the station and the rolling stocks is unlimited.
3. Dwelling time at the origin station and terminal station of the trip for each train is not considered.
4. The difference between the infrastructure of stations is not considered. In the real word, the infrastructure in some small-scale stations is so poor that they are not suitable to serve as an origin station or terminal station. In this paper, we assume that all stations are qualified to serve as an origin station or terminal station for additional trains.
## 2 Computational Modeling
### Validation of Numerical Results  
After performing numerical simulations, using Mesh1.2 and Transient Blade Row, the values for the pump stage flow rate Q, head H, and hydraulic efficiency coefficient \(\eta_{\mathrm{H}}\) are obtained.  
In Figure 5, the results obtained both experimentally and through numerical simulations are presented.  
Figure 4: A diagram of the experimental setup (system). Reproduced with permission from [PERSON] Investigation of the influence of the Radial diffuser and the return guide vanes on the performance of a multistage centrifugal pump. PhD thesis published by the University of Ruse, Ruse, Bulgaria, 1983.  
Figure 5: The validation of numerical results includes (**a**) relationships regarding the impact of flow rate on head and hydraulic efficiency, obtained through experimental methods (as seen in Ref. [2]) and numerical simulations; (**b**) relative errors \(\delta_{\mathrm{H}}\) and \(\delta_{\mathrm{n}}\) given as functions of the flow rate.  
To evaluate the accuracy of the results obtained, the relative errors of the head \(\delta_{\rm H}\) and the hydraulic coefficient of efficiency \(\delta_{\rm n}\) are calculated by applying the following equations:  
\[\delta_{\rm H}=\frac{\left|\rm H_{exp}-\rm H_{CFX}\right|}{\rm H_{exp}}100\% \tag{11}\]  
and  
\[\delta_{\rm n}=\frac{\left|\rm n_{H,exp}-\rm n_{H,CFX}\right|}{\rm n_{H,exp}}100\% \tag{12}\]  
where \(\rm H_{exp}\) and \(\rm n_{H,exp}\) are the values of head and hydraulic coefficient of efficiency obtained experimentally, while \(\rm H_{CFX}\) and \(\rm n_{H,CFX}\) are obtained after performing numerical simulations.  
In Figure 5b, the relationship demonstrating the impact of the flow rate on the relative errors (deviations) \(\delta_{\rm H}\) and \(\delta_{\rm n}\) is presented. The largest relative error of the head reaches 8%, and the hydraulic coefficient of efficiency is 5%. According to Ref. [1], p. 614, for academic studies with no commercial risk, the targeted tolerances on head and power may be limited to \(\pm\)10%.
## 2 Materials and Methods  
### BDS and GPS Data  
The CMONOC consists of 260 continuous stations, 28 of which were installed in 1999, the remaining sets of which have operated since 2010, and 62 of which have deployed with BDS/GPS dual module Trimble NETR9 receivers since 2015. The raw data can be obtained by asking the data center of CMONOC ([[http://www.neis.cn/](http://www.neis.cn/)]([http://www.neis.cn/](http://www.neis.cn/))). Figure 1 shows the spatial distribution of 62 BDS/GPS dual module stations. A total of 884 daily results are estimated with BDS and GPS observations from day 213 of 2015 to day 365 of 2017. The first 60 solutions in 2017 and 44 stations with almost full-time occupation history were used to estimate the accuracy of positioning results from different satellite systems. The signals from 14 BDS satellites can be tracked. However, due to the extraordinary large clock errors in C02 satellite of GEO, 13 BDS satellites, including 4 GEO, 5 IGSO, and 4 MEO satellites, were included during the data processing in this study.
# An Automatic Dry Sieving Mechanism for a Lunar Brick Payload
## 3 Results
### Influence of Aperture Size  
The influence of different aperture sizes is an important aspect to address. All tests in this study were conducted using LHS-1 regolith at a fixed angle of 45 degrees and a frequency of 7.5 Hz, differing from the previous 9.8 Hz tests. This lower frequency resulted in a slightly higher sieve amplitude. Aperture sizes of 500, 250, and 125 were evaluated.  
Sieve blocking data, presented in Figure 8, revealed that the percentage of blocked pores increased as aperture size decreased. These results validate the previously known fact that dry aperture-based sieving becomes more challenging as particle size decreases [5], as stated in the introduction.  
Figure 6: Cumulative fine fraction percentage of dried and undried LMS-1 simulant at a 45\({}^{\circ}\) sieve angle.  
Figure 7: Cumulative fine fraction percentage of LHS-1 simulant with different amplitudes at a 45\({}^{\circ}\) sieve angle.  
As shown in Figure 9, sieving with a 500 \(\upmu\)m aperture produced a lower fine fraction compared to the 9.8 Hz tests (Figure 2), particularly in the 250 \(\upmu\)m particle size range. For this range, the cumulative fine fraction was approximately 5% at 9.8 Hz but dropped to around 1% at 7.5 Hz. This observation is consistent with the findings in Section 3.4, where an increased amplitude showed a reduction in sieving efficiency. When the aperture size was reduced to 250 \(\upmu\)m, no particles above 250 \(\upmu\)m were observed, and a notable reduction in the 125 \(\upmu\)m range was detected, though the pan fraction remained relatively unchanged in comparison with the 500 \(\upmu\)m aperture sieve. Finally, for the 125 \(\upmu\)m aperture test, no particles exceeded this size threshold, and a decrease in the pan fraction was observed. Therefore, the dramatic increase in sieve blocking, as shown in Figure 8, likely reduces the sieving efficiency in the range close to the aperture size.
## 1 Introduction
In order to deal with the issue, the gain adaptation algorithm was taken into account. The integration of the gain adaption algorithm and the super-twisting sliding mode control can benefit the formation maneuvers of uncertain multi-robot systems with the unknown boundary [28]. However, the design in [28] was only presented for the single-input-single-output systems and it cannot be directly extended to a multiple-input-multiple-output system as the formation maneuvers of multi-robots. In this paper, we focused on this field, worked at the issue, and sought to its solution. The purpose was to investigate an adaptive-gain super-twisting sliding mode control design for the formation maneuvers of multi-robot systems. The remainder is presented as follows. Section 2 introduces the modeling of a single mobile robot, as well as the modeling of a leader-follower pair of multi-robot systems. Section 3 presents the design of the adaptive-gain super-twisting sliding mode control and adopts the Lyapunov theory to analyze the closed-loop system stability. In Section 4, we implement the adaptive-gain super-twisting sliding mode control on a multi-robot system platform. Some numerical results and comparisons are illustrated in Section 4. Finally, conclusions are drawn in Section 5. The highlights and contributions of the paper can be summarized by  
* The multiple-input-multiple-output dynamics of the formation problem were formulated. * An adaptive-gain super-twisting sliding mode control method was developed by the formation maneuvers of uncertain multi-robot systems. * The control method is with the guaranteed closed-loop stability in the sense of Lyapunov. * The adaptive gains were theoretically bounded even if the boundaries of the uncertainties and disturbances were unknown.
## 3 Experiment
### Experiment Result  
In order to better reflect the improved prediction performance of LSTM model based on RNN model, LSTM and RNN algorithm are established as the comparison of neural network in this paper. The experiment was implemented on a computer equipped with Intel i7 3.4 GHz CPU, 16 GB memory and NVIDIAGTX1060 GPU. Both algorithms were trained 100 times under the same experimental conditions. In our experiment, we used 25 sets of extrusion cycle data collected at the 1# measuring point to make predictions. The prediction results and original load data of the five sets of extrusion cycles in the test set are shown in Figure 8. Under the same experimental environment and training times, the prediction results of the load data during the service process of the extruder can be seen. Due to the problems of gradient disappearance and gradient explosion, the unmodified RNN algorithm can not meet the prediction requirements in the burst stage of data, although there has been a slight fitting in the rising and falling trend. The predicted load of LSTM algorithm has similar extrusion cycle characteristics with the actual extrusion load, and the predicted results are closer to the actual data, which reflects the strong memory and learning ability of LSTM network in time series.  
Figure 7: Stress time history of each measuring point.  
According to the prediction result indicators of the two models on the test set, the loss function values of different models are shown in Table 1. The MSE, RMSE and MAE values of LSTM and RNN algorithm are 0.405, 0.636, 0.502 and 4.807, 2.193, 1.144, respectively. It is found that compared with RNN model, the prediction data error of LSTM network is closer to zero. The higher prediction accuracy further reflects the prediction performance of LSTM network, so LSTM model can better adapt to the situation of random load prediction and meet the needs of load spectrum extrapolation.
# Joint Communication-Motion Planning in Networked Robotic Systems
## 2 Conventional Relay-Assisted Robot System
### Joint Communication-Motion Planning: Decide
#### 2.3.2 JCMP Solutions
Similarly, \(w\|x_{r,k}-x_{r,k-1}\|\) is convex, so the function \(J\) is also convex. Therefore, the motion planning problem of Equation (9) is a convex optimization problem; hence, we may obtain the optimal position of the relay robot in each time step by using the interior point method.