esa-sceva/satcom-chunk-collection huggingface dataset:
## 3 Compensation Correction Models for the Off-Axis TMA Telescope  
To start with, we take SM as the compensator as an example to construct its corresponding compensation correction model, and the target objects to be compensated are TM misalignments and PM figure errors. Here, PM is chosen as the coordinate reference. To this end, Equations (5)-(7) can be modified as  
\[ \begin{array}{l}C_{5,C}^{SM}+C_{5,L}^{SM}+C_{5,O}^{SM}=C_{5}-C_{5,C}^{TM}-C_ {5,L}^{TM}-C_{5,Q}^{TM}-(n^{\prime}-n)_{(FIGURERE)}C_{5,C}\\ C_{6,C}^{SM}+C_{6,L}^{SM}+C_{6,Q}^{SM}=C_{6}-C_{6,C}^{TM}-C_{6,L}^{TM}-C_{6,Q }^{TM}-(n^{\prime}-n)_{(FIGURERE)}C_{6,C}\end{array} \Bigg{\}}, \tag{8}\]  
\[ \begin{array}{l}C_{7,C}^{SM}+C_{7,L}^{SM}=C_{7}-C_{7,C}^{TM}-C_{7,L}^{TM}-(n ^{\prime}-n)_{(FIGURERE)}C_{7,C}\\ C_{8,C}^{SM}+C_{8,L}^{SM}=C_{8}-C_{8,C}^{TM}-C_{8,L}^{TM}-(n^{\prime}-n)_{(FIGURERE )}C_{8,C}\end{array} \Bigg{\}}, \tag{9}\]  
\[ \begin{array}{l}C_{9,C}^{SM}=C_{9}-C_{9,C}^{TM}-\left(n^{\prime}-n\right)_{ (FIGURERE)}C_{9,C}.\end{array}  \tag{10}\]  
In Equations (8) and (9), the terms containing superscripts \(SM\) and \(TM\), respectively, represent the contribution of SM misalignments and TM misalignments to the aberration fields, and their numerical values can be solved by Equations (2)-(4). After the system being corrected, the net aberration fields induced by perturbation parameters is zero, so \(C_{5-9}=0\) in Equations (8) and (9). We aim to calculate the compensation adjustments of SM when the misalignments of TM and figure errors of PM are known. To achieve that, Equations (8)-(10) need to satisfy the aberration field compensation mechanism described in the previous section, as shown in the following equations:  
\[ \begin{array}{l}C_{5,C}^{SM}=-\left[C_{5,C}^{TM}+(n^{\prime}-n)_{(FIGURE)}C _{5,C}\right]\\ C_{5,Q}^{SM}=-C_{5,Q}^{TM}\\ C_{6,C}^{SM}=-\left[C_{6,C}^{TM}+(n^{\prime}-n)_{(FIGURE)}C_{6,C}\right]\\ C_{6,L}^{SM}=-C_{6,L}^{TM}\\ C_{6,Q}^{SM}=-C_{6,Q}^{TM}\end{array}
## 3 Results
### EOs Characterization  
The average results of TPC in the extracted eucalyptus EO are presented in Table 5 and Figure 6. The TPC is expressed in mg of polyphenols per gram of eucalyptus. From the results obtained, there are two conclusions that can be taken:  
* The longer the extraction time, the higher the TPC obtained in the EO;
* EO extracted with PEF application has a higher average TPC when compared to the traditional method (control).  
Figure 5: Results of yield thyme EO extracted with and without (Control) PEF application and different distillation times.  
An ANOVA single factor analysis was done to validate the results obtained, and statistical significance was obtained, showing that for the EO extraction from eucalyptus, the TPC is higher with the application of PEF pre-treatment in comparison with the traditional method.  
For the EO extracted after PEF application and 30 min HD, considering the higher average extracted yield, +17%, as shown in Table 4, it was expected that the TPC would also be higher than the one verified for the traditional extraction, +27%. However, for the 60 min distillation time, as there is not a significant yield difference, +2%, as shown in Table 4, it was interesting to observe an increase of +12% in the TPC with the extraction upon PEF application, which suggests that PEF application, on its own, allows for a higher extraction of polyphenols.
# Multimodal Power Management Based on Decision Tree for Internet of Wearable Things Systems
## 4 Experimental Results
### ML-Decision Tree Power Management Results
As one can notice from Figure 11 shows that the ML-DPMS prevents the system from shutting down by applying two large sleep periods in samples 79 and 80, resulting in an energy consumption of 1.53 J. This represents a 39.6% reduction in energy consumption compared to the uniform strategy's 2.52 J.  
Figure 10: ML-decision tree results for test case scenario 2: (**a–c**) SpOZ, Temperature and Heart rate measurements; (**d**) Oscillatory supercapacitor’s voltage; and (**e**) ML-decision tree classification results. Figure 9: Comparative analysis result of ML-Decision tree and uniform power management for test scenario 1. Considering the same samples marked on the square red of Figures 8 and 10, the results on both test cases demonstrate the smart and adaptive behavior of the decision tree-DPMS.
# Mining Deformation Life Cycle in the Light of InSAR and Deformation Models
## Materials and Methods
### Deformation Modelling  
#### 2.2.1 Generalised Dynamic Subsidence Modelling  
Based on the equation introduced by [PERSON] [30], the dynamic subsidence (dependent on time) was determined as follows:  
\[\frac{d_{w}(t)}{dt}=C[w_{k}(t)-w(t)], \tag{10}\]  
where \(C\) is a constant coefficient of proportionality called the time factor, which is independent of time, describing the rate of vertical displacements in time through rock mass; \(w_{k}(t)\) is a steady subsidence (asymptotic) caused by an exploitation of a panel with a shape at the moment \(t\); \(w(t)\) is a dynamic subsidence of a point in the moment \(t\); and \(t\) is the time measured from the commencement of exploitation.  
Figure 6 shows an example of the functions \(w_{k}(t)\) and \(w(t)\). Assuming an immediate exploitation of a part of a seam, the solution of Equation (10) takes the following form:  
\[w(t)=w_{k}T(t), \tag{11}\]  
when \(w_{k}(t)=w_{k}=const\), and the initial value \(w(0)=0\). \(T(t)\) is the so-called [PERSON] function of time, which takes the following form:  
\[T(t)=1-e^{-ct}. \tag{12}\]  
These relations were introduced by [PERSON] 60 years ago; however, modern analysis of subsidence has enabled the generalisation of Equation (14) [2,32]:  
\[T(t)=\Theta(t)q(t), \tag{13}\]  
where \(\Theta(t)\) stands for the principal function of time:  
\[\Theta(t)=1-\sum_{i=1}^{n}A_{i}exp[-c_{i}t], \tag{14}\]  
and  
\[q(t)=\left\{\begin{array}{l}0\ for\ t<0\\ 1\ for\ t\geq 0\end{array}\right.. \tag{15}\]  
\(A_{i}\) is a parameter of the equation, \(c_{i}\) is a time factor of the \(i-th\) exponential component, \(n\) is the number of exponential components, and \(0<A_{i}\leq 1\) is the participation of \(i-th\) component \(A_{i}\) of the elementary exploitation with time factor \(c_{i}\). To prevent the function \(\Theta(t)\) from taking a negative value, \(A_{i}\) factors must also fulfil the following condition:  
\[\sum_{i=1}^{n}A_{i}\leq 1. \tag{16}\]  
Figure 6: Distribution of steady \(w_{k}(t)\) and dynamic \(w(t)\) subsidence [2].  
For modern mining conditions characterised by a high rate of advance and exploitation breaks (weekends and holidays), the model to describe the dynamic subsidence should have two components, as follows (17):  
\[\Theta(t)=1-A_{1}exp(-c_{1}t)-A_{2}exp(-c_{2}t), \tag{17}\]  
where \(A_{1}\) and \(c_{1}\) are parameters describing the immediate mining influences; \(A_{2}\) and \(c_{2}\) are parameters describing residual mining influences (residual subsidence after exploitation) whereby \(A=A_{2}<1\) and \(A_{1}=1-A_{2}\). The generalised function of time (13) is similar to the creeping function of rheological models [46].
# Planning and Scheduling with Uncertainty in the Steel Sector: A Review
## 2 Uncertainty in Scheduling: Definition and Approaches  
The steel industry involves different production steps, each one with their own characteristics and problematics which translates into specific planning and scheduling procedures. However, in most cases they can be considered to be a complex Hybrid Flow Shop (HFS) scheduling problem with hard constraints. This problem is based on the necessity to process a given set of jobs through various processing stages, with one or more parallel machines on each stage optimizing an established objective function. All the jobs must follow the same stages processing route [7]. The HFS scheduling problem can be expressed as a mixed integer linear programming (MILP) problem. Let \(x\) denote the continuous variables that represent the starting and finishing times (or processing times) of the jobs and let \(y\) denote the binary variables referring to the selection of tasks to be processed and the machines in which they are allocated. Considering \(c\) and \(d\) as the correspondent coefficient vectors for the decision variables \(x\) and \(y\), the HFS can be formulated in the following way:  
\[\text{Min }(c^{T}x\ +\ d^{T}y) \tag{1}\]  
Subject to \(Ax\ +\ By\ \leq\ p\ \big{|}x\ \geq\ 0;\ y\ \in\ \{0,\ 1\};\ x\ e\ R^{n},\ y\ \in\ R^{m}\) where the constraints (\(Ax\ +\ By\ \leq\ p\)) are time limitations due to tasks durations, sequence requirements and other process-related restrictions. The parameters \(A\) and \(B\) represent the constraint matrixes associated with decision variables \(x\) and \(y\) respectively. The parameter \(p\) corresponds to the maximum threshold.  
[PERSON] and [PERSON] [8] state that slight modifications in the nominal values of this type of model may lead to infeasible solutions. The uncertainties responsible for these modifications can be of very different nature, like disruptions in the processing times, unexpected equipment stoppages or non-fulfillment of target specifications of the order. Hence, the presence of uncertainty becomes one of the main factors impacting the correct realization of schedules in steel manufacturing processes.  
There are many studies in the literature that analyze and classify the approaches in the scheduling uncertainty across different sectors [3; 6; 9]. Most of the authors agree that there are two main groups in which these techniques can be divided: proactive scheduling solutions and reactive scheduling solutions.
# Bridge Health Monitoring via Displacement Reconstruction-Based NB-IoT Technology
## 3 Bridge Health Monitoring Experiment  
To validate the aforementioned displacement reconstruction method and damage indicators, three different experiments are introduced in this section.
# A Low Sampling Rate Receiver Design for Multi-Antenna Multi-User OFDM Systems
## 4 Simulation Results
### Parp  
Another concern was whether the proposed scheme would raise the PAPR of the transmit signal. High PAPR increases the hardware costs of power amplifiers (PAs) and ADCs since it has to increase the resolution to cope with the high dynamic input signal. The simulated CCDF of PAPR for both systems are shown in Figure 8. We can see that the proposed scheme did not raise the PAPR of the transmission signal and it even produced some gain over the OFDM system.
## 1 Introduction
[22] investigated the acoustic radiation efficiency of local resonance-based band-gap materials in both infinite structures and corresponding finite structures, with a specific focus on the radiation efficiency variation affected by the correlation between the resonant frequency and the critical frequency of the plate. It was first found that the band-gap property may increase the radiation efficiency of the LR plate. [PERSON] et al. [23] investigated the suppression of vibration and acoustic radiation in a sandwich plate through the use of a periodic design by the finite-element method (FEM). [PERSON] et al. [24] derived the average radiation efficiency of a sandwich plate with periodically inserted LR resonators theoretically. Recently, [PERSON] et al. [25; 26] used the LR band gaps to increase the efficiency of sound radiation employing defect modes on a phononic crystal. Although research has been conducted focusing on acoustic radiation in LR structures, more studies can be done to further obtain valuable acoustical characteristics of the LR structure in the low-frequency range. In this paper, the low-frequency vibration and radiation performance of the LR plate attached with periodic multiple resonators is studied. Following the introduction, the theoretical models are built for the forced response and the total radiation efficiency of the finite LR plate in Section 2. A general model of the boundary conditions is adopted by using linear and torsional springs for the finite LR plate. In Section 3, the band-gap property in the infinite LR plate and vibration attenuation in its finite counterpart are discussed. Furthermore, the acoustic radiation from the finite LR plate is analyzed, with a focus on the effect of the boundary conditions of the plate itself and the damping characteristic of the resonators on the acoustic radiation property. Finally, the conclusions are summarized in Section 4. The theory built in this paper and the corresponding findings can guide the multi-band-gap design of the LR plate for noise control.
## 5 Performance Evaluation
### Comparison of BSMH and Other Benchmarks
#### 5.4.7 Network Lifetime  
The network lifetime achieved by the protocols are shown in Figure 20. As shown, the network lifetime achieved by BSMH (especially with high values of \(\epsilon\)) is much higher than that of the other protocols. LVGR attains the second-best performance in most of the cases. GPSR and EDGR show the smallest network lifetime. With \(\epsilon=1.2\), BSMH results in the network lifetime which is higher than 1.1 times that of LVGR, 1.1 times that of EDGR and 1.2 times that of GPSR in 1-n communication, for all network topologies. Specifically, in the best cases, BSMH with \(\epsilon=1.2\) can extend the network lifetime by the factors of 1.5, 2.4 an 1.9 compared to LVGR, EDGR and GPSR. Regarding the n-n communication, BSMH with \(\epsilon=1.2\) achieved the network lifetime higher than 1.1 times those of LVGR, EDGR and GPSR in all topologies. In the best cases, the ratios of the network lifetime achieved by BSMH to those achieved by LVGR, EDGR and GPSR are 1.8, 3.4 and 2.0, respectively.  
Figure 19: Packet forwarding ratio distribution regarding Topology 4. The x-axis represents the node orders that are sorted by the descending order of the packet forwarding ratio. The y-axis represents the packet forwarding ratios and the x-axis represent the orders of the nodes. (**a**) 1-n communication. (**b**) n-n communication.  
Generally, the decrease of \(\epsilon\) results in the decrease of the network lifetime of BSMH. When reducing \(\epsilon\) to 0.3, the network lifetime attained by BSMH is still higher than LVGR, EDGR and GPSR in all topologies excepting Topology 6 in 1-n communication. Specifically, in the best cases, the ratios of the network lifetime of BSMH with \(\epsilon=0.3\) to those of LVGR, EDGR and GPSR are 1.3, 1.9 and 1.7 in the 1-n communication, and 1.3, 2.5 and 1.8 in the n-n communication, respectively.  
Regarding Topology 6 in 1-n communication, it can be seen that BSMH with \(\epsilon=0.3\) attains a worse performance than LVGR. This phenomenon can be explained similarly as in Section 5.4.6, i.e., the diversity of routing paths determined by LVGR is increased thanks to the presence of many small holes, while the diversity of routing paths determined by BSMH is reduced due to the small spaces between the holes.  
Another observation is that the network lifetimes achieved by 1-n communications are much smaller than those achieved by n-n communications. This can be seen by comparing Figure 19(a) and Figure 19(b). This phenomenon can be explained by the so-called hotspot problem caused by the high traffic load around the destination.
## 3 Discussion
### Limitations  
There are some limitations of the current experiment. First, the nonadjacent layouts (\(A^{\prime}S\) and \(A^{\prime}S\)) occurred only second, which means that in the transfer task the impact of adjacency was overwhelmed by learning effects; it also means that the full range of interactions between the variables could not be tested. Secondly (as detailed in Section 1.1.2), by shearing parallel with the octave axis, the angles of the pitch axis and the angle of the major second axis covaried, so these two effects cannot be disambiguated; furthermore, the angle of the octave axis was invariant (it was always vertical) so not tested. Thirdly, only melodies were tested--we would expect different results for bass lines (where perfect fifths and fourths are prevalent) or for harmony, where thirds are also prevalent. Fourthly, all of the pitch layouts tested were rather similar in their overall form--this similarity is a natural consequence of good experimental design, which requires changing only the variables of interest across conditions, but it may limit generalizability. Finally, other covarying aspects of the layouts were not independently tested (e.g., adjacencies or angles of other intervals).  
Most of these limitations can be overcome by conducting further experiments, although it would not be feasible to address all of them at once. For instance, the nonadjacent layouts could be presented first and third; the shears could be made parallel with the pitch axis or with the major second axis--doing both, in conjunction with this experiment, would enable the effects of the pitch, octave, and M2 axes' angles to be fully disambiguated; differing musical contexts, such as chord progressions or bass lines, could be trained and tested; a wider range of layouts, with configurations distinctly different from those considered here, could be used.  
With respect to the results, limitations can be seen in the ceiling effect achieved quickly for some of the tasks, particularly with the second and third layouts played. The experiment allowed for training with audiovisual performances for 4 separate instances (one watching the audiovisual sequence, and the remaining three playing along with the sequence). For the scale task, this was sufficient for participants to excel in the immediate retention test; conversely, for the arpeggio task, this may not have been enough training because performances in the immediate retention were too poor to analyse. For the transfer task, 20 s of exploration was allowed prior to the first performance on each layout. This is not a standard figure, but was used to avoid a floor performance for this untrained task. However, for the second and third layouts, this may have helped participants too much because ceiling performance was reached quickly. Selecting training period lengths and tasks with the appropriate difficulty are important in the design of learning experiments. A task of appropriate difficulty can ensure that a learning effect can be measured.
## 3 Characteristics of an Ideal Bone Grafting Material  
An ideal bone graft has all three of the aforementioned properties (osteoinduction, osteoconduction and osteogenic capabilities) as well as being easy to harvest and available in the desired quantity, with minimal risks for infectious disease transmission and low cost.  
The autograft has all bioactive properties, being the easiest to incorporate and infectious risk free, but is associated with significative donor site morbidity and is available in a limited quantity.  
Vascularized bone graft is a form of bone transplant, in which both the arteries and veins of the transplanted bone segment are anastomosed to a nearby host. In this kind of graft, all osteocytes and osteoprogenitor cells are preserved and graft incorporation is realized by primary or secondary bone healing, not by creeping substitution like for a fracture [9]. The main advantage of this graft type is the maintaining of bone strength during the entire integration process [10].  
Allografts are harvested from living donors or (most of the time) from cadavers. The advantages of this kind of graft are related to the easiness of harvesting and to the disposable quantity and forms (structural or morselized). Graft processing decreases the immune response and removes substances that may transmit different diseases. On the other hand, this process, especially gamma radiation, affects the mechanical properties of the graft by polypeptide chain splitting and water molecule radiolysis. At the same time, its ability to stimulate bone healing by osteogenic and osteoinductive properties are compromised due to the destruction of all cellular elements [11]. Demineralized bone matrix (DBM) is a form of processed allograft consisting of collagens, non-collagenous proteins, BMPs and other growth factors which are responsible for osteoinduction and osteoconduction. The osteoinductive properties of DBM are greater than those of allografts. Improved osteoconductive properties can be obtained by mixing DBM with bone chips [8].  
Synthetic calcium salt-based bone substitutes need to be similar in structure and strength to human bone. They are strictly osteoconductive, so the role in bone healing is limited. Adding collagen, growth factors and even MSCs to these synthetic substitutes may add osteoinductive or even osteogenic properties to these materials. The advantages are related to the quantity, different forms (powders, pellets, blocks or coatings on implants), lack of risk of infection and availability. Bone tissue engineering and three-dimensionalprinting are generating promising products which could provide new perspectives in the future.  
Trabecular metal is a 3D-processed tantalum with excellent biocompatibility and resistance to corrosion. It is structurally similar to cancellous bone with very high porosity [12]. Due to the high friction coefficient, the primary stability of this kind of metal is very high, which makes it widely used in revision arthroplasties with large structural bone defects.
# Transformation of Trigonometric Functions into Hyperbolic Functions Based on Cable Statics
## Appendix C  
Based on the following relationship:  
\[\sin\theta=\tanh\theta_{h}. \tag{10}\]  
using the change of variable \(w=\tanh\theta_{h}\):  
\[\sin\theta=w. \tag{11}\]  
The Euler constant expression with complex numbers is used:  
\[\frac{e^{\theta i}-e^{-\theta i}}{2i}=w.\]  
The Euler constant expression with complex numbers is used:  
\[\frac{e^{2\theta i}-1}{2i\times e^{\theta i}}=w. \tag{12}\]  
The expression is multiplied, obtaining, by solving for 1:  
\[e^{2\theta i}-2i\times e^{\theta i}w=1. \tag{13}\]  
\(w^{2}\) is added to both sides of the equation:  
\[e^{2\theta i}-2i\times e^{\theta i}w-w^{2}=1-w^{2}.\]  
The sum of squares is completed:  
\[\Big{(}e^{\theta i}-i\times w\Big{)}^{2}=1-w^{2}. \tag{14}\]  
The equation is solved for \(e^{\theta i}\) for positive values, yielding:  
\[e^{\theta i}=i\times w+\sqrt{1-w^{2}}, \tag{15}\]  
and \(\theta\) is solved for, using the relation \(-i=1/i\):  
\[\theta=-i\ln\Bigl{(}i\times w+\sqrt{1-w^{2}}\Bigr{)}. \tag{16}\]  
By replacing \(w=\tanh\theta_{h}\), it is obtained that:  
\[\theta=-i\,\ln\Bigl{(}i\tanh\,\theta_{h}+\sqrt{1-\tanh^{2}\theta_{h}}\Bigr{)}. \tag{17}\]  
By replacing the identity \(1-\tanh^{2}\theta_{h}=\operatorname{sech}^{2}\theta_{h}\):  
\[\theta=-i\,\ln(i\,\tanh\theta_{h}+\operatorname{sech}\theta_{h}). \tag{18}\]  
Finally, the identity can be expressed in terms of \(\sinh\theta_{h}\) and \(\cosh\theta_{h}\):  
\[\theta=-i\,\ln\frac{i\,\sinh\theta_{h}\pm 1}{\cosh\theta_{h}}. \tag{19}\]