esa-sceva/satcom-chunk-collection huggingface dataset:
## 2 The Principle of DS Positioning with LEO Communication Satellites  
### DS Calculation of LEO Communication Satellite Signals  
Due to the asynchronous nature of LEO communication satellites, there is relative motion between users and the LEO satellite orbiting the Earth, which causes the user's signal reception frequency to deviate from the original signal frequency, leading to the doppler effect. The extra frequency generated by this doppler effect is termed the doppler shift.  
As shown in Figure 1, LEO communication satellite A orbits the Earth at a speed of \(V_{s}\). The signal emitted by satellite A at time t can be represented by \(u_{S}=U_{t}\cos(\omega_{t}t+\phi_{0})\), where \(\omega_{t}\) is the angular frequency of the signal, and \(\phi_{0}\) is the initial phase of the signal. The signal received by the user is as follows:  
\[u=U\cos[\omega_{t}(t-\tau)+\phi_{0}], \tag{1}\]  
where \(\tau=\frac{\tau}{c}\) is the signal propagation time-delay caused by the relative motion of satellite A and the user; \(r=r_{0}-V_{r}t\) is the change in distance between satellite A and the user; \(r_{0}\) is the initial distance between satellite A and the user; \(V_{r}=V_{s}\cos\alpha\) is the radial velocity between satellite A and the user, \(V_{s}\) is the speed of satellite A; \(\alpha\) is the angle between \(V_{s}\) and the user's line of sight. Therefore, it can be calculated that the phase of the user's received signal is as follows:  
\[\phi=\omega_{t}\left(t-\frac{r_{0}-V_{r}t}{c}\right)+\phi_{0}, \tag{2}\]  
For Equation (2), by taking the derivative of phase to time, the angular frequency received by the user can be obtained as follows:  
\[\omega_{r}=\frac{d\phi}{dt}=\omega_{t}\left(1+\frac{V_{r}}{c}\right), \tag{3}\]  
Based on the Equations (1)-(3), it can be concluded that the instantaneous frequency received by the user is different from the signal frequency emitted by satellite A. When considering only the relative motion, its frequency difference is doppler shift as follows:  
\[f_{d}=2\pi\omega_{r}-2\pi\omega_{t}=f_{t}\frac{V_{r}}{c}, \tag{4}\]  
where \(V_{r}=V_{s}\cos\alpha\), \(f_{t}=2\pi\omega_{t}\) is the transmission frequency of the signal. From the above Equation (4), we can conclude that the magnitude of DS depends on the satellite signal frequency and relative motion velocity between satellite A and the user, and the positive or negative of DS depends on the direction of relative motion, which is determined by \(\alpha\).
## 3 Results and Discussion
### Powder X-ray Diffraction  
In order to confirm the formation of a new solid phase belonging to the CAT-TEO cocrystal, powder X-ray diffraction studies (PXRD) were performed. The PXRD pattern of CAT-TEO ground with dichloromethane after 15 min of grinding time was different to  
\begin{table}
\begin{tabular}{c c c c c c c} \hline  & **vO-H** & **\(\Delta\)(vO-H)** & **vC=O** & **\(\Delta\)(vC=O)** & **vN-H** & **\(\Delta\)(vN-H)** \\ \hline CAT-H & 3443, 3321 & — & — & — & — & — \\ CAT & 3444, 3320 & — & — & — & — & — \\ TEO & — & — & 1705, 1662 & — & 3120 & — \\ TEO-H & 3360 & — & 1708, 1695, 1642 & 3, –10, –20 & 3131 & 11 \\ CAT-TEO-H & 3517, 3454 & 73, 314 & 1699, 1666, 1629 & \(-\)6, 4, \(-\)33 & N.O. & — \\ CAT-TEO & 3151 & \(-\)293, \(-\)169 & 1714, 1704, 1633 & 9, –1 *, –29 & N.O. & — \\ CAT-TEO-MIX & 3345, 3324 & — & 1705, 1662 & — & 3120 & — \\ \hline \end{tabular}
\end{table}
Table 1: O-H, C=O and N-H stretching frequencies (cm\({}^{-1}\)) CAT-H (catechol ground with water), CAT (catechol), TEO (theophylline), TEO-H (theophylline ground with water), CAT-TEO-H (catechol and theophylline ground with water), CAT-TEO (catechol ground with dichloromethane), CAT-TEO-MIX (physical mixture of catechol and theophylline). (*) under the spectral resolution. N.O. = not observed.  
the starting solids CAT and TEO, and also to the hydrated CAT-TEO-H ground mixture (Figure 3). The PXRD pattern of TEO-H is similar to that reported for the theophylline hydrate [18]. The absence of the signals of CAT at low 20 in the XRPD diffractograms of the anhydrous CAT-TEO ground mixture suggests the complete conversion of CAT and TEO into the CAT-TEO cocrystal. The PXRD patterns of CAT-TEO showed characteristic peaks at 20 = 9.0\({}^{\circ}\) 10.5\({}^{\circ}\), 13.1\({}^{\circ}\), 14.7\({}^{\circ}\), 15.8\({}^{\circ}\) 16.5\({}^{\circ}\), 17.6\({}^{\circ}\), 20.3\({}^{\circ}\), 22.9\({}^{\circ}\), 26.3\({}^{\circ}\), 29.0\({}^{\circ}\).
## 2 Terahertz Time-Domain Spectroscopy of High-Permittivity Substrates  
### Materials  
The materials characterized in this work are three of the most popular high-permittivity microwave substrates, made commercially available by Rogers Corporation: RO30101(tm), RT/duroid 6010.2 LMTM, and TMM101 TM [24]. The first two are ceramic-filled PTFE composites for use in commercial microwave and RF applications. RO3010 exhibits negligible permittivity dispersion up to 50 GHz and an almost copper-matched coefficient of thermal expansion (CTE). The third one is a thermoset microwave laminate with low thermal coefficient and low frequency dispersion of dielectric permittivity (in the microwave range), copper-matched CTE, and high thermal conductivity facilitating heat dissipation and removal.  
Table 1 summarizes the main material and dielectric properties of the three investigated samples. It is stressed that in all cases, the values of their relative permittivity \(\varepsilon_{\mathrm{r}}^{\prime}\) and loss tangent \(\tan\delta\) (\(\varepsilon_{\mathrm{r}}:=\varepsilon_{\mathrm{r}}^{\prime}(1-j\tan\delta)\) being the complex-valued relative permittivity), as provided by the manufacturer at 10 GHz, are very similar: \(\varepsilon_{\mathrm{r}}^{\prime}\simeq 10\) and \(\tan\delta\simeq 0.002\). However, it has been shown in scarcely available literature data that the dielectric properties of standard microwave substrates can significantly differ in the sub-TTE spectral range [10; 11]. Moreover, the dielectric permittivity and loss tangent values are usually extracted by inversion algorithms that produce a discrete set of frequency-dependent values that do not necessarily satisfy the Kramers-Kronig relations, essential to preserve causality in the frequency-domain dielectric function [25]. In this work, we investigated the dispersion of the complex permittivity of the three benchmark materials via THz-TDS by accurately fitting to a single-term Lorentzian model [25], which provided a readily available analytic and consistent expression to be used both in frequency- and time-domain simulations, such as the broadly used finite-difference time-domain method [26; 27].
# Dynamic Observer Modeling and Minimum-Variance Self-Tuning Control of EDM Interelectrode Gap
## 2 EDM Interelectrode Gap Model Based on Plate Capacitor
### Analysis of \(\beta\)  
It can be learned from Equation (6) that \(\beta\) should be a constant, but the dielectric properties of the insulating working fluid in which electrodes were immersed changed during the discharge process, resulting in \(\beta\) not being constant in the test. Because the insulating working fluid media had good dielectric properties under the initial test conditions, in the single-pulse discharge test, the metal particles, carbon particles, and colloidal particles generated during the discharge process were diffused into the insulating medium. Since these materials have certain electrical conductivity that is equivalent to a piece of iron plate inserted into the insulating medium of the plate capacitor, and this effect is equivalent to the interelectrode gap decrease of the plate capacitor, the capacitance value \(C_{g}\) of the plate capacitor therefore increases. From Formula (2), we can see that the time constant \(\tau\) will increase, and so the product \(\beta\) of the interelectrode gap \(d\) and the time constant \(\tau\) will increase. However, with the auxiliary effect of interelectrode flushing, the metal particles, carbon particles, and colloidal particles in the interelectrode insulating medium will reach saturation at a certain concentration, and as the discharge continues, \(\beta\) will not change substantially.
# Theory of Edge Effects and Conductance for Applications in Graphene-Based Nanoantennas
## 1 Introduction
One can clearly expect that the error of such a non-consistent approach may be ignored as being very small, providing the size of the system is rather large. However, it means that the effect of the Fresnel transmission-reflection dominates the field forming, whereas the antenna efficiency decreases. Nevertheless, it is impossible to say a priori what is the validity bound of such a simplification. This problem becomes especially relevant for graphene-based structures due to the corresponding large geometrical size disparity for applications in different graphene devices. The advancement in graphene synthesis methods make it possible to grow graphene samples from 2.1 nm to few centimeters [6; 44; 45; 46; 47]. The detail description of optical graphene conductivity requires a self-consistent analysis. Such a self-consistent approach determines the produced electromagnetic field acting on electrons over their motion by taking into consideration the finite-size configuration and using an appropriate microscopic model for the edge. The formulation of such a self-consistent analysis is one of the main contributions of this paper. One of the important results of this paper, is the analysis of edges effects (shape of finite extend) and determining the corresponding error when self-consistency is not prevailed. It is important to note that edge effects do not only add up to the quantitative differences in the value of conductivity. Edge effects are also able to dramatically affect the special physical mechanism of charge transport. This causes the necessity of formulating the theory in terms of optical conductance, which is essential for applications in antenna design. This paper is organized as follows: models of the edge of a graphene ribbon based on the Dirac- fermion concept are first discussed in Section 2. Thereafter, based on using the Kubo approach and the concept of general susceptibility [48], we analytically obtain an expression for the surface conductance of a terminated (finite) graphene sheet. Results of numerical simulations together with a discussion are presented in Section 3. Conclusion and outlook are finally provided in Section 4.
# Voice Activity Detection Using Fuzzy Entropy and Support Vector Machine
## 2 Proposed Methodology
### Classifier
#### 2.4.2 \(k\)-Nearest Neighbor (\(k\)-NN)  
The \(k\)-nearest neighbor algorithm classifies unknown samples based on the closest training samples in the feature space [29; 30]. The distance or the similarity measure determines the closeness of the \(k\)-nearest neighbor. Here, Euclidian distance is used to compute the nearest neighbor for the new feature vector. The class with majority of the neighboring votes is declared as the class of the new feature vector. Here \(k\)-NN classifier is considered to show the significance of FuzzyEn feature.
## 4 Design Considerations and Implementation Challenges
### Integration with Structural Systems  
The integration of supplementary damping devices into structural systems necessitates a comprehensive investigation of the complex interplay between these dissipative mechanisms and the primary structure. [PERSON] et al. [136] have shown that this process often entails extensive modifications to existing structural elements or the introduction of novel components to facilitate efficient force transfer from the dampers to the main structural system. According to these studies, the design methodology must ensure the primary structure's capacity to withstand the additional forces induced by the dampers without compromising its structural integrity. Furthermore, recent investigations by [PERSON] et al. [137] and [PERSON] et al. [138] emphasize that the integration approach must address architectural constraints, serviceability criteria, and potential implications for other building systems, including mechanical, electrical, and plumbing (MEP) networks. Their findings suggest that this multifaceted optimization problem requires advanced numerical modeling techniques and sophisticated performance-based design frameworks to achieve optimal structural performance under various loading scenarios.  
Effective integration also requires a comprehensive methodology for structural analysis and design. As demonstrated by [PERSON] et al. [139] engineers must utilize sophisticated modeling techniques that accurately reflect the combined behavior of the primary structure and the supplementary damping system. Their research emphasizes the necessity of non-linear time-history analyses to evaluate performance under diverse seismic conditions. [PERSON] et al. [140] have shown that the design must take into account the varying response characteristics of the structure with and without the activation of dampers, as their studies reveal that certain damping devices may remain inactive during minor events or wind loads. Furthermore, recent work by [PERSON] [141] highlights that the integration process should tackle constructability challenges. Their findings underscore the importance of addressing issues such as connection details, installation sequencing, and quality control measures to ensure that the dampers function as intended once they are incorporated into the structural system. These studies collectively emphasize the complexity of integrating supplementary damping systems and the need for advanced analytical approaches to ensure optimal performance.
# Investigating Models for the Transcription of Mathematical Formulas in Images
## 1 Introduction  
Speech synthesis has advanced significantly in its ability to read textual content accurately [1]. This progress relies on solid transcriptions to convert written text into spoken language. However, a notable limitation arises when it comes to processing images. While text within images can be transcribed using optical character recognition (OCR) technology, the process of converting visual elements, such as mathematical formulas, into spoken words is more difficult than textual content. This is particularly evident in educational materials and scientific documents where formulas are still often expressed as embedded images. A perfect transcription of formulas in images would not only help make coursebooks with mathematical formulas more accessible for blind people, but also help sighted people who want to familiarize themselves with the course content without reading, e.g., during sporting activities or when driving.  
However--to the best of our knowledge--there is no work that tackles the problem of transcribing mathematical formulas in images. Figure 1 illustrates the two possible processes for transcribing mathematical formulas. In the first approach, the image of the formula is converted into LaTeX code using mathematical expression recognition (MER) [2; 3; 4; 5; 6]. This LaTeX code then serves as input for a natural language processing (NLP) model, which produces the transcription of the formula. In the second approach, the image of the formula is converted into its transcription using a vision-language model (VL), which is able to combine image analysis and text generation [7].  
Since there was no existing dataset that covered the whole pipeline from the image of the formula as input to the final transcription as output, we created a new dataset called _Formula2 Text_, which is publicly available in our GitHub repository ([[https://github.com/ficht74/Formula2](https://github.com/ficht74/Formula2) Text]([https://github.com/ficht74/Formula2](https://github.com/ficht74/Formula2) Text), accessed on 21 January 2024). _Formula2 Text_ is based on the existing dataset _IM2 LATEX-230K_[8], which we reduced, cleaned, and augmented with English transcriptions.  
Consequently, our contributions are as follows:  
* We are the first to tackle the problem of transcribing images of mathematical formulas.
* We created a benchmark dataset for this task: _Formula2 Text_.
* We investigated state-of-the-art MER, NLP, and VL models for this task.
* We share our code and dataset with the research community in our GitHub repository.  
In the next section, we will describe the challenges in the process of the transcription of mathematical formulas. We will provide an overview of related work in Section 3. In Section 4, we will present our experimental setup. Our experiments and results will be described in Section 5. In Sections 6 and 7, we will conclude our work and indicate possible future steps.
## 3 Natural Products: A New Source of Molecules with Antitumor Activity
### Flavonoids
#### 3.2.1 Quercetin  
Quercetin is the most representative bioactive compound of the flavanols group, and the one with the greatest presence in foods consumed daily. It can be found in onions, apples, grapes, broccoli, or tea [66]. This compound has been shown to be an excellent antioxidant and anti-inflammatory in vitro, also presenting an antitumor and antimicrobial effect [92]. Numerous in vivo and in vitro studies have analyzed the mechanisms of action by which quercetin exerts its antitumor effect. It mainly acts by regulating the cell cycle, inhibiting cell proliferation and growth through the modulation of different molecular pathways such as PI3K/AKT/mTOR and MAPK/ERK1/2. The cytotoxic effect of this compound has been shown in CRC lines HCT-15 and RKO at doses up to 300 uM [93] and with IC\({}_{50}\) of 50, 100, and 50 uM in CRC lines CT26, MC38, and HT29 after 24 h of treatment, respectively [94]. The combination of quercetin with other bioactive compounds, such as curcumin, has also been shown to enhance the antiproliferative effect in different types of cancer by modulating the Wnt/\(\beta\)-catenin signaling pathway as observed in in vitro studies [95]. This compound also induces cell death through autophagy and apoptosis of tumor cells by increasing the expression of pro-apoptotic proteins and reducing the expression of anti-apoptotic proteins. In addition, it possesses anti-angiogenic and anti-metastatic activity, inhibiting VEGF protein expression and the EMT process increasing E-cadherin and decreasing mesenchymal markers such as N-cadherin, vimentin, and Snail. Lastly, in CRC quercetin inhibits tumor invasion and migration by regulating the expression of matrix metalloproteinases (MMPs) [92]. In in vivo studies, it is involved in reducing tumor size, reducing the number of precancerous lesions, suppressing metastasis, and reducing resistance to chemotherapy drugs [96].  
This compound has also been shown to synergize with doxorubicin. Thus, a study that was carried out in the SW620 cell line observed that quercetin improves the cytotoxic activity of doxorubicin acting at the p-GP level [24]. On the other hand, encapsulation of the compound and its use together with doxorubicin increases cell growth inhibition in the CT26 cell line, reducing cardiac toxicity in murine models [97].  
Although quercetin has not been generally encased in formulations, [PERSON] et al. encapsulated this compound in a film containing chitosan nanoparticles and showed it to be an effective delivery system in CRC. It produced an effective cytotoxic effect on the Caco-2 line, exerting its effect through cell cycle arrest in G0/G1 phase and inducing apoptosis [98].
## 4 FEA Data Construction
### Database Construction
\begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline
**Variable** & **Unit** & **Min** & **Max** & **Mean** & **Median** & **Var** & **Std** & **Skewness** \\ \hline \(b_{f}\) & mm & 298 & 933 & 554.3 & 411 & 53,298.1 & 230.9 & 0.55 \\ \(t_{f}\) & mm & 20.6 & 86 & 49.7 & 38.1 & 532.6 & 23.1 & 0.36 \\ \(d\) & mm & 902 & 2800 & 1701.2 & 1550 & 572,580.6 & 756.7 & 0.37 \\ \(l_{x}\) & mm\({}^{4}\) & 3.29 \(\times 10^{9}\) & \(\times 10^{11}\) & 1.09 \(\times 10^{11}\) & 2.85 \(\times 10^{10}\) & 1.92 \(\times 10^{22}\) & 1.39 \(\times 10^{11}\) & 1.09 \\ \(l_{y}\) & mm\({}^{4}\) & 9.77 \(\times 10^{7}\) & \(\times 10^{10}\) & 3.27 \(\times 10^{9}\) & 4.44 \(\times 10^{8}\) & 1.92 \(\times 10^{19}\) & 4.38 \(\times 10^{9}\) & 1.25 \\ \(L\) & m & 22.55 & 70 & 42.5 & 38.75 & 357.863 & 18.917 & 0.37 \\ \(L_{b}\) & m & 1.611 & 35 & 7.3 & 5 & 45.98 & 6.8 & 2.35 \\ No. of bracings & & 1 & 13 & 7.2 & 7 & 15.13 & 3.9 & \(-\)0.04 \\ \(\beta_{T}\) & N \(-\) mm/rad & 0 & \(\times 10^{11}\) & 6.76 \(\times 10^{9}\) & 1.71 \(\times 10^{9}\) & 1.80 \(\times 10^{20}\) & 1.34 \(\times 10^{10}\) & 5.08 \\ \(S\) & m & 0 & 11.2 & 3.59 & 2.8 & 7.844 & 2.8 & 1.25 \\ \(C_{bb}\) & & 1 & 1.667 & 1.08 & 1.038 & 0.019 & 0.137 & 3.28 \\ \(C_{bu}\) & & 1 & 1.471 & 1.19 & 1.316 & 0.033 & 0.181 & 0.02 \\ \(f_{bu}\) & MPa & 6.2 & 450 & 203.172 & 203.114 & 9564.74 & 97.8 & 0.14 \\ \(f_{y}\) & MPa & 235 & 450 & 336.25 & 330 & 5929.688 & 77.0 & 0.23 \\ \(F_{n,L}\) & MPa & 6.2 & 44.7 & 28.4 & 30.5 & 70.5 & 8.4 & \(-\)0.87 \\ \(F_{n,L_{b}}\) & MPa & 24.8 & 450 & 291.2 & 308.3 & 9049.0 & 95.1 & \(-\)0.31 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Ranges of design parameters for input parameters used in this study.
## 6 Coal Burst Prediction of 76 Working Face in Wuyang Mine
### Coal Burst Prediction of 76 Working Face
#### 6.2.2 Local Stability Analysis of 76 Working Face  
According to the analysis of Figure 14, the supporting stress on the 76 working face is roughly distributed in a \"saddle shape\". The saddle-shaped distribution of abutment stress is significantly influenced by the additional stress energy transferred from the edges of adjacent goafs. This transferred stress contributes to the peak abutment stress values at 30 m and 265 m, which correspond to increased local coal burst risks, as shown in Figure 14. From both sides of the working face to about 30.0 m away from both sides, it shows an upward trend. At 30.0 m and 265.0 m away from the left goaf, the abutment stress reaches its peak value of 31.1 MPa, then shows a downward trend, and finally stabilizes at the original rock stress of 15.1 MPa.  
The bearing strength of coal in the 76 working face is approximately distributed in a trapezoidal shape, showing an upward trend from 0 to 15.0 m on both sides of the working face and reaching its maximum bearing strength of 30.0 MPa at x = 15.0 m.  
Since the abutment stress and bearing strength of the 76 working face are symmetrically distributed, the coal near the left goaf is taken as an example for analysis. It is found that at x = 0-15.0 m, the slope of the bearing strength curve of the working face is greater than that  
Figure 14: The 76 working face \(\sigma_{\rm x}\)–R\({}_{\rm x}\)–x relationship curve.  
of the abutment stress curve. The bearing strength curve remains unchanged after reaching a peak of 30.0 MPa at x = 15.0 m, while the abutment stress continues to show an upward trend from x = 15.0-30.0 m, reaching a peak of 31.1 MPa at x = 30.0 m. The abutment stress begins to decrease after partially exceeding the bearing strength, eventually reducing to 15.1 MPa and stabilizing.  
The coal burst risk at a specific point is highest at the peak, that is,  
\[\mathrm{J}=\mathrm{\eta}\frac{\mathrm{\sigma}_{x}}{\mathrm{R}_{x}}=(1.0{\sim}1.5)\times\frac{31.1}{30}=1.04{\sim}1.55 \tag{14}\]  
The possibility of coal burst at this point is J > 1, indicating that the 76 working face of Wuyang Mine has a local coal burst risk (represented by the yellow dotted line area in Figure 14).