esa-sceva/satcom-chunk-collection huggingface dataset:
## 4 Ion Current
### Current and Propellant Use  
The current use (\(\eta_{b}\)) is of importance for Hall thrusters as those devices are not operated with direct ion current control. A Hall thruster provides thrust when delivering a  
Figure 7: Cylindrical coordinate system used to express the current density \(j_{i}\). The latter is constant on a ring of radius \(y\) and thickness \(ds\).  
discharge current (\(I_{d}\)) that incorporates both ion and electron contribution. The current use is the ratio between the experimental ion current and \(I_{d}\).  
\[\eta_{b}=\frac{I_{i}}{I_{d}}. \tag{6}\]  
This ratio is around 0.8 for HTs [34,67]. That means about 20% of the current is provided by the electrons which do not contribute to the thrust. The propellant mass use \(\alpha\) is the ratio of the ion mass flow rate to the propellant mass flow rate. It corresponds to the fraction of the propellant mass flow rate injected into the discharge channel that is ionized. This quantity directly characterizes the ionization efficiency, hence it must be maximized. The propellant use reads [68,69]  
\[\alpha=\frac{\dot{m_{i}}}{\dot{m}}=\frac{1}{\dot{m}}m\sum_{n=1}\frac{I_{n+}}{ ne}, \tag{7}\]  
where \(\dot{m_{i}}\) and \(\dot{m}\) are the ion mass flow rate and the atom mass flow rate, respectively, \(m\) is the atomic mass, \(e\) is the elementary charge and \(I_{n+}\) the current associated with ions having a \(n+\) electric charge. Please note that multiple-charged xenon ions with charges up to 5+ have been detected in the plume of high-power Hall thruster. As the multiple-charged ion fraction is often unknown, the ion beam is assumed to be solely composed of singly-charged ions. The propellant use \(\alpha\) is then given by the following formula:  
\[\alpha=\frac{1}{\dot{m}}\frac{I_{i}}{e}m. \tag{8}\]  
Please note that the above equation overestimates the value of \(\alpha\) when multiple-charged ions are present in the thruster plasma plume [68]. For high-power Hall thrusters this ratio lies between 85% and 95%. For low-power HTs the current use is much lower with values around 70%. In all cases accurate FC measurements are used to get more precise and reliable values for the current ionization as this quantity plays a key role in HT optimization.
## 4 Boundary and Initial Conditions  
The boundary conditions at the free surface and bottom of the \(j\)th annular sub-layer are given by the following expressions, respectively.  
\[\frac{\partial u_{j}^{s}(r,z,t)}{\partial z}|_{z=0}\,=0 \tag{5a}\] \[\frac{\partial u_{j}^{s}(r,z,t)}{\partial z}|_{z=H}\,=-\bigg{(}\frac{k_{j}^{s}u _{j}^{s}(r,z,t)}{E_{j}^{s}}+\frac{\delta_{j}^{s}}{E_{j}^{s}}\frac{\partial u_{ j}^{s}(r,z,t)}{\partial t}\bigg{)} \tag{5b}\]  
where \(E_{j}^{s}\frac{\partial u_{j}^{s}(r,z,t)}{\partial z}\) refers to the internal stress of the soil. \(k_{j}^{s}u_{j}^{s}(r,z,t)\) and \(\delta_{j}^{s}\frac{\partial u^{s}(r,z,t)}{\partial t}\) are the external forces related to stiffness and damping, respectively. According to the force equilibrium conditions, Equation (5b) can be established.  
Figure 2: The derivation procedure of complex stiffness.  
When \(r\rightarrow\infty\), the longitudinal displacement of surrounding soil tends toward zero. Namely,  
\[\lim_{r\rightarrow\infty}u(r,z,t)=0 \tag{6}\]  
The continuity and equilibrium conditions at the outer interface of the \(j\)th sub-layer are  
\[u_{j}^{\mathrm{s}}(r,z,t)\big{|}_{r=r_{j+1}}=u_{j+1}^{\mathrm{s}}(r,z,t)\big{|}_ {r=r_{j+1}} \tag{7a}\] \[G_{j}^{\mathrm{s}}\frac{\partial u_{j}^{\mathrm{s}}(r,z,t)}{\partial r}+c_{j}^{ \mathrm{s}}\frac{\partial^{2}u_{j}^{\mathrm{s}}(r,z,t)}{\partial t\partial r} \big{|}_{r=r_{j+1}}=G_{j+1}^{\mathrm{s}}\frac{\partial u_{j+1}^{\mathrm{s}}(r, z,t)}{\partial r}+c_{j+1}^{\mathrm{s}}\frac{\partial^{2}u_{j+1}^{\mathrm{s}}(r,z,t)}{ \partial t\partial r}\big{|}_{r=r_{j+1}} \tag{7b}\]  
where \(G_{j}^{\mathrm{s}}\frac{\partial u_{j}^{\mathrm{s}}(r,z,t)}{\partial r}+c_{j} ^{\mathrm{s}}\frac{\partial^{2}u_{j}^{\mathrm{s}}(r,z,t)}{\partial t\partial r }\big{|}_{r=r_{j+1}}\) and \(G_{j+1}^{\mathrm{s}}\frac{\partial u_{j+1}^{\mathrm{s}}(r,z,t)}{\partial r}+c _{j+1}^{\mathrm{s}}\frac{\partial^{2}u_{j+1}^{\mathrm{s}}(r,z,t)}{\partial t \partial r}\big{|}_{r=r_{j+1}}\) are the shear stress of the \(j\)th and (\(j\)+1)th, respectively, sub-layers. Based on the stress equilibrium condition at the interface between the \(j\)th and (\(j\)+1)th sub-layers, Equation (7b) is built.  
The equilibrium conditions of the pile are expressed as the following forms:  
\[EPAP\frac{duP}{dz}\bigg{|}_{Z=0}+\rho^{\mathrm{p}}AP(v^{\mathrm{p}}r_{1}s)^{2} \frac{duP}{dz}\big{|}_{z=0}=-p(t) \tag{8a}\] \[\frac{k^{\mathrm{p}}+s\delta^{\mathrm{p}}}{EPAP}u^{\mathrm{p}}+\frac{duP}{dz}+ \frac{\rho^{\mathrm{p}}AP(v^{\mathrm{p}}r_{1}s)^{2}}{EPAP}\frac{duP}{dz}\big{|} _{z=H}=0 \tag{8b}\]  
where \(\frac{k^{\mathrm{p}}+s\delta^{\mathrm{p}}}{EPAP}u^{\mathrm{p}}\) denotes the external supporting force beneath the pile toe. \(\frac{duP}{dz}+\frac{\rho^{\mathrm{p}}AP(v^{\mathrm{p}}r_{1}s)^{2}}{EPAP}\frac {duP}{dz}\) is the internal stress of the pile. According to the force equilibrium condition beneath the pile toe, Equation (8b) can be established.  
The coupled condition of the first disturbed sub-layer and pile is given by  
\[u_{1}^{\mathrm{s}}(r,z,t)\big{|}_{r=r_{1}}=u^{\mathrm{p}}(z,t). \tag{9}\]
# Characteristics and Vaporization Potential of Fermentation Waste of Greengage (_Prunus mume_)
## 3 Results
### Antioxidant Capacity  
In this section, the antioxidant capacity of the waste sample was evaluated by both ABTS and DPPH methods. The samples of fresh greengage were also tested to provide a comparative references.  
Figure 5 shows the DPPH radical scavenging of fresh fruit and fermentation waste. The lower value ifor the fermentation waste shows that the fresh greengage exhibited a higher DPPH radical scavenging capacity than the waste (7.84 umol TE/g EPW and 5.39 umol TE/g EPW, respectively). Nevertheless, 5.39 umol TE/g EPW was still far from exhausted since lower values of around 3 umol TE/g EPW for plum fruit are previously reported in the literature [38], which makes the valorization of the waste necessary.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Numbers** & **CAS** & **Substracts** & **Concentration (mg/L)** \\ \hline
1 & 78-70-6 & Linalool & 14.33 \(\pm\) 1.09 \\
2 & 2270-57-7 & 3,7-Dimethyl-6-octen-3-ol & 9.26 \(\pm\) 1.06 \\
3 & 10482-56-1 & Terpineol & 25.19 \(\pm\) 1.87 \\
4 & 119-36-8 & Methyl salicylate & 4.803 \(\pm\) 0.81 \\
5 & 17283-81-7 & 4-(2,6,6-trimethyl-1-cyclohex-1-yl)butan-2-one & 11.08 \(\pm\) 0.94 \\
6 & 3301-94-8 & \(\delta\)-Nonlactone & 9.94 \(\pm\) 0.29 \\
7 & 14901-07-6 & \(\beta\)-ionone & 24.33 \(\pm\) 5.68 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Key Bioactive Compounds Found in the Fermentation Waste Extract.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Numbers** & **RT (min)** & **Compound Name** & \(\begin{array}{c}\textit{m/z}\\ \textbf{Calculated}\end{array}\) & \(\begin{array}{c}\textit{m/z}\\ \textbf{Experimental}\end{array}\) & **Formula** \\ \hline
1 & 5.576 & Neochlorogenic acid & 353.30078 & 353.08801 & C\({}_{16}\)H\({}_{18}\)O\({}_{9}\) \\
2 & 7.017 & Chlorogenic acid & 353.30078 & 353.08765 & C\({}_{16}\)H\({}_{18}\)O\({}_{9}\) \\
3 & 5.576 & 7-Hydroxycounarine & 161.13420 & 163.03923 & C\({}_{9}\)H\({}_{6}\)O\({}_{3}\) \\
4 & 7.114 & 3-O-Feruloylquinic acid & 367.32736 & 367.10349 & C\({}_{17}\)H\({}_{20}\)O\({}_{9}\) \\ \hline \hline \end{tabular}
\end{table}
Table 2: Key Phenolic Compounds Found in the Fermentation Waste Extract.  
The results of ABTS radical scavenging are illustrated in Figure 6. Similar remarks can be drawn: the fermentation waste again presented lower antioxidant capacity than the fresh one, with the value of 9.80 umol/g EPW, while previous works reported around 6 umol TE/g FW for yellow plum [38,39].  
In general, the position and counts of the hydroxyl groups on the aromatic rings of the phenolic compounds affect the activity of free radicals; thus phenolic compounds (including flavonoids) contribute to free radial scavenging [40]. In this case, the fermentation waste had a lower TPC and TFC value of than for fresh fruit, which resulted in lower DPPH and ABTS radical scavenging.
## 2 Fungal Pigments Found on Paper
### Melanin  
Melanin is an ubiquitous, widely distributed dark brown to black pigment in animals, plants, and microorganisms [81]. It is an insoluble and non-digestible, negatively charged polymer formed by oxidative polymerization of phenolic or indolic compounds [82; 83; 84]. There are a few forms of melanin existing in living organisms, including fungi: allomelanins, eumelanins, and pheomelanins. Eumelanins are characterized as black-brown insoluble melanin pigments partially derived from the oxidative polymerization of L-dopa via 5,6-dihydroxyindole intermediates. Pheomelanins represent a subgroup of melanins containing sulfur obtained by the oxidation of cysteinyldopa precursors via benzothiazine and benzothiazole intermediates. These pigments are alkali-soluble with a yellow to brown color [85]. Allomelanins are defined as melanins containing phenolic, catecholic, and 1,8-dihydroxymorphthalene (1,8-DHN) units [86].  
Melanins were previously described as compounds resistant to degradation by hot acids, hot concentrated alkaline solutions, and bleaching by strong oxidizing agents, while nowadays, they stand for melanins, compounds insoluble in aqueous or organic solvents [87]. As a consequence of melanin's recalcitrant nature, it is difficult to achieve a detailed chemical analysis of melanin. Additionally, the use of hazardous chemical methods for the purification of melanin makes it harder to chemically analyze them since the chemicals used in the purification process can modify their structure [87; 88; 89]. Microscopic analysis of fungi has suggested that the melanins, in general, have a granular shape and are enclosed in the fungal cell wall [60]. Many filamentous fungi, also including paper deteriorogens [2; 18], in the genera _Alternaria_, _Aspergillus_, _Auricularia_, _Cladosporium_, _Epicocum_, _Eurotium_, _Magnapothe_, _Penicillium_, _Phomopsis_, _Sporothri_, _Stachybottrys_, and _Wangiella_, have been shown to synthesize melanin [90]. This pigment serves as a protection from disadvantageous conditions for fungal species, even though it is not essential for their development. It has been shown that fungi that produce melanin are more resistant to UV light-induced damage, damage caused by radioactive oxidative species, temperature extremes, different hydrolytic enzymes, antimicrobial drugs, and many other harmful factors [54; 91; 92]. Recently, it has been discovered that due to the production of melanin fungi, particularly _Cladosporium_ and _Alternaria_, species could survive extreme conditions, such as those in industrial and roadside areas. For instance, _Cladosporium_ spp., _Alternaria alternata_, and _Aurebosidium pullulans_ were found to colonize the walls of the damaged reactor at Chernobyl, where they were exposed to extreme levels of radiation [93]. Melanin protects conidia against hydrolysis and digestion by different enzymes secreted by other microorganisms as well as against bacterial and fungicidal proteins of animal origin [83]. Thus, it can be concluded that melanin contributes to fungal pathogenesis and survival in unfavorable conditions.
## 3 Blind Demodulation of CDS-SS Signals Based on Particle Filters
### Blind Demodulation of CDS-SS Signals under Colored/Non-Gaussian Noises Condition
In this paper, under the conditions of non-cooperative communication (unknown transmitter structure) and colored or non-Gaussian noises, the intercepted CDS-SS signals containing 200 bits at SNR = 7 dB are blindly demodulated by the proposed PF-based algorithm, and no error is found. Figure 5(a) shows the message \(\hat{b}_{k}\) estimated by PF at SNR = 7 dB; Figure 5(b) shows the result of lowpass filtering; Figure 5(c) shows the original transmitted binary message \(-b_{n}\). In [25], the PF is used to estimate the parameter of the chaotic system with the requirement that the structure of the chaotic map is known. For comparison in the simulation, the algorithm in [25] is also modified by the fact that the colored or non-Gaussian noises are formulated by ARMA models, and then the parameters that model the noises are included in the state vector. A nonlinear RPROP neural network is developed to blindly demodulate (unknown transmitter structure) the CDS-SS signals in [16]. Figure 6 gives the bit-error rate (BER) performances of the algorithm in [25], the nonlinear RPROP neural network algorithm in [16], the UKF-based algorithm in [15] and the proposed PF-based algorithm with the noises in Equations (40) and (41). The BER of the proposed algorithm is about \(10^{-5}\) at SNR = 7 dB. It can be concluded that the BER performance of the proposed PF-based algorithm is better than the nonlinear RPROP neural network and the UKF-based algorithm on the non-cooperative communication condition (unknown transmitter's structure), and approaches the level the algorithm in [25] that is belong to the cooperative communication (known transmitter's structure) could achieve. Figure 5: **(a)** The message \(\hat{b}_{k}\) estimated by PF when \(\beta\) = 0.9 at SNR = 7 dB; **(b)** the result of lowpass filtering; **(c)** the original transmitted binary message \(b_{n}\).
# Fine-Grained Detection of Pavement Distress Based on Integrated Data Using Digital Twin
## 5 Results and Discussion
### Comparison of the Results for Different Virtual-to-Real Ratios
In order to dig into the influence of the number of real data in the training set on the ability of effective feature extraction of the YOLOv5 model in the pavement-distress detection task, under the condition of 3:1 virtual-to-real ratio, this paper further trains the YOLOv5 network with 25, 50, 75 and 100 real images combined with the corresponding number of virtual data forming integrated datasets, respectively, and tests them on the same 100 real pavement-distress images. The results show that the MAP of the model trained with 25 real images is about 50%, and when the number of real images is increased to 75, the MAP increases by almost 30%, reaching 76.19%. If the number of real images is increased to 100, the detection accuracy is further improved (MAP:76.53%), but the improvement is not significant. These results demonstrate that training the network model using 75 and 100 real images is sufficient for the model to extract the most discriminative features of the pavement-distress images, justifying the setting of 100 real images to train the YOLOv5 network in this paper. The MAP of the YOLOv5 network trained using different numbers of real data is shown in Table 5. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline  & **Transverse Crack** & **Longitudinal Crack** & **Cross Crack (CO)** & **Alligator Crack (AC)** & **Pothole (P)** \\ \hline Measured dataset & & & & & \\ (0:1) & 35.04 & 22.81 & 52.81 & 28.87 & 57.96 & 39.50 \\ Traditional data augmentation & & & & & \\ (3:1) & 50.49 & 36.77 & 54.07 & 32.2 & 60.95 & 46.90 \\ Integrated dataset & & & & & \\ (3:1) & 52.12 & 70.05 & 96.97 & 80.56 & 82.95 & 76.53 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Comparison of two data augmentation methods. Figure 12: Precision-recall curves of five types of defects based on integrated datasets with different virtual-to-real ratios. Detection results of YOLOv5 network for (**a**) transverse cracks (**b**) longitudinal cracks (**c**) cross cracks (**d**) alligator cracks (**e**) potholes. \begin{table}
\begin{tabular}{c c c c c c} \hline \multicolumn{2}{c}{**Integrated Dataset**} & \multicolumn{4}{c}{**Number of Images**} \\ \hline Training set & Real images & 25 & 50 & 75 & 100 \\ Virtual-to real (3:1) & Virtual images & 75 & 150 & 225 & 300 \\ \hline Test set & 100 & 100 & 100 & 100 & 100 \\ Total set & 200 & 300 & 400 & 500 \\ MAP\% & 49.85 & 50.33 & 76.19 & 76.53 \\ \hline \end{tabular}
\end{table} 
Table 5: The MAP of the YOLOv5 network trained using a different number of real data.
# Parametric Study on the Buckling of Unbraced Steel Frames under Fire Situation
## 2 Materials and Methods
### Methodology Used to Determine Buckling Lengths in Fire  
For the critical columns in fire, as explained in Section 2.2, the following methodology was followed. First, a thermal analysis using the software Elefir-EN v1.4.5 [31] was carried out considering uniform temperature in the sections. Then, the elastic critical amplifier in fire (\(\alpha_{cr,fi}\)) was calculated for the same assumptions using linear buckling analysis in CAST3M 2015 [32]. The temperatures were varied between 20 \({}^{\circ}\)C and 1100 \({}^{\circ}\)C. Finally, the buckling length in fire, \(l_{fi}\), can be computed as follows:  
\[N_{cr,fi}=\alpha_{cr,fi}N_{Ed,fi} \tag{6}\]  
\[l_{fi}=\pi\sqrt{\frac{k_{E,\theta E}I}{N_{cr,fi}}} \tag{7}\]  
\[k_{fi}=\frac{l_{fi}}{l_{real}} \tag{8}\]  
where \(N_{cr,fi}\) is the critical buckling load of the column, \(N_{Ed,fi}\) is the axial force in the column under fire conditions, \(l_{real}\) is the column length, and \(k_{fi}\) is the associated buckling coefficient.
## 3 Results
### Logistic Regression  
In the logistic regression analysis, the dependent variable was whether a participant experienced falls during the 12-month follow-up period (1: yes, 0: no). The independent variables included the TUG score (used for the aged 60-70 and 70 or older groups), TUG cut-off (0: TUG \(\geq\) 6.9 s [risk of falling], 1: TUG \(<\) 6.9 s) for the aged 50-60 years group, and other variables that showed a statistically significant association with falls during the follow-up period. The outcome measures that demonstrated a statistically significant effect on the dependent variable (\(p\) \(<\) 0.05) were as follows: TUG (a), HoF (b), UpExt (c), and benzodiazepine use (d) in all participants; TUG cut-off (e) and HoF (b) in the aged 50-60 years group; TUG (a), UpExt (c), and number of medications per day (f) in the aged 60-70 years group; and TUG (a), HoF (b), and benzodiazepine use (d) in the aged 70 or older group (Table 3).  
The probability of suffering a fall, \(pr(Fall)\), can then be calculated as:  
\[\text{Adults aged 50 years or older }pr(Fall)=\frac{1}{1+e^{0.185(a)-0.848(b)-0.585(c)-0.834(d)}} \tag{1}\]  
\begin{table}
\begin{tabular}{l c c c c c c} \hline \hline
**Models** & \(\mathbf{\beta}\) & **SE** & **Wald** & \(\mathbf{p}\) & **OR** & **95\% CI** \\ \hline \(\geq\)50 years & & & & & & \\  (a) TUG & \(-\)0.185 & 0.022 & 67.424 & \textless{}0.001 & 0.83 & 0.80–0.87 \\  (b) HoF (1) & 0.848 & 0.263 & 10.382 & 0.001 & 2.34 & 1.39–3.91 \\  (c) UpExt (1) & 0.585 & 0.285 & 4.212 & 0.040 & 1.79 & 1.11–21.4 \\  (d) Benzodiazepepines (1) & 0.834 & 0.280 & 8.856 & 0.003 & 2.30 & 1.33–3.99 \\
50–60 years & & & & & & \\  (e) TUG cut-off (1) & \(-\)2.528 & 0.832 & 9.234 & 0.002 & 0.08 & 0.02–0.41 \\  (b) HoF (1) & 1.666 & 0.689 & 5.856 & 0.016 & 5.29 & 1.37–20.41 \\   Constant & \(-\)1.136 & 0.448 & 6.443 & 0.011 & 0.32 & - \\
60–70 years & & & & & & \\  (a) TUG & \(-\)0.173 & 0.072 & 5.806 & 0.016 & 0.84 & 0.73–0.97 \\  (c) UpExt (0) & \(-\)1.345 & 0.468 & 8.245 & 0.004 & 0.26 & 0.10–0.65 \\  (f) Medications/day & 0.215 & 0.086 & 6.214 & 0.013 & 1.24 & 1.05–1.47 \\ \(\geq\)70 years & & & & & & \\  (a) TUG & \(-\)0.056 & 0.027 & 4.444 & 0.035 & 0.95 & 0.90–0.99 \\  (b) HoF (1) & 1.125 & 0.347 & 10.497 & 0.001 & 3.08 & 1.56–6.09 \\  (d) Benzodiazepepines (1) & 0.797 & 0.362 & 4.836 & 0.028 & 2.22 & 1.09–4.51 \\ Constant & \(-\)1.093 & 0.356 & 9.422 & 0.002 & 0.34 & - \\ \hline \hline \end{tabular}  
* TUG cut-off (0: TUG \(\geq\) 6.9 s (risk of falling), 1-TUG \(<\) 6.9 s), HoF (1: yes, 0: no), UpExt (1: yes, 0: no), Benzodiazepepines (1: yes, 0: no).  
\end{table}
Table 3: Factors associated with falls among community-dwelling adults aged 50 and older, identified through logistic regression.  
Adults aged 50-60 years : \(pr(Fall)=\dfrac{1}{1+e^{1.136+2.528(e)-1.666(b)}}\)  
\[\text{Adults aged 60--70 years : }pr(Fall)=\dfrac{1}{1+e^{0.173(a)+1.345(c)-0.215(f)}} \tag{3}\]  
\[\text{Adults aged 70 years or older : }pr(Fall)=\dfrac{1}{1+e^{1.093+0.056(a)-1.125(b)-0.797(d)}} \tag{4}\]
## 3 Results and Discussion
### DFT Calculated CH\({}_{4}\) and H\({}_{2}\)O Adsorption on Coal
#### 3.1.3 Co-Adsorption of CH\({}_{4}\) and H\({}_{2}\)O on Coal Molecules  
As demonstrated in Section 3.1.2, both CH\({}_{4}\) and H\({}_{2}\)O prefer aromatic planes over alkane chains. Therefore, CH\({}_{4}\) and H\({}_{2}\)O may be adsorbed competitively on the aromatic planes of coal. To quantitatively investigate their intermolecular interactions, we examined the co-adsorption of CH\({}_{4}\) and H\({}_{2}\)O and calculated the adsorption energy of CH\({}_{4}\) in the presence of a nearby H\({}_{2}\)O and vice versa. The geometries and energies of six co-adsorption structures are shown in Figure 3.  
A comparison between Figure 3a,c and row 4 of Table 3 suggest that the presence of a nearby CH\({}_{4}\) has a negligible influence on the adsorption of H\({}_{2}\)O, even if the distance between CH\({}_{4}\) and H\({}_{2}\)O is as small as 3.43 A. The same conclusion holds for CH\({}_{4}\) adsorption. As shown in Figure 3d,f and row 2 of Table 2, the adsorption energy of CH\({}_{4}\) above aromatic planes is around 22 kJ/mol, regardless of whether a nearby H\({}_{2}\)O molecule is present.  
The results in Figure 3 suggest CH\({}_{4}\) and H\({}_{2}\)O have rather weak interactions. They will neither enhance nor weaken the adsorption of each other. The results also imply that H\({}_{2}\)O does not have the ability to dispel CH\({}_{4}\) from the coal surface if CH\({}_{4}\) is already adsorbed on the surface. Water is usually found in CBM wells. In some cases, water coexists with coal in the well, and the CBM well needs to be dewatered before the extraction. In other instances where the CBM wells are fractured, external water is introduced through the fracturing fluid. This conclusion implies that water does not facilitate the desorption of CH\({}_{4}\) from the coalbed. In Section 3.2, the effect of water on the desorption of CH\({}_{4}\) from the coal surface is further investigated from the MD point of view.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**No.** & **Adsorption Site** & **Representative Adsorption Structures and Energies** \\ \hline
1 & \begin{tabular}{c} Hydrogen bonding with \\ as proton donor \\ \end{tabular} & \
\begin{tabular}{c} \\ NH \\ or \\ as proton donor \\ \end{tabular} &
\begin{tabular}{
## 4 Video Compression Sub-Application Layer Protocol for WVSN
### M-Frame Transmission in Dynamic Periods
#### 4.3.2 Spdf  
The function is used to find total number of pixels which will be sent using D-Frame compression method. It is defined as follows:\[SPDF=\sum_{i=1}^{N-1}\left(BP_{D(i)}\right)\times\left(\{1-P_{i}\}\right)\times AP _{i} \tag{3}\]  
In this equation, \(BP_{D(i)}\) is number of blocks with priority level \((i)\), \(AP_{i}\) is the average of priority level range and \(P_{i}\) is probability of dropping data packets with priority level \((i)\). The Algorithm.3 in Figure 6, is used to decide when an M-Frame should be transmitted.  
In this algorithm, \(\partial\in\)[0, 1] is a coefficient that affects energy saving and video quality. Using a lower value of \(\partial\) leads to M-Frame being sent to a high frequency, which results in more energy and bandwidth consumption. It causes, however, better video quality. Higher values of \(\partial\) causes lower video quality and more energy and bandwidth saving.