esa-sceva/satcom-chunk-collection huggingface dataset:
# DLI-Based DP-QPSK Reception Scheme for Short-Range Optical Communication
## 2 Structure and Basic Principle
The raw data is recovered using subsequent devices. It is noteworthy that the LPF used here is a manifestation of the low-pass characteristics of the hardware, which result from the limitations of the hardware itself. For example, limitations in the frequency response of the photodiodes prevent high-frequency components from passing through it. Assuming that the responsibilities of photodiodes are the same, all being equal to \(\alpha\), the differential delay in the time domain is \(\tau\), and the signal at the input of DP-DLI is \(E(t)=A\ \exp[j(\varphi(t)+\varphi_{n})]\), where \(A\) is the amplitude, \(\varphi(t)\) is the carrier phase, and \(\varphi_{n}\) is the signal phase. The optical signal at the output of the DP-DLI can be expressed as:  
\[E_{1u,2u,1v,2v}=\frac{j}{2}[E(t)e^{\pm j\frac{\tau}{4}}\pm E(t-\tau)]. \tag{5}\]  
According to the square-law characteristic of photodiodes, the converted photocurrent is (taking \(E_{1u}(t)\) as an example here):  
\[i_{PD}(t)= \frac{\sqrt{2}\alpha A^{2}}{4}(\sqrt{2}+\cos\Delta\varphi_{n}- \sin\Delta\varphi_{n}). \tag{6}\]  
After the balanced photodetectors, the two electrical signals can be written as:  
\[ \begin{array}{l}i_{u}(t)=\frac{\sqrt{2}}{2}\alpha A^{2}(\cos\Delta\varphi_{ n}-\sin\Delta\varphi_{n}),\\ i_{v}(t)=\frac{\sqrt{2}}{2}\alpha A^{2}(\cos\Delta\varphi_{n}+\sin\Delta \varphi_{n}).\end{array}  \tag{7}\]  
where \(\Delta\varphi_{n}\) is the phase difference between adjacent symbols.
## 3 Problem Formulation  
In this section, we first formulate an optimization problem for our QoS-guaranteed joint resource allocation framework for NR with SUL. The proposed QGJRA-SUL framework involves three parameters for joint optimization, as described below:  
1. SUL admission: Considering the dynamic change of the wireless environment, SUL admission needs to be dynamically optimized by adjusting \(\delta\).
2. TDD pattern: As shown in Figure 2, a hard slicing scheme of the NR band for multiple slices with the same \(\lambda\) is proposed. \(\lambda\) needs to be dynamically optimized for the load between the downlink and the uplink.
3. Band slicing scheme: The hard slicing scheme \(\mathbf{w}\) represents an isolated bandwidth allocation scheme for both the downlink and uplink.  
The detailed steps of the QGJRA-SUL framework are shown in Algorithm 1, where we assume that the BS continuously reconfigures the above three parameters \(\delta,\lambda,\mathbf{w}\) with period T. The description of the system state as the input of the DRL solution is detailed in Section 4.  
```
1:repeat
2:\(\delta,\lambda,\mathbf{w}\leftarrow\) DRL-based solution
3:for slice \(m=1\to M\)do
4:for UE \(n=1\rightarrow|\mathcal{N}_{m}|\)do
5:if\(\gamma_{m,i}^{d,x}<\delta\)then
6:\(x_{m,i}=sul\);
7:else
8:\(x_{m,i}=nr\);
9:endif
10:endfor
11:endfor
12: The TDD pattern \(\lambda\) in Equation (4) divides \(\tau\) into downlink duration \(\lambda\tau\) and uplink duration \((1-\lambda)\tau\) in the time domain.
13:for slice \(m=1\to M\)do
14:for\(d\in\mathcal{D}\)do
15: Set the bandwidth allocated to slice \(m\) to \(w_{m}^{d}\);
16:endfor
17:endfor
18: Base station provides communication services to UEs;
19:for\(t=0\to T-1\)do
20:endfor
21: System State \(\rightarrow\) DRL-based solution;
22:until The Base station shutdown.
```  
**Algorithm 1** The QGJRA-SUL framework The objective of QGJRA-SUL is to guarantee the slice QoS satisfaction rate as much as possible while balancing the slice load via the joint optimization of the SUL admission, TDD pattern, and band slicing scheme. The utility function of each period \(T\) can be formulated as  
\[U=q-\beta\cdot\varsigma. \tag{10}\]  
The first part of (10) is to maximize the QoS satisfaction rate, and the second part, \(-\beta\cdot\varsigma\) is a penalty item to balance the slice load. \(\beta\) is the weight of the penalty item to make the trade-off between the QoS satisfaction rate and the slice load balance. The optimal state of the system is that \(q=1\) and \(\varsigma=0\), which means the QoS satisfaction rate of each slice is 1, and all slices have the same load. With a traffic model \(\mathbf{g}=\{g^{d}_{m,n}(t)|m\in\mathcal{M},n\in\mathcal{N},d\in\mathcal{D},t \in[0,T-1]\}\), the QoS satisfaction rate \(q(\lambda,\mathbf{w},\delta,\mathbf{g})\) is influenced by the three parameters mentioned above and the traffic model. Hence, the problem is formulated as follows.  
\[\mathbf{P}: \max_{\delta,\lambda,\mathbf{w}}q-\beta\cdot\varsigma\] \[\text{s. t. }(1),(3),(4),(8),\] \[0<w^{d}_{m}, \tag{11}\] \[\sum_{m\in\mathcal{M}}w^{d}_{m}=W^{nr} \tag{12}\]
# Experimental Study on the Efficacy of Water Infusion for Underground Mining of a Coal Seam
## 3 Experimental Program  
### Laboratory Test Program  
The selected coal samples used for the laboratory test program in this study originated from Coal seam No 14-5 (Khe cham III coal mine, Quang Ninh, Vietnam) (See Figure 3). In total, 18 coal samples were taken from three different sections (i.e., six samples per section) along Coal seam No 14-5. The performance of all laboratory tests followed Vietnamese standards (TCVN 2012), such as those for the moisture content (TCVN 4196), bleeding (C 940), compressive strength (D 4832), flowability (D 6103), specific gravity (TCVN 4195), unit weight (TCVN 4202), permeability (TCVN 8723), and direct shear test (TCVN 4199). Table 1 summarizes all of the general characteristics of the coal samples from the laboratory test program.  
\begin{table}
\begin{tabular}{c c c c} \hline
**Properties** & **Section 1** & **Section 1** & **Section 1** \\ \hline Moisture content (\%) & 4.901 & 4.85 & 4.617 \\ Unit weight (g/cm\({}^{3}\)) & 1.422 & 1.414 & 1.419 \\ Specific gravity & 1.521 & 1.51 & 1.518 \\ Permeability (cm/s) & 0.000380 & 0.000339 & 0.000362 \\ Color & Black & Black & Black \\ \hline \end{tabular}
\end{table}
Table 1: General characteristics of the coal samples.  
Figure 3: Location coal seam No 14-5 (Khe cham III coal mine, Quangninh, Vietnam).  
Figure 2: Principle of effective stress with saturated soil (reproduced with permission from [PERSON], Principle of Effective Stress published by John Wiley & Sons [16]).  
In addition to the above general characteristics, the relationship between strength properties (i.e., from direct shear tests) and moisture content with time was also investigated in the laboratory to evaluate the appropriate parameters (e.g., water injection time and the optimum moisture content) for water infusion works in the field. The effect of moisture content (i.e., 12 different moisture contents) on the strength properties of coal was performed first to determine the optimum moisture content of the coal specimen. After that, the coal with the optimum moisture content was subjected to direct shear tests to determine the strength properties with respect to time. The tests were performed every 2, 18, 24, 36, 43, 48, and 51 h.
# Comparison of Temperature Dependent Carrier Transport in FinFET and Gate-All-Around Nanowire FET
## 2 Materials and Methods  
The cross-sectional transmission electron microscopy (TEM) images [8; 15] of the devices under test are shown in Figure 1. Both GAA NW-FETs and FinFETs were fabricated using the high-k replacement metal gate (HK-RMG) process [7; 16; 17]. The diameter of nanowire (\(D_{inv}\)) is 8 nm for GAA NW-FETs. In the case of FinFETs, the fin width (\(W_{fin}\)) is 5 nm and the fin height (\(H_{fin}\)) was 26 nm.  
Both GAA NW-FETs and FinFETs were fabricated based on a conventional bulk FinFETs process flow [15] with the following particularities in the case of GAA NW-FETs, as shown in Figure 2. First, in order to suppress the short channel effect, a ground plane (GP) isolation implant was used [8]. Implanted boron reduced the punch through via a parasitic channel underneath the bottom of the nanowire so that it improves the gate control in the subthreshold region. The second difference is the channel formation process. For fin formation on both devices, a self-aligned double patterning (SADP) process is conducted using SiN spacers while maintaining uniform shallow trench isolation (STI) filling. To make nanowires, SiGe/Si/SiGe/Si epitaxial layers were grown before the SADP process, and the sacrificial SiGe layer was removed with the vapor HCl etch process before the HK-RMG process. Furthermore, the temperature of the STI densification step was reduced from 1050 to 750 \({}^{\circ}\)C to avoid SiGe/Si intermixing and a consequent loss of nanowire shape controllability [18]. In this study, gate lengths \(L_{G}\) = 30 nm and 70 nm were used for the electrical characterization.  
The Keysight B1500A was used for the electrical measurements. The gate-source bias (\(V_{GS}\)) was swept from \(-0.5\) to 1.5 V (step = 50 mV) in the linear region at \(V_{DS}\) = 50 mV. The electrical characterizations were carried out under various temperature conditions from 25 to 125 \({}^{\circ}\)C.  
Figure 1: TEM cross-sectional images of NMOS: (**a**) gate-all-around nanowire field effect transistors (GAA NW-FETs); and (**b**) fin field effect transistors (FinFETs). Two nanowires are stacked in GAA NW-FETs.
## 2 Materials and Methods
### Physical-Layer Security Analysis: Colluding Eavesdroppers
\left(\begin{array}{c}\tilde{\gamma_{e}}\\ \gamma_{e}\prod_{j=1}^{n_{e}}E\left[X_{j}^{2}\right]\mu_{ej}K_{j}\left(1+ \kappa_{ej}\right)\end{subarray}\right), \tag{9}\]  
where \(\tilde{\gamma_{E}}\) is the average received SNR at E, \(\beta_{e}^{\prime}=\mu_{e1}K-\mu_{e2}K+r_{1}-r_{2}+1,\cdots,\mu_{e1}K-\mu_{ en_{e}}K+r_{1}-r_{ne}+1,1\), and  
\[c_{x,e}= 2\prod_{j=1}^{n_{e}}\left[\frac{\left[2\mu_{ej}K_{j}\sqrt{ \kappa_{ej}\left(1+\kappa_{ej}\right)}\right]^{2\gamma_{j}+\mu_{ej}K_{j}-1}}{ (r_{j})!2^{2\gamma_{j}+\mu_{ej}K_{j}-1}}\right]\prod_{j=1}^{n_{e}}\left[ \frac{\left[\mu_{ej}K_{j}\left(1+\kappa_{ej}\right)\right]^{\mu_{e1}K-\mu_{ jj}K_{j}+r_{1}-r_{j}}}{\kappa_{ej}^{\frac{\mu_{ej}K_{j}-1}{2}}\exp\left( \kappa_{ej}\mu_{ej}K_{j}\right)}\right]\] \[\times\prod_{j=1}^{n_{e}}\left[\frac{\mu_{ej}K_{j}\left(1+\kappa_ {ej}\right)^{\frac{\mu_{ej}K_{j}+1}{2}}}{\Gamma\left(r_{j}+\mu_{ej}K_{j} \right)}\right].\]  
Proving the accuracy of (9), the PDF of \(\gamma_{E}\) is plotted in Figure 2 with Monte-Carlo simulations. Using (9) and ([28] Equation (26)), the CDF of \(\gamma_{E}\) can be given by  
\[F_{\gamma_{E}}(\gamma_{e}) = \sum_{r_{1}=0}^{\infty}\sum_{r_{2}=0}^{\infty}\cdots\sum_{r_{n_{ e}}=0}^{\infty}\frac{c_{x,e}}{2}G \begin{subarray}{c}n_{e}&1\\ 1&n_{e}+1\end{subarray} \left(\begin{array}{c}\tilde{\epsilon}^{\prime}_{e} \\ \tilde{\gamma_{E}}K\end{subarray}\right)\left(\gamma_{e}\frac{\prod_{j=1}^{n_{e} }E\left[X_{j}^{2}\right]}{\gamma_{E}K}\right)^{\mu_{\alpha}K+r_{1}}, \tag{10}\]  
where \(\epsilon^{\prime}=1-\mu_{e1}K-r_{1}\), \(\eta_{e}^{\prime}=-\mu_{e1}K+\mu_{e2}K-r_{1}+r_{2},\cdots,-\mu_{e1}K+\mu_{e^{ \prime}n_{e}}K-r_{1}+r_{n_{e}},0\), \(-\mu_{e1}K-r_{1}\), and \(A=\prod_{j=1}^{n_{e}}E\left[X_{j}^{2}\right]\mu_{ej}K_{j}\left(1+\kappa_{ej}\right)\). Figure 2: The PDF of the received SNR at the eavesdropper (\(\gamma_{E}\)) for multiple values of cascade level of the wiretap channel (\(n_{e}\)) and multiple number of antennas at E (\(K\)). \(\kappa_{e}=1\) and \(\mu_{e}=2\).
## 5 Data Analyses and Results
### DIC Analyses
#### 5.2.3 Analyses of the Landslide Deformation
Therefore, the displacement magnitude effect induced an important or total variation on the morphology. Figure 10: DIC displacement maps derived from CSK SAR absolute amplitude images (in ascending geometry) and analyzed with COSI-Corr software. The extracted vector field (white arrows) of the landslide area (red polygon) is reported. Grey coloring corresponds to areas with loss of correspondence between the pre- and post-failure images. Figure 14: DIC displacement map retrieved from shaded Digital Terrain Models (DTMs) derived images with COSI-Corr (**A**) and GOM Correlate (**B**) software. The white arrows show the displacement vector field. The red polygons show the landslide boundary. Grey coloring corresponds to areas with loss of correspondence between the pre- and post-failure images. Figure 12: DIC displacement map retrieved from descending CSK SAR temporal average amplitude images with COSI-Corr software. The white arrows show the displacement vector field. The red polygons show the landslide boundary. Grey coloring corresponds to areas with loss of correspondence between the pre- and post-failure images. Figure 13: DIC displacement map retrieved from LANDSAT 8 OLI-TIRS (Operational Land Imager-Thermal Infrared Sensor) images and analyzed with COSI-Corr software. White arrows show the displacement vector field. The red polygon shows the landslide boundary. Grey coloring corresponds to areas with loss of correspondence between the pre- and post-failure images. In Figures 10, 11b and 14b, certain portions of the NE and E sectors of the landslide are characterized by a lack of signal where any type of results can be retrieved. In the areas immediately surrounding the landslide, no movement has been registered as shown by the green tones in each DIC displacement map.
# Low-Profile Harmonic Transponder for IoT Applications
## 5 Conclusions  
In this paper, a novel harmonic transponder is presented. In order to efficiently convert the received fundamental frequency, the transponder receiving antenna was matched to the diode input impedance at 2.45 GHz. In addition, for efficiently transmitting the converted second harmonic, the corresponding antenna was matched at 4.9 GHz. Moreover, the CL was compared for a matched and biased diode, for which similar values of CL were achieved for both cases. However, biasing the diode does not necessitate a matching condition at the expense of having a supply voltage of \(\approx\)100 mV and thus, more weight and volume. The introduced transponder was fabricated and a range measurement was conducted, which fit very well with the calculations. Two main research directions will be investigated in the near future. The first one is the insertion of another encoding bit to the tag structure to implement the multi-bit harmonic transponder. The second direction is the employment of the developed tags in indoor localization systems, besides the integration to the printed diode.  
Concept and theoretical development, M.K.; numerical analysis, M.K, A.F. and A.B., T.K.; writing of manuscript, M.K. Finally, all authors together analyzed the simulation and measurement results, discussed among themselves and completed the manuscript edition. All authors have read and agreed to the published version of the manuscript.  
This research work was partially funded by the Drulde (INTERREG-PROJEKT) and the APC is funded by the Open Access Publication Fund of the University of Duisburg-Essen.  
Not applicable.  
The authors declare no conflict of interest.
###### Abstract  
To investigate the deformation characteristics of shield tunnel linings under ground surcharge, finite element software was employed to create a detailed three-dimensional model of the staggered assembly of the shield tunnel lining. This model includes components such as precast concrete segments, reinforcements, and joints (comprising bent bolts, washers, and bolt sleeves). Additionally, the model accounts for interface frictions between segments and the interactions between different rings. The reliability of the numerical model was verified based on the results of a full-scale model test. Additionally, the model accounts for interface frictions between segments and the interactions between different rings. Changes in tunnel convergence, joint tensioning, bolt stresses, reinforcement stresses, and concrete crack development were systematically analyzed. The results indicate the following: (1) the deformation mode of the lining structure under ground surcharge resembles a \"transverse ellipse\". Joints located near the haunch opened along the outer arc, while those near the vault and bottom opened along the inner arc. The restraining effect of the bolts on joints opening in the inner arc was greater than that on the outer arc. Notably, when the opening of the inner arc reached 4.9 mm, the bolt stress escalated to the yield strength of 640 Mpa. (2) Under larger loads, the lining structure's joints are susceptible to greater deformation, resulting in the tensile yielding of local reinforcement within these joints. (3) Cracks predominantly occur near the haunch, vault, and bottom of the lining structure, with the central angle of crack distribution ranging between 70\({}^{\circ}\) and 85\({}^{\circ}\).  
ground surcharge; shield tunnel; lining structure; deformation characteristics; numerical analysis +
Footnote †: journal: Applied  
0000-0001-9993-3333][PERSON], [PERSON]-[PERSON], [PERSON]-[PERSON], L.-[PERSON], D. Numerical Analysis of Ground Surcharge Effects on Deformation Characteristics in Shield Tunnel Linings. _Appl. Sci._**2024**, _14_, 2328. [[https://doi.org/10.3390/app14062328](https://doi.org/10.3390/app14062328)]([https://doi.org/10.3390/app14062328](https://doi.org/10.3390/app14062328))
## Materials and Methods
### Con A Immobilisation Protocol
#### 2.2.4. Con A Immobilisation  
Con A was added at a concentration of 1 mg mL\({}^{-1}\) in an aqueous 20 mM MOPS buffer of pH 5.5 containing 10 mM CaCl\({}_{2}\) and 10 mM MnCl\({}_{2}\). The Ca\({}^{2+}\) and Mn\({}^{2+}\) ions play the role of co-factors [38] required to activate the protein for glucose binding. The MOPS buffer containing Con A was further diluted 10-fold in 50 mM Boric acid to a final concentration of 0.1 mg mL\({}^{-1}\) protein. The covalent coupling of Con A to the silane layer (catalysed using a water soluble carbodiimide) involved conjugation of the amine groups on the protein to the carboxyl groups on the silane. The water soluble carbodiimide (EDAC) was dissolved to a final concentration of 0.5 mg mL\({}^{-1}\). EDAC catalyses an activation of the carboxyl for the coupling of primary amines to yield amide bonds. Accordingly, 100 \(\upmu\)L of freshly prepared solution was dispersed on the silanised quartz surface for at least 2 h at room temperature to permit the amide bonds to be completed (Figure 1c,d). After the immobilisation process, the wafers were removed from the solution, washed with MOPS buffer and DI water three times. Thereafter, the sample surface was dried under a nitrogen stream.  
Figure 1: Schematic representation of various steps of the immobilisation protocol: (**a**) hydroxylation, (**b**) silanisation, (**c**) Con A immobilisation, and (**d**) chemical reaction between the functional groups of the silane and the Con A, (**e**) Dextran binds to immobilised Con A, (**f**) Glucose competitive binds to Con A and replaces dextran.
## 2 Definitions and Known Results
### Graph Width Parameters  
In this subsection, we briefly review the definitions of graph width parameters. We only give the definitions of graph width parameters that will be needed in our proofs. Definitions of the other graph width parameters can be found as follows: For the definitions of path-width, tree-width, branch-width, and band-width, see e.g., [18]. For the definitions of carving-width, clique-width, and boolean-width, see e.g., [19; 20; 21], respectively. Note that the decision problems related to graph width parameters considered in this paper are all minimization problems.  
As some of graph width parameters are based on decomposition trees, let us first review the notion of a decomposition tree. Given a tree \(T\), let us denote the set of leaves of \(T\) by \(L(T)\). For an edge \(e\) in \(T\), \((T\backslash e)_{1}\) and \((T\backslash e)_{2}\) denote the two subtrees obtained from \(T\) by removing \(e\). Given a graph \(G=(V,E)\) and a tree \(T\) such that \(|L(T)|=|V|\), let \(f_{T}\) be a bijection from \(L(T)\) to \(V\). For each edge \(e\) in \(T\), we denote the subset of \(V\) mapped by \(f_{T}\) from the leaves in \((T\backslash e)_{i}\) as \((V\backslash e)_{i}\) for \(i\in\{1,2\}\). That is, \((V\backslash e)_{i}=\{f_{T}(v):v\in L((T\backslash e)_{i})\}\). Note that \((V\backslash e)_{i}\) obviously depends on \(T\) and \(f_{T}\). In this paper, we will refer to a pair \((T,f_{T})\) satisfying the following conditions as a _decomposition tree_ of \(G=(V,E)\):  
* \(T\) is a subcubic tree with \(|V|\) leaves, where a tree is _subcubic_ if every vertex in \(T\) has degree \(1\) or \(3\);
* \(f_{T}\) is a bijection from \(L(T)\) of \(T\) to \(V\).  
We denote the set of tree decompositions of \(G\) by \(\mathscr{D}_{G}\).  
**Cut-width:**: For a graph \(G=(V,E)\), let \(\pi:V\rightarrow\{1,\ldots,|V|\}\) be an ordering of \(V\). Let \(S_{\pi}(i):=\{\pi^{-1}(1),\ \pi^{-1}(2),\ \ldots,\ \pi^{-1}(i)\}\), \(\partial_{e}(\pi,i):=E(S_{\pi}(i),\overline{S_{\pi}(i)})\). Then, \(cutw(G):=\min\limits_{\pi}\max\limits_{1\leq i\leq n}|\partial_{e}(\pi,i)|\).
**Rank-width:**: For a graph \(G=(V,E)\), let \(T\) be a subcubic tree and \(f_{T}\) be a bijection from \(L(T)\) to \(V\). Then, \(rw(G):=\min\limits_{(T,f_{T})\in\mathscr{D}_{G}}\max\limits_{e\in E(T)}rank \big{(}M\big{[}(V\backslash e)_{1},(V\backslash e)_{2}\big{]}\big{)}\).
**Maximum induced matching-width**: For a graph \(G=(V,E)\) and a subset \(A\) of \(V\), we denote the size of a maximum induced matching in the bipartite graph \((A,\overline{A};E(A,\overline{A}))\) by \(mim(A)\). Then, \(mimw(G):=\min\limits_{(T,f_{T})\in\mathscr{D}_{G}}\max\limits_{e\in E(T)}mim(( V\setminus e)_{1}))\).
## 3 Results and Discussions
### Density Studies
model and their deviations are presented in Tables 4 and 5. In both (ethanol + 1-hexanol and ethanol + 1-octanol) binary liquid systems, it was observed that the deviation of density takes the following order: \(\Delta\rho_{\rm MNM}>\Delta\rho_{\rm HT}>\Delta\rho_{\rm YG}>\Delta\rho_{\rm R}\). This study demonstrated that the APD of the density is more in the Mchaeweh-Nasrifar-Mashfeghian model and least in the [PERSON] et al. model, amongst the models used in this work. Also, the theoretical calculations made on the density of binary mixtures using various models gave the conclusion that the density values estimated from [PERSON] et al. [34] are the most suitable ones for predicting the density of both binary mixtures, Ethanol + h-Hexanol and Ethanol + 1-octanol. Thus, it is worth mentioning that the basic assumptions used in the model of [PERSON] et al. [34] and the assumptions applied in that model are well-suited for estimating the closer value of the density for the studied binary mixtures. \begin{table}
\begin{tabular}{c c c c c c} \hline \multirow{3}{*}{\begin{tabular}{c} **Mole Fraction** \\ **of Ethanol** \\ \end{tabular} } & \multirow{3}{*}{\begin{tabular}{c} **Density (Experimental** \\ **Values) kg/m\({}^{3}\)** \\ \end{tabular} } & \multicolumn{3}{c}{**Theoretical Density (kg/m\({}^{3}\))**} \\ \cline{3-5}  & & **Mahseh–Nasrifar-Mashfeghian** & \begin{tabular}{c} **[PERSON] and** \\ **[PERSON]** \\ **Model (\(\rho_{\rm MNM}\))** \\ \end{tabular} & \
\begin{tabular}{c} **[PERSON] and** \\ **(\(\rho_{\rm HT}\))** \\ \end{tabular} &
\begin{tabular}{c} **[PERSON] et al.** \\ **Model (\(\rho_{\rm R}\))** \\ \end{tabular} \\ \hline
0.00 & 807.6 & 654.2 & 844.9 & 839.7 & 839.2 \\ \hline
0.14 & 805.6 & 656.6 & 847.9 & 842.9 & 842.2 \\ \hline
0.28 & 802.9 & 658.8 & 850.5 & 845.6 & 844.7 \\ \hline
0.49 & 798.6 & 661.5 & 853.6 & 848.9 & 847.8 \\ \hline
0.64 & 794.8 & 663.3 & 855.2 & 850.6 & 849.5 \\ \hline
0.77 & 791.2 & 664.4 & 855.9 & 851.5 & 850.4 \\ \hline
0.87 & 787.7 & 665.1 & 856.1 & 851.8 & 850.7 \\ \hline
0.95 & 785.7 & 665.5 & 856.0 & 851.8 & 850.7 \\ \hline
1.00 & 783.9 & 665.6 & 855.9 & 851.6 & 850.7 \\ \hline
**APD from experimental** & & & & \\
**values** & & & & & \\ \hline \end{tabular}
\end{table} 
Table 4: Experimental and theoretical density of binary liquid system of Ethanol + 1-Hexanol at 303.15 K.