esa-sceva/satcom-chunk-collection huggingface dataset:
## 4 Digital Watermarking System for JPEGs
### DCT Domain Embedding  
The process adapts to the input image colour space: YCbCr for JPEG disk images and RGB for stand-alone COCO2017 images. We propose the following embedding approach to balance imperceptibility with robustness.  
DCT applies to each selected block \(B_{i}\) in each colour channel:  
\[\text{DCT}(B_{i})\to C_{i}(u,v) \tag{7}\]  
The watermark bit \(W_{i}\) is embedded in the mid-frequency coefficient C(4, 4) in each channel, selected by zigzag scanning (shown in Figure 2) for its optimal balance between perceptual masking and robustness. This coefficient position remains relatively stable under common image transformations and offers good imperceptibility. The embedding strength is determined adaptively based on the perceptual mask described in Section 4.9.  
For YCbCr colour space,  
\[C_{Y}(4,4)^{\prime} =C_{Y}(4,4)+\alpha_{Y}\times W_{b}\times M(4,4) \tag{8}\] \[C_{Cb}(4,4)^{\prime} =C_{Cb}(4,4)+\alpha_{Cb}\times W_{b}\times M(4,4)\] (9) \[C_{Cr}(4,4)^{\prime} =C_{Cr}(4,4)+\alpha_{Cr}\times W_{b}\times M(4,4) \tag{10}\]  
For RGB colour space,  
\[C_{R}(4,4)^{\prime} =C_{R}(4,4)+\alpha_{R}\times W_{b}\times M(4,4) \tag{11}\] \[C_{G}(4,4)^{\prime} =C_{G}(4,4)+\alpha_{G}\times W_{b}\times M(4,4)\] (12) \[C_{B}(4,4)^{\prime} =C_{B}(4,4)+\alpha_{B}\times W_{b}\times M(4,4) \tag{13}\]  
For greyscale images,  
\[C(4,4)^{\prime}=C(4,4)+\alpha W_{b}\times M(4,4) \tag{14}\]  
where \(C(4,4)^{\prime}\) represents the modified coefficient after watermarking, \(W_{b}\) is the watermark bit value (0 or 1), and \(M(4,4)\) denotes the perceptual mask value at position (4, 4). The channel-specific embedding strength factors (\(\alpha_{Y}\), \(\alpha_{Cb}\), \(\alpha_{Cr}\), \(\alpha_{R}\), \(\alpha_{G}\), \(\alpha_{B}\), \(\alpha\)) are derived from the adaptive threshold calculation to ensure optimal perceptual masking in each colour space.
## 3 Results and Discussion
### AFM LON on TaS\({}_{2}\) Surfaces
#### Dynamic-Tip LON  
The AFM-LON studies were first conducted using the classical oxidation procedure in which the tip is oscillating during the process (_dynamic-tip_ LON). In these samples, the LON produced massive oxide formations with a rippled topography (Figure 1b). This ripple oxide formation by _dynamic-tip_ LON was found to be very sensitive to the experimental conditions. Oxide dots created at the same values of voltages and times exhibit not only different topologies (different number of rings) but also different heights and widths.  
This observation can be related to the fact that the size of an oxide pattern by LON generally depends on the size of the meniscus, and this is dependent on the tip-to-sample distance (among other parameters). Shorter tip-substrate spacing favors the formation of the water meniscus while an increase in the tip-to-sample distance leads to a linear decrease in the meniscus width [24; 25]. In our case, the tip-to-sample distance was found to have a threshold value from which the size of the pattern grew significantly as can be seen in Figure 2a. The tip-to-sample distance was checked by recording the so called force-distance curve. This distance can be adjusted by choosing the corresponding amplitude of oscillation and by fitting the set point in tapping mode. In general, a set point of 1.5 V was initially tuned in order to achieve a reasonable surface proximity for LON purposes. As the tip-to-sample distance was decreased, the oxide width and height grew. The standard 12-14 nm tip-to-sample distances led to precise nano-dot writing. As the tip was pushed closer to the surface, uncontrolled massive oxide formations were fabricated. Interestingly, it was also observed that the number of the outer rings of the ripple formations grew in an inversely proportional manner with respect to the tip sample distance: three outer rings for \(d_{\text{ts}}\) = 14 nm, two outer rings for \(d_{\text{ts}}\) = 15 nm and a single outer ring for \(d_{\text{ts}}\) = 16 nm. So for a bigger water meniscus (shorter tip-to-sample distance), a bigger oxide motif is formed and there is more space for the formation of a ripple structure with a larger number of rings.  
As observed for other materials [26], it was also found that there is always a threshold potential from which the oxide started to form. Then, at a constant tip-sample distance, the size of the whole pattern is governed by the pulse time duration (\(t_{\text{ox}}\)). In Figure 2b it is shown a set of three oxidized dots performed at \(d_{\text{ts}}\) \(\sim\)13 nm and voltage pulse, \(V_{\text{ox}}\) = \(-\)21 V, with increasing time of oxidation 100 ms, 200 ms, 300 ms, respectively. The formations grew in number of rings, height and width as the pulse time was increased.  
Finally, some experiments were performed at a positive bias instead of a negative bias and similar results were obtained. As expected, the polarity of the voltage pulse did not affect the oxidation outcome given the metallic nature of the TaS\({}_{2}\) conducting flakes [27].
# The Design and Implementation of a Novel Open Source Massive Deployment System
## 5 Discussion
### Comparisions with Other System Deployment Solutions  
The proposed flexible architecture and the Clonezilla implementation can provide better features than other proprietary or open source software. The comparisons between the Clonezilla and other nine software packages (which include six open source and three proprietary solutions) are summarized in Table 5. All of the open source programs are released under the GPL license, except for OpenStack Ironic, which is released under the Apache License. Two of them, i.e., FOG and OpenGnSys, also use the Partclone as the file system imaging engine. This offers the advantage of open source software, which allows the development and contribution of the software to be used and recognized by others. As shown in Table 5, Clonezilla is superior to the proprietary software in the supporting of more file systems. In addition, Clonezilla is also superior to other open source software. Clonezilla can be started from a live system, supports the massive deployment of disks in a computer, and provides a client-server mechanism which can be used for massive deployment in large-scale computers. Based on the comparison results, the proposed novel architecture and the Clonezilla implementation in this research have more features. These aspects show that the developed massive deployment system in this study can be a better choice for system administrators.  
\begin{table}
\begin{tabular}{l c c} \hline \hline \multirow{2}{*}{**Commercial Proprietary Product**} & \multirow{2}{*}{**Price (USS)**} &
\begin{tabular}{c} **Cost Savings in Using** \\ **Clonezilla Live (\%)** \\ \end{tabular} \\ \hline SySTOR 1 to 31 Multiple USB Thumb Drive & 2360 & 91.5 \\ Duplicator/USB Flash Card Copier (USB-31) [50] & 2750 & 92.7 \\ BestDuplicator Premium-M Series-31 Target (1 to 31) & 2789 & 92.8 \\ USB Duplicator/Multiple Flash USB Card Copier [51] & 2345 & 91.5 \\
1-To-31 USB Duplicator [52] & 2561 & 92.2 \\ \hline \hline \end{tabular}
\end{table}
Table 4: Commercial USB flash drive duplicator cost and cost saving percent for using Clonezilla live.
# A Service-Constrained Positioning Strategy for an Autonomous Fleet of Airborne Base Stations
## 6 Evaluation and Results  
In this section, some numerical simulations have been carried out to evaluate both the scheduler and the proposed positioning strategy. Tables 1, 2, and 3 presents all the parameters used in the simulations. Some of them have been obtained from the literature and others have been adjusted during the simulations process (\(\mu\), \(\mu_{BH}\), \(\triangle\), \(\gamma\), \(T_{it}\) and \(grid\)).  
\begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline \hline
**Parameter** & \(P_{T}\) & \(P_{T_{int}}\) & \(f_{e}\) & \(BW_{A}\) & \(G_{T}\) & \(G_{R}\) & \(k_{b}\) & \(T\) & \(F\) & \(\alpha\) \\ \hline Value & 25 dBm & 28 dBm & 2 GHz & 20 MHz & 3 & 3 & 1.38 \(\times 10^{23}\) J/K & 290 K & 5 dB & 9.6 \\ \hline
**Parameter** & \(\beta\) & \(\xi_{LOS}\) & \(\xi_{NLOS}\) & \(\mu\) & \(\mu_{BH}\) & \(\triangle\) & \(B_{BH}^{total}\) & \(\gamma\) & \(T_{it}\) & \(grid\) \\ \hline Value & 0.28 & 1 dB & 20 dB & 3 & 5 \(\times 10^{5}\) & 52 m & 180 MHz & 14 kHz & 0.3 s & 50 m/unit \\ \hline \hline \end{tabular}
\end{table}
Table 1: General parameters for the communications field.  
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Parameter** & \(F_{m}\) & \(C_{D}\) & \(\Omega\) & \(\alpha_{P}\) & \(M\) \\ \hline Value & 0.75 & 1.3 & 20 rad/s & 10\({}^{\circ}\) & 2 Kg \\ \hline \hline \end{tabular}
\end{table}
Table 3: Specific parameters for the UAV model.
## 2 Analysis of the Reverse Torque and Vibration in the Mud Pump
### Relationship between Mud Pump Reverse Torque and Rotational Speed  
To establish the relationship between the mud pump's reverse torque and rotational speed, a three-dimensional model of the mud pump flow channel was established by using the three-dimensional modeling software Solidworks (version 2018), and its cutaway view is shown in Figure 7. The model was meshed by using the Mesh tool in ANSYS Workbench (Version 2020 R1) and automatic meshing was used for the division. A total of 239,462 grids were divided, as shown in Figure 8. Except for the difference in the analysis model, the rest of the settings are identical to those used when analyzing single-stage pumps and will not be repeated here.  
\begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline \hline
**Rotational Speed (rpm)** & **1400** & **1410** & **1420** & **1430** & **1440** & **1450** & **1460** & **1470** & **1480** & **1490** & **1500** \\ \hline Pressure difference between inlet and outlet (MPa) & 0.658 & 0.662 & 0.672 & 0.685 & 0.695 & 0.705 & 0.715 & 0.725 & 0.734 & 0.746 & 0.756 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Relationship between inlet and outlet pressure difference and rotational speed.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Rotational Speed (rpm)** & **Useful Work (kW)** & **Calculated Reverse Torque (N-m)** \\ \hline
1400 & 22.06 & 273.17 \\
1410 & 22.19 & 272.83 \\
1420 & 22.53 & 275.06 \\
1430 & 22.96 & 278.35 \\
1440 & 23.29 & 280.39 \\
1450 & 23.63 & 282.53 \\
1460 & 23.96 & 284.51 \\
1470 & 24.29 & 286.46 \\
1480 & 2 Figure 5: Relationship between the calculated and simulated values as they vary with the rotational speed.  
Figure 6: Relationship between the error and rotational speed as they vary.  
Figure 7: The cutaway view of the mud pump flow channel.  
To establish the relationship between the reverse torque and rotational speed of the mud pump within the speed range from startup to normal operation, 24 sets of analytical experiments were conducted at different pump speeds. The reverse torque values at 24 different speeds were obtained, and a torque-speed relationship curve was plotted based on the analytical experimental data, as shown in Figure 9. The analysis results indicate that the reverse torque of the mud pump increases approximately linearly with an increase in the rotational speed. According to the actual operating conditions, as the pump speed increases, the fluid in the pump moves rapidly accordingly. At a high speed, the excitation force of the fluid becomes higher, resulting in an increase in the reverse torque. This effect is especially significant in the areas with a high fluid velocity. The analysis results are consistent with the actual operating conditions. The minimum reverse torque is \(-320.4\) N-m at 0 rpm, while the maximum reverse torque is 3620.28 N-m at 1500 rpm. The value of the maximum reverse torque provides a reference for the selection of motors.
## 3 Results
### Dsc  
Figure 3 presents the representative heat flow plots for the CM, EDM, and OF. One definite endothermic peak occurred during the heating cycle (lower curve) of CM (Figure 3A) and OF (Figure 3C), and two indistinct exothermic peaks occurred during the cooling cycle (upper curve), whereas the DSC result of EDM showed one definite endothermic peak as well as two definite exothermic peaks (Figure 3B). Austenite start temperatures of CM, EDM and OF were 27.53, 33.91, and \(-8.8\)\({}^{\circ}\)C, respectively, and austenite finish temperatures of CM, EDM and OF were 58.3, 52.36, and 39.2 \({}^{\circ}\)C, respectively.  
Figure 2: SEM images of fractured surface after cyclic fatigue resistance test. (**A–C**) Fractured surface of HyFlex CM, HyFlex EDM, and OneFlare after test performed at RT, ductile fracture area was marked with yellow boundary; (**D–F**) magnified images of box area of (**A–C**), respectively; (**G–I**) fractured surface of HyFlex CM, HyFlex EDM, and OneFlare after test performed at BT, ductile fracture area was marked with yellow boundary; (**J–L**) magnified images of box area of (**G–I**), respectively.  
The lower curve is the heating cycle and the upper curve is the cooling cycle. The austenite start temperature (As) and austenite finish temperature (Af) are shown in the heating curve.  
Figure 3: Representative DSC results of HyFlex CM (**A**), HyFlex EDM (**B**), and OneFlare (**C**).
## 5 DoS and DDoS Defense
### Defenses against XML-DoS and HTTP-DoS Attacks
A request must go through the HTTP header filtering (HTTP floods, non-existing SOAP Action usage and content-length outliers) and then through actual XML content filtering (SOAP feature outlier detection and SOAP Action or WS-Addressing spoofing). This defense mechanism has proved to be successful at detecting and mitigating all listed vulnerabilities. In addition, it might even be able to handle unknown vulnerabilities with minimal time overhead. **Flexible, Collaborative, Multilayer, DDoS Prevention Framework (FCMDPF). ** [PERSON] et al. (2016) propose a framework composed of (1) an Outer attack Blocking (OB) at the edge router; (2) a Service Traceback Oriented Architecture (STBOA); (3) and a flexible advanced entropy based (FAEB) layer. From a blacklist database table (IP source), the OB layer blocks or forwards the incoming request. The STBOA layer is designed to validate whether the incoming request is launched by a human (real web browser) or by an automated tool (bots). A puzzle or random number is sent to the client or the requester to solve. After verification, if the puzzle or random number are correct, the request is forwarded to the next level. Otherwise, it is immediately blocked and a blacklist is updated. The FAEB layer computes entropy of overall requests to determine flash crowds or HTTP attacks. The entropy of incoming requests that are launched towards hot pages of the website determines the flash crowd. In the case of an HTTP attack, the blacklist is updated. The disadvantage of this framework lies in the information on the blacklist and its updates. **Using CAPTCHA to Mitigate HTTP-DoS Attacks. ** [PERSON] et al. (2016) propose an architecture to migrate HTTP-DoS attacks with (1) a feature extractor; (2) a clustering unit; (3) a workload calculator and (4) a filter. With a navigation log, the extractor module extracts: browsing length ratio, average stay time and the HTTP request rate to identify user groups. Every T interval, the clustering module samples the user traffic. Experiments show that for T = 15 min offers a good performance. By using the clustering report, the workload calculator computes the size and density of each cluster. The load is calculated both with the computational overhead (pageload factor) and the network bandwidth usage (number of bytes transferred for each request). Finally, if the workload exceeds a certain threshold, for each cluster, the filter provides a mechanism to filter traffic from such sources. The difficulty is to set the value of threshold as it should be proportional to the capacity of the web server. If the workload exceeds a threshold and a cluster is highly dense, then the users are suspected to be bots. The potential attackers are then challenged with a CAPTCHA to eliminate false positives.
# A Review of Multimodal Interaction in Remote Education: Technologies, Applications, and Challenges
## 4 Keyword and Correlation Analysis
### Correlation Analysis
#### 4.2.3 Feedback  
The prevalence in many studies highlights its key importance in multimodal technology practice. Maintaining an efficient provision of education is an ongoing area of research, especially in student and teacher contexts where debates often revolve around understanding and challenge, emphasizing feedback in student-teacher interaction and learner adaptation. The connection between system, model, and feedback suggests that this study is examining integrating automated and AI-powered systems of feedback, including applications in speech communication and automated testing systems, as shown in Figure 5. Furthermore, the connection between learning, cognition, and feedback suggests that methods of feedback are now being created in accordance with cognitive science to better aid in learning outcomes & optimize instructional experience.
## 2 System Model
### Baseline Scheduling Algorithm with Sub-Flow Division
#### 2.4.1 Stream Preprocessing, Filtering, and Sub-Flow Division
74:duration for a sub-stream if \(F_{(idx)}\) was to be divided based on \(T_{first\_period}\)'s scale
75:if\(target\_substream\_duration>0\)and\(t_{(idx)}>target\_substream\_duration\)then\(\triangleright\) Only divide if original stream is longer than target sub-stream duration
76:\(N_{(idx)}\leftarrow[t_{(idx)}/target\_substream\_duration]\). 77:if\(N_{(idx)}>1\)then\(\triangleright\) If sub-flow division is determined
78:for all\(x=1\) to \(N_{(idx)}\)do
79:if\(x<N_{(idx)}\)then
80:\(a_{(idx),x}\leftarrow[t_{(idx)}/N_{(idx)}]\). 91:else
92:\(a_{(idx),x}\gets t_{(idx)}-(N_{(idx)}-1)\cdot[t_{(idx)}/N_{(idx)}]\). 10:\(\triangleright\) Last sub-stream takes remainder \(\triangleright\) No sub-flow division, \(N_{(idx)}=1\)
11:else
12:\(a_{(idx),1}\gets t_{(idx)}\). 13: Store \(A_{(idx)}\), \(N_{(idx)}\), and \(\{a_{(idx),x}\}\) for \(F_{(i)}\). 14:return\(\mathcal{T}\), and parameters (\(A_{i}\), \(N_{i}\), \(\{a_{i,x}\}\)) for \(F_{i}\in\mathcal{S}_{sched}\). ```  
**Algorithm 1** Stream Preprocessing, Filtering, and Sub-Flow Division Parameter Calculation
# Effectiveness of Electrode Design Methodologies for Fast EDM Slotting of Thick Silicon Wafers
## 2 Materials and Methods  
### Experimental Setup  
All the experiments in this study have been conducted on the silicon workpiece. The initial shape of the silicon workpiece was round, with a diameter of 300 mm. EXCETEK W 350G wire EDM, Taichung City, Taiwan, was used to cut the round silicon into a rectangular shape to fit in the rise of the die-sinking EDM. The dimension and specifications of the silicon workpiece are shown in Table 1.  
The higher melting point and brittleness of silicon make the selection of the EDM electrode tricky and crucial. Graphite has good electrical conductivity, thermal conductivity, and a very high melting point compared to silicon. The machinability of the electrode, along with other electro-thermal properties, was considered while choosing an electrode material for this study, since the electrodes were machined to produce different arrays and heights of electrode legs. In this research study, graphite material of grade Poco-3 was used as an electrode (Entegris, Poco Materials, Billerica, MA, USA). The properties of Poco-3 graphite, as obtained from the product specification from Entegris website, are shown in Table 2. The dimensions of the Poco-3 graphite block are 1\({}^{\prime\prime}\)\(\times\) 1\({}^{\prime\prime}\)\(\times\) 2\({}^{\prime\prime}\) in length, breadth, and height, respectively. The tolerance of the Poco-3 electrode is \(\pm\)0.005\({}^{\prime\prime}\) and grounded on 6 sides.  
All the experiments for slotting silicon workpieces using graphite electrodes were carried out on the die-sinking EDM machine EXCETEK(r) ED 400, Taichung City, Taiwan. EDM oil (hydrocarbon oil) was used as a dielectric and all the experiments were carried out in submerged conditions, where a low and constant dielectric flow was used for flushing debris efficiently. The specifications of the EXCETEK(r) ED 400 die-sinking machine, Taichung City, Taiwan, are listed in Table 3.  
\begin{table}
\begin{tabular}{c c} \hline \hline
**Description** & **Data** \\ \hline Workpiece material & Silicon \\ Workpiece length & \(\sim\)110 mm \\ Workpiece width & \(\sim\)80 mm \\ Workpiece thickness & \(\sim\)3.74 mm \\ Density & 2.33 gm/cm\({}^{3}\) \\ Resistivity & 0.0–0.05 \(\Omega\)cm \\ Melting point & 1414 \({}^{\circ}\)C \\ Boiling point & 3265 \({}^{\circ}\)C \\ \hline \hline \end{tabular}
\end{table}
Table 1: Material properties and specification of Silicon workpiece.  
\begin{table}
\begin{tabular}{c c} \hline \hline
**Description** & **Data** \\ \hline Electrode material & Graphite \\ Grade & Poco-3 \\ Average particle size & \(<\)5 \(\upmu\)m \\ Flexural strength & 13,300 psi (935 kg/cm\({}^{2}\)) \\ Compressive strength & 18,100 psi (1273 kg/cm\({}^{2}\)) \\ Hardness & 73 shore \\ Electrical resistivity & 615 \(\upmu\Omega\)-in \\ Melting point & 3650 \({}^{\circ}\)C \\ \hline \hline \end{tabular}
\end{table}
Table 2: Material properties of graphite electrode [34] (obtained from the open-source product specification from Entegris website).
## 4 Some Numerical Examples  
In this section, we present some preliminary numerical results to illustrate the main result, Theorem 1. All codes were written in Matlab 2013b and run on Sumsung i-3 Core laptop.  
**Example 1**.: _We find a numerical example in \((\mathbb{R}^{3},\|\cdot\|_{2})\) of the problem considered in Theorem 1 of the previous section. Now, take_  
\[C:=\{x=(x_{1},x_{2},x_{3})\in\mathbb{R}^{3}:\langle a,x\rangle\geq b\},\]  
_where \(a=(2,-6,1)\) and \(b=-4\). Then we have_  
\[P_{C}(x)=\frac{b-\langle a,x\rangle}{\|a\|_{2}^{2}}a+x.\]  
_Let \(Q:=\{x=(x_{1},x_{2},x_{3})\in\mathbb{R}^{3}:\langle c,x\rangle=d\}\), where \(c=(3,5,7)\) and \(d=2\). Then we have_  
\[\Pi_{Q}(x)=P_{Q}(x)=\max\Big{\{}0,\frac{d-\langle c,x\rangle}{\|c\|_{2}^{2}} \Big{\}}c+x.\]  
_Suppose that the mapping \(T\) in Theorem 1 is defined as \(T:=P_{C}\), the metric projection on \(C\). Then the problem considered in Theorem 1 reduces to the problem:_  
\[\text{Find}\;\;x\in F(T)\cap C(=C)\;\;\text{such that}\;\;Ax\in Q. \tag{48}\]  
_Let \(\mathcal{F}\) denote the set of solutions of the problem (48) with \(\mathcal{F}\
eq\emptyset\). Furthermore, let_  
\[\alpha_{n}=\frac{1}{n+1},\;\;\beta_{n}=\frac{n}{8(n+1)},\;\gamma_{n}=\frac{n} {8(n+1)},\;\delta_{n}=\frac{3n}{8(n+1)},\;\;A=\left(\begin{array}{ccc}4&-6&- 8\\ -5&1&-5\\ -8&-5&4\end{array}\right).\]  
_Then our iterative processes (20) becomes_  
\[\left\{\begin{array}{l}x_{n}=P_{C}\big{(}u_{n}-s_{n}A^{T}(I-P_{Q})Au_{n} \big{)},\\ u_{n+1}=P_{C}\Big{[}\frac{u}{n+1}+\Big{(}1-\frac{1}{n+1}\Big{)}\Big{(}\frac{n} {2(n+1)}u+\frac{n}{8(n+1)}x_{n}+\frac{3n}{8(n+1)}P_{C}x_{n}\Big{)}\Big{]}\end{array}\right. \tag{49}\]  
_for each \(n\geq 1\). Now, we make different choices of \(u\), \(u_{1},s_{n}\) and take \(\frac{\|x_{n+1}-x_{n}\|}{\|x_{2}-x_{1}\|}<10^{-2}\) as our stopping criterion._  
**Case I.** Take \(u=(1,1,1),\;u_{1}=(3,0,4)\) and \(s_{n}=0.0137\). Then we have the numerical analysis tabulated in Table 1 and show in Figure 1.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline \(s_{n}\) & **Time Taken** & **Number of Iterations** & \(\|x_{n+1}-x_{n}\|_{2}\) & \(\|u_{n+1}-u_{n}\|_{2}\) \\ \hline \multirow{6}{*}{0.0137} & \multirow{6}{*}{0.0400} & 2 & 0.6758 & 4.2169 \\  & & 3 & 0.0122 & 0.0453 \\  & & 4 & 0.0177 & 0.0497 \\  & & 5 & 0.0158 & 0.0265 \\  & & 6 & 0.0146 & 0.0194 \\  & & 7 & 0.0130 & 0.0154 \\  & & 8 & 0.0113 & 0.0127 \\  & & 9 & 0.0098 & 0.0107 \\  & & 10 & 0.0085 & 0.0091 \\  & & 11 & 0.0074 & 0.0079 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Example 1, case I.  
**Remark 2**.: _We make the following comments from Example 1. We observe that different choices of \(s_{n}\) has no effect in terms of number of iterations obtained and the time taken for the convergence of our algorithm._