esa-sceva/satcom-chunk-collection huggingface dataset:
## 3 Results and Discussion
### Porosity Measurements and Gas Storage Capacity of **1-3**
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Polyphosphate** & **S\({}_{\text{BET}}\) (m\({}^{\text{2}}\)/g)** & **Pore Volume (cm\({}^{\text{3}}\)/gm)** & **Average Pore Diameter (nm)** \\ \hline
**1** & 82.7 & 0.11 & 2.43 \\
**2** & 213.5 & 0.32 & 1.96 \\
**3** & 86.1 & 0.13 & 2.43 \\ \hline \hline \end{tabular}  
* Polyphosphates **1-3** have a tetrahedral geometry with sp\({}^{3}\) hybridized phosphorus core [53]. The CO2 sorption isotherms for **1-3** (Figure 8) showed no apparent adsorption-desorption hysteresis, indicating possible reversible adsorption of CO2 within the pores of **1-3** at 323 K and 40 bars. The CO2 uptake for polyphosphates **1**, **2**, and **3** was 2.04, 6.00, and 4.57 wt %, respectively (Table 4). The high CO2 uptake could be due to the high S\({}_{\text{BET}}\) of the polyphosphates and strong van der Waals interaction and hydrogen bonding between CO2 and the polyphosphates. In addition, polyphosphates **1-3** contain strong Lewis base sites that help in capturing CO2. Indeed, POPs containing heteroatoms (O, N, S, or P) can capture CO2 selectively over nitrogen and methane [54; 55; 50; 56].  
The CO2 uptake using carbon-containing materials such as porous nanocarbons in the presence of additives (e.g., ethylenediamine and potassium oxalate) as media for CO2 adsorption was 1.9-4.6 mmol/g at 25 \({}^{\circ}\)C [27]. While carbon fibers containing polyacrylonitrile in the presence of potassium hydroxide led to a CO2 uptake of 2.7 mmol/g at 25 \({}^{\circ}\)C and 1 atm [28]. The CO2 uptake  
\end{table} 
Table 3: Porosity properties of **1-3**. using organotin complexes containing telmisartan as adsorbent media was in the range of 3.6-7.1 wt % at 323 K and 50 bars [51]. Polyphosphates containing benzidine showed a remarkable CO\({}_{2}\) uptake (1.8-14.0 wt %) at 323 K and 50 bars [50]. Polyphosphate **2** (_meta_-phosphate) was more effective in CO\({}_{2}\) uptake as compared with **1** (para-phosphate) and **3** (ortho-phosphate). The _meta_-phosphate geometry of **2** imparts a highly distorted network to this POP as compared to **3** and **1**. The extended surface area resulted in high CO\({}_{2}\) uptake. Polyphosphate **1** has the least distorted geometry and the lowest surface area, because of which the CO\({}_{2}\) uptake is lowest among the three polyphosphates. A similar observation has been previously made when _tris_(formylphenyl)phosphates containing benzidine were used as media for CO\({}_{2}\) capture [50].
# Early Evidence That Soil Dryness Causes Widespread Decline in Grassland Productivity in China
## 2 Materials and Methods
### Methods
#### 2.2.1 Interannual Correlation Measures
The specific formula is described as follows:  
\[P(-\text{GPP}>90\%\,|\text{VPD}>90\%)=\frac{1-P(-\text{GPP}>90\%)-P(\text{ VPD}>90\%)+C(-\text{GPP}>90\%,\text{VPD}>90\%)}{1-P(\text{VPD}>90\%)}\]  
Note that it takes a threshold above a certain value of atmospheric VPD to initiate a decline in ecosystem GPP, so we used \(-\text{GPP}\) to calculate the conditional probability in the bivariate relationship. Here, the conditional probability of \(P(-\text{GPP}>90\%\,|\,\text{VPD}>90\%)\) is identical to that of \(P(\text{GPP}<10\%\,|\,\text{VPD}>90\%)\). Therefore, above equation can be interpreted as the conditional probability of an event occurring with a GPP below \(10\%\) in the case of VPD above \(90\%\). It is expressed as follows:  
\[P(\text{GPP}<10\%\,|\text{VPD}>90\%)=\frac{1-P(\text{GPP}<10\%)-P(\text{ VPD}>90\%)+C(\text{GPP}<10\%,\text{VPD}>90\%)}{1-P(\text{VPD}>90\%)}\]  
We used percentages to define the degree of atmospheric drought and the degree of ecosystem GPP deficit, defining all samples with VPD values above \(90\%\), \(70\%\), and \(50\%\) as \begin{table}
\begin{tabular}{c c c} \hline \hline
**Copula** & **Expression of Distribution Function** & **Range of \(\theta\) Values** \\ \hline Gumbel & \(\exp\left(-\left[\left(-\ln u\right)^{\theta}-\ln v^{\theta}\right]^{1/ \theta}\right)\) & \((1,+\infty)\) \\ t & \(\int_{-\infty}^{t-1(u)}\int_{-\infty}^{t-1(v)}\frac{1}{2\pi\sqrt{1-\theta}} exp\left[1+\frac{\delta^{2}-28\delta t+\epsilon^{2}}{k(1-\theta^{2})} \right]^{-\frac{1+2}{2}d\delta t}\) & \((-1,1),k\
eq 0\) \\ Gaussian & \(\int_{-\infty}^{\infty-(u)}\int_{-\infty}^{\infty-(v)}\frac{1}{2\pi\sqrt{1- \theta^{2}}}exp\left[1+\frac{\delta^{2}-28\delta t+\epsilon^{2}}{k(1-\theta^{2 })}\right]^{-\frac{1+2}{2}d\delta t}\) & \((-1,1),k\
eq 0\) \\ \hline \hline \end{tabular}
\end{table} 
Table 1: _Cont._severe, moderate, and mild atmospheric drought and all samples with GPP values below 10%, 30%, and 50% as severe, moderate, and mild vegetation deficit. Unlike atmospheric drought, a soil drought event can only be recognized as occurring when soil moisture falls below a certain threshold. We focused on the joint probability of extreme SM (below 10%, 30%, 50%) and GPP (below 10%, 30%, 50%). Thus, the conditional probability of a decline in ecosystem GPP in the presence of an extreme soil drought event can be derived by combining the [PERSON] equation described as:  
\[P(\text{GPP}<10\%|\text{SM}<10\%)=\frac{C(\text{GPP}<10\%,\text{SM}<10\%)} {P(\text{SM}<10\%)}\]  
Similarly to atmospheric drought, we defined severe, moderate, and mild soil drought for all samples with SM values below 10%, 30%, and 50%.
## 3 Experimental Results
The crater parameters of all the impact craters obtained in the experiments are listed in Table 2, including the depth \(H\), the diameter \(D\), the volume \(V\), the depth-diameter ratio \(H\)/\(D\), the dimensionless depth \(H\)/\(l\), the dimensionless diameter \(D\)/\(d\), and dimensionless volume \(V\)/\(ld^{2}\) of the craters. After the impact, the projectiles were deformed, eroded and broke into small pieces, all of which fell to the ground. No projectile was observed to have stuck in the impact crater. The remainders of  
\begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline
**Shot No. ** & \(\rho_{p}\)/\(\rho_{t}\) & \(H\) **(cm)** & \(D\) **(cm)** & \(V\) **(cm3)** & \(H\)/\(D\)** & \(H\)/\(l\)** & \(D\)/\(d\)** & \(V\)/\(ld^{2}\)** & **Target No. ** \\ \hline
1 & 1.71 & 5.89 & 26.85 & 1133 & 0.22 & 1.61 & 14.65 & 91.98 & T26 \\
2 & 1.71 & 6.90 & 34.80 & 2288 & 0.20 & 1.88 & 19.01 & 186.36 & T01 \\
3 & 1.71 & 7.25 & 50.51 & 5195 & 0.14 & 1.98 & 27.60 & 423.38 & T13 \\
4 & 1.71 & 8.03 & 48.94 & 5838 & 0.16 & 2.19 & 26.70 & 474.22 & T02 \\
5 & 1.71 & 9.33 & 54.50 & 9033 & 0.17 & 2.55 & 29.77 & 735.36 & T32 \\
6 & 3.02 & 6.13 & 31.12 & 1510 & 0.20 & 2.01 & 20.46 & 213.79 & T24 \\
7 & 3.02 & 8.41 & 37.12 & 2694 & 0.23 & 2.76 & 24.40 & 382.18 & T20 \\
8 & 3.02 & 8.76 & 49.49 & 5530 & 0.18 & 2.87 & 32.54 & 784.50 & T19 \\
9 & 3.02 & 9.76 & 49.42 & 6576 & 0.20 & 3.20 & 32.47 & 931.05 & T04 \\
10 & 3.02 & 9.74 & 61.07 & 10,130 & 0.16 & 3.20 & 40.12 & 1435.18 & T30 \\
11 & 6.86 & 7.77 & 31.90 & 1738 & 0.24 & 3.32 & 27.45 & 550.55 & T22 \\
12 & 6.86 & 9.94 & 51.43 & 6012 & 0.19 & 4.27 & 44.30 & 1916.72 some projectiles were recovered carefully after the impact experiments. Figure 9 shows the photographs of the typical recovered projectiles. The effects of deformation and damage of the projectiles on impact craters will be a topic of more detailed study in the future.
## 1 Introduction
Therefore, this study preserves the complete bat algorithm process, augmenting it with non-dominated sorting and crowding distance calculations from NSGA-II, establishing the multi-objective bat algorithm (MOBA) to provide comprehensive optimization strategies. In algorithmic frameworks, the selection of hyperparameters profoundly impacts performance. Discovering suitable hyperparameters necessitates numerous experiments, which prove time-consuming and intricate and do not assure optimal findings. This paper addresses the critical role of hyperparameter selection in algorithmic performance and introduces reinforcement learning to enhance parameter tuning in multi-objective optimization algorithms. It discusses the integration of NSGA-II and SARSA into NSGA-RL by [PERSON] et al. [9] and the use of Q-learning by [PERSON] et al. [10] to refine the parameters for MOPSO. The comparison highlights the risk differences between Q-learning and SARSA, emphasizing SARSA's lower risk and superior learning effectiveness [11]. This paper proposes applying an enhanced-learning-based multi-objective bat algorithm to the task-offloading decision-making process in edge computing, addressing the trade-off between latency and energy consumption. The distinctive features of this study can be summarized as follows:  
1. This study optimizes edge computing task-offloading decisions to address network latency and energy consumption issues, aiming to prolong the lifespan of smart devices. 2. Retaining the bat algorithm's (BA) single-objective optimization process, we introduce multi-objective optimization to create the multi-objective bat algorithm (MOBA). This approach proposes multiple objective decisions to select candidates from intricate solution variances, fostering evolutionary progress. 3. Enhanced-learning SARSA is integrated to automatically adjust the hyperparameters of the multi-objective bat algorithm, simplifying complex hyperparameter experiments and statistical analyses. Moreover, we introduce an automated mechanism to adjust the search scope, enhancing overall performance. 4. Customized multi-objective functions are devised within the edge computing framework, considering intelligent mobile devices' remaining energy and computational capacities. A custom-enhanced learning reward function is also proposed based on the edge computing objective function.
## 4 Resource Allocation Mechanism
### Interference Clustering + Improved Genetic Algorithm  
For the joint allocation of bandwidth and power, many scholars have adopted genetic algorithms to solve them. However, as mentioned in Section 3.1, with the increase of the number of beams, the search space for all beams to be optimized together is very large, which will lead to slow convergence of the algorithm and cannot obtain a satisfactory solution.  
In addition, in order to avoid CCI, many articles set a distance threshold. More specifically, it is generally considered that there is no interference if the distance between two cells exceeds four times the radius of the cell, i.e., non-adjacent cells. On the one hand, it is inaccurate to measure interference based on distance. From the antenna model in Section 3.3, we can easily discover that the change of gain with an off-axis angle is not monotonic, and the distance between two cells is not in a one-to-one correspondence with their off-axis angle. On the other hand, it is unrealistic to restrict adjacent cells from being illuminated at the same time slot in order to avoid CCI, which will cause the beam to hop back and forth between two adjacent hot spots.
## 3 Materials and Methods
### The EduDCM Framework
#### 3.1.3 Heuristic Alignment  
The tentative labels generated by the LLM are refined by aligning them not only with predefined categories but also with specific examples in the knowledge base. Using Sentence-BERT, each unannotated utterance and the sampled examples are embedded into a high-dimensional semantic space. The cosine similarity between the embedding vectors is calculated as follows:  
\[\text{Sim}(u,e)=\frac{1}{m}\sum_{j=1}^{m}\frac{\vec{u}\cdot\vec{e}_{j}}{\|\vec{u }\|\|\vec{e}_{j}\|} \tag{1}\]  
where \(\vec{u}\) represents the embedding of the unannotated utterance, \(\vec{e}_{j}\) represents the embedding of the \(j\)-th sampled example from the knowledge base, and \(m\) is the number of sampled examples. The mean similarity \(\text{Sim}(u,e)\) is used to determine alignment. If \(\text{Sim}(u,e)\geq\theta\), the utterance is considered aligned with the category associated with the sampled examples. The threshold \(\theta=0.88\) was determined experimentally to balance precision and recall. Additionally, context-aware embeddings aggregate the surrounding utterances to improve alignment in complex or ambiguous scenarios. When no matches  
Figure 1: Workflow of the EduDCM framework. This figure illustrates the four key stages of the EduDCM framework: first, LLM-Driven Context-Aware Label Generation, where unannotated text is processed by an LLM to generate labeled text; second, Knowledge Base Construction, where a knowledge base built from the TalkMoves dataset supports classification into three pedagogical categories; and finally, Heuristic alignment and semantic disambiguation, where annotated text is aligned with knowledge base examples through semantic similarity, with context embeddings used to refine the alignment and dynamically adjust thresholds to ensure accuracy.  
meet the threshold, a dynamic adjustment mechanism iteratively lowers \(\theta\) or expands the search to neighboring categories, formalized as  
\[\theta^{\prime}=\theta-\Delta\theta \tag{2}\]  
where \(\Delta\theta\) is the adjustment step size.
## 3 Influence of Boundary Distance in the Integral Response Deformation Method
### Influence of the Bottom Artificial Boundary Distance
#### 3.2.2 Soil Stress  
Figure 8 presents the shear stress distributions in the geotechnical medium under varying \(R_{B}\). As \(R_{B}\) increases, the shear stress levels in the soil surrounding the structure gradually decrease, indicating a weakening of the constraints imposed by the bottom boundary. Specifically, when \(R_{B}\leq 1.0\), the bottom boundaries are too close to the structure, imposing excessive constraints and causing elevated stress levels in the surrounding area, especially near the floor. As \(R_{B}\) increases to the range of 2.0-3.0, the shear stress levels around the structure decrease significantly, although residual boundary effects remain observable. When \(R_{B}\geq 3.0\), the influence of the bottom boundary on the soil stresses becomes negligible, and the shear stress distribution stabilizes to a converged state.  
A comprehensive analysis reveals that the bottom boundary distance plays a crucial role in the computational accuracy of the IRDM. When the bottom boundary is too close to the structure, the intensified constraints imposed by fixed boundaries distort the stress distributions in the surrounding soil, thereby undermining computational accuracy and resulting in reliability. To ensure the validity of the IRDM, the vertical distance from the structural floor to the bottom boundary should be set to at least three times the vertical height of the underground structure while also adhering to prescribed lateral boundary distance requirements.
# Autonomous Intersection Management by Using Reinforcement Learning
## 3 Methodology
### Brake-Safe Control
#### 3.3.1 Model  
The vehicles' longitudinal can be modeled as follows. Let \(x_{i}=(y_{i},v_{i})^{\prime}\in X_{i}\) be the state of vehicle \(i\), consisting of the longitudinal position \(y_{i}\) and velocity \(v_{i}\) along its path \(\varphi_{i}\). Note that the state \(x_{i}\) here is different from state \(s_{i}\). The state and control constraints are given as \(X_{i}=[0,\bar{y_{i}}]\times[0,\bar{v_{i}}]\) and \(U_{i}=[\underline{u_{i}},\bar{u_{i}}]\). \(\bar{y_{i}}\) is the end point of the given path. Vehicles are considered as leaving the system if \(y_{i}=\bar{y_{i}}\). \(\underline{u_{i}}\) and \(\bar{u_{i}}\) represent the minimum and maximum acceleration values.  
The evolution of state is described by the differential equation  
\[\dot{y_{i}}(t)=v_{i}(t) \tag{1}\]  
\[\dot{v_{i}}(t)=u_{i}(t)\delta\Big{(}u_{i}(t),v_{i}(t)\Big{)}, \tag{2}\]  
where \(\delta\) is a binary function that ensures \(v_{i}\in[0,\bar{0}_{i}]\) at all times. That is, \(\delta(u_{i}(t),v_{i}(t))=1\) except for \((v_{i}(t)=0)\cap(u_{i}(t)<0)\) and for \((v_{i}(t)=\bar{v_{i}})\cap(u_{i}(t)>0)\), i.e., if (1) the velocity \(v_{i}(t)\) is zero and the accelerate \(u_{i}(t)\) is negative or (2) the velocity \(v_{i}(t)\) reaches the maximum value and the accelerate \(u_{i}(t)\) is positive, then the output \(\delta\) function will be zero. Let \(y_{i}(t,u_{i}x_{i}(t_{0}))\) denote the position of vehicle \(i\) at time \(t\), starting from \(x_{i}(t_{0})\).  
For a pair of vehicles \(i\), \(j\in N\) such that vehicle \(j\) has priority over \(i\), the authors denote **completed obstacle region**\(R_{\varphi(j)<\sigma(i)}\) the set of positions \((y_{i}\),\(y_{j})\) leading to a collision or a violation of priority \(\sigma(j)<\sigma(i)\) (i.e., vehicle \(i\) crossed the intersection earlier than vehicle \(j\)).
# Full-Field Strain Determination for Additively Manufactured Parts Using Radial Basis Functions
## 2 Surface Strain Determination  
We assume that a DIC-system provides a set of coordinates of so-called facet points \(\vec{x}_{k}(t_{n})\), \(k=1,\ldots,n_{\mathrm{D}}^{(n)}\), at time \(t_{n}\), \(n=0,\ldots,n_{\mathrm{DIC}}\). Here, \(n_{\mathrm{DIC}}\) represents the number of times pictures of a \"configuration\" are taken. Thus, \(n_{\mathrm{D}}^{(n)}\) is the number of spatial coordinates at time \(t_{n}\). The coordinates in the initial configuration of a \"material point\" \(\vec{X}_{k}=\vec{x}_{k}(t_{0})\) are used to calculate the displacement of the \(k\)-th point \(\vec{u}_{k}(\vec{X}_{k},t_{n})=\vec{x}_{k}(t_{n})-\vec{X}_{k}\). These are \(n_{\mathrm{D}}^{(n)}\) displacement vectors at time \(t_{n}\), which can vary depending on whether \(\vec{x}_{k}(t_{n})\) can be detected by the DIC-system or not. There are several questions to be treated. First, what is the displacement of a material point \(\vec{X}_{k}\) at time \(t_{n}\) if the DIC-system is not able to detect \(\vec{x}_{k}(t_{n})\) in time properly? Second, how can one determine the in-plane strain tensors that are based on some in-plane gradient? Third, how can one obtain the spatial velocity (or even the in-plane strain-rate tensor)? Thus, particular interpolation concepts in space and time are required. The interpolation in time is commonly performed by a linear interpolation, whereas two local concepts are employed for spatial interpolations. The first local approach uses a linear tangential surface which is based on a regression analysis of points around the evaluation point, see [3], and in more detail [4]. Alternatively, shape functions from the finite element method are chosen, where the triangulation is the simplest approach [4; 5; 6]. The first approach has the disadvantage that multiple interpolations are required. The second approach, however, only leads to piece-wise continuous displacements, so that the strains have jumps. This can be circumvented for principal strains (or stretches) by averaging at the measurement points, but with the disadvantage that this is not applicable to the principal strain directions. In this context, gradients are only calculable in the interior of the local interpolation regions, but not at the bounds. A further disadvantage is the necessity to find the element for a given point that is required for the evaluation. This leads to additional computational effort. Thus, we are interested in a global interpolation scheme. For this purpose, we use radial basis functions. In this article, the question is followed, what accuracy can be expected for smooth and rough surfaces?  
In the first step, the theory of strain determination in curvilinear surfaces is recapped in Section 2.1. Afterwards, Section 2.2 discusses the concept using RBFs, followed by an investigation of RBFs in strain determination in Section 2.3.
# Data-Driven Analysis of Outdoor-to-Indoor Propagation for 5G Mid-Band Operational Networks
## 2 Background, Related Work, and Contributions
### Relevant Experimental Studies
Both studies showed that the MPC power decay factor at 3.5 GHz is lower than the one observed at 28 GHz; however, the cluster decay rate is higher at 3.5 GHz than at 28 GHz. In [13], it was also observed that CIRs at 28 GHz could be characterized by a single cluster of paths, while more than one cluster is likely to exist at 3.5 GHz. In particular, as also shown in [10], the authors highlighted that the RMS delay spread at 3.5 GHz is higher than at 28 GHz. Similarly, the path loss analysis at 3.5 GHz to 28 GHz was carried out in [11; 31] an indoor environment. Both studies showed that the path loss exponent is lower at 3.5 GHz than at 28 GHz in both LOS and NLOS cases. In [6], the authors discussed RMS delay spread and path loss, showing that RMS delay spread increases with path loss. In [45], the authors presented large-scale radio channel measurements, performed in urban and suburban environments of different countries, in a frequency range from 0.8 GHz up to 73 GHz. This work presents an overview of the path loss model adopted in the recommendation ITU-R P.1411-10 (2019-08) and gives the data analysis with the approach to derive this adopted path loss model. It is worth to highlight that this work is one of the few works that analyzes how different channel parameters (RMS delay spread and path loss in this case) are mutually correlated, thus taking a further step towards better understanding the relationships among propagation characteristics. As anticipated in Section 1, beamforming strategy is an integral part in the design and deployment of a 5G network; however, it is worth remarking that none of the above studies addressed the impact of beamforming strategies on channel propagation characterization. A comparison table of this presented research work with the existing literature is given is Table 1.
## 3 Numerical Uncertainty Analysis
### Evaluation of the Results
#### 3.2.1 Sparsity  
Because the coefficients \(-\frac{k}{m}\) and \(-\frac{d}{m}\) to be identified appear only in the second row of Equation (7), the results corresponding to the second row of Equation (7) were selected for the evaluation. That means that the real NNZC equals two and the signal \(\vec{q}(t)\) is used to deliver the spectrum for further evaluation.  
To compare the NNZC with these two methods, the results from the data set \(Ord=3\) and \(\epsilon_{N}=0.005\) were used at first as an example to present the distribution of NNZC. As shown in Figure 3, 8847 out of 10,000 examples identified by LSST had six or seven coefficients. By contrast, 9606 NNZCs identified by the LSPL method had exactly two coefficients.  
Figure 2: Comparison of the amplitudes of velocity signals with initial states \(\mathbf{x}(0)\), \(\mathbf{x}_{1}^{*}(0)\), and \(\mathbf{x}_{2}^{*}(0)\).  
The median, 0.25 quantile, and 0.75 quantile were chosen to represent the NNZCs of all 25 MCSs with five different noise factors and five polynomial orders in Figure 4. The total numbers of candidate functions for each polynomial order are marked by horizontal lines with corresponding colors, which are also the maximum possible values of NNZC. The classic combination of mean value and standard deviation is not appropriate under this circumstance because the distribution of NNZC is strongly asymmetric, as shown in Figure 3. On the left side of Figure 4, the NNZC of the LSST method has a clear dependency on the noise factor \(\epsilon_{N}\) and polynomial order \(Ord\). Except for the identification with \(Ord=1\), more coefficients were identified with a higher noise factors. From left to right, the curves for each order \(Ord>1\) increase steeply on the low noise side and then flatten on the high noise side, which indicates a saturated character.  
On the contrary, the NNZC of the LSPL method does not rise substantially with the noise factor \(\epsilon_{N}\); see Figure 4b. The medians of all MCSs do not vary from the true number of coefficients. Only in the MCSs with \(Ord\geq 3\) and \(\epsilon_{N}\geq 0.0075\), a change of the 0.75 quantile occurs up to 3. Compared to LSST, the LSPL method identifies the sparsity of the numerical model with a significant advantage of precision, which means that LSPL has a lower risk of overfitting.  
Figure 4: Median and quantile of NNZC with methods (**a**) LSST and (**b**) LSPL. The horizontal dotted lines mark the maximal numbers of candidate functions for each polynomial order.  
Figure 3: Distribution of NNZC of the methods (**a**) LSST and (**b**) LSPL, \(Ord=3\), \(\epsilon_{N}=0.005\).