esa-sceva/satcom-chunk-collection huggingface dataset:
## 3 Calculation Results
In Figure 4, the spectral response of the NF absorption, calculated based on Equation (30), is also plotted in the evanescent region of \(u>1\). For all the dipole positions, the spectral response of the NF absorption becomes closer to the total spectral power density at the larger normalized in-plane wave vectors. Thus, the contribution of the NF absorption to the total power dissipation spectrum becomes more important than that of the SP modes when the in-plane wave vector becomes very large in the evanescent region. To further investigate how the dipole emitter position in the EML affects the power dissipation of the dipole emitter, the relative radiated power of all the optical modes is calculated. The polarization-dependent relative optical power of each optical mode induced by a dipole emitter together with the total power dissipation is calculated by [9; 12]  
\[F_{\parallel(\perp),total}^{TE(TM)}=\int_{0}^{\infty}K_{\parallel(\perp)}^{ TE(TM)}(u)du^{2}=\int_{0}^{\infty}K_{\parallel(\perp)}^{TE(TM)}(u)udu, \tag{31}\]  
\[F_{\parallel(\perp),out}^{TE(TM)}=\int_{0}^{u_{crit}}K_{\parallel(\perp),out} ^{TE(TM)}(u)du^{2}=\int_{0}^{u_{crit}}K_{\parallel(\perp),out}^{TE(TM)}(u)udu, \tag{32}\]  
\[F_{\parallel(\perp),abs}^{TE(TM)}=\int_{0}^{u_{crit}}K_{\parallel(\perp),abs} ^{TE(TM)}(u)du^{2}=\int_{0}^{u_{crit}}K_{\parallel(\perp),abs}^{TE(TM)}(u)udu, \tag{33}\] \begin{table}
\begin{tabular}{c c c c} \hline
**Dipole Position (nm)** & **TM0** & **TM1** & **TM2** \\ \hline \(10\) & \(1.849+0.0211i\) & \(2.133+0.0521i\) & \(2.636+0.1447i\) \\ \hline \(125\) & \(1.852+0.0211i\) & \(2.125+0.0521i\) & \(2.605+0.1447i\) \\ \hline \(240\) & \(1.849+0.0211i\) & \(2.123+0.0521i\) & \(2.650+0.1447i\) \\ \hline \end{tabular}
\end{table} 
Table 2: Effective mode indices of TM modes obtained by the Lorentzian line shape-based fitting to the total power dissipation spectrum. \[F_{\parallel,\text{WG}}^{\text{TE}}=\int_{u_{crit}}^{\infty}K_{\parallel}^{\text{TE} }(u)du^{2}=\int_{u_{crit}}^{\infty}K_{\parallel}^{\text{TE}}(u)udu, \tag{34}\]  
\[F_{\parallel(\perp),\text{WG}}^{\text{TM}}=\int_{u_{crit}}^{1}K_{\parallel(\perp )}^{\text{TM}}(u)du^{2}=\int_{u_{crit}}^{1}K_{\parallel(\perp)}^{\text{TM}}(u) udu, \tag{35}\]  
\[F_{\parallel(\perp),\text{SP}}^{\text{TM}}=\int_{1}^{\infty}K_{\parallel(\perp ),\text{SP}}^{\text{TM}}(u)du^{2}=\int_{1}^{\infty}K_{\parallel(\perp),\text{SP }}^{\text{TM}}(u)udu, \tag{36}\]  
\[F_{\parallel(\perp),\text{NF}}^{\text{TM}}=\int_{1}^{\infty}K_{\parallel(\perp ),\text{NF}}^{\text{TM}}(u)du^{2}=\int_{1}^{\infty}K_{\parallel(\perp),\text{ NF}}^{\text{TM}}(u)udu, \tag{37}\]  
where \(u_{crit}=n_{air}/n_{EML}\) indicates the normalized in-plane wave vector for the critical angle. In general, the optical power dissipation of the air mode (\(0\leq u\leq u_{crit}\)) is divided into the out-coupled air mode and absorption loss [22; 36].
## 3 Proposed Methods
### Heuristic Scheduling Methods  
The heuristic scheduling methods follow the algorithm framework of RS, but without the state prediction and rule-based reasoning steps. Furthermore, the calculation of the target weight is changed to a deterministic calculation method. According to the target selection strategies mentioned in RS, three weight calculation strategies are proposed including the observation-priority strategy, data transmission-priority strategy, and electricity-priority strategy. The observation priority strategy allows the satellite to observe more targets, the data transmission-priority strategy allows the satellite to acquire more data transmission opportunities, and the electricity-priority strategy allows the satellite to obtain more charging electrical energy. Furthermore, three heuristic scheduling methods were constructed corresponding to different target selection strategies including the observation-priority heuristic algorithm (OPH), data transmission-priority heuristic algorithm (DPH), and the electricity-priority heuristic algorithm (EPH). Among all of these algorithms, OPH draws upon the existing method [34; 35] using the strategy of maximum backward time slack, while DPH and EPH are two heuristic methods that we proposed based on the mission scenario analysis in this study.  
The target weight calculation in OPH can be calculated as  
\[w_{i}=\frac{v_{i}\text{max}\Big{(}\Delta t_{lbS,i}^{p}\Big{)}}{t_{e}-t_{s}}. \tag{23}\]  
The target weight calculation in DPH can be expressed as  
\[w_{i}=c_{o}\frac{v_{i}\text{max}\Big{(}\Delta t_{lbS,i}^{p}\Big{)}}{t_{e}-t_{s }}+c_{d}status_{datatrans}^{i}. \tag{24}\]  
The target weight calculation in EPH can be expressed as  
\[w_{i}=c_{o}\frac{v_{i}\text{max}\Big{(}\Delta t_{lbS,i}^{p}\Big{)}}{t_{e}-t_{s }}+c_{e}flag_{ele}\big{(}1-\big{|}\varphi_{power}-\varphi_{i}\big{|}\big{)}. \tag{25}\]
###### Abstract  
Background: In cases of moderate to severe dental discoloration, vital tooth whitening usually requires a prolonged treatment time if it is to obtain satisfactory outcomes. Variations in the clinical efficacy of whitening products in terms of their concentration and application time mean that we need to be aware of the real bleaching capacity of each whitening method and each product. This randomized clinical trial aimed to analyze with a spectrophotometer the effect of the number of in-office vital tooth whitening sessions (one or two) on the number of weeks of ensuing home whitening until color stability was obtained. Methods: Twenty patients with moderate/severe discoloration were treated with combined vital tooth whitening. Ten patients were treated with a single in-office session consisting of two applications of a product containing 40% hydrogen peroxide, followed by home treatment with individualized splints and a 16% carbamide peroxide gel (Group 1S). The other ten patients (Group 2S) were treated in two in-office sessions with two applications of the same product as Group 1S, followed in the same way by home treatment. Results: Comparing the two groups (1S and 2S), no significant differences in Euclidean distance (\(\Delta\)E) were found after in-office whitening, or when color stabilization was obtained and home whitening ceased. Significant differences in the number of weeks of home whitening until color stabilization reached the same outcomes were found between 1S and 2S; 1S required a mean of 11.6 weeks home whitening, while 2S required 8.2 weeks. Conclusions: Combined tooth whitening with two in-office sessions significantly reduces the number of weeks (by three to four weeks) of subsequent home tooth whitening needed to reach color stabilization.  
combined vital tooth whitening; hydrogen peroxide; carbamide peroxide; tooth discoloration
## 4 Results and Discussion  
### Simulation Results  
In order to determine the influence of the nozzle geometry and the carrier gas flow on the present oxygen concentration, a parameter sweep of the carrier gas volume flow and shield gas volume flow were carried out for both nozzles. Results are shown in Figures 6 and 7.  
Figure 6: Parametric sweep of the carrier gas volume flow and shield gas volume flow of the three-jet nozzle. **Top**: Oxygen concentration in an isometric view. **Bottom**: Oxygen concentration on workpiece surface.  
As can be seen from Figures 6 and 7, the three-jet nozzle is more sensitive to a variation in the carrier and shield gas volume flow in relation to the coaxial nozzle. From a carrier gas flow to shield gas volume flow ratio of greater than 0.4, the three-jet nozzle exhibits significantly higher oxygen concentrations. Furthermore, the oxygen concentration on the substrate surface is more homogeneous for the coaxial nozzle.
# Generalized Paxos Made Byzantine
## 2 Background and Overview
### Paxos and Its Variants
#### 2.1.2 Fast Paxos  
Fast Paxos observes that it is possible to improve on the previous latency (in terms of common case message steps) by allowing proposers to propose values directly to acceptors [12]. To this end, the protocol distinguishes between fast and classic ballots, where fast ballots bypass the leader by sending proposals directly to acceptors and classic ballots work as in Basic Paxos. The reduced latency of fast ballots comes at the additional cost of using a quorum size of \(n-e\) instead of a classic majority quorum, where \(e\) is the number of faults that can be tolerated while using fast ballots. In addition, instead of the usual requirement that \(n>2f\), to ensure that fast and classic quorums intersect, a new requirement must be met: \(n>2e+f\). This means that if we wish to tolerate the same number of faults for classic and fast ballots (i.e., \(e=f\)), then the total number of replicas is \(3f+1\) instead of the usual \(2f+1\) and the quorum size for fast and classic ballots is the same. The optimized commit scenario occurs during fast ballots, in which only two messages broadcasts are necessary: _phase 2a_ messages between a proposer and the acceptors, and _phase 2b_ messages between acceptors and learners. This creates the possibility of two proposers concurrently proposing values to the acceptors and generating a conflict, which must be resolved by falling back to a recovery protocol.
# A Multiple-Step, Randomly Delayed, Robust Cubature Kalman Filter for Spacecraft-Relative Navigation
## 6 Numerical Simulations
### Simulation Results and Analyses  
Monte Carlo simulations were conducted to evaluate the effectiveness of several filters for estimation. Then, the root-mean-square error (\(RMSE\)) and the average RMSE (\(ARMSE\)) of the state estimations were calculated, as follows:  
\[RMSE_{k}(i)=\sqrt{\frac{1}{M}\sum_{m=1}^{M}\left(\hat{\pi}_{k}^{m}(i)-x_{k}^{m} (i)\right)^{2}} \tag{67}\]  
\[ARMSE(i)=\frac{1}{k_{n}-k_{0}}\sum_{k=k_{0}}^{k_{n}}RMSE_{k}(i) \tag{68}\]  
where \(M\) denotes the number of Monte Carlo simulations. \(k\) is the \(k\)-th instant, and \(\hat{\pi}_{k}^{m}\) and \(x_{k}^{m}\) are the estimation and the true value, respectively.  
Figures 8-11 compare the performances of the CKF, ORD-CKF, MRD-CKF, and MRD-DCSCKF. The simulation results show that CKF had the worst estimation. The performance of ORD-CKF was between CKF and MRD-CKF because ORD-CKF could only handle one-step randomly delayed measurements. The performance of MRD-CKF was significantly better than CKF and ORD-CKF because it could handle multiple-step randomly delayed measurements. There is no doubt that MRD-DCSCKF had the best performance among all filters. MRD-DCSCKF adopts the multiple-step randomly delayed filtering framework in combination with the DCS kernel function, which enables its ability to address both delayed measurements and outliers.  
Figure 7: The nominal trajectory of the chief spacecraft.  
Figure 8: RMSEs of the position with CKF, ORD-CKF, MRD-CKF, and MRD-DCSCKF.  
Figure 9: RMSEs of the velocity with CKF, ORD-CKF, MRD-CKF, and MRD-DCSCKF.  
Figure 11: RMSEs of the gyro drift with CKF, ORD-CKF, MRD-CKF, and MRD-DCSCKF.  
Figure 10: RMSEs of the attitude with CKF, ORD-CKF, MRD-CKF, and MRD-DCSCKF.  
Figure 12: Position error.  
Figure 13: Velocity error.  
Simulations to investigate the effects of delay probability on the MRD-DCSCKF were conducted, and Figures 16-19 show the ARMSEs from 450 to 600 s with delay probabilities of \(0\leq p\leq 0.2\). It is clear that MRD-DCSCKF achieved the highest estimation accuracy among the four filters.  
Figure 14: Attitude error.  
Figure 15: Gyro drift error.  
Figure 16: ARMSEs of position under different delay probabilities.  
Figure 17: ARMSEs of velocity under different delay probabilities.  
Figure 19: ARMSEs of gyro drift under different delay probabilities.  
Figure 18: ARMSEs of attitude under different delay probabilities.  
Figure 21: ARMSEs of velocity under different perturbing parameters.  
Figure 20: ARMSEs of position under different perturbing parameters.
## 3 Results  
Baseline characteristics of CS, CS70, CS90, and CG are shown in Table 1. Frequency of male gender, DM, HT, and age were proven to be significantly higher among CS when compared to CG (\(p\) = 0.0004, \(p\) < 0.00002, \(p\) < 0.00002, and \(p\) < 0.00002, respectively). Statistically significant differences between CS70 and CS90 groups were not found. The Tth111I, N363S, or ER22/23 EK-_NR3C1_ genotypes were found to be in Hardy-Weinberg equilibrium in both CS and CG (\(p\) > 0.05). The three loci were then examined for the level of LD in the entire group (\(n\) = 205). The estimated values of D' were equal to 1 for each pair of loci. The results of an association of the Thh111I, N363S, or ER22/23 EK polymorphisms of the _NR3C1_ gene with CA stenosis are summarized in Table 2. We did not observe any significant association between the occurrence of the disease and the variants tested. No significant association between Thh111I, N363S, or ER22/23 EK-_NR3C1_ polymorphisms and the severity of CA stenosis were found when CS70 vs. CS90 were compared (Table 3). Moreover, no significant associations were found among Thh111I, N363S, or ER22/23 EK alleles or haplotypes and the occurrence or severity of CA stenosis (Tables 2 and 3). \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Parameter** & **CG (\(n\) = 88)** & **CS (\(n\) = 117)** & \(p\) **CG vs. CS a** & **CS70 (\(n\) = 61)** & **CS90 (\(n\) = 56)** & \(p\) **CS70 vs. CS90 a** \\ \hline Male gender & 39.77\% & 64.96\% & 0.0004 & 65.57\% & 64.29\% & 1.00 \\ \hline Age years & 60.14 \(\pm\) 8.25 & 72.61 \(\pm\) 7.96 & \textless{}0.00002 & 72.98 \(\pm\) 7.24 & 72.20 \(\pm\) 8.66 & 0.656 \\ \hline BMI (kg/m\({}^{2}\)) & 27.40 \(\pm\) 3.85 & 27.74 \(\pm\) 3.80 & 0.674 & 28.07 \(\pm\) 3.90 & 27.39 \(\pm\) 3.66 & 0.304 \\ \hline Dyslipidemia & 73.86\% & 64.96\% & 0.223 & 62.30\% & 67.86\% & 0.565 \\ \hline DM & 14.77\% & 49.57\% & \textless{}0.00002 & 49.18\% & 50.00\% & 1.00 \\ \hline HT & 54.55\% & 86.32\% & \textless{}0.00002 & 85.25\% & 87.50\% & 0.792 \\ \hline Smoking & 12.50\% & 12.82\% & 1 & 11.48\% & 14.29\% & 0.784 \\ \hline \hline \end{tabular}  
* CC—control group; CS—patients with CA stenosis; CS70—patients with 70–99% stenosis; CS90—patients with 90% or more stenosis; DM—diabetes mellitus; HT—arterial hypertension. Data are given as mean \(\pm\) SD or %. a \(p\)-values were calculated with Mann–Whitney test for quantitative variables and with [PERSON]’s exact test for qualitative variables.  
\end{table} 
Table 1: Baseline characteristics of CG and CS.
## 2 Materials and Methods  
### Sample Preparation  
The studied soil was a diatom-kaolin mixture (DKM) comprising Georgia kaolin (RP-2; Active Minerals International, Baltimore, MD, USA) and diatom from Changbai Prefecture, Jilin, China. Figure 1 gives the mineral and chemical compositions of kaolin and diatom as revealed by X-ray diffraction and X-ray energy-dispersive spectroscopy: diatom comprises quartz and opal with no clay minerals, which is consistent with the high contents of Si and O elements; kaolin has a dominant mineral content of kaolinite with traces of illite and quartz, in which the content of illite and quartz are ca. 1.8% and 1.2%, respectively. Table 1 summarizes the physical properties of the diatom and kaolin as determined by ASTM standards. Diatom has lower \(G_{\rm S}\) (2.25), significantly higher specific surface area (179.5 m\({}^{2}\)/g), higher activity (\(A_{\rm d}\)) (0.87), and cation exchange capacity (32.3 meq/100 g) compared with kaolin.  
DKM samples with varying diatom proportions (0-100%) in terms of dry mass ratio were prepared to investigate the influence of diatom content on the consistency limits of fine-grained DS. To ensure that the water in diatom materials is completely removed before preparing DKM with a certain diatom content, the diatoms and kaolin materials were dried at 105 \({}^{\circ}\)C for 24 h. The DKM samples were prepared by thoroughly mixingdiatom and kaolin using mechanical stirring. For convenience, each prepared DKM sample was indexed as \"diatom content D-kaolin content K\", where D refers to the diatoms and K refers to the kaolin; for example, the DKM sample indexed as 40D-60K contained 40% diatoms and 60% kaolin.
## 3 Results and Discussions
### Effect of Co-Existing Ions  
For the estimation of the method's tolerance limit towards the ions that co-exist in the sample matrix, the effect of coexisting ions was studied. In order to have satisfactory tolerance, the analyte recovery must remain between 85 and 115% in the presence of other ions. For Cu and Pb, the material shows satisfactory selectivity for 5000 mg L\({}^{-1}\) K\({}^{+}\), 5000 mg L\({}^{-1}\) Na\({}^{+}\), 100 mg L\({}^{-1}\) Ca\({}^{2+}\) and Mg\({}^{2+}\), 500 ug L\({}^{-1}\) As\({}^{3-}\), 500 ug L\({}^{-1}\) Bi\({}^{3+}\), 15,000 mg L\({}^{-1}\) Cl\({}^{-}\) and 15,000 mg L\({}^{-1}\) NO\({}_{3}\)\({}^{-}\), 1000 mg L\({}^{-1}\) SO\({}_{4}\)\({}^{2-}\), 10,000 mg L\({}^{-1}\) NH\({}_{4}\)\({}^{+}\) for their quantification. However, for the remaining analytes, i.e., Ba, Cd, Ni and Zn, the tolerance limit for co-existing ions was found to be 1000 mg L\({}^{-1}\) K\({}^{+}\), 1000 mg L\({}^{-1}\) Na\({}^{+}\), 50 mg L\({}^{-1}\) Ca\({}^{2+}\) and Mg\({}^{2+}\), 500 ug L\({}^{-1}\) As\({}^{3-}\), 500 ug L\({}^{-1}\) Bi\({}^{3+}\), 15,000 mg L\({}^{-1}\) Cl\({}^{-}\) and 15,000 mg L\({}^{-1}\) NO\({}_{3}\)\({}^{-}\), 1000 mg L\({}^{-1}\) SO\({}_{4}\)\({}^{2-}\), 10,000 mg L\({}^{-1}\) NH\({}_{4}\)\({}^{+}\).
## 4 Solution Procedure
### Upper Bounds
#### 4.1.3 Lagrangian Decomposition (LD)  
When the Lagrangian multipliers \(\zeta_{jlt}\) and \(\chi_{it}\) are fixed, the relaxed model can be decomposed into two subproblems. The first (SubP1) determines the facility locations. After solving this problem, the set of locations would be categorized as \(I_{o}\in I\) that refers to the located and opened facilities and \(I_{No}\in I\) that would be the set of locations that there is not opened facilities in them and we have \(I=I_{o}\cup\ I_{No}\) and \(I_{o}\cap\ I_{No}=\varnothing\). For \(I_{o}\in I\) the second subproblem is defined as (SubP2) that assigns modules to each opened facility and allocates the demand points to the modules. SubP1 and Subp2 are as follows:  
\[\begin{array}{c}\text{(SubP1)}\\ Z_{LD1}=\text{ Max}\ \sum\limits_{i\in I}\sum\limits_{l\in T}\chi_{it}\beta_{i}v_{i} \end{array} \tag{11}\]  
Subject to (7) and (8).  
\[\begin{array}{c}\text{(SubP2)}\\ Z_{LD2}=\text{ Max}\ \sum\limits_{i\in I_{o}}\sum\limits_{l\in T}\sum\limits_{l\in T}(\sum \limits_{j\in I}\left(\alpha_{j}g_{ij}a_{jlt}-\zeta_{jlt}-\chi_{it}a_{jlt} \right)\ x_{ijlt}-\sum\limits_{k_{i}\in K_{i}}h_{ilk,l}y_{ilk,l}\ )+\sum\limits_{j\in I}\sum\limits_{l\in L}\sum \limits_{l\in T}\zeta_{jlt}\\ \end{array} \tag{12}\]  
Subject to (2), (4), (5), and (8).  
As the constraints (3) are relaxed there is no restricting constraint for the amount of coverage for demand points and they can have any positive value. The valid inequality (13) is added to SubP2 (as well as to LR1 and LR2), which is a redundant constraint for the primal MMCMCLP. The SubP2 is solved with the addition of (13) to obtain results for variables \(y_{ilk,l}\) and \(x_{ijlt}\). An interesting feature of the SubP2 is that this problem can be decomposed and solved for each \(i\in I_{o},l,t\).  
\[x_{ijlt}\leq\sum\limits_{k_{i}\in K_{j}}y_{ilk,l}\ \forall i\in I_{o},j,l,t\]  
We use the subgradient method to compute \(Z_{LD}=Z_{LD1}+Z_{LD2}\).
## 5 Taxonomy of Technology-Enabled Smart City Applications in 6G Networks
### Edge-Cloud Computing  
Cloud computing is a technological paradigm that enables on-demand access to a shared pool of configurable computing, storage, and network resources over the internet [124]. It is based on a pay-per-use model and can be provisioned with minimal management effort. With the emergence of the IoT and big data analytics applications in various domains such as healthcare [125; 126; 127], education [128; 129; 130], transportation [131], banking [132; 133], energy utilities [134; 135], and entertainment [136; 137], cloud computing provides a sandbox for data processing and storage, enabling the deployment of compute-intensive smart city applications [138]. However, considering the distance between the IoT devices and the remote cloud servers, the latency requirements of time-critical applications may be violated. Consequently, mobile edge computing has been introduced, which provides computing and storage resources close to the IoT devices. For applications with low latency requirements, the service request can be directed to the nearest edge computing site. However, the computing capabilities of edge servers are low compared to the remote cloud servers, leading to the high processing time for compute-intensive applications. Thus, an integrated edge-cloud computing system is often used to handle compute-intensive and/or time-critical applications [139; 140]. However, the underlying 6G networks should consider the energy efficiency [141; 142; 143; 144; 145; 146; 147; 148], optimal resource provisioning and scheduling [149; 150; 151; 152], and contextual-aware application partitioning [153; 154; 155; 156; 157; 158; 159; 160; 161; 162; 163; 164] requirements of this integrated system.  
In summary, smart city applications have stringent requirements, in terms of an ultra-low latency, high data rate, reliability, energy efficiency, and security that should be fulfilled by the next-generation 6G networks. These applications, underpinned by emerging technologies such as the IoT, HC, blockchain, XR, and edge-cloud computing, provide a lot of potential for unprecedented services to citizens. However, smart urbanism [165] is seen as critical for the success of a smart city. Governments should put in place plans to address some inherent issues to the deployment of AI-sensing and data-driven smart applications. In particular, privacy concerns should be addressed as personal data is collected continuously. In addition, people's fear that this paradigm shift to smart cities may generate unemployment in some professions should be dealt with. Furthermore, worries of losing social face-to-face interactions with government entities, which would rely on sensing and digital devices to collect personal data for improving services, have to  
Figure 17: Blockchain-enabled Integrated Internet of Vehicles (IoV)-Edge-Cloud environment.  
be taken care of. Consequently, smart urbanism advocates incremental changes to cities rather than a massive one.
## 3 Results and Discussion
### Hardness Results  
The hardness values (HV) of pure copper before and after ECAP passes as a function of ECAP passes is shown in Figure 5. Before ECAP process, the hardness was 51 HV for all slurry velocities. After the first pass of ECAP, the hardness values dramatically increased, but the rate of hardness decreased as the number of passes increased. After four ECAP passes for the samples subjected to low slurry velocities (2.7 m/s and 3.8 m/s) the maximum hardness value reached \(\sim\)152 HV (enhancement of 198%) while, at high velocity (5.4 m/s), the maximum hardness was \(\sim\)115 HV (125.5%).  
The increases of HV values after the first ECAP pass are attributed to the generation of dislocations, increase of dislocation density and formation of the ultrafine-grained structure. At low velocities, the material loss due to E-C is low, so the resistance to penetration is high. More details of the mechanism of materials hardness and strength due to the severe plastic deformation for various materials are discussed in [11; 12].