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The whole AP procedure terminates after a fixed number of iterations or after the center decisions stay unchanged for some number of iterations.
The IGP index is based on the idea of probability and statistics, so it is a Coarse-grained estimate from the point of view of granular computing.
Therefore, when the average IGP index value are the same, the maximum number of classes is treated as optimal number of clusters.
Therefore, the optimal number of clusters is 13.
And the optimal number of clusters is obtained respectively according to IGP index. 2) The number of clusters of each sub-datasetare calculated respectively.

Clustering is an important tool for data analysis, unsupervised learning, data graining and information compression.
The function number of KP is () and the function number of KP is ().
(1) The LKP of and is and ;,,is the functional perfection degree, functional number and level number of KP respectively.,, is the functional perfection degree, functional number and level number of KP respectively.
is the same functional number as that of KP in .
Let , i.e, the level number of LKP is the same.

The remelting zone between layers ensures good metallurgical bonding between adjacent layers and enables the newly formed grains to grow along the deposition direction through epitaxial growth on the solidified layer.
The variation of the phase-field variable with time can be obtained by solving the phase variation of the free energy functional: ∂ϕα∂t=-β≠αiMαβiδFδϕα-δFδϕβ (6) where Mαβ is the interfacial mobility and i is the number of phases in the grid.
In order to solve the chemical free energy, it is necessary to analyze the Gibbs free energy of the system: G=α=1nNαi=1uμαicαi (7) where Nα is the number of phases and u is the number of alloying elements.
In the calculation domain, the number of cells/dendrites in the steady-state growth was counted along the X direction (i.e. perpendicular to the growth direction), and then the average primary dendrite spacing under different solidification conditions was estimated by dividing the width of the calculation domain by the number of cells/dendrites.
The simulation results show that even if the cooling rate is as high as 1.33 × 106k/s, the segregation of Nb will still occur between the cellular grains.

The reason is that a large number of fatigue failures have been observed beyond 107 cycles in high strength materials and at stress lower than the conventional fatigue limit [1].
(1) Where Ni,s is equal to the total number of inclusions located at the surface, Ni,v is the total number of inclusions in the whole specimen volume, di and d are the size of inclusions and the diameter of specimen, respectively.
(2) Where Ni is the number of cycles for subsurface crack initiation and Ns is the number of cycles for surface crack initiation.
In dry air, kw ≈1.is the dimensionless unit increment of energy for dislocations in cycling. ψ= r/l is the ratio of inclusion radius r to grain radius l. φ= ∆σ/2k is the ratio of stress amplitude ∆σ to the resistance of dislocation movement k.
What’s more, some other models on the formation of FGA have been proposed, for instance, the “hydrogen embrittlement-assisted cracking” by Murakami et al. [1], the “depressive decohesion of spherical carbide” by Shiozawa et al.[4], the “cyclic compression between crack faces” by Nakamura et al.[22], and the “grain refinement and local stress decreasing” by Grad et al.[23].

In the investigations of the cellular responses of cells, two aspects were considered: the number of growing cells and their morphological features.
Generally, limited number of materials, including ceramics and glasses can bond directly to the living bone without encapsulation by fibrous tissues but TiO2 shows good bone-binding ability on implants surface [2].
Changes in the number of viable cells on the scaffolds after 1, 3, and 7 days in culture were quantitatively assessed by MTS test.
The intensity of the color produced is therefore directly proportional to the number of viable cells in culture, and thus to their proliferation in vitro.
The interaction between bone marrow cells and TiO2 foam surface can be observed at the grain boundary (Fig. 5).

Electrostatic and steric repulsion forces inhibit aggregation and attachment of particles to grain surfaces [35, 36].
Nelson and Ginn [60] formulated a correlation equation to predict the collector contact efficiency () for colloid filtration in Happel’s sphere-in-cell porous media model: (2) where is a factor accounting for the particle flux into the Happel sphere, is , is porosity, is a function of porosity accounting for the impact of neighboring grains on the flow field, is a dimensionless number characterizing the van der Waals force, is a dimensionless number characterizing the effect of relative particle and collector sizes, is , is a dimensionless number characterizing the effect of gravitational sedimentation, and is a dimensionless number characterizing the effect of Brownian diffusion.
Several soil properties, including grain size and pore size distribution, porosity, mineralogy, organic matter content, and hydraulic conductivity, will be measured using standard methods.

Table 4: Applied brazing fillers, by manufacturer's instruction material number melting range [°C] ultimate tensile strength Rm [MPa] yield strength Rp0.2 [MPa] CuSi3Mn1 2.1461 910 - 1025 340 - 460 > 120 CuAl7 2.0921 1030 - 1040 380 - 450 180 CuSn6+P 2.1020 910 - 1040 > 260 > 150 Fig. 6: Overview of a brazed joint and its heat-affected-zone (HAZ); HCT600XD, CuSi3Mn1; scale 100 and 200 µm Boundary base material / filler HAZ: fine-grained zone / coarse-grained zone HAZ: coarse-grained zone Length of HAZ Test parameters.
At this for cyclic loading critical region the coarse grained zone, the fine-grained region, and the unaffected material is closely located.

Optical (OM) and scanning electron microscope (SEM) analyses were carried out to elucidate actual particle size and volume fraction as well as matrix grain size and distribution of intermetallics.
Indeed, the fracture surface corresponding to initial fatigue crack growth mainly developed through the matrix and intersected only a relatively low number of alumina particles (Fig. 7a).
Moving on toward the region corresponding to final growth stage, the fracture surface underwent a progressive modification with an increasing number of fractured ceramic particles exposed on the crack path, as depicted in Fig. 7b.
Their results highlighted that ceramic particles in MMCs are much stronger barriers for short cracks than many other microstructural defects such as grain boundaries and that the threshold for the short crack growth (i.e. the fatigue limit) could be directly related to the ability of the particles to trap the crack-tip cyclic plasticity.
· On the contrary, in the high-cycle fatigue regime, during early stages of crack propagation, the crack path mainly develops through the matrix and intersects only a relatively limited number of alumina particles.

The scrapers can remove of melted fine-grained rocks (sandy loam, loam, clay) in natural deposit, as well as pre-loosened strong (dense, semi-scaly, rocky) rocks [3].
Besides for large inclusions in coarse-grained or loose rock, it is possible to jam these elevators.
The use of an elongated hopper is rational from the economic point of view: an increase in the volume of the hopper leads to a reduction in the number of movements of the scraper for the transfer of rock mass.
Based on the repeated experiment number for laboratory conditions equaled to 5, and taking into account the constant error of the measuring apparatus ±3%, the average experimental error should not exceed 10…14% [22].
The determination of the most economical set of machines for specific mining conditions is a fairly long and time-consuming process involving a number of repetitive calculations.

Compared with the traditional way, it can significantly decrease the number of trials and improve the accuracy.
Over a period of nearly half a century, a large number of beneficial fracture criteria for the fracture prediction and prevention were extensively conducted and well documented [2-5].
This poor workability can be associated with the high-temperature oxidation and coarse grains [17].
It indicates that if critical fracture model for other metal alloys in hot forming were also a linear relationship, the critical fracture model would be developed after only limited experiment times, and further effectively decrease the number of trials and reduce the costs.