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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.

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).

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.

The abundant SOx species on S-ZrO2(s) and S-ZrO2(se) may inhibit the growth of grain.
IR spectra of S-ZrO2(p) heated at 400, 520 and 620°C 8009001000110012001300 S-ZrO2(p) (620ºC) (520ºC) (400ºC) ZrO2·nH2O 1000 1033 Transmittance Wave number / cm-1 1270 1080 1140vapor pressure are shown in Fig.6.
The syntheses of S-ZrO2(se) and S-ZrO2(s) were conducted for the purpose of an increase in the surface area and a resultant rise in the number of surface SOx species.
An increase in the number of surface SOx species and resultant rise in conductivities were achieved.

Experimental results Non-oriented (NO) silicon iron alloys are soft magnetic materials with an approximate anisotropic grain texture.
Some mathematical interpolations (Fig. 3) prove that the NO FeSi and Co-based amorphous alloys, obeys a simple linear law: (5) where the microstructural information is now carried by n0, which represents the limiting number of simultaneously active MO's when f→0 and by the magnetic field H0.
Prediction of the number of the active magnetic objects n versus the dynamic field Hexc in a 0.65 mm thick NO FeSi lamination (M800-65A) at peak polarization Jp = 0.5 T (left figure) and in case of a 11 μm thick Co-based amorphous ribbon annealed under longitudinal applied magnetic field at peak polarization Jp = 0.02 T (right figure).
Acknowledgement This work was supported by a grant of the Romanian Ministry of National Education, UEFISCDI, project number PN-II-PT-PCCA-2011-3.2-0373.

Taking solid material for example, solid material contains several scales such as the atomics structure, crystal structure, grain structure and element in macro-scale, in which they may present great differences in physical behaviour.
As shown in Fig. 3, contact interface between particle and matrix cracking cracks who make a third crack boundary.means crack boundary,means the crack boundary of inclusion particles crack boundary,means the crack boundary of substrate, so we can find that at it still satisfy: Fig.3 Voronoi Cell with Interface Debonding (1) At and,because of the cracking, the two boundary has no restraint,so satisfy the following boundary conditions (on border) (2) (on border) (3) Introduction of Lagrange multiplier method can get the Surplus energy functional (4) The total energy (5) is the unit of energy,e is the number of units, To get one order variation is described unit internal stress strain relationship of the Euler equation (6)
All nodes of the elements related to the point should be read, then the number of this point should be instead of zero, the rest points are stored.
After going though the entire nodes, a grope of nodal numbers could be obtained, in which the anticlockwised nonzero ones are the boundaries of the member.

As friction is formed by three items that's anchoring strength, micro convex body plastic deformation force, hard micro convex body and grinding grain furrow force, the change of sliding speed between friction pairs to be able to affect the surface temperature of friction pair.
Due to a large number of friction work is transformed into heat when the friction pair in high speed the temperature between friction pair lifts quickly, cause friction pair softening surface, between the friction pair actual contact area increases, the contact point has the agglutination, so after bonding, tear, and adhesive, and torn cycle process, cause serious adhesive wear, therefore the friction pair wear serious, this and wear along with the speed of change law is consistent.
(a) 0.84m·s-1 200N (b) 0.84m·s-1 400N Fig.6 25CrMn ring wear surface of SEM Comparison in Fig.6 (a), (b) can be found when imposing 200N load of friction pairs, there are a large number of plow wrinkles plastic deformation on frictional surfaces resulting from plough effect, while have the obvious plastic flow and trace of the material flaking.
This is because as the applied load increases, friction between worn surface of severe plastic deformation, deformation work has increased, resulting in real contact area and increase in the number of micro-convex body contact, slightly convex body onto the depth increases, last making serious wear phenomena of friction pairs.

In the observation channel, built 500 mm from the support, the first fatigue crack was observed at the number of 320 thousand cycles.
Fig. 4 Experimental studies: a) beam scheme with numbered steel dowels, b) steel beam (dowels 1’ to 9’) after cutting, c) steel beam (dowels 1 to 9).
I (Figs. 8a, b) is fine-grained, which could be affected by the cutting technology (oxygen-acetylene cutting).
The product of the remaining number of cycles to the maximum crack length – from 37 to 238 mm (destruction of steel beam) and average speed shows clear decrease of crack propagation speed.

The gaseous allocations from the system of furnaces released into the atmosphere are a problem number one in pollution abatement of the environment by production of cement today.
The detailed composition and structure of clinker for HBC production are not given, but it is clear that in order to ensure activity, the belite must be present in the clinker composition in its hight-temperature polymorphic modifications, and the cement’s grain composition must be carefullyselected.
Over the past 10-15 years, the number of publications devoted to the use of biomineralization phenomenon for obtaining various types of building materials is rapidly increasing.
Therefore for receiving qualitative cement it is necessary to work properly at all these stages, to observe a number of requirements.

A number of studies were found in literature regarding the performance, deformation characteristics, and processing techniques of the two-component armor systems, which generally referred to ceramic/metal or ceramic/composite armors.
Meanwhile, linear scanning images of EDS determined that a large quantity of Fe, Cr atoms entered the intermediate nearby Ti-6-Al-4V alloy while a number of Ti atoms also passed through the mid-ceramic to come into the intermediate nearby 42CrMo steel, as shown in Fig. 5.
Fig.5 EDS linear scanning images from 42CrMo steel to the mid-ceramic and further to Ti-6Al-4V alloy Fig.6 FESEM image of the microstructure of the mid-ceramic Fig. 7 The hardness distribution curve of the FG multilayer composite In addition, FESEM images showed that the mid-ceramic was composed of a number of very fine ceramic phases such as TiC1-x, TiB and TiB2, of which the majority were smaller than 1 μm in size, and some ones even resided in the range of 100~200 nm in size, as shown in Fig. 6.
Furthermore, because of the loss of a large quantity of the mid-ceramic liquid, there was only low atomic concentration of C and B in the remained mid-ceramic liquid, so TiB2, TiB and TiC solids hardly grew even if they nucleated in the mid-ceramic liquid, finally, ultrafine grained microstructure was achieved in the mid-ceramic after rapid solidification of the mid-ceramic, as shown in Fig. 6.