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The macroscopic state of the system is determined by the occupation numbers ns.
Thus the partition function form (1) could be written as      11' ' ' ' ,' 1 = exp 2 s s s ss s s ss s s s s s ns Z i n W U D D                           . (3) The additional field variables  and  describe the attractive or repulsive nature of interaction, that allows taking into account the combination of states representing different combinations of occupation numbers.
For a practical case, one always has some number of B-type particles in the A-B binary system =Bs sNn (considering a canonical ensemble).
The number of realistic interactions, for which the inverse operator can be found analytically, is limited.
It should be emphasized that this equilibrium state defined by (11) is only valid for a space-limited systems with the boundaries (grain boundaries, external free boundaries, etc.).

Peaks at 522 and 976 cm-1 correspond to Si, the peak at 1332 cm-1 is related to diamond and the peaks at 1134 cm-1 and 1540 cm-1 are ascribed to the amorphous network (trans-polyacetylene at the grain boundaries).
Fig. 1b shows typical COF versus number of cycles curves recorded during the sliding tests on the NCD films against Si3N4.
number of peaks along the scan line) were obtained from it and are reported in Table 1.
A number of grooves on the NCD surface decreases from Fig. 2a to Fig. 2c and only two grooves can be found in Fig. 2c.
Therefore, the number of grooves decreases with increasing frequency (from 2 Hz to 10 Hz) and sliding distance (from 14 400 to 108 000 cycles).

Al2O3-Fe-based cermet is the introduction of iron particles into the ceramic matrix, which greatly refine the Al2O3 grain, and enhance the toughness and strength of ceramics, has great practical significance [3, 4].
Content Numbering Low-grade bauxite /% Kaolin /% Quartz /% Iron powder /% Water content /% Stationary time /day 1 50 35 15 0 7 2 2 50 33 13 4 7 2 3 50 31 11 8 7 2 4 50 29 9 12 7 2 5 50 27 7 16 7 2 6 50 25 5 20 7 2 Performance Testing Determination of Bulk Density, Water Absorption and Apparent Porosity.
Numbering Dry weight Weight after corrosion /g Surface area/ mm2 Corrosion rate / g/dm2·h /g 1 86.85 85.91 114.60 0.034 2 86.09 85.26 140.80 0.025 3 98.34 97.65 141.82 0.020 4 112.53 111.54 145.68 0.028 5 110.38 109.73 146.72 0.018 6 125.62 124.54 148.80 0.030 Table 3 shows that the corrosion rate of specimen No. 1 is the maximum, which is 0.034 g/dm2·h, the corrosion rate of specimen No.5 is the minimum, which is 0.018 g/dm2·h.
Numbering Diameter /cm Thickness /cm Bear pressure / KN compressive strength/ g/dm2·h 1 7.2 1.4 169.54 41.66 2 7.3 1.5 202.39 48.42 3 7.2 1.2 215.27 52.90 4 7.5 1.3 352.28 79.79 5 7.2 1.2 284.59 69.94 6 7.2 1.1 366.17 89.99 As can be seen from the above table, with the increase of iron powder content, the compressive strength of the specimen is gradually increasing.
Numbering P b /mm h / mm Bending strength / MPa /KN 1 0.24 41.6 9.6 9.39 2 0.09 40.3 8.0 5.23 3 0.18 43.0 10.1 6.16 4 0.43 41.4 9.9 15.90 5 0.09 43.6 9.6 3.36 6 0.14 44.0 10.3 4.50 As can be seen from the above table, the bending strength of No.4 is the largest, which is 15.90MPa.

Wang, Influence of coarse aggregates’ shape index and gradation in self-compacting concrete’s rheological behavior and working performance, Concrete, 1(2011): 75-80 , At the same time, a large number of admixtures used during the production have obvious economic, social and environment benefits, which has a very wide range of applications.
Therefore, preferable aggregate grading must satisfy the following three conditions: small porosity to decrease the cement content and ensure compactness; small total surface area to decrease water demand for moisting the surface of aggregate; a small number of fine grains to meet the requirement of concrete workability.
Table 2 Properties of SCC with different aggregate grading Test serial number Coarse aggregate strategy Slump//cm T500 /s Slump flow /cm Compression strength/MPa Splitting tensile strength/MPa 3d 28d 3d 28d S1 ZCS1 24 9 61 21.7 35.6 1.71 2.28 S2 ZCS2 24 9 62 20.9 34.8 1.61 2.14 S3 ZCS3 25 8 65 23.4 37.6 1.74 2.31 As seen in Table 3, the workability of SCC can be obviously improved by choosing the proper sand percentage under the same coarse aggregate grading.
Table3 Properties of SCC with different aggregate grading Test serial number Sand percentage/% Slump/cm T500/s Slump flow /cm Compression strength/MPa Splitting tensile strength/MPa 3d 28d 3d 28d S4 45 21 11 56 22.3 35.7 1.83 2.59 S5 47 22 11 57 20.8 34.5 1.72 2.46 S6 49 21 8 59 19.8 32.7 1.68 2.16 Different from the change of fluidity of concrete mixture, the strength index of SCC decreases with the increasing sand percentage.
Table 4 Properties of SCC with different shape index* Test serial number Shape index I Slump/cm T500/s Slump flow /cm Compression strength/MPa Splitting tensile strength/MPa 3d 28d 3d 28d S8 0.3712 21 11 56 20.15 34.47 168 2.48 S9 0.3959 22 11 57 20.69 34.78 1.71 2.47 S10 0.4316 24 7 62 21.56 35.50 1.82 2.55 S11 0.4403 21 8 59 23.03 36.65 1.91 2.63 *：shape index：I＝I=∑αi×pi，αi is sphericity distribution interval, pi is the probability ofαi to total region.

Metal powders and pore inducers were blended together with diamond grains for sufficient time to guarantee a homogeneous distribution of the initial materials.
Quite a number of micro-cracks distribute on the surface of base metal of the porous wheel I as shown in Fig.7(a).
Coupled with the experimental results of the grinding forces and the surface topographies of the two wheels after a certain number of grinding passes, it is shown that wheel I exhibits better self-sharpening ability because high porosity within it provides more space for debris and make the diamond grits easy to emerge in the grinding process.
This is why quite a number of micro-cracks distribute on the matrix surface of the porous wheel I after it grinded for a period of time at a higher rotating speed and bigger depth of cut.
SEM observations revealed that quite a number of micro-cracks distribute on the matrix surface of the porous wheel I while much more serious erosion o and burning on the base metal was observed on the wheel II.

The numbers of the stator and rotor slots were 36 and 28, respectively.
The material of the model core was 0.5 mm thickness non-oriented silicon steel sheet, and the total number of lamination was 20.
The number of stator winding in each phase was equal to 120.
The number of the sampling points, the sampling frequency and the number of the measured points were 20000, 1MHz and 2400, respectively.
[7] K.Senda, M.Ishida, K.Sato, M.Komatubara, T.Yamaguchi: Localized Magnetic Properties in Grain-oriented Silicon Steel Measured by Stylus Probe Method.

The formation of metatitanic acid in the thermal hydrolysis of TiOSO4 by self-generating seeded goes through a series of steps involving ionic reaction, olation and oxolation, nucleation, grain growth and aggregate to the final form [6].
The Volume ratio of pre-adding water to TiOSO4 solution influenced the number and activity of the seed crystal, thereby influenced nucleation, crystallization and aggregation process, eventually determined morphology and pigment properties of the product.
With rising pre-adding volume ratio, number and activity and dispersion of seed crystals increased [9] bringing about the formation rate of initial nuclei and secondary nuclei enlarging, resulting in forming the smaller hydrated TiO2 particles.
Colloid Ti4+ accumulate gradually as the extension of time, homogeneous nucleation dominant, instantly generate a large number of nuclei and finer the primary particles, the rate of hydrolysis sharp increase.
The Volume ratio of pre-adding water to TiOSO4 solution influenced the number and activity of the seed crystal, thereby influenced nucleation, crystallization and aggregation process, eventually determined morphology and pigment properties of the product.

, based on the principle of multi-objective planning, According to the multi-grade standards, the evaluation index can translate into measurable evaluation scores through conversion function, and then an overall evaluation is obtained according to the evaluation objects , and judge the merits based on the final score, This method is used to evaluate the object with comparison, ordering, and rarely used for classification.We have a new try to apply it to grade the risk .Calculate the maximum and minimum efficiency coefficient for each classification. to determine the efficiency coefficient demarcation point, and make the classification more reasonable. the improved evaluation steps as follows: 2.1 Set the classification standard Classification standard is the max and min value of corresponding evaluation of some category, the max limit value is the max standard of one category, and the min value is the min standard. set evaluation standard vector is Y=(y1,y2,…,ym) , classification number
is m, and standard value number is m+1, classification standard value is kj(j=0,1,2,…,m+1) 2.2 Indentify standard coefficient of standard value Standard coefficient is the level coefficient of corresponding standard value, Objectively reflect the different levels of evaluation criteria value, it is used to calculate the index of the actual value corresponds to the standard value, the standard value for each category, there is a corresponding coefficient.
Standard coefficients is represented with number ranged between 0-1 , record as λj (j=1,2,…,m+1) .Calculate formulation as follows: For efficiency index that the larger value is the better: (1) For cost-type index that the smaller value is the better: (2) In the formulation, λj is the standard coefficient; kj is the standard value; xmax is the max index; xmin is the min index. 2.3 Determine the weight of each index Entropy method is used here.
Sites dominated by coarse-grained granite bedrock, interspersed with granitic porphyry vein-in the meantime, part of the tunnel under water-rich Sandy layers, construction risk is significant. 4.2 Standard coefficient of standard value of categories In the establishment of the index system for evaluation of surrounding rock stability, span, groundwater surroundings, construction management belong to the benefit indicators, that is,the higher the value, the lower the stability of the surrounding rock, the greater the risk of collapse in tunnel.
Table 4 Comparative results of surrounding rock number individual indicators total level actual Vp depth span groundwater surroundings management 1 0.0765 0.01456 0.05537 0.0551 0.045 0.02 0.26653 II II~III 2 0.20094 0.02136 0.05411 0.1121 0.03 0.022 0.44051 III III 3 0.26979 0.01728 0.0511 0.1406 0.105 0.02 0.60377 IV III~ IV 4 0.0306 0.01256 0.05537 0.0342 0.0075 0.028 0.16823 I I Conclusions 1.

Fig.1 Installation of Signal Acquisition System Data analysis is conducted by acquiring one CMV every 1m and one Evd value every 20m during rolling compaction operations [4-5]. 2 Analysis of Test Results 2.1 Relationship between test indices and roller passes With increasing number of roller passes, subgrade becomes more and more dense and accordingly, CMV and Evd increase.
Relationship between the CMV and roller passes Fig.3 Relationship between the Evd and roller passes From the relationship between test indices and roller passes, it can be seen, with increasing number of roller passes, both CMV and Evd show clear increasing trend, which can roughly reflect the relationship between test indices and compaction state. 2.2 Statistical analysis of test indices Test data are random variables.
Table 2 Statistics of Test Results for 4 Roller Passes Number of roller passes Statistical item CMV EVd/MPa Pass 1 Average 5.5 36.5 Variance 3.4 97.9 Coefficient of variation 0.63 2.68 Pass 2 Average 8.2 54.7 Variance 6.5 174.3 Coefficient of variation 0.8 3.18 Pass 3 Average 10 63.2 Variance 8.7 238.1 Coefficient of variation 0.88 3.76 Pass 4 Average 9.8 74.8 Variance 2.03 228.01 Coefficient of variation 0.21 3.05 It can be seen from the table that the coefficient of variation of CMV is smaller than that of EVd, indicating the CMV test method can better reflect the state of subgrade compaction than EVd test method.
The reasons are as follows: (1) impact of data volume: to analyze the probability, for the same target value, the greater the number of samples collected, the smaller the coefficient of variation is.
Table 3 Statistics of the Correlation between CMV and Test Indices Number of roller passes Coefficient EVd Pass 1 Coefficient A 10.0 Coefficient B 15.7 Correlation coefficient R 0.56 Pass 2 Coefficient A 8.6 Coefficient B 9.8 Correlation coefficient R 0.69 Pass 3 Coefficient A 8.8 Coefficient B 25.2 Correlation coefficient R 0.56 Pass 4 Coefficient A 8.4 Coefficient B 14.8 Correlation coefficient R 0.66 From the fitting curve and the statistics of correlation, the correlation between CMV and Evd is not very high, which is affected by: (1) the filling materials are coarse grained gravel with uneven distribution.

The node set is defined by , where is the total number of nodes.
(6) denotes the number of the elements in . 1.2.
(8) where and are the graph numbers of and .
In training graph clustering and prototype selection step, the stopping threshold and representative prototype number of each sub-category are two parameters to be set.
Shapiro: Unsupervised template learning for fine-grained object recognition, in Proc.