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Online since: December 2010
Authors: Jun Guo, Yun Sheng Wang, Bin Zhang, Xin Ya Song, Xian Li Li
We define sampling period as t. the main factors causing memory consumption is call frequency of web services, basic consumption of memory resources in server systems’ running and the total server memory consumption in last interval, the k+2 input nodes of BP network is, and the server’s total consumption memory in period t-1; the hidden layer 1 and hidden layer nodes number (2k+5); the output node number 1 as the server’s total memory consumption of the period t.
Choosing of hidden nodes number seriously influences the performance of BP network, fewer nodes will lead to poor approximation ability and weak fault tolerance, and more nodes will lead to large scale of BP, long learning time and not minimum error.
In this paper, we initially set the hidden nodes as 2N+1 and eliminate the useless hidden units through continuous learning, until find the best reasonable numbers.
The aging degrees of different stages are different, and we propose an adaptive fine-grained rejuvenation strategy for related services based on the rejuvenation queue and the server ageing state.
First, automatically collecting the total server memory consumption and the number of each service’s calls of multiple cycles in the high reliable stage, initially establishing and fixing the aging model; secondly judging the server status by the server memory consumption.
Choosing of hidden nodes number seriously influences the performance of BP network, fewer nodes will lead to poor approximation ability and weak fault tolerance, and more nodes will lead to large scale of BP, long learning time and not minimum error.
In this paper, we initially set the hidden nodes as 2N+1 and eliminate the useless hidden units through continuous learning, until find the best reasonable numbers.
The aging degrees of different stages are different, and we propose an adaptive fine-grained rejuvenation strategy for related services based on the rejuvenation queue and the server ageing state.
First, automatically collecting the total server memory consumption and the number of each service’s calls of multiple cycles in the high reliable stage, initially establishing and fixing the aging model; secondly judging the server status by the server memory consumption.
Online since: May 2014
Authors: Mats Karlberg
i = 1…n, n= number of el
To include strip profile effects the strip width is in the model approximated to consist of a discrete number of fibres.
Eq. 10 has been implemented to the FE model where all temperature trajectories inside the discretised domain continuously are computed whereas the absolute strength level can be formulated as (12) The base strength parameter, σb is typically dependent on chemical composition, ferrite grain size and phase composition etc. which are to be evaluated in the ROT section.
The yield stress was measured at a number of positions along the head and tail parts of the strip where deviations normally are expected.
Number Grade Length [m] Coil radius[m] Width [m] Thickness [mm] Head samples [pcs] Tail samples [pcs] ÄS 110471 HSLA-grade 199 0.72 1.538 6 12 11 The calculations were made for 10800s (3h) on a mesh consisting of 20x20 elements.
To include strip profile effects the strip width is in the model approximated to consist of a discrete number of fibres.
Eq. 10 has been implemented to the FE model where all temperature trajectories inside the discretised domain continuously are computed whereas the absolute strength level can be formulated as (12) The base strength parameter, σb is typically dependent on chemical composition, ferrite grain size and phase composition etc. which are to be evaluated in the ROT section.
The yield stress was measured at a number of positions along the head and tail parts of the strip where deviations normally are expected.
Number Grade Length [m] Coil radius[m] Width [m] Thickness [mm] Head samples [pcs] Tail samples [pcs] ÄS 110471 HSLA-grade 199 0.72 1.538 6 12 11 The calculations were made for 10800s (3h) on a mesh consisting of 20x20 elements.
Online since: June 2014
Authors: Hong Yan Zhao, Jun Zhang, Jian Qiang Zhang
Identification and state section includes identification information and state information, such as data module code, version number, security classification, etc.; Content section includes equipment technical data, such as the descriptive information, maintenance procedures information etc...
Namely Identification information(such as data module code, title, version number, publication date, the language used and etc.) and state information (such as security scale, the responsibility units and the preparation units, technical standards, application information, quality verification status , skill level, for the change reason used and etc.).
The code consists of English characters and numbers but avoids using “I” and “O”.
ICN YYYYYY YY Y Y YYYYY NNNNN XXX AY X prefix type distinguish systems difference systems divide responsibility cooperate sides information order edition number systems difference secret scale data unit code Project coding is a encoding scheme based on the type identification.
Summary Native XML database possess unparalleled advantage and potential camper with other databases in dealing with XML documents, the disadvantages of native XML database are the lack of fine-grained data processing capabilities, not suitable for processing XML documents and so on.
Namely Identification information(such as data module code, title, version number, publication date, the language used and etc.) and state information (such as security scale, the responsibility units and the preparation units, technical standards, application information, quality verification status , skill level, for the change reason used and etc.).
The code consists of English characters and numbers but avoids using “I” and “O”.
ICN YYYYYY YY Y Y YYYYY NNNNN XXX AY X prefix type distinguish systems difference systems divide responsibility cooperate sides information order edition number systems difference secret scale data unit code Project coding is a encoding scheme based on the type identification.
Summary Native XML database possess unparalleled advantage and potential camper with other databases in dealing with XML documents, the disadvantages of native XML database are the lack of fine-grained data processing capabilities, not suitable for processing XML documents and so on.
Online since: January 2017
Authors: Abdelouahid El Amri, Abdelaltif Khamlichi, M. El Yakhloufi Haddou
The cyclic thermal load occurs by nature in a small number of cycles, but the stresses generated by the restrained thermal expansion may be far beyond the elastic limit.
Low cycle fatigue (LCF) is isothermal fatigue where the strain amplitude during fatigue cycling exceeds the yield strength and causes inelastic deformations so that the material suffers from damage in a short number of cycles [7].
LCF is isothermal fatigue where the strain range during fatigue cycling exceeds elastic strain range and causes inelastic deformations so that the material exhibits a short number of cycles to failure [7].
Number LiTH-IKP-S-459.
Thermo-mechanical and isothermal fatigue of a coated columnar-grained durectionally solidified nickel-base superalloy.
Low cycle fatigue (LCF) is isothermal fatigue where the strain amplitude during fatigue cycling exceeds the yield strength and causes inelastic deformations so that the material suffers from damage in a short number of cycles [7].
LCF is isothermal fatigue where the strain range during fatigue cycling exceeds elastic strain range and causes inelastic deformations so that the material exhibits a short number of cycles to failure [7].
Number LiTH-IKP-S-459.
Thermo-mechanical and isothermal fatigue of a coated columnar-grained durectionally solidified nickel-base superalloy.
Online since: July 2021
Authors: Yelena Kolganova, Anna Azarova, Boris Soldatov, Nikolai Koval, Georgiy Sanamyan
The advantages are manifested due to a significant reduction in labor intensity and cost while processing a large number of parts.
Processing Media Grain-Size Characteristics Choice Principles Taking into account the direction of the research, we will analyze the methods of intensification of vibration processing based on the combination of processing and activating media in relation to finishing and cleaning processing of parts of electronic equipment, which primarily involves removing burrs and preparing surfaces for coating.
Characteristic Designation Experience Number 1 2 3 4 5 6 7 8 The coefficient that defines the ratio of the volume KV Х1 0,1 0,7 0,1 0,7 0,1 0,7 0,1 0,7 Mass of granules of the activating medium, ma Х2 0,1 0,1 3 3 0,1 0,1 3 3 Mass of granules of the processing medium, mm Х3 0,02 0,02 0,02 0,02 0,2 0,2 0,2 0,2 The intensity of the treatment process Р 1 Y1 0,028 0,036 0,035 0,032 0,022 0,03 0,02 0,036 2 Y2 0,026 0.034 0,028 0,038 0,025 0,032 0,024 0,034 3 Y3 0,028 0,034 0,03 0,034 0,022 0,028 0,028 0,03 4 Y4 0,024 0,038 0,034 0,033 0,021 0,033 0,024 0,031 5 Y5 0,021 0,034 0,028 0,036 0,019 0,03 0,025 0,32 Table 2.
The values of the coefficients bi AlMg4.5Mn CuZn38Pb1.5 bi bi b0 0,03159351 0,025324365 b1 0,010814815 0,01375447 b2 -0,029757344 -0,030648148 b3 0,00861552 0,001759259 b11 0,017592593 0,011965812 b22 -0,000574713 -0,00037414 b33 0 0 b12 0,000526511 0,000451632 b13 0 0 Verification of the obtained criteria of dependence on a given significance level a = 0.05 and the number of degrees of freedom f according to the standard confirms the hypothesis that the nature of the distribution of experimental data is close to the normal distribution law of independent random variables.
//MATEC Web of Conferences. - 2018. - Vol. 224: International Conference on Modern Trends in Manufacturing Technologies and Equipment (ICMTMTE 2018). - Article Number: 03011
Processing Media Grain-Size Characteristics Choice Principles Taking into account the direction of the research, we will analyze the methods of intensification of vibration processing based on the combination of processing and activating media in relation to finishing and cleaning processing of parts of electronic equipment, which primarily involves removing burrs and preparing surfaces for coating.
Characteristic Designation Experience Number 1 2 3 4 5 6 7 8 The coefficient that defines the ratio of the volume KV Х1 0,1 0,7 0,1 0,7 0,1 0,7 0,1 0,7 Mass of granules of the activating medium, ma Х2 0,1 0,1 3 3 0,1 0,1 3 3 Mass of granules of the processing medium, mm Х3 0,02 0,02 0,02 0,02 0,2 0,2 0,2 0,2 The intensity of the treatment process Р 1 Y1 0,028 0,036 0,035 0,032 0,022 0,03 0,02 0,036 2 Y2 0,026 0.034 0,028 0,038 0,025 0,032 0,024 0,034 3 Y3 0,028 0,034 0,03 0,034 0,022 0,028 0,028 0,03 4 Y4 0,024 0,038 0,034 0,033 0,021 0,033 0,024 0,031 5 Y5 0,021 0,034 0,028 0,036 0,019 0,03 0,025 0,32 Table 2.
The values of the coefficients bi AlMg4.5Mn CuZn38Pb1.5 bi bi b0 0,03159351 0,025324365 b1 0,010814815 0,01375447 b2 -0,029757344 -0,030648148 b3 0,00861552 0,001759259 b11 0,017592593 0,011965812 b22 -0,000574713 -0,00037414 b33 0 0 b12 0,000526511 0,000451632 b13 0 0 Verification of the obtained criteria of dependence on a given significance level a = 0.05 and the number of degrees of freedom f according to the standard confirms the hypothesis that the nature of the distribution of experimental data is close to the normal distribution law of independent random variables.
//MATEC Web of Conferences. - 2018. - Vol. 224: International Conference on Modern Trends in Manufacturing Technologies and Equipment (ICMTMTE 2018). - Article Number: 03011
Online since: August 2013
Authors: Jian Li Yang, Jing Liu, Mei Li Du, Chun Xia Yu
Fig 1 Experimental process flow diagram
3 Experimental procedure
3.1 The raw coal crushing.Use jaw crusher to crush, in order to prevent crushing excessively, break once will use sets of sieve to sieve, remove the grain size we need, which is larger than the size continues to break, repeat the above procedure.
3.2 Raw coal screening.Vibrating screen grading, dry coal sample, shrink specimen, stop the machine every 5min, check one time by hand screening, when check, remove the sieve on the enamel plate from top to bottom by hand sieve, screening by hand for a minute, the weight of screen underflow is not more than 1% of the weight of oversize, so sieve netly.
Table 1 The experimental results of kerosene as collector Number Kerosene /μL Octanol/μL Clean coal yield/ % Clean coal ash /% Tailings yield /% 1 90 10 89.61 7.91 10.37 2 100 10 89.73 7.19 10.26 3 110 10 88.52 9.49 11.46 Table 2 The experimental results of diesel oil as collector Number Diesel oil /μL Octanol/μL Clean coal yield/ % Clean coal ash /% Tailings yield /% 1 90 10 84.47 8.60 15.52 2 100 10 85.47 9.47 14.51 3 110 10 85.47 9.77 14.52 We use clean coal yield, clean coal ash and tailings yield to draw column chart, do analysis and comparison by it, when select collector is 100μL, the results shown in Figure 2.
Table 3 The experimental results of drainage oil as collector Number drainage oil /μL octanol/μL Clean coal yield/ % Clean coal ash /% Tailings yield /% 1 90 10 89.33 10.57 10.67 2 100 10 88.87 10.60 11.11 3 110 10 89.73 9.16 10.25 Figure 2 The column chart of flotation 4.2 Study flotation use emulsified drainage oil as collector agent.We use OP emulsifier in experiment, which is a condensation compound of alkylphenol and ethylene oxide, is a non-ionic surfactant, the appearance is a viscous liquid which is colorless to pale yellow, solve in water easily, with excellent homogeneously staining, emulsification, wetting, diffusion and other properties.
Table 4 Emulsion drainage oil flotation experimental results Number Vo:Vw Convert dranage oil/μL Clean coal yield / % Clean coal ash /% Tailings yield /% 1 3:7 45 90.00 10.06 9.98 2 4:6 60 88.13 8.76 11.86 3 5:5 75 87.73 8.94 12.25 4 6:4 90 88.67 8.63 11.32 5 7:3 105 88.53 9.86 11.45 Using the above data plot in Figure 3.
Table 5 Emulsion drainage oil collector flotation experimental results Number Convert dranage oil /μL octanol/μL Clean coal yield/ % Clean coal ash /% Tailings yield /% 1 90 10 90.13 9.34 9.85 2 100 10 88.27 9.95 11.71 3 110 10 89.87 9.71 10.12 Draw column chart analysis with clean coal yield, clean coal ash and tailings yield when take collector 110μL and octanol 10μL, the results are shown in Figure 4: Figure 4 Column chart of kerosene, diesel, drainage oil and emulsified drainage oil flotation Seen from Figure 4, adding a certain amount collector, clean coal yield is 89.87%, clean coal ash is 9.71% and tailings yield is 10.12% when collector is emulsified drainage oil.
Table 1 The experimental results of kerosene as collector Number Kerosene /μL Octanol/μL Clean coal yield/ % Clean coal ash /% Tailings yield /% 1 90 10 89.61 7.91 10.37 2 100 10 89.73 7.19 10.26 3 110 10 88.52 9.49 11.46 Table 2 The experimental results of diesel oil as collector Number Diesel oil /μL Octanol/μL Clean coal yield/ % Clean coal ash /% Tailings yield /% 1 90 10 84.47 8.60 15.52 2 100 10 85.47 9.47 14.51 3 110 10 85.47 9.77 14.52 We use clean coal yield, clean coal ash and tailings yield to draw column chart, do analysis and comparison by it, when select collector is 100μL, the results shown in Figure 2.
Table 3 The experimental results of drainage oil as collector Number drainage oil /μL octanol/μL Clean coal yield/ % Clean coal ash /% Tailings yield /% 1 90 10 89.33 10.57 10.67 2 100 10 88.87 10.60 11.11 3 110 10 89.73 9.16 10.25 Figure 2 The column chart of flotation 4.2 Study flotation use emulsified drainage oil as collector agent.We use OP emulsifier in experiment, which is a condensation compound of alkylphenol and ethylene oxide, is a non-ionic surfactant, the appearance is a viscous liquid which is colorless to pale yellow, solve in water easily, with excellent homogeneously staining, emulsification, wetting, diffusion and other properties.
Table 4 Emulsion drainage oil flotation experimental results Number Vo:Vw Convert dranage oil/μL Clean coal yield / % Clean coal ash /% Tailings yield /% 1 3:7 45 90.00 10.06 9.98 2 4:6 60 88.13 8.76 11.86 3 5:5 75 87.73 8.94 12.25 4 6:4 90 88.67 8.63 11.32 5 7:3 105 88.53 9.86 11.45 Using the above data plot in Figure 3.
Table 5 Emulsion drainage oil collector flotation experimental results Number Convert dranage oil /μL octanol/μL Clean coal yield/ % Clean coal ash /% Tailings yield /% 1 90 10 90.13 9.34 9.85 2 100 10 88.27 9.95 11.71 3 110 10 89.87 9.71 10.12 Draw column chart analysis with clean coal yield, clean coal ash and tailings yield when take collector 110μL and octanol 10μL, the results are shown in Figure 4: Figure 4 Column chart of kerosene, diesel, drainage oil and emulsified drainage oil flotation Seen from Figure 4, adding a certain amount collector, clean coal yield is 89.87%, clean coal ash is 9.71% and tailings yield is 10.12% when collector is emulsified drainage oil.
Online since: November 2012
Authors: Alexanders Urbahs, Mukharbiy Banov, Vladislav Turko
Physical Basis
In works sanctified to the physical processes of endurance and fatigue stregnth, the following stages of cracks’ origin and propagation are distinguished: the origin of microcracks at the level of size of grain, confluence of microcracks and formation of the magistral main crack’s focus, growth of this main crack to its critical length, and lead to resulting speed-up destruction of inspected unit [3].
To the well-known models that describe the fatigue destruction phenomenological, and that is why are most applied at fatigue strength design, takes the Weibull model of “weak link”: (2) where N – number of load cycles, a, b, m –CDF parameters (respectively position, scale and mode parameters), model of casual accumulation of plural fatigues modest damages (H.Kordonsky, M.Stepnov, V.Kogaev and other): (3) where N - number of load cycles, N0 –cycle sensibility factor, a,b - CDF parameters (respectively position and scale) Evidently, that for satisfactory description of fatigue durability three parameters of CDF are required.
In papers [6, 8] it is shown that at the low levels of loading (large values of the fatigue endurance or the high level of reliability) the CDF is well described by two-parameter expression: (4) where τ = lgN – the logarithm of number of load cycles, а, b – CDF parameters of position and scale Comparing different CDF with fracture character of fatigue destruction it is possible to mark the following, that the model of Weibull “weak link” (2) describes brittle and semibrittle destruction, while the model of an accumulation of many modest fatigue damages (3) is semiductile destruction.
So it results in the model of maximums distribution [6] or to CDF expression (4), where а –position parametrs, b – scale parametrare, Г’(1) = -0,5772…Euiler constant tied with mathimatical expectation Mτ and variance D{τ}: Mτ=a+bГ'1 (5) D{τ}=π2b2/6 (6) Summary A hypothesis on that a full-size construction can be presented as an association of eventual number of some local zones is offered.
Simplest model of the scale effect based on the hypothesis of local volumes Strength of Materials, 1986, Volume 18, Number 4, Pages 455-460
To the well-known models that describe the fatigue destruction phenomenological, and that is why are most applied at fatigue strength design, takes the Weibull model of “weak link”: (2) where N – number of load cycles, a, b, m –CDF parameters (respectively position, scale and mode parameters), model of casual accumulation of plural fatigues modest damages (H.Kordonsky, M.Stepnov, V.Kogaev and other): (3) where N - number of load cycles, N0 –cycle sensibility factor, a,b - CDF parameters (respectively position and scale) Evidently, that for satisfactory description of fatigue durability three parameters of CDF are required.
In papers [6, 8] it is shown that at the low levels of loading (large values of the fatigue endurance or the high level of reliability) the CDF is well described by two-parameter expression: (4) where τ = lgN – the logarithm of number of load cycles, а, b – CDF parameters of position and scale Comparing different CDF with fracture character of fatigue destruction it is possible to mark the following, that the model of Weibull “weak link” (2) describes brittle and semibrittle destruction, while the model of an accumulation of many modest fatigue damages (3) is semiductile destruction.
So it results in the model of maximums distribution [6] or to CDF expression (4), where а –position parametrs, b – scale parametrare, Г’(1) = -0,5772…Euiler constant tied with mathimatical expectation Mτ and variance D{τ}: Mτ=a+bГ'1 (5) D{τ}=π2b2/6 (6) Summary A hypothesis on that a full-size construction can be presented as an association of eventual number of some local zones is offered.
Simplest model of the scale effect based on the hypothesis of local volumes Strength of Materials, 1986, Volume 18, Number 4, Pages 455-460
Online since: March 2014
Authors: Atsushi Sugeta, Jinta Arakawa, Hiroyuki Akebono, Masahiko Kato, Yoshiichirou Hayashi, Ryota Tanegashima, Motoki Kakuta
The run-out number is N=1×107 cycle.
C Si Mn P S Ni Cr N Al Ca O 0.049 0.50 0.83 0.040 0.004 3.62 12.82 0.027 0.010 <0.0005 0.00063 HV σ0.2[MPa] σB[MPa] 280 594 829 Amplitude Vibrational frequency shot distance shot extent shot material shot grain size Time 50mm 20kHz 20mm 76mm×26mm SUJ2 f4.0mm 20sec Fig. 1 Schematic illustration of specimen.
Fatigue tests Figure. 5 shows the results of fatigue tests, which indicates the relationship between stress amplitude at the notch root and number of cycles to failure.
The results of simulation are shown in Fig. 8, which indicates the relationship between crack length, 2a, and number of cycles normalized by simulated number of cycles to failure of Virgin specimen, N/Nf|Virgin.
In Fig. 8, it was assumed that both fatigue cracks in USP specimen and Virgin specimen initiated at the same number of cycles based on experimental results of fatigue crack propagation behavior.
C Si Mn P S Ni Cr N Al Ca O 0.049 0.50 0.83 0.040 0.004 3.62 12.82 0.027 0.010 <0.0005 0.00063 HV σ0.2[MPa] σB[MPa] 280 594 829 Amplitude Vibrational frequency shot distance shot extent shot material shot grain size Time 50mm 20kHz 20mm 76mm×26mm SUJ2 f4.0mm 20sec Fig. 1 Schematic illustration of specimen.
Fatigue tests Figure. 5 shows the results of fatigue tests, which indicates the relationship between stress amplitude at the notch root and number of cycles to failure.
The results of simulation are shown in Fig. 8, which indicates the relationship between crack length, 2a, and number of cycles normalized by simulated number of cycles to failure of Virgin specimen, N/Nf|Virgin.
In Fig. 8, it was assumed that both fatigue cracks in USP specimen and Virgin specimen initiated at the same number of cycles based on experimental results of fatigue crack propagation behavior.
Online since: November 2013
Authors: Dan Lv
Year
1950
1960
1970
1980
1990
2000
2010
Number of farms [ten thousand]
538
372
295
244
214
200
220
Average farm size [acres]
212
313
374
426
460
430
418
Table 1 Statistic of the number and average scale of the American Farm
Data sources: American "Statistical Abstract" 1975, 1982, 2011
Each year more than 40% of the grain and oil crops and more than 10% of the animal products are for export. with only about 1.8% of the country's population feeding the 300 million people in the United States.
In view of this, the environmental protection agency (EPA) in American has launched a number of new laws and regulations to strengthen environmental protection agriculture in recent years.
In general, use biomass waste in agricultural process as new energy materials, applying biomass biochemistry technology into family farm. 3.2 Implant concept of "green chemistry", implement the agricultural cleaner production The modern agriculture with the feature of highly intensification and a large number of chemical inputs is causing an increasingly serious environment pollution problem.
At the same time, as a business individuals, if family farm flowed out a large number of land, it may lead to a lot of liquidity is occupied by a expensive rents, and the contradiction of no capacity to manage land.
Each year more than 40% of the grain and oil crops and more than 10% of the animal products are for export. with only about 1.8% of the country's population feeding the 300 million people in the United States.
In view of this, the environmental protection agency (EPA) in American has launched a number of new laws and regulations to strengthen environmental protection agriculture in recent years.
In general, use biomass waste in agricultural process as new energy materials, applying biomass biochemistry technology into family farm. 3.2 Implant concept of "green chemistry", implement the agricultural cleaner production The modern agriculture with the feature of highly intensification and a large number of chemical inputs is causing an increasingly serious environment pollution problem.
At the same time, as a business individuals, if family farm flowed out a large number of land, it may lead to a lot of liquidity is occupied by a expensive rents, and the contradiction of no capacity to manage land.
Online since: November 2020
Authors: Alexander Yuryevich Mironenko, Alexander Konstantinovich Chepak, Leonid Lazarevich Afremov
The presence of a phase transition was determined by the behavior of the magnetic susceptibility χ, which was calculated using three order parameters — magnetic Mma, cluster Mcl, and percolation Mpr, which were determined using the following relationships:
Mma=1NiNmasi, (8)
Mcl=1NiNclsi, (9)
Mpr=1NiNprsi, (10)
magnetic susceptibility was calculated in a known manner:
χ=NtM2-M2, (11)
here N=L2; Nma, Ncl and Npr – the number of nodes in the lattice, the number of
In the region far from the phase transition, the average number of ncl clusters is almost constant; therefore, Nma and Ncl are proportional to the concentration of magnetic atoms, unlike Mpr, which is determined by an infinite cluster whose size Npr does not change in this region.
Since the number of magnetic particles in a cluster is less than the number of magnetic particles (NclBinder, Critical properties from Monte Carlo coarse graining and renormalization, Phys.
In the region far from the phase transition, the average number of ncl clusters is almost constant; therefore, Nma and Ncl are proportional to the concentration of magnetic atoms, unlike Mpr, which is determined by an infinite cluster whose size Npr does not change in this region.
Since the number of magnetic particles in a cluster is less than the number of magnetic particles (Ncl