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It represents the frequency of occurrence of earthquakes as a function of magnitude: , (1) where N is the cumulative number of earthquakes with magnitude larger than M and a and b are constants.
Analysis and results The data is separated into different depth ranges for calculation of the frequency magnitude distribution according to the number of the events.
As normal stress levels increase with depth, the earth becomes more close-grained, resulting in a greater area of contact.
For example, the small events may precede the big earthquake and the big event always accompanied with a number of aftershocks.
The probability (P) that a magnitude event will develop into a larger event is given by the ratio of the number .

Assume Y is diffraction intensity and X is diffraction angle(2θ), so the target function for fitting is, (1) where stands for the total diffraction intensity of crystal fraction at X, is the t-th diffraction intensity at X, stands for the total intensity of non-crystalline fraction, and N is the number of crystal diffraction peaks.
For the non-crystalline fraction, the Seventh Polynomial is selected for interpolation and fitting, that is, (3) Select the proper undetermined coefficients ft,At,Pt,Wt,a,b,c,d,e,f,g,h , trying to make the curve Ycal(X) determined by calculating and experimental curve Yobs(X) overlapping, so the following evaluation function, (4) tends to zero, that is, the minimal value, where m is the number of discrete data points in Tibetan medicine XRD patterns.
The obtained peak type data after making peak resolution Serial number Peak intensity [CPS] Peak position[º] FWHM[º] 14# a 104.8 15.03 1.338 b 143.1 17.67 2.596 c 69.36 20.59 2.361 d 135.8 22.91 2.214 25# a 101.9 15.9 4 b 221.6 21.99 3.713 27# a 98.49 15.43 0.0629 b 200 15.52 4.913 c 170.4 22.3 3.504 50# a 76.42 18.56 6.984 Note: Here the a,b,c,d are signs marked in Fig. 1-4.
It can be found in Fig.2 that there are two crystal peaks with large FWHM, the crystalline grain being large, which the specific data can be seen in Table 1.For the sample 27#, it presents 'Twin Peak' as a whole, yet being a little different from sample 25#.
Handling this kind of pattern with peak resolution proves to be a little difficult, for its being sensitive to peak height and peak number.

Silica sand, with a specific gravity of 2.61 and grain sizes ranging from 105 to 120 μm, was used in the study.
It is rational that the value of cracking number is highest around middle of specimen because the cement matrix stress is theoretically maximized at the around middle of sector.
It is obvious that, there is significant difference in number of cracking distribution between all the specimen(when compared at same tensile stress).
As the replacement of EXA 10% the total width decrease, but the number of cracks increase.
The shrinkage compensating UHS-SHCC ties exhibited crack distribution, and the resulting greater number of cracks.

Now, the development of seismic rock physics research has actually exceeded the seismic interpretation of the requirements of a large number of rock physics theory tentacles out into the seismic data has been unable to distinguish the pore space.
Rock and fluid properties through a variety of research and development of effective medium model, speed and attenuation factors of a large number of experimental tests have summed up the experience in relation to certain formulas, rock physics model thus has been able to establish a means of allowing people to rock composition, such as porosity and particle structure, fluid saturation and stress, many of the reservoir rock to quantify the elastic and inelastic characteristics.
For the reservoir rock is usually high pressure tends asymptotically towards the flat line, after reaching vary only the first step confining pressure and pore pressure between, there is no absolute "effective pressure Guidelines"; pressure depends on the grain boundaries.
In a large number of speed porosity theoretical formulas and empirical relationships, the time average equation is widely used in accordance with the mineral composition and pore fluid rocks to estimate the seismic velocity, or speed based on the measured value and the rock type and pore fluid composition to estimate porosity.
A large number of experimental observations indicate that the velocity almost always increases with frequency and when the waves propagate through the rock always decay.

（7） In preceding equations, iu and ju are the velocity along the i and j directions, m/s; ix and jx are the node coordinates on the i and j directions, m; ρ is the fluid density, k/m³; P is the pressure force, Pa; iF is the volume force, N; µand tµ are viscosity coefficient of laminar flow and turbulent flow respectively, Pa·s effµ is effective viscosity coefficient, Pa·s ; Pr and Prt are Prandtl number of laminar flow and turbulent flow respectively; θ is the temperature, ºC; TS is source item. k is turbulent kinetic energy，ε is turbulent kinetic energy losing rate.
They come from the commendatory number of Launder and Spalding: 44.11=C 、 92.12=C 、 09.0=µC 、 0.1=kσ 、 3.1=εσ [4] .
Analysis of Coupled Results Effect of Superheat on Coupled Result Effect of superheat on coupled temperature distribution The temperature distribution in strip blank at superheat 10°C and 30°C are shown in Fig.4(a, b) (The number on the curve means the isothermal value).
Crystal grain gets the great refining and the secondary interdendritic distance decreases greatly, but it is column structure basically seen from Fig.5.
More homogeneous organization can be gained in strip thickness direction when the point of pouring decreases to a proper temperature number and the roll-casting velocity and press is more proper, which is shown as Fig.5(b).

RFA at implant placement RFA at healing period of 4weeks Number Mean ± SD Number Mean ± SD machined 4 78.000±2.160 4 75.250±5.500 anodized 4 77.250±2.754 3 78.333±2.887 anodized+IBDA 4 78.750±2.500 3 77.000±2.646 Table 2.
RFA at implant placement RFA at healing period of 8weeks Number Mean ± SD Number Mean ± SD machined 4 76.750±4.272 4 76.667±1.528 anodized 4 75.500±5.447 4 78.500±1.291 anodized+IBDA 4 72.000±9.764 4 73.500±4.950 2.
Additionally, the presence of the residual stress in coating HA results in crack nucleation due to large grain size and growth in post-processing of HA coatings, implantation and postoperative surgery, or even in detachment of HA coatings fragments, which can irritate bone tissues.

In these structures, a number of intriguing physical properties have been discovered, such as the temperature-dependent exchange [1], unusual variation in the interlayer coupling with a change in the thicknesses of the nonmagnetic [2 and 3] and magnetic [4] layers, and spin-glass-like behavior [5].
As is known, the intensity of the absorption line at the magnetic resonance determined as an area under the resonance curve is proportional to the number of absorption centers.
It is seen that surface roughness, i.e., the grain size, strongly depends on deposition rate.
Based on these frequencies, we decomposed the observed NMR curves in the component lines whose number and location allowed us to conclude on the magnetic phase composition of the films.
In our case, the expression for the free energy per unit area is , (1) where J is the interlayer coupling constant, is the external magnetic field, is the magnetization of the th ferromagnetic layer, is the angle of in-plane magnetization counted from the direction of an external magnetic field, is the number of a magnetic layers, and is the magnetic layer thickness; the z axis is perpendicular to the film plane.

The main phase of all the samples can be identified as LiFePO4 with an ordered olivine structure indexed to orthorhombic Pnmb (JCPDS card number: 40-1499) [34].
The diffraction peak intensity becomes strongest at 800°C, and peak width at half height become smaller, which indicates that the crystallinity, grain size and ordering of local structure increase, and the lattice strain releases with the increase of the sintering temperature [42].
This behavior could be attributed to the effect of carbon reducing the size of LiFePO4 grains [10,44].
When the preparing time extends to 16 h, the crystal grains grow and accompany with the agglomeration.
There is no remarkable segregation of carbon in the mapping area according to Fig. 11, which indicates carbon is uniformly coated on the surface of LiFePO4 grains.

Business Bureau of China reported that new oil well in service was emerging with a rate of 10×10 4 every year, and the total number of oil well had exceeded 80×10 4.
Grain refinement is the most effective method to increase both the strength and impact toughness.
As for quenching and tempering steel, increasing quenching temperature is usually used to improve the strength and impact toughness, but often accompanied with grain coarsening.
Microalloying elements such as Ti and Nb could constrain the growth of austenite grains.
NbC and TiN precipitate in grain boundary could prevent the growth of austenite grains, while the solid solution of Nb in austenite is in favor of strength.

Spark plasma sintering (SPS) processing of monolith and composite ceramics materials has been recognized to offer a number of advantages over conventional sintering approaches.
It was concluded, by some, that SPS has the potential of enhanced densification and suppressed grain growth due to a fast heating rate and apparent low firing temperature.
The grain size was estimated from the full width at half maximum (FWHM) by the Scherrer equation [8] and confirmed by TEM and line intercept method by SEM.
The improvement in fracture toughness in TZP-3Y20A/50% HA samples could be attributable to the decrease of porosity, saying HA content increases from 40 to 50%, more HA get fill in the pores of the continuously porous skeleton fabricated by fine grains of ZrO2 and Al2O3.
Hardness slightly decreases at 1400 °C can be observed, this is probably caused by the influence of grain size on the hardness of the sintered composite, that is, coarser grain size lead to lower hardness [13].