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The specimens was broken at number of cycles of 630442.
The Betti numbers are one of the invariant in a homology.
In 2-dimensional case, the Betti numbers are consisting of two numbers.
The other is b1= H1(X), which is the number of holes.
Because the Betti numbers are invariant, the shape of the grain has nothing to do with the Betti numbers.

In this study a number of thermal treatment schemes over a wide range of temperatures between 120˚ to 350˚ C and times (30 – 120 minutes) have been experimented in an effort to understand the effect of thermal treatment on tensile properties of vacuum die cast modified aluminum alloy A356.
This is because ultra fine grain structure present in die castings due to severe chill rate often approaches almost similar microstructural condition of solution heat treatment.
Hanna et al. [10] have reported that fine eutectic silicon along with fine primary aluminum grains improves mechanical properties.

The total Gibbs energy is given as a summation of the products of chemical potential of species and molar numbers of species in the system as follows; (1) N: number of species C: chemical potentials of species X: molar number of speciesThe main problem of minimization of the Gibbs energy can be formulated as follows; mim G (2) subject to AX = B (3) X > 0 (4) Here, A is the stoichiometric number matrix and B: is total mole numbers of elements This main problem can be converted to the following dual problem using the duality [8]: maximize (6) subject to (7) where L is the elemental chemical potentials; (8) This dual problem gives the basis of understanding the generalized chemical potential diagrams as shown in Fig. 1.
This quantity can be represented by the plane that has the slope corresponding to the given stoichiometric numbers.
Eq.(7) is graphically given as the surface and the inside of the polyhedron consisting of stable compound planes having fixed stoichiometric number and the Gibbs energy.
By changing the initial stoichiometric numbers, we obtain the respective equilibrium states for a whole stoichiometric number region.
Stoichiometric numbers are represented by a slope of a flat plane in a chemical potential space.

The common point of experiment conditions of lower left corner, selected case number 1 to 9, is purity of copper 4N.
Macro and microstructures were sound structure with few impurities on and/or inner grain boundaries.
Figure 4 shows electrical resistivity vs Vickers hardness of the selected case number from 1 to 9 OFHC copper.
Figures 5 and 6 indicate the oxygen content and total impurities of the selected case number from 1 to 9 OFHC copper.
Vickers hardness of the selected case number from 1 to 9 OFHC copper. 0123456789 5 10 15 20 25 Oxygen Content (ppm) Selected Case Number 5 ppm Raw Material Figure 5: Oxygen content of the selected case number from 1 to 9 OFHC copper. 0123456789 0 10 20 30 40 50 60 40 ppm Total Impurities (ppm) Selected Case Number Raw Material Figure 6: Total impurities of the selected case number from 1 to 9 OFHC copper. 4.

Table 1 Number of repeated combing The feed amount per cycle[mm] Number of repeated combing Forward feed Back feed 4.2 4.9 5.5 4.7 4.4 5.0 5.2 4.0 4.6 From table 1 it can be known that when feed mode is the same, the shorter the length in feed amount per cycle is, the bigger the number of the repeated combing will be, so the combing efficiency can be improved; when the length of feed amount per cycle decreases from 5.2mm to 4.7mm, the number of repeated combing can be increased by 10%.
When the length of feed mount per cycle is identical, the number of repeated combing of back feed is larger than that of forward feed.
The main process parameters of the comber and combing preparation are shown in table 4 Table 3 Fiber parameters Test term Numerical value Classer's staple [mm] 28.5 1%fiber span length [mm] 36.1 Average length(n) [mm] 21.0 Content of fiber below 12.5mm [%] 6.8 Neps number[grain·g-1] 46 Mic value 4.4 Fiber strength [cN·tex-1] 3.1 Table 4 The processing parameter of combing preparation and comber Experiment project Project 1 Project 2 Project 3 UNllapE32 Super lap machine Bat weight [ktex] 72 72 77.7 Tex of feeding sliver [tex] 4500 4500 4500 Blending number 24 24 26 Drawing times 1.453 1.453 1.453 Total drawing multiple of combing preparation 7.265 7.265 7.265 E65 comber The feed amount per cycle [mm] 5.2 4.7 4.7 Speed [pliers sequence·min-1] 450 450 450 Ekartement gauge [mm] 9.6 9.6 9.6 Feed mode Back feed Back feed Back feed Scale of detaching dial 0.5 0.3 0.5 Nip gauge of main drawing area [mm] 45 45 45 Nip gauge of pre drawing area [mm] 54 54 54 Pre drawing multiple 1.37 1.37 1.37
This is because that the decreasing length of feed amount per cycle can increase the number of repeated combing of cylinder to tuft (as table 1), and can increase the fiber straightness of combed sliver, the structure of combed sliver is therefore improved.
Table 5 Comparisons of yarn qualities Experiment project project 1 project 2 project 3 Percentage of noil 18.99 18.87 19.18 Output [kg·h-1] 65 59 64 Yarn unevenness CV [%] 13.05 12.94 12.87 -40%thin place [entris·km-1] 119 118 111 -50%thin place number [entris·km-1] 2 4 3 +35%thick place number [entris·km-1] 376 363 338 +50%thick place umber [entris·km-1] 34 28 26 +140% neps number [entris·km-1] 286 257 208 +200%neps number [entris·km-1] 58 58 42 IPI-stat value [entris·km-1] 781 738 657 IPI stat value [entris·km-1] 94 84 71 Notes: IPI- is the sum of statistical value of -40% thin place, +35% thick place and +140% nep: IPI is the sum of statistical value of +50% thick place, -50% thin place, and +140% nep: The effect of bat weight on yarn quality Fix the length of feed amount per cycle, and increase the bat weight from 72g/m to 77.7g/m, carry on the spinning experiment according to process parameters of comber and combing preparation in table 4, the test result of yarn quality parameters

Additionally, large numbers of grain boundary provide a short cut for heat energy to diffuse from shear zone to the inside of workpiece and promote the deformation of workpiece material.
The coordination numbers in workpiece are marked by different colors.
The atoms with coordination number seven and eight lie in shear zone and the coordination number more than eight seems mainly located at the tool-workpiece interface.
That is to say, any atoms with coordination number more than six can be treated as metastable phases.
The overcoordinated atoms are coded by according to the coordination number.

Around the deposited particle’s periphery (in the jetting region) the temperatures are significant, this lends itself to the presence of grain refinement at the periphery of sprayed particles and the propagation of dynamic recrystallization which is closely coupled with the thermal softening of the particle.
A number of studies [1-6] sought to understand the deformation sequences and the bonding mechanism associated with the CS technique.
Microstructure of the Al coating material (gray areas are single phase Al with limited porosity appearing as black areas) A cold spray sample presented herein was produced alongside a number of other specimens [24] by a Kinetic Metallization (KM).
The particle drag coefficient were calculated according to the local Reynolds number and Henderson’s correlation by evaluating the gas nozzle exit velocity (1025 m/s) based on the gas stagnation temperature (140°C), pressure (620 kPa), and the He gas thermodynamic properties using a 1-dimensional isentropic model.
Excessive temperatures, however, can lead to localized stress relaxation, grain refinement at the periphery of sprayed particles and the prorogation of dynamic recrystallization in the narrow band along the periphery which is closely coupled with the thermal softening of the particle.

MTT test was applied to quantitatively assess the number of viable cells attached and grown on the scaffolds.
Nano-HA, with an average grain of less than 100nm, was obtained from our lab.

The silica fume is in amorphous form, and it has some special powder properties such as ultra fine grain size and high specific surface area and high chemical activity, these provide favorable foundation for low energy consumption process of recycling the powder.
And a large number of manpower and material resources consumed to overstock the low quality micro silica powder with ferrosilicon production increased more and more. 
CONCLUSIONS The silica fume is in amorphous form, and it has some special powder properties such as ultra fine grain size and high specific surface area and high chemical activity, these provide favorable foundation for low energy consumption process of recycling the powder.

To achieve improvements in the mechanical properties, fine grain size, homogeneous microstructure and high density are desirable.
Hence significant grain growth takes place.
Acknowledgements The authors thank DPT (the State Planning Organization of Turkey) for providing financial support for this work under project number 2001K120590.