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Adding their inertia moments suitably, one can obtain as a result the reduction at the DOF (degree of freedom) of the system.
On the basis of these data, it is possible by use of the well known solving analytic or numerical procedures to calculate the values of the natural frequencies (e.g. by means of numerical methods based on the Jacobi eigenvalue algorithm [11]).
A stage of the two-stage gear (a) and the separated assembly of the countershaft (b) In the case of high values of the mesh stiffness (in relation to the other spring parameters in the system) after performing the reduction of the inertia moments on the input shaft, one can obtain the 2-DOF system described by the formula (8) where: and If the stiffness k1 and k2 are significantly lower than the stiffness of the countershaft kw23 and the meshes have very high values of stiffness (in relation to the other spring parameters in the system), then after the reduction of parameters on the input shaft the natural frequency is expressed by the formula
(10) For the vibrations of the gear wheels in relation to the countershaft (the stiffness of the input shaft, output shaft and mesh stiffness are neglected), after the reduction parameters on the countershaft, one can obtain the natural frequency of the equivalent system as (11) where: An analysis of dynamics in the system for varying stiffness of the countershaft-numerical calculations For the two-stage reducer, as we mention above, the important dynamic phenomena appear only on the high-speed stages.
The data for spur gears have included: z1 = 20÷31; z2 = 40÷61; z3 = 20÷41; z4 = 40÷61 – numbers of teeth for the first and second stage, respectively, mn1 = 2÷4 mm; mn2 = 2÷4mm – pitch modules, bw1= 20÷80 mm; bw2 = 20÷80 mm – face width of wheels.

Because of the higher dislocation density the yield strength will be increased what goes along with the reduction of elongation.
The result of the heat treatment is a reduction of the accumulated dislocations in the strain hardened material [10].
The use of the FLD is a further step to gain a better understanding of the materials´ behavior and acquire more data for the simulation of IHT.
The measured data are plotted using a simple linear regression function.
This effect can be interpreted as a reduction of the dislocations and the associated strain hardening.

For example, the statute of “Management Measures on Urban Waste”, issued in 2007, pinpointed the principles of waste reduction, recycling, and recovery (3R principle) [6-8].
According to the government, the methods included consulting work reports and literatures, analyzing the results and data from these literatures and reports.
Data resource: China Statistics Yearbook on Environment from 2007 to 2011 [9-13] According to Hangzhou Environment Bulletin, the total MSW amount has increased year by year.
Incineration has been proven as an attractive method of MSW treatment due to the primary advantages of harmless control, volume reduction (about 90%), mass reduction (about 70%) and energy recovery.
Lo, Waste management in Guangdong Cities: The waste management literacy and waste reduction preferences of domestic waste generators.

Expert assessments show that 80% of the projected GHG emission reduction can be reached by improvement of vehicle efficiency and introduction of alternative fuels [3].
The major challenge in reaching this goal is that the necessary reductions in the carbon emissions by vehicles must be achieved without disruptions in transportation patterns and population mobility.
Since there is no available experimental data that suggest numeric values of the coefficients in the Wiebe model adjusted to the gaseous fuel compositions considered in the current work, an approach suggested in [13] was applied.
Laminar flame velocity for each of the considered gaseous fuel compositions was estimated based on the published experimental data.
In the case of engine feeding by methanol steam reforming products the working mixture leaning up to λ=1.45 ensured more than double reduction of NOx emissions as compared to the reference liquid fuel – methanol.

The data clearly shows that the density value was slightly decreased with increasing temperature.
The evaporation of volatile alkali metal oxides and partial melting at high temperature is likely a main reason for the density reduction [4].
The related dielectric data are also listed in Table 1.
Moreover, small reduction of Tc was observed with increasing the sintering temperature (Fig. 4(d)).
Therefore, a reduction of polarization for crystal structure with the tetragonal symmetry can be occurred (for the 1250°C ceramics).

Through data-driven way, non-parametric method forms a convex linear envelope as the production frontier, which does not involve the estimation of parameters of functions.
Not only analytical method, but also the processing of data is important for the correctness and accuracy of the empirical results.
Conclusion and policy implication Based on the cross-province panel data, this article uses SFA method to analyze the effect of FDI and foreign trade on energy technical efficiency in the Yangtze Delta region.
study on the provincial panel data, Modern Management Science, 5 (2013) 78-86.
E., Coelli T.J., A model for technical inefficiency effects in a stochastic production frontier for panel data, Empirical Economics, 20 (1995)325-332

The data so generated will eventually enable us quantifying the resilience figures for the pipe segment system for cases pertaining to variation of flow, inlet temperature and inlet pressure (Case-I, II & III).
System resilience data is estimated from Fig.1 by evaluating the area under the stress-strain curve employing numerical integration technique.
Pipe system resilience data can also be estimated from Fig.2 by evaluating the area under the stress-strain curve employing numerical integration technique.
Pipe system resilience data is estimated from Fig.3 by evaluating the area under the stress-strain curve employing numerical integration technique.
However, analyzing all the available data, the reason for this stress declining phenomena is found to be fairly straight-forward.

The increase in water molecules release and reduction of molecular oxygen release from the barium cerate, irradiated by high-energy ions is found during vacuum constant rate heating.
It is suggested that the partial reduction from В4+ to В3+ of the cations in the lattice B-sites takes place under irradiation due to formation of oxygen vacancies.
The state of the surface relief according to atomic-force microscopy data is also in agreement with the results of SEM.
Unfortunately, the adsorption band region of carbonate structures (1300-1600 cm-1) overlaps the region of OH group bending vibrations, complicating data interpretation.

It results in the reduction of the wafer removal rate, and a pad conditioner or diamond disk must be frequently employed to refresh the pad surface.
It was found from experimental data that the diamonds which were located outside, originally protruded more highly and with crest lines oriented upward wore faster.
It was found that the wafer removal rate reduced gradually with the use of pad conditioner as compared with that of a large reduction when the pad conditioner was not applied during the polishing process [3].
Table 1 Experimental data of worn area Original relative height Outmost annulus （r=20mm） Middle annulus （r=15mm） Innermost annulus （r=10mm） （μm） （μm 2） （μm 2） （μm 2） 240~249 311 x 308 230~239 298 286 234 220~229 245 234 162 210~219 196 186 124 It can be seen that the worn area of the diamonds at the outmost ring is larger than that of the diamonds at the middle and inner annuluses.

The results compare fairly with those obtained from DNS data.
All data are non-dimensional and obtained from the cross section at the outlet of the duct where x=25.
As for velocity, as is shown in Fig. 1(a)(b), the time-averaged velocity along z axis obtained from the modified k-ω is in good agreement with DNS data from [8].
In addition, the DNS from [8] used 38384.4 CPU hours to get a fully developed result, while the current implementation only requires 170.75 CPU hours, a large reduction in time making this currently proposed model suitable for industrial simulation.
A modified k-ω model is also developed and validated against DNS data in MHD square duct flow with electric insulating walls.