Sentence examples for and using the uniform from inspiring English sources
Passing to the limit as (varepsilonto0) and using the uniform continuity of (u_{i}) on the compact set (Itimes[-r,r]), we obtain lim_{varepsilonto0} frac{u^{i}_{r} varepsilon)}{[alpha_{i}]_{q}}=0, which yields the desired result.
Passing to the limit (deltarightarrow0) and using the uniform bounds of those quantities, we recover the system and the initial condition u_{t}+ ucdotnabla)u-triangle u+nabla p=f quad text{in } Omega _{1}, qquad u x,0)=u_{0}.
Write begin{aligned} (A_m - A_n)f = A_m (f - f_m) + (A_m B_m - A_n B_n)h + A_n (f_n - f) end{aligned}and use the uniform boundedness of (A_n) to show that (A_n f) converges.
It was found that a suitable cross-sectional distance of less than 3 km should be adopted when simulating hyperconcentrated floods, and the results using the uniform allocation mode can agree better with measurements than other two allocation modes.
Experimental results varying with position of the substrate are fitted to the theory of evaporation and the simulation of film uniformity using the uniform evaporation method was examined.
To compare the results, their effective isotropic elastic modulus, E = 16.42 GPa and ν = 0.32 for cortical bone and E = 0.482 GPa and ν = 0.26 for cancellous bone, were deduced using the uniform strain and uniform stress isotropic bounds of Voigt and Reuss to describe the behavior of the first isotropic model.
As one application of the technique, we successfully produced a large area of highly uniform hexagonally packed gold nanoposts and nanoholes in gold thin film using the uniform HCP nanoholes and nanopillars of photoresist for lift-off process, as shown in Fig. 5a and b.
The proposed model, which allows for the varying local fluid thermophysical properties inside the flow path, can be applied for both dry and wet working conditions by using the uniform enthalpy equations.
The objects were uniformly distributed throughout the environment, and all object properties were determined using the uniform probability distribution with different values possible for each axis.
Hence a small-sized problem is generated by using the uniform distribution, and it is solved with the Lingo 8 software.
