Sentence examples for boundary rotation from inspiring English sources
Noor studied the Hankel determinant of Bazilevic functions in [15] and of functions with bounded boundary rotation in [16 19].
The simultaneous evolution of high boundary misorientations was ascribed to the subgrain boundary rotation for accommodating further strains.
Deformation at temperatures and strain rates between 1040 1140 °C and 0.1 0.001/s resulted in a transition of dominant deformation mechanisms from dislocation based plasticity to grain boundary rotation and sliding.
It has three stages: (1) formation of elongated cells and subgrains; (2) increased misorientation between neighboring grains and breakup of elongated grains into smaller units; and (3) rotation of boundaries by grain boundary rotation and formation of equiaxed structure.
From Brannan [7] representation form for functions with bounded boundary rotations, we have (2.3).
For we obtain the well-known classes and of analytic functions with bounded radius and bounded boundary rotations, respectively.
Also, V k ( 0 ) = V k, the class of functions of bounded boundary rotations and V 2 ( η, 0 ) = C denotes the class of convex functions of complex order.
Then, for η ≠ 0 (complex), 0 ≤ ρ < 1, f ∈ V k if and only if ( 1 + 1 η z f ′ ′ ( z ) f ′ ( z ) ) ∈ P k , z ∈ E. We note that for η = 1, we have the class V k of bounded boundary rotations of order ρ introduced by Padmanabhan and Parvatham [1].
For λ = 0, we obtain the class V k of analytic functions with bounded boundary rotations of order σ studied by Padmanabhan et al. [2] and when σ = 0 and λ = 0, we get the class V k discussed by Paatero [3], see also [4 8].
Several mechanisms may contribute concurrently to the plastic deformation of nanocrystalline materials (grain-boundary sliding, grain-boundary rotation, and the generation of dislocations at grain-boundaries) [84].
All of these three effects may increase the resistance for grain-boundary sliding, grain-boundary rotation, and the generation of dislocations at grain-boundaries.
