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In contrast, the directional distance function scales point A to point A' on the boundary in the direction of increasing desirable outputs from y 1 to y 2 and decreasing undesirable outputs from b 2 to b 1.
Such a scheme requires only solving a set of one-dimensional problems, and the grid can be easily fit to the boundary in the direction of each of these problems.
(ii) The free boundary (Gamma(t)) is a surface of class (C^{1,lambda}) at each time (tin[0,T)), and the normal velocity (V_{n} x,t)) of the free boundary in the direction of its normal n at position x is uniformly bounded, sup_{substack{ tin 0,T) mathbf{x}inGamma(t)} }biglvert V_{n}(mathbf{x},t bigrvert < infty.
When a precipitate β is growing at the expense of a matrix α, there is a flux J 1 (mol m− 2 s− 1) of atoms crossing the boundary in the direction of the precipitate and a flux J 2 of atoms going back to the matrix.
(ii) The free boundary (Gamma(t)) is a surface of class (C^{1,alpha}) at each time (tin[0,T) ), and the normal velocity (V_{n}(mathbf{x},t)) of the free boundary in the direction of its normal n at position x is uniformly bounded, mathop{sup_{tin 0,T)}}_{mathbf{x}inGamma(t)} biglvert V_{n}(mathbf{x},t) bigrvert < infty.
In both groups, however, a majority of subjects exhibited a change in their perceptual boundary in the direction of the /∫/-end of the continuum.
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The thickness of the hypertrophic zone was defined as the distance along the longitudinal axis of the local growth plate boundaries in the direction of the cell columns from the top edge of the most cranial cell to the bottom edge of the most caudal cell.
Subjects in the adult group exhibited a reliable change in boundary location in the direction of /∫/ (i.e., an adaptive shift) following the period of speech practice, t(12) = 2.44, p<.05.
The energy Equation (4) is solved iteratively by moving the boundaries in the directions of decreased energy.
Eriugena, then, has a dialectical understanding of the relation of God and man which can be viewed as orthodox from one point of view, but which is always transgressing the boundaries of orthodoxy in the direction of a view which has God and man mutually contemplating themselves and each other, in an endless, eternal play of theophanies.
The drift at the edge of the boundary layer is oriented in the direction of wave propagation in the transitional flow regime, while this drift is oriented in the opposite direction in the turbulent flow regime.
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