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But in this situation one or both of boundary values can be a pressure above zero.
To the authors' knowledge, few results on third-order differential equations with inhomogeneous three-point boundary values can be found in the literature.
The solution is an iterative process and setting boundary values can be a problem whereas co-current operation can be solved easily as a group of partial differential equations with known initial values.
For example, if 4 categories are assumed for precursor CVS, then one set of boundary values can be determined by assuming 20% of CVS observations in the first category, 30% in the second, 30% in the third, and 20% in the last category.
By expanding variables at a discretized time interval, a non-linear coupled space/time domain problem with initial and boundary values can be converted into a series of recursive linear boundary value problems, the variations of variables can be described more precisely via a self-adaptive computing procedure, and the non-linear iteration can be avoided.
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For any function in the Dirichlet boundary condition (1.5), there is a set of the functions of Neumann boundary condition (1.10), where is corresponding to the complex equation (1.4) one by one, namely if we know the boundary value and one complex equation in (1.4), then the boundary value can be determined.
The definition of the applicability domain (AD) of a QSAR model is very useful to define boundaries whereby the obtained predicted values can be trusted with confidence.
Although these results cannot at present be used as a bloom metric to assess ecological status, due to a lack of reference conditions and class boundary values, they can be used to support classification decisions by expert judgement (Aroviita et al. [2012]).
But the results of [4] show that if α < p − 1, one can define the trace of u on the boundary, and the homogeneous boundary value condition can be defined as usual.
Whether the usual Dirichlet homogeneous boundary value condition can be imposed depends on whether (a_{i}(x)) is degenerate on the boundary or not.
For more difficult and nonconvex domains such as crescents we demonstrate how the right choice of charge points is connected to how far into the complex plane the solution of the boundary value problem can be analytically continued, which in turn depends on both domain shape and boundary data.
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