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We will deal with the question of rationality of ringed surfaces and discuss the usefulness of the so called P-curves for constructing rational ringed-surface-blends.
Especially a method for constructing rational adaptive blends which bypass a given obstacle (or more given obstacles when needed) is thoroughly discussed and its functionality is demonstrated on a number of examples.
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The former was especially important in giving a systematic way to construct rational maps from given topological/combinatorial data.
The fact that the Darboux frame is rotation-minimizing along lines of curvature of a smooth surface is invoked to construct rational surface patches whose boundary curves are lines of curvature.
As is well known, the Wronskian technique can also be applied to construct rational solutions, positons, negatons, complexitons, and interaction solutions of the nonlinear equations.
Three linear methods for constructing a rational S matrix from phase shifts are presented and compared.
We present a method for constructing a rational quadratic Bezier patch that interpolates a portion of a quadric surface, and clarify the geometric and parametric degrees of freedom inherent in any such construction.
The second requirement of constructing a rational economic order is the ability to define, without reference to the understandings of individual economic actors and their contexts, an objective hierarchy of preferences.
Butts, says Sternberg, approaches every new project in a systematic way, starting with an exhaustive literature search, communicating her reasons for doing the study, constructing a rational and reasonable methodology, learning the necessary techniques, and locating the right people to collaborate with.
Not everybody wants to hear this, but accepting this truth is the price we must pay for constructing a rational protectionist policy that will protect industries that do deserve protection.
Perhaps that's the biggest problem with content marketing: It's a rational construct, based on rational assumptions.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com