Support region

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This is the most basic and simplest of the analyses that we can do. It determines how much of the limit curve is modified when one control point is moved. That part which is dependent on a given control point is called the support region of that point. Pedantically both of these refer to an interval in parameter space, but since that corresponds to a piece of the curve we can also use support to refer to that. 

This gives a more precise meaning to the term support width. It is the width in abscissa units of the closure15 of the abscissa region over which the basis function is non-zero (the support region). 

B closure is a technicality which allows us to ignore the fact that the basis function can be zero at isolated points of the support region. 

By looking at the extent of influence of one control point after 0,l,2,oo refinements, in the cubic B-spline scheme we can see that the refined polygons converge towards the basis function, and the last non-zero entry converges towards the end of the support region. 

In a previous chapter we saw that we should expect to see discontinuities of some derivative in the limit curve at places corresponding to the ends of the support region. 

Then we expect derivatives lower than the k th to be continuous at the end of the support region, and the next derivative to have a discontinuity. 

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A low stiffness material may have some additional adverse effects. A low stiffness material will experience a loss of tension in the film in the field-supported region of operation at a lower electric field. Further, many soft materials would be more prone to puU-in failure due to mechanical instabilities resulting from film defects or thinner film regions (a source of dielectric failure in softer insulating films) [10]. 

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Meshless Methods, Fig. 2 Weight function, support region, and approximated function... 

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B.2.1.1. Transit Particles pass support region repeatedly in particles finite steps. This produces an equivalent scattering and diffusion process. 

In and near the support region there arise non-adiabatic phenomena due to violation of the constancy of both the first and second invariants. This affects the motion of transit as well as trapped particles. 

Another less obvious non-adiabatic effect arises from the finiteness of the drift steps (x ) of Fig. 2. With each step (x ) in the azimuthal direction of the main internal coil, there is an associated step (x ) in the direction along the supports, as given by the perturbed F-surfaces of Fig. 3. Since the steps C(x>j) are finite, however, the earlier predicted cancellation of the contributions during a complete passage through the support region ... 

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