Lifting Theorem as a Special Case of Abstract Interpolation Problem

1996 ◽  
Vol 15 (4) ◽  
pp. 789-798 ◽  
Author(s):  
S. Kupin
Keyword(s):  
Interpolation Problem ◽  
Abstract Interpolation Problem ◽  
Special Case

scholarly journals A generalization of Hermite's interpolation formula in two variables

1974 ◽  
Vol 18 (4) ◽  
pp. 402-410 ◽  
Author(s):  
M. M. Chawla ◽  
N. Jayarajan
Keyword(s):  
Interpolation Problem ◽  
Cartesian Product ◽  
Interpolation Formula ◽  
Interpolation Polynomial ◽  
Cartesian Grid ◽  
Rectangular Grid ◽  
Partial Derivatives ◽  
Fixed Order ◽  
Derivatives Of ◽  
Special Case

Spitzbart [1] has considered a generalization of Hermite's interpolation formula in one variable and has obtained a polynomial p(x) of degree n + Σnj=0 = rj in x which interpolates to the values of a function and its derivatives up to order rj at xj, j = 0, 1,···n. Ahlin [2] has considered a bivariate generalization of Hermite's interpolation formula. He has developed a bivariate osculatory interpolation polynomial which agrees with f(x, y) and its partial and mixed partial derivatives up to a specified order at each of the nodes of a Cartesian grid. However, the above interpolation problem considered by Ahlin assumes that the values of partial and mixed partial derivatives of the same fixed order k – 1 are available at every point of the rectangular grid. It may also be observed that Ahlin's formula is essentially a Cartesian product of a special case of Spitzbart's formula in one variable.

Extreme self-sacrifice beyond fusion: Moral expansiveness and the special case of allyship

2018 ◽  
Vol 41 ◽  
Author(s):  
Daniel Crimston ◽  
Matthew J. Hornsey
Keyword(s):  
General Theory ◽  
Biological Markers ◽  
Natural Environment ◽  
Relevant Dimension ◽  
Special Case

AbstractAs a general theory of extreme self-sacrifice, Whitehouse's article misses one relevant dimension: people's willingness to fight and die in support of entities not bound by biological markers or ancestral kinship (allyship). We discuss research on moral expansiveness, which highlights individuals’ capacity to self-sacrifice for targets that lie outside traditional in-group markers, including racial out-groups, animals, and the natural environment.

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