In 2015 he was elected as a fellow of the American Mathematical Society " for contributions to arithmetic potential theory, computational number theory, and arithmetic dynamics ".
42.
He made important contributions to linear elasticity : the Somigliana integral equation, analogous to Green's formula in potential theory, and the Somigliana dislocations are named after him.
43.
Analogously, the " static term " in the electromagnetic Li�nard Wiechert potential theory of the fields from a moving charge, does not suffer from either aberration or positional-retardation.
44.
Kellogg is known for his work on potential theory, which was the subject of his dissertation and also his famous 1929 textbook " Foundations of Potential Theory ".
45.
His " Ueber Riemann's Theorie der algebraischen Funktionen und ihre Integrale " ( 1882 ) treats complex analysis in a geometric way, connecting potential theory and conformal mappings.
46.
;Fine topology ( potential theory ) : On Euclidean space \ R ^ n, the coarsest topology making all subharmonic functions ( equivalently all superharmonic functions ) continuous.
47.
Kellogg is known for his work on potential theory, which was the subject of his dissertation and also his famous 1929 textbook " Foundations of Potential Theory ".
48.
At very low Reynolds numbers ( based on the diameter of the circular member ) the streamlines of the resulting flow is perfectly symmetric as expected from potential theory.
49.
He used the moving frame method with success only matched by its inventor; he preferred in complex manifold theory to stay with the geometry, rather than follow the potential theory.
50.
Other potential theories include the aggressive redrawing of congressional boundaries known as gerrymandering, from a more historical perspective the loss of party alignment, or the simple fact of being an incumbent.
