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.
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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.
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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 ".
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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.
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;Fine topology ( potential theory ) : On Euclidean space \ R ^ n, the coarsest topology making all subharmonic functions ( equivalently all superharmonic functions ) continuous.
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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.
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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.
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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.
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