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There is one more definition that we shall need: it is closely linked to an important theorem in the structure of semisimple Lie groups [52, 60].
Proposition 3.1 is linked to Theorem 2.1 of Section 2 in the subsequent result.
A posthumous work of 1665 by Pascal on the "arithmetic triangle" now linked to his name (see binomial theorem) showed how to calculate numbers of combinations and how to group them to solve elementary gambling problems.
In this paper, we will use the following local linking Theorem A to prove our theorems.
We have designed these techniques as part of a project to link automatic theorem provers to the interactive theorem prover Isabelle.
In this paper, we want to get a (C) c sequence by a linking theorem (Theorem 2.1, in [11]).
In [4], the authors used the mountain pass theorem, a linking theorem, and Clark's theorem to establish the existence of multiple solutions for a fractional difference boundary value problem with a parameter.
In [3], Micheletti and Pistoia used a variational linking theorem to investigate the existence of two solutions for a more general nonlinearity (g(cdot,u)).
It is also shown that the linked cluster theorem for Feynman graphs extends to generalized Feynman graphs.
Michael Atiyah and Isadore Singer are to share the $875,000 award for their proof of a theorem that links two very different areas of mathematics--topology and differential equations.
We shall use the following variant weak linking theorem to prove our result.
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