Infinite Congruence Theorem
Integration by parts is used as an essential step in deriving the Infinite Congruence Theorem. The derivation follows from the Linear congruence theorem combined with fractal geometry. The result highlights the convenience to express integral equations with respect to the derivatives of the integrand. The results of this theorem have given rise to new numerical techniques for solving integral equations. The theorem has been in heavy use in the field of quantum computing as a result.
Read more about this topic: Integration By Parts
Famous quotes containing the words infinite, congruence and/or theorem:
“Since [man] is infinitely removed from comprehending the extremes, the end of things and their beginning are hopelessly hidden from him in an impenetrable secret; he is equally incapable of seeing the nothing from which he was made, and the infinite in which he is swallowed up.”
—Blaise Pascal (1623–1662)
“As for butterflies, I can hardly conceive
of one’s attending upon you; but to question
the congruence of the complement is vain, if it exists.”
—Marianne Moore (1887–1972)
“To insure the adoration of a theorem for any length of time, faith is not enough, a police force is needed as well.”
—Albert Camus (1913–1960)