1
[see also: consequence, effect, outcome, achievement] Let n→∞, applying Lemma 5. The result is......
As a result, B is isomorphic to C.
As usual, we can rephrase the above result as a uniqueness theorem.
Slightly refining a result of [8], Davenport proved......
The method of proof of Theorem B can be adapted to extend the right-to-left direction of Mostowski's result by showing that......
It is hoped that a deeper understanding of these residues will help establish new results about the distribution of modular symbols.
We could have adopted an approach to proving Theorem 2 along a line of reasoning which bears greater resemblance to the treatment of the analogous result in Section 1.
In the course of writing this paper we learned that P. Fox has simultaneously obtained results similar to ours in certain respects.
There is a related result concerning primitivity.
The results have been encouraging enough to merit further investigation.
We show that one can drop an important hypothesis of the saddle point theorem without affecting the result.
This rests on a result of Kummer.
2
The resulting formula exhibits u as the Laplace transform of x. [Not: “The obtained formula'']
We can solve the resulting equations successively for c1,...,cn.
Their study resulted in proving the conjecture for k=1.
The demand that each entry be a perfect square results in nine equations. [Note the subjunctive be.]
Less than 1 in p of its points will result in a quartic with ideal class number p.
Lebesgue discovered that a satisfactory theory of integration results if the sets Ei are allowed to belong to a larger class of subsets of the line.
[Do not write: “It results that'' if you mean: It follows that.]