Simple Analytic Proof Research Articles

Remarks on Bodenmiller's theorem

The original version ofBodenmiller's Theorem states that the three circles with the diagonals of a complete quadrilateral as diameters intersect in the same two points. We provide a simple analytic proof of this fact which yields a much more general result. Furthermore we discuss some special configurations appearing in this context.

A simple proof of some congruences for colored generalized frobenius partitions

In this paper we present a very simple analytic proof of some congruences for generalized Frobenius partitions with k colors. The proof highlights yet another combinatorial property of these objects.

On the exact evaluation of 〈det Up〉 in a lattice gauge model

A simple analytic proof of Green and Samuel's conjecture on the behaviour of 〈det U p〉 in lattice QCD 2 is found by exploiting the formal analogy of the model with the representation of multimonopole solutions. Our method also leads to an exact evaluation of 〈det U p〉 for large N in the weak coupling regime and to a simple weak coupling 1 N expansion.

Simple Analytic Proof of the Prime Number Theorem

(1980). Simple Analytic Proof of the Prime Number Theorem. The American Mathematical Monthly: Vol. 87, No. 9, pp. 693-696.

Simple Analytic Proof of the Prime Number Theorem

Simple Analytic Proof of the Prime Number Theorem

A Simple Analytic Proof of a General | chi 2 Theorem

A Simple Analytic Proof of a General | chi 2 Theorem

A Simple Analytic Proof of a General χ2 Theorem

Many of the applications of the x2 distribution can be justified as particular cases of a general theorem. It is the purpose of this paper to state and give a simple analytic proof of this theorem. Two of the more basic x2 principles are stated as corollaries of the general theorem. The usual procedure in developing the applications of x2 is to treat each application more or less independently. When proofs are included they usually involve geometry in n-space, the moment generating function, the Laplace transform, or the algebra of quadratic forms. The proof given here makes use of none of these methods. It does make use of the Jacobian in the change of variables in a multivariate differential (or multiple integral).

Least squares, and a generalisation of the »Student»-Fisher theorem

Abstract 1. Following the methods employed by Steffensen 1 a simple analytical proof of a generalisation of the »Student»-Fisher theorem is obtained. Geometrical proof of this generalisation has been given by Sterne.2