MATHEMA TICS: M. MORSE THE CRITICAL POINTS OF A FUNCTION OF n VARIABLES BY MARSTON MORSE

A New Modification of Morse Potential Energy Function

Interaction of meso — tetrakis (p-sulphonato phenyl) porphyrin (hereafter abbreviated to TSPP)with Na+ has been examined using HF level of theory with 6-31G* basis set. Counterpoise (CP)correction has been used to show the extent of the basis set superposition error (BSSE) on thepotential energy curves. The numbers of Na+ have a significant effect on the calculated potentialenergy curve (includ...

Mathema Tics: D. Maharam

for some N. The only difficulty in the proof of these statements, beyond the methods already used in §§1-4, is the possibility that surfaces in $3 may have boundary values which are constant on some arcs of the circumference. Statement (1) yields a modified Morse theory; the usual requirement is that every k-cap contain a minimal surface g for which D [g] = a. But by assigning type numbers to b...

The Critical Points of a Function

A Brief History of Morse Homology

Morse theory was originally due to Marston Morse [5]. It gives us a method to study the topology of a manifold using the information of the critical points of a Morse function defined on the manifold. Based on the same idea, Morse homology was introduced by Thom, Smale, Milnor, and Witten in various forms. This paper is a survey of some work in this direction. The first part of the paper focuse...

Homotopy Type and Critical Values

Take M , a finite-dimensional differentiable manifold, and f : M → R a smooth function. Such a function f is called a Morse function if it has no degenerate critical points. Morse theory allows us to connect the topology, in particular the homotopy type, of M with the behavior of f on M . In the following sections, we will state and prove two important theorems in Morse theory. Using these two ...