Morse inequalities, a function space integral approach

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...

Morse Inequalities for a Dynamical System

Witten’s Proof of Morse Inequalities

Both properties do not depend on the choice of coordinates. The index ind (x) is the number of negative eigenvalues of Hess (f) (x). Let mp = mp (f) be the number of critical points of index p. Let bp = bp (M) = dimH (M) be the dimension of the p de Rham cohomology group. 0→ Ω (M) d −→ Ω (M) d −→ ... d −→ Ω (M) d −→ 0 This is called the de Rham complex. Note that d = 0. If ω = dα, then dω = 0. ...

Morse Inequalities and Zeta Functions

Morse inequalities for diffeomorphisms of a compact manifold were first proved by Smale [21] under the assumption that the nonwandering set is finite. We call these the integral Morse inequalities. They were generalized by Zeeman in an unpublished work cited in [25] to diffeomorphisms with a hyperbolic chain recurrent set that is axiom-A-diffeomorphisms which satisfy the no cycle condition. For...

New integral inequalities for $s$-preinvex functions

In this note, we give some estimate of the generalized quadrature formula of Gauss-Jacobi$$underset{a}{overset{a+eta left( b,aright) }{int }}left( x-aright)^{p}left( a+eta left( b,aright) -xright) ^{q}fleft( xright) dx$$in the cases where $f$ and $left| fright| ^{lambda }$ for $lambda >1$, are $s$-preinvex functions in the second sense.