Rotary and percussive drilling prediction using regression analysis


KAHRAMAN S.

INTERNATIONAL JOURNAL OF ROCK MECHANICS AND MINING SCIENCES, vol.36, no.7, pp.981-989, 1999 (Journal Indexed in SCI) identifier identifier identifier

  • Publication Type: Article / Article
  • Volume: 36 Issue: 7
  • Publication Date: 1999
  • Doi Number: 10.1016/s0148-9062(99)00050-9
  • Title of Journal : INTERNATIONAL JOURNAL OF ROCK MECHANICS AND MINING SCIENCES
  • Page Numbers: pp.981-989

Abstract

It has recently been conjectured that the eigenvalues $\lambda$ of the Dirac operator on a closed Riemannian spin manifold $M$ of dimension $n\ge 3$ can be estimated from below by the total scalar curvature: $$ \lambda^2 \ge \frac{n}{4(n-1)} \cdot \frac{\int_M S}{vol(M)}. $$ We show by example that such an estimate is impossible.