J.J. Thomsen: Vibration and Stability: Advanced Theory, Analysis and Tools. Springer, Berlin, Germany, 2003. (See in particular pp. 59 for composite Eigenvalue problems, Dunkerley and Southwell’s formulas).

has been cited by the following article:

• TITLE: Computing Dark Energy and Ordinary Energy of the Cosmos as a Double Eigenvalue Problem

  AUTHORS: Mohamed S. El Naschie

  KEYWORDS: Double Eigenvalues, Weyl Scaling, Magueijo-Smolin Energy Formula, Dark Energy, Einstein’s Relativity, E-Infinity Theory

  JOURNAL NAME: Journal of Modern Physics, Vol.6 No.4, March 19, 2015

  ABSTRACT: We compute the dark energy and ordinary energy density of the cosmos as a double Eigenvalue problem. In addition, we validate the result using two different theories. The first theory is based on Witten’s 11 dimensional spacetime and the second is based on ‘tHooft’s fractal renormalization spacetime. In all cases, the robust result is E(O) = mc2/22 for ordinary energy and E(D) = mc2(21/22) for dark energy. Adding E(O) to E(D) we obtain Einstein’s famous equation which confirms special relativity, although it adds a quantum twist to its interpretation. This new interpretation is vital because it brings relativity theory in line with modern cosmological measurements and observations. In particular, we replace calculus by Weyl scaling in all computation which is essentially transfinite discrete.