Mono-Duality in Static Systems

  • David Yang Gao
Part of the Nonconvex Optimization and Its Applications book series (NOIA, volume 39)


The governing equations of equilibrium in nonlinear systems are amazingly beautiful. Their structure is repeated throughout the field equations of mathematical physics and of discrete systems of networks. By introducing abstract notations, we are able to see unifying structures in the different theories. Through pure mathematical analysis, the intrinsic inner beauty in physical nature can be revealed.


Saddle Point Variational Problem Bilinear Form Duality Theorem Legendre Transformation 
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  1. 1.
    Leonard Euler (1707–1783), a great mathematician from Switzerland. During his life he published a total of 886 books and mathematical memoirs, and produced thirteen children (all but five of whom died very young).Google Scholar
  2. 2.
    Joseph Louis Lagrange, 1736–1813, was born in Turin of Italian-French ancestry. His most valuable book Mechanique Annlutique was published in 1788. In this work, Lagrange unified the science of mechanics, and, as Hamilton said, made of it “a kind of scientific poem”.Google Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2000

Authors and Affiliations

  • David Yang Gao
    • 1
  1. 1.Department of MathematicsVirginia Polytechnic Institute and State UniversityBlacksburgUSA

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