## Contributions to the Calculus of Variations: Theses Submitted to the Department of Mathematics of the University of Chicago and a Bibliography |

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12 of Eai accessory extremaloids admissible arc analogous arc E^g Bliss boundary value problem calculus of variations characteristic numbers coefficients composite arc conjugate point conjugate system constants corners COROLLARY definition denote determinant different from zero differential equations element end-conditions equa equations 3:2 equivalent problem exist extremal arc family of composite family of extremals focal point following theorem function F function H(x G. A. Bliss Hamiltonian function Hence hoxh identically zero infinitesimal contact transformation integral intersection interval inverse problem Jacobi equations Lemma linearly independent matrix minimizing arc multiplier rule necessary condition neighborhood non-singular normal obtained original problem orthogonal parameter family principal curvature problem of Bolza problem of Lagrange prove quadratic form region satisfy the condition satisfying the equations second variation subarc sufficiency theorem tangent tensor tions transversality vanish variables vectors xb+1 yi(x