The paper defines conjugate points for systems of second-order ODEs and discusses their properties.
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5 results for “eigendistributions”
problem Defining and analyzing conjugate points for systems of second-order ordinary differential equations.
method Using Jacobi fields and eigendistributions of the Jacobi endomorphism, the paper extends the concept of conjugate points to a generalization of locally symmetric spaces and Lagrangian systems with symmetry.
result The paper provides a comprehensive analysis of conjugate points for various types of systems of second-order ordinary differential equations.
The aim of this paper is to classify compact, simply connected Kähler manifolds which admit J-invariant Killing tensor with two eigenvalues of multiplicity 2 and n-2 and with constant eigenvalue corresponding to 2-dimensional eigendistribution.
The abstract conjectures and proves conditions for scalar-flat Kähler surfaces with specific tensor properties.
problem Conditions for scalar-flat Kähler surfaces with special tensor properties.
method Conjecture and prove in three special cases.
result The conjecture is proven in three special cases.
Deep random feature models are analyzed for their performance with exact asymptotic expressions.
problem Understanding the performance of deep random feature models.
method Established a novel universality result and used the convex Gaussian Min-Max theorem.
result Exact asymptotic expressions for the performance of deep random feature models are derived.
New geometric structures derived from Hessian metrics and tensors.
problem Constructing geometric structures from Hessian metrics and tensors.
method Introduced a family of Hessian metrics and constructed a -tensor field.
result Derived golden and metallic structures from the tensor field.