Abstract: The author gives several definitions, including the definition of linear vector spaces, inner products, and Hilbert spaces. He defines linear operators and the Hilbert adjoint operator, and ...
In this paper, the algebraic, geometric and analytic multiplicities of an eigenvalue for linear differential operators are defined and classified. The relationships among three multiplicities of an ...
The RH proof presents a complete resolution of the Riemann Hypothesis (RH) based on a spectral-theoretic construction. The core idea is the realization of a self-adjoint operator whose spectrum ...
Abstract: First-order optimization algorithms, often preferred for large problems, require the gradient of the differentiable terms in the objective function. These gradients often involve linear ...
This work presents the mathematical/theoretical framework of the “nth-Order Feature Adjoint Sensitivity Analysis Methodology for Response-Coupled Forward/Adjoint ...
Edited by Joel E. Cohen, The Rockefeller University, New York, NY, and approved December 6, 2011 (received for review August 23, 2011) These results were found for finite-dimensional models. But the ...
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