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Perturbation theory of eigenvalue problems
Franz Rellich,B. J. Berkowitz +1 more
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The article was published on 1969-01-01 and is currently open access. It has received 600 citations till now. The article focuses on the topics: Inverse iteration & Eigenvalue perturbation.read more
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A Matricial Boundary Value Problem Which Appears in the Transport Theory
TL;DR: In this article, the authors studied the boundary value problem Tφ′ = −Aφ (I-P)φ(0), Pφτ = 0, where T = T ∗, A = A ∗, P 2 = P, P ∗ T = TP, T invertible The motivation to consider such problem comes from the transport theory The behavior of values of τ for which there is a nontrivial solution (exceptional values) is investigated using the indicator function.
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CMCpy: Genetic Code-Message Coevolution Models in Python
TL;DR: CMCpy is an object-oriented Python API and command-line executable front-end that can reproduce all published results of CMC models and presents novel analytical results that extend and generalize applications of perturbation theory to quasispecies models and pioneer the application of a homotopy method for quasipecies with non-unique maximally fit genotypes.
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Complex D convergence and diagonal convergence of matrices
TL;DR: In this article, it was shown that for complex matrices of order n ⩽ 3 diagonal convergence, D C convergence and boundary convergence are all equivalent, and an example of a 4 by 4 matrix that is D C convergent but not diagonally convergent is constructed.
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Gradient Flows for Sampling: Mean-Field Models, Gaussian Approximations and Affine Invariance
TL;DR: In this article , the affine invariance property of gradient flows was studied for the Kullback-Leibler divergence, and it was shown that the gradient flows resulting from this choice of energy do not depend on the normalization constant.
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A note on semilinear elliptic equation with biharmonic operator and multiple critical nonlinearities
TL;DR: In this article, the existence and non-existence of nontrivial weak solutions of the weak version of the problem with multiple critical nonlinearities was studied. And the existence of nonsmooth solutions was established using the Mountain-Pass theorem by Ambrosetti and Rabinowitz.