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Showing 1 to 6 of 6 for “"Comparison Theorems"”.
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Comparison Theorems in Elliptic Partial Differential Equations with Neumann Boundary Conditions
… the data are rearranged. Specifically, we prove comparison theorems on spherical shells, spheres, and hemispheres, showing that under rearrangement of the data, the solution's convex mean increases. We also obtain similar weighted comparison results in balls.</p>
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Eigenvalue comparison theorems for certain boundary value problems and positive solutions for a fifth order singular boundary value problem.
Comparison of smallest eigenvalues for certain two point boundary value problems for a fifth order linear differential equation are first obtained. The results are extended to (2n+1)-order and (3n+2)-order boundary value problems. Methods used for these results involve the theory of $u_0$-positive …
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Positive Solutions, Existence Of Smallest Eigenvalues, And Comparison Of Smallest Eigenvalues Of A Fourth Order Three Point Boundary Value Problem
… where $1-\frac{\sqrt{3}}{3}\le p < 1$. A comparison theorem for smallest positive eigenvalues is then obtained. Using the same theorems, we will extend the problem to the fifth order via the Green's Function and again via Substitution. Applying the comparison theorems and the properties of …
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Analytic calculations of MHD equilibria and of MHD stability boundaries in fusion plasmas
… with the ideal MHD energy principle. Stability comparison theorems are presented. The main conclusion can be summarized in two points. (1) In systems with ergodic magnetic field lines, ideal MHD accurately predicts marginal stability, even in fusion grade plasmas. (2) In closed field line …
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Geometrical approximation methods for the discrete spectra of Schrödinger operators
… [Special characters omitted.] . Several new comparison theorems for the eigenvalues of a pair of Schrödinger equations [Special characters omitted.] , i = 1, 2, are introduced. These theorems allow the comparison function [Special characters omitted.] to intersect at a finite number of …
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Polynomial methods in statistical inference: Theory and practice
… quadrature. Furthermore, by proving new moment comparison theorems in the Wasserstein distance via polynomial interpolation and majorization techniques, we establish the statistical guarantees and adaptive optimality of the proposed procedure, as well as oracle inequality in misspecified models. …