Results 211 to 220 of about 51,027 (249)

Liouville Theorems for Generalized Harmonic Functions

Potential Analysis, 2002
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DOES LIOUVILLE'S THEOREM IMPLY QUANTUM MECHANICS?

International Journal of Modern Physics B, 1999
The essentials of quantum mechanics are derived from Liouville's theorem in statistical mechanics. An elementary solution, g, of Liouville's equation helps to construct a differentiable N-particle distribution function (DF), F(g), satisfying the same equation.
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A Liouville Theorem for Harmonic Maps

American Journal of Mathematics, 1995
The main result of the author is a Liouville type theorem for harmonic maps with domain \(M\), a complete Riemannian manifold of nonnegative Ricci curvature, and range \(N\), a simply-connected complete Riemannian manifold with sectional curvature bounded above by \(-a^2\), \(a>0\).
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The Poincar�?Lyapunov?Liouville?Arnol'd theorem

Functional Analysis and Its Applications, 1994
The author presents the following theorem: Let \(M\) be a symplectic manifold of dimension \(2n\). Suppose that a Hamiltonian flow \(X_H\), \(H \in C^\infty (M)\), possesses \(k\) \((1 \leq k \leq n)\) integrals in involution \(H= F_1,F_2,\dots, F_k\) and that there exists a \(k\)-dimensional compact connected submanifold \(S \subset M\) invariant ...
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Nonlinear Liouville theorems

1997
Proceeding del Meeting Reaction Diffusion Systems, Lecture Notes in Pure and Applied Mathematics, Marcel Dekker Inc.
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A Strong Version of Liouville's Theorem

The American Mathematical Monthly, 2008
1. THE MAIN RESULT. Liouville's theorem states that every bounded holomor phic function on C is constant. Let us recall that holomorphic functions / on open subsets U of the complex plane have the mean value property, that is, for every closed disk B(z,r) in U, the value of / at its center z is equal to the average of the values of f on the circle S(z ...
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Phragmen-Liouville-type theorems and Liouville theorems for a linear parabolic equation

Mathematical Notes of the Academy of Sciences of the USSR, 1985
The author proves some results of Phragmén-Lindelöf type and some Liouville type theorems applying to a class of linear parabolic equations with measurable coefficients.
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Learning nonlinear operators via DeepONet based on the universal approximation theorem of operators

Nature Machine Intelligence, 2021
Lu Lu, Pengzhan Jin, Guofei Pang
exaly  

Experimental quantum key distribution certified by Bell's theorem

Nature, 2022
David Nadlinger, C j Ballance, Kirill Ivanov   +2 more
exaly  

Another Approach to Liouville Theorem

Mathematische Nachrichten, 1982
Bojarski, B., Iwaniec, T.
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