Results 151 to 160 of about 24,283 (189)

Liouville’s theorems for Lévy operators

Mathematische Annalen
45 pages; minor ...
Tomasz Grzywny, Mateusz Kwaśnicki
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THE LIOUVILLE THEOREM INVOLVING QUANTUM EFFECT

Acta Mathematica Scientia, 1986
Summary: In this article we have shown, if the wave packets are used to describe the dynamical states of particles in a many-particle system, we can get a set of Langevin-type equations, instead of the classical canonical equations of Hamilton. At the same time a diffusion-type Liouville theorem involving quantum effect is resulted instead of the ...
Bao, Keda, Liu, Fusui
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Liouville theorems for some nonlinear inequalities

Proceedings of the Steklov Institute of Mathematics, 2008
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CARISTI, GABRIELLA, D'AMBROSIO L, MITIDIERI, ENZO   +2 more
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On Liouville’s Theorem for Biharmonic Functions

SIAM Journal on Applied Mathematics, 1971
The following theorem, called Liouville's theorem, is well known. THEOREM 1. Any harmonic function bounded either above or below in all of n-space is constant. The reader is referred to the excellent book by Protter and Weinberger [1] for the proof of the above theorem.
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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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