Results 151 to 160 of about 49,771 (197)
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1998
Abstract This result has a long history. For diffeomorphisms of class C in ℝ Liouville established the result in 1850 [204] along the lines we discussed in the chapter on conformal geometry. The relaxation of the differentiability hypotheses and the local injectivity assumptions are significant steps since the aim is to describe the ...
Tadeusz Iwaniec, Gaven Martin
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Abstract This result has a long history. For diffeomorphisms of class C in ℝ Liouville established the result in 1850 [204] along the lines we discussed in the chapter on conformal geometry. The relaxation of the differentiability hypotheses and the local injectivity assumptions are significant steps since the aim is to describe the ...
Tadeusz Iwaniec, Gaven Martin
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Liouville’s Theorem for the Drifting Laplacian
Bulletin of the Malaysian Mathematical Sciences Society, 2022zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Fan Chen, Qihua Ruan, Weihua Wang
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2014
A complex number α is said to be an algebraic number if there is a non-zero polynomial \(f(x) \in \mathbb{Q}[x]\) such that f(α) = 0. Given an algebraic number α, there exists a unique irreducible monic polynomial \(P(x) \in \mathbb{Q}[x]\) such that P(α) = 0. This is called the minimal polynomial of α.
M. Ram Murty, Purusottam Rath
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A complex number α is said to be an algebraic number if there is a non-zero polynomial \(f(x) \in \mathbb{Q}[x]\) such that f(α) = 0. Given an algebraic number α, there exists a unique irreducible monic polynomial \(P(x) \in \mathbb{Q}[x]\) such that P(α) = 0. This is called the minimal polynomial of α.
M. Ram Murty, Purusottam Rath
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Liouville theorem for X-elliptic operators
Nonlinear Analysis: Theory, Methods & Applications, 2009zbMATH Open Web Interface contents unavailable due to conflicting licenses.
KOGOJ, ALESSIA ELISABETTA +1 more
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Liouville’s theorems for Lévy operators
Mathematische Annalen45 pages; minor ...
Tomasz Grzywny, Mateusz Kwaśnicki
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THE LIOUVILLE THEOREM INVOLVING QUANTUM EFFECT
Acta Mathematica Scientia, 1986Summary: 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, 2008zbMATH Open Web Interface contents unavailable due to conflicting licenses.
CARISTI, GABRIELLA +2 more
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On Liouville’s Theorem for Biharmonic Functions
SIAM Journal on Applied Mathematics, 1971The 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, 2002zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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DOES LIOUVILLE'S THEOREM IMPLY QUANTUM MECHANICS?
International Journal of Modern Physics B, 1999The 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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