Examples of 'liouville' in a sentence
Meaning of "liouville"
Liouville refers to a mathematical concept related to the density of solutions in a particular mathematical space. It is often used in the context of complex analysis and dynamical systems
How to use "liouville" in a sentence
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liouville
Liouville showed these numbers are all transcendental.
This equation is known as the Liouville equation.
Liouville numbers and transcendence.
To the east is the comparably sized Liouville.
Liouville lambda function.
This sum is transcendental because it is a Liouville number.
Liouville showed that all Liouville numbers are transcendental.
It has a form of Liouville type theorem.
Number theory in the spirit of Liouville.
Liouville formulated the problem that is solved by the Risch algorithm.
Every surface of revolution is a Liouville surface.
The Liouville numbers are precisely those numbers having infinite irrationality measure.
The Polyakov action must be supplemented by the Liouville action to describe string fluctuations.
The Liouville equation is valid for both equilibrium and nonequilibrium systems.
The case with zero diffusion is known in statistical mechanics as the Liouville equation.
See also
The Liouville equation describes the time evolution of the phase space distribution function.
The conformal anomaly due to matter induces a Liouville term in the effective action.
Any Liouville number must have unbounded partial quotients in its continued fraction expansion.
Starting from the Liouville equation.
Liouville transformations relate Schrödinger equations with different potential landscapes but identical scattering properties.
That number is now known as the Liouville Constant.
The crater Liouville on the Moon is named after him.
That number is currently referred to as the Liouville Constant.
The Liouville transformation transforms this operator isospectrally into the Schrödinger operator.
Where λ is the Liouville function.
The Liouville numbers and hence the U numbers are uncountable sets.
On the exact Hausdorff dimension of the set of Liouville numbers.
So is the Liouville function, an important function in number theory.
Numbers are called Liouville numbers.
The formula is named after the French mathematician Joseph Liouville.
Which are Liouville.
Posthumous publication of the mathematical manuscripts of Évariste Galois by Joseph Liouville.
Below, we will show that no Liouville number can be algebraic.
Also outlined an analogy between this system and gravitation in two dimensions, via liouville gravity.
All Liouville numbers are transcendental, but not vice versa.
It should not be confused with the CGHS model or Liouville gravity.
A Liouville number can thus be approximated ‘ quite closely ' by a sequence of rational numbers.
However, not every transcendental number is a Liouville number.
Moreover, the Liouville numbers form a dense subset of the set of real numbers.
Therefore, we conclude that any such x is a Liouville number.
Of the Liouville function, which gives the parity of the number of prime factors.
Unfortunately, not every transcendental number is a Liouville number.
Sturm - Liouville theory is a theory of a special type of second order linear ordinary differential equation.
He found surprising applications of ω-languages in the study of Liouville numbers.
Sometimes V is also called the Liouville vector field, or radial vector field.
Where a is an arbitrary parameter, and if u is a solution of the Liouville equation.
We approach liouville type properties for $ \ varphi $ - laplaciano and make a geometric application for killing graphs.
Subsequently, we shall prove existence and uniqueness to this Liouville equation.
Hence a Liouville number, if it exists, can not be rational.
These theories may be understood as non-diagonal extensions of Liouville theory.
