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Hace 4 días · Niels Henrik Abel in 1823 , and Joseph Liouville in 1832 . The early development of these concepts in the abstract form had led to the definition of the “left” and “right” Riemann-Liouville fractional derivatives of a non-integer order \(\alpha \) .
Hace 5 días · A generalized Liouville equation and magnetic stability. Alireza Ataei, Douglas Lundholm, Dinh-Thi Nguyen. This work considers two related families of nonlinear and nonlocal problems in the plane $\R^2$. The first main result derives the general integrable solution to a generalized Liouville equation using the Wronskian of two ...
Hace 5 días · $\begingroup$ Liouville's Theorem is quite non-trivial. Its proof may not be long, but the proof uses several preliminary results, especially, Cauchy's Theorem. The behavior of sums of convergent power series is very different from that of polynomials.
7 de dic. de 2021 · In this section, we show that Bessel's functions. ϕn(x) =Jν(μnx ℓ) (n = 1, 2, 3, …) ϕ n ( x) = J ν ( μ n x ℓ) ( n = 1, 2, 3, …) are orthogonal when parameters μ n are positive roots of some transcendent equation involving Bessel functions of the first kind. Orthogonal means that. ϕn(x),ϕk(x) =∫ℓ 0 Jν(μnx ℓ)Jν(μkx ℓ ...
Hace 5 días · Joseph Liouville showed that the Liouville constant is transcendental. A decimal representation of this number starts 0.1100010000000...; in what place to the right of the decimal point will the next non-zero digit appear? (Hint: they are seen in places 1, 2, 6 - these numbers start a well-known sequence) Hint
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Hace 3 días · The Rössler attractor is the attractor for the Rössler system, a system of three non-linear ordinary differential equations originally studied by the German biochemist Otto Eberhard Rössler (born 20 May 1940). Rössler, O. E. (1976), "An equation for continuous chaos", Physics Letters A, 57 (5): 397--398.
Hace 5 días · It was founded by Joseph Liouville and published continuously by leading French Mathematicians - among the latest: Jean Leray, Jacques-Louis Lions, Paul Malliavin and presently Pierre-Louis Lions.
