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As an illustration of this, the parity cycle (1 1 0 0 1 1 0 0) and its sub-cycle (1 1 0 0) are associated to the same fraction 5 / 7 when reduced to lowest terms. In this context, assuming the validity of the Collatz conjecture implies that (1 0) and (0 1) are the only parity cycles generated by positive whole numbers (1 and 2 ...
More specifically, the Millennium Prize version of the conjecture is that, if the elliptic curve E has rank r, then the L-function L(E, s) associated with it vanishes to order r at s = 1. Hilbert's tenth problem dealt with a more general type of equation, and in that case it was proven that there is no algorithmic way to decide whether a given ...
Many mathematical problems have been stated but not yet solved. These problems come from many areas of mathematics, such as theoretical physics, computer science, algebra, analysis, combinatorics, algebraic, differential, discrete and Euclidean geometries, graph theory, group theory, model theory, number theory, set theory, Ramsey theory, dynamical systems, and partial differential equations.
For example, if s=2, then 𝜁(s) is the well-known series 1 + 1/4 + 1/9 + 1/16 + …, which strangely adds up to exactly 𝜋²/6. When s is a complex number—one that looks like a+b𝑖, using ...
X-Plane is a flight simulation software initially launched by Laminar Research in 1995. Commercial desktop versions are sold for macOS, Windows, and Linux. In addition, Laminar Research also distributes FAA-certified versions for professional use. A mobile version has been available for Android, iOS, and webOS since 2009 as well.
Laminar Research is a small software company based in Columbia, South Carolina, and dedicated to providing software that accurately reflects the laws of physics. Laminar's flagship product is the flight simulator X-Plane. [1] The game works with Macintosh, Microsoft Windows, and Linux. They also have mobile versions for iPhone, iPad, and Android.
The Bell X-2 (nicknamed "Starbuster" [1]) was an X-plane research aircraft built to investigate flight characteristics in the Mach 2–3 range. The X-2 was a rocket-powered, swept-wing research aircraft developed jointly in 1945 by Bell Aircraft Corporation, the United States Army Air Forces and the National Advisory Committee for Aeronautics (NACA) to explore aerodynamic problems of ...
This statement, due to Tunnell's theorem (Tunnell 1983), is related to the fact that n is a congruent number if and only if the elliptic curve y 2 = x 3 − n 2 x has a rational point of infinite order (thus, under the Birch and Swinnerton-Dyer conjecture, its L-function has a zero at 1). The interest in this statement is that the condition is ...