Related examples To illustrate, the solution 3^3 + 6^3 = 3^5 has bases with a common factor of 3, the solution 7^3 + 7^4 = 14^3 has bases with a common factor of 7, and 2^n + 2^n = 2^{n+1} has bases w ...
The first is principally devoted to consideration of direct problems over (typically) the integers, that is, determining the structure of hA from the structure of A: for example, determining which ele ...
A smooth structure on a manifold M is a collection of smoothly equivalent smooth atlases. Here, a smooth atlas for a topological manifold M is an atlas for M such that each transition function is a sm ...
Poincaré's question At the beginning of the 20th century, Henri Poincaré was working on the foundations of topology—what would later be called combinatorial topology and then algebraic topology. He ...
Mordell (1922) proved Mordell's theorem: the group of rational points on an elliptic curve has a finite basis. This means that for any elliptic curve there is a finite sub-set of the rational points o ...
The Navier–Stokes equations Main article: Navier–Stokes equationsIn mathematics, the Navier–Stokes equations are a system of nonlinear partial differential equations for abstract vector fields of a ...
Most known and nontrivial (i.e. interacting) quantum field theories in 4 dimensions are effective field theories with a cutoff scale. Since the beta-function is positive for most models, it appears th ...
The Riemann zeta function is defined for complex s with real part greater than 1 by the absolutely convergent infinite series\zeta(s) = \sum_{n=1}^\infty \frac{1}{n^s} = \frac{1}{1^s} + \frac{1}{2^s} ...
Let X be a compact complex manifold of complex dimension n. Then X is an orientable smooth manifold of real dimension 2n, so its cohomology groups lie in degrees zero through 2n. Assume X is a K?hler ...
The relation between the complexity classes P and NP is studied in computational complexity theory, the part of the theory of computation dealing with the resources required during computation to solv ...
The Institute is run according to a standard structure comprising a scientific advisory committee that decides on grant-awarding and research proposals, and a board of directors that oversees and appr ...
The question is whether, for all problems for which an algorithm can verify a given solution quickly (that is, in polynomial time), an algorithm can also find that solution quickly. The former describ ...
Differential technological development is a strategy proposed by transhumanist philosopher Nick Bostrom in which societies would seek to influence the sequence in which emerging technologies developed ...
A study published in the journal Computers in Human Behavior was conducted between 1992 and 1994 surveying first-year college students across various countries. The overall percentage of the 3,392 stu ...
In the beginnings of the scientific revolution, scientists such as Robert Boyle found themselves in conflict with those such as Thomas Hobbes, who were skeptical of whether science was a satisfactory ...
