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A sequence of random variates X_0, X_1, ... with finite means such that the conditional expectation of X_(n+1) given X_0, X_1, X_2, ..., X_n is equal to X_n, i.e., ...

In many cases, the Hausdorff dimension correctly describes the correction term for a resonator with fractal perimeter in Lorentz's conjecture. However, in general, the proper ...

The Ochoa curve is the elliptic curve 3Y^2=2X^3+386X^2+256X-58195, given in Weierstrass form as y^2=x^3-440067x+106074110. The complete set of 23 integer solutions (where ...

A polyhedral graph on five nodes. There are two topologically distinct pentahedral graphs which, through duality, correspond to the skeletons of the square pyramid (left ...

Petersson considered the absolutely converging Dirichlet L-series phi(s)=product_(p)1/(1-c(p)p^(-s)+p^(2k-1)p^(-2s)). (1) Writing the denominator as ...

It is possible to describe a set of positive integers that cannot be listed in a book containing a set of counting numbers on each consecutively numbered page. Another form ...

A Lie algebra over a field of characteristic zero is called semisimple if its Killing form is nondegenerate. The following properties can be proved equivalent for a ...

A Lie group is called semisimple if its Lie algebra is semisimple. For example, the special linear group SL(n) and special orthogonal group SO(n) (over R or C) are ...

The tau conjecture, also known as Ramanujan's hypothesis after its proposer, states that tau(n)∼O(n^(11/2+epsilon)), where tau(n) is the tau function. This was proven by ...

The tritetrahedron, also called the "boat polyhedron," is the name given in this work to the concave (non-regular) octahedron formed by joining three regular tetrahedra ...