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The mean square displacement (MSD) of a set of N displacements x_n is given by <|x|^2>=sum_(k=1)^N|x_k|^2. It arises particularly in Brownian motion and random walk problems. ...

The modified spherical Bessel differential equation is given by the spherical Bessel differential equation with a negative separation constant, ...

Let q be a positive integer, then Gamma_0(q) is defined as the set of all matrices [a b; c d] in the modular group Gamma Gamma with c=0 (mod q). Gamma_0(q) is a subgroup of ...

A generalization of calculus of variations which draws the relationship between the stationary points of a smooth real-valued function on a manifold and the global topology ...

Let E be the largest and e the smallest power of l in the HOMFLY polynomial of an oriented link, and i be the braid index. Then the Morton-Franks-Williams inequality holds, ...

The Moscow-Soicher graph is a weakly regular graph on 672 vertices with parameters (nu,k,lambda,mu)=(672,110,28,(0,18)). It is distance-regular but not distance-transitive ...

What is the longest ladder that can be moved around a right-angled hallway of unit width? For a straight, rigid ladder, the answer is 2sqrt(2), which allows the ladder to ...

Müntz's theorem is a generalization of the Weierstrass approximation theorem, which states that any continuous function on a closed and bounded interval can be uniformly ...

Let rho(x)dx be the fraction of time a typical dynamical map orbit spends in the interval [x,x+dx], and let rho(x) be normalized such that int_0^inftyrho(x)dx=1 over the ...

Let H be a subgroup of a group G. The similarity transformation of H by a fixed element x in G not in H always gives a subgroup. If xHx^(-1)=H for every element x in G, then ...