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The system of partial differential equations U_t = [V,W] (1) V_t = [W,U] (2) W_t = [U,V], (3) where [A,B] denotes the commutator.

For b>a>0, 1/b<(lnb-lna)/(b-a)<1/a.

The Napoleon crossdifference is the crossdifference of the Napoleon points. It has triangle center function alpha_(1510)=((b^2-c^2)[2cos(2A)-1])/a and is Kimberling center ...

Given the center of a circle, divide the circle into four equal arcs using a compass alone (a Mascheroni construction).

The integral transform defined by (Kphi)(x)=int_0^inftyG_(pq)^(mn)(xt|(a_p); (b_q))phi(t)dt, where G_(pq)^(mn) is a Meijer G-function. Note the lower limit of 0, not -infty ...

Two real algebraic manifolds are equivalent iff they are analytically homeomorphic (Nash 1952).

The unit of information obtained by using the natural logarithm lnx instead of the base-2 logarithm log_2x=lgx when defining entropy and related information theoretic ...

The natural domain of a function is the maximal chain of domains on which it can be analytically continued to a single-valued function.

The "natural exponential function" is the name sometimes given in elementary contexts to the function f(x)=e^x, where e =2.718... is the base of the natural logarithm. While ...

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 ...