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The Enneper surfaces are a three-parameter family of surfaces with constant negative curvature (and nonconstant mean curvature). In general, they are described by elliptic ...

There exists an absolute constant C such that for any positive integer m, the discrepancy of any sequence {alpha_n} satisfies ...

Let sigma(n) be the divisor function. Then lim sup_(n->infty)(sigma(n))/(nlnlnn)=e^gamma, where gamma is the Euler-Mascheroni constant. Ramanujan independently discovered a ...

A function of the coordinates which is constant along a trajectory in phase space. The number of degrees of freedom of a dynamical system such as the Duffing differential ...

Applying the Kaprekar routine to 4-digit number reaches 0 for exactly 77 4-digit numbers, while the remainder give 6174 in at most 8 iterations. The value 6174 is sometimes ...

Pairs of points of a line, the product of whose distances from a fixed point is a given constant. This is more concisely defined as a projectivity of period two. If ...

The so-called Malthusian equation is an antiquated term for the equation N(t)=N_0e^(lambdat) describing exponential growth. The constant lambda is sometimes called the ...

A problem in the calculus of variations. Let a vessel traveling at constant speed c navigate on a body of water having surface velocity u = u(x,y) (1) v = v(x,y). (2) The ...

If there exists a critical region C of size alpha and a nonnegative constant k such that (product_(i=1)^(n)f(x_i|theta_1))/(product_(i=1)^(n)f(x_i|theta_0))>=k for points in ...

For some range of r, the Mandelbrot set lemniscate L_3 in the iteration towards the Mandelbrot set is a pear-shaped curve. In Cartesian coordinates with a constant r, the ...