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Define f(x_1,x_2,...,x_n) with x_i positive as f(x_1,x_2,...,x_n)=sum_(i=1)^nx_i+sum_(1<=i<=k<=n)product_(j=i)^k1/(x_j). (1) Then minf=3n-C+o(1) (2) as n increases, where the ...

A smooth function is a function that has continuous derivatives up to some desired order over some domain. A function can therefore be said to be smooth over a restricted ...

The problem of finding the curve down which a bead placed anywhere will fall to the bottom in the same amount of time. The solution is a cycloid, a fact first discovered and ...

Let h:{0,1}^(l(n))×{0,1}^n->{0,1}^(m(n)) be efficiently computable by an algorithm (solving a P-problem). For fixed y in {0,1}^(l(n)), view h(x,y) as a function h_y(x) of x ...

Whirls are figures constructed by nesting a sequence of polygons (each having the same number of sides), each slightly smaller and rotated relative to the previous one. The ...

A palindromic prime is a number that is simultaneously palindromic and prime. The first few (base-10) palindromic primes are 2, 3, 5, 7, 11, 101, 131, 151, 181, 191, 313, ...

A sequence whose terms are integers. The most complete printed references for such sequences are Sloane (1973) and its update, Sloane and Plouffe (1995). Neil Sloane ...

A Lambert series is a series of the form F(x)=sum_(n=1)^inftya_n(x^n)/(1-x^n) (1) for |x|<1. Then F(x) = sum_(n=1)^(infty)a_nsum_(m=1)^(infty)x^(mn) (2) = ...

The Neuberg cubic Z(X_(30)) of a triangle DeltaABC is the locus of all points P whose reflections in the sidelines BC, CA, and ABform a triangle perspective to DeltaABC. It ...

Roundoff error is the difference between an approximation of a number used in computation and its exact (correct) value. In certain types of computation, roundoff error can ...