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If 0<=g(x)<=1 and g is nonincreasing on the interval [0, 1], then for all possible values of a and b, int_0^1g(x^(1/(a+b)))dx>=int_0^1g(x^(1/a))dxint_0^1g(x^(1/b))dx.

A p×q submatrix of an m×n matrix (with p<=m, q<=n) is a p×q matrix formed by taking a block of the entries of this size from the original matrix.

A function defined for all possible input values.

A curve which intersects some straight line in an infinity of points (but for which not every point lies on this curve).

The geometric centroid of a quadrilateral lamina is the center of its Wittenbauer's parallelogram.

n-dimensional Euclidean space.

The binomial coefficient (n; k) is the number of ways of picking k unordered outcomes from n possibilities, also known as a combination or combinatorial number. The symbols ...

The Smarandache function mu(n) is the function first considered by Lucas (1883), Neuberg (1887), and Kempner (1918) and subsequently rediscovered by Smarandache (1980) that ...

An amicable quadruple as a quadruple (a,b,c,d) such that sigma(a)=sigma(b)=sigma(c)=sigma(d)=a+b+c+d, (1) where sigma(n) is the divisor function. If (a,b) and (x,y) are ...

A Brier number is a number that is both a Riesel number and a Sierpiński number of the second kind, i.e., a number n such that for all k>=1, the numbers n·2^k+1 and n·2^k-1 ...