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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 ...

A perfect matching of a graph is a matching (i.e., an independent edge set) in which every vertex of the graph is incident to exactly one edge of the matching. A perfect ...

A quartic equation is a fourth-order polynomial equation of the form z^4+a_3z^3+a_2z^2+a_1z+a_0=0. (1) While some authors (Beyer 1987b, p. 34) use the term "biquadratic ...