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Assume that f is a nonnegative real function on [0,infty) and that the two integrals int_0^inftyx^(p-1-lambda)[f(x)]^pdx (1) int_0^inftyx^(q-1+mu)[f(x)]^qdx (2) exist and are ...

The Euclidean plane parametrized by coordinates, so that each point is located based on its position with respect to two perpendicular lines, called coordinate axes. They are ...

The only nonassociative division algebra with real scalars. There is an 8-square identity corresponding to this algebra. The elements of a Cayley algebra are called Cayley ...

A description of an object by properties that are different from those mentioned in its definition, but are equivalent to them. The following list gives a number of examples. ...

An (infinite) line determined by two points (x_1,y_1) and (x_2,y_2) may intersect a circle of radius r and center (0, 0) in two imaginary points (left figure), a degenerate ...

The geodesics in a complete Riemannian metric go on indefinitely, i.e., each geodesic is isometric to the real line. For example, Euclidean space is complete, but the open ...

The term "continuum" has (at least) two distinct technical meanings in mathematics. The first is a compact connected metric space (Kuratowski 1968; Lewis 1983, pp. 361-394; ...

The complex lattice Lambda_6^omega corresponding to real lattice K_(12) having the densest hypersphere packing (kissing number) in twelve dimensions. The associated ...

The cross-correlation of two complex functions f(t) and g(t) of a real variable t, denoted f*g is defined by f*g=f^_(-t)*g(t), (1) where * denotes convolution and f^_(t) is ...

Decimal is the base-10 notational system for representing real numbers. The expression of a number using the decimal system is called its decimal expansion, examples of which ...