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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 term "Cartan algebra" has two meanings in mathematics, so care is needed in determining from context which meaning is intended. One meaning is a "Cartan subalgebra," ...

Let g be a finite-dimensional Lie algebra over some field k. A subalgebra h of g is called a Cartan subalgebra if it is nilpotent and equal to its normalizer, which is the ...

The term "Cartesian" is used to refer to anything that derives from René Descartes' conception of geometry (1637), which is based on the representation of points in the plane ...

According to Pólya, the Cartesian pattern is the resolution method for arithmetical or geometrical problems based on equations. The first step is to translate the question ...

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 ...

A Cartesian tensor is a tensor in three-dimensional Euclidean space. Unlike general tensors, there is no distinction between covariant and contravariant indices for Cartesian ...

A method for verifying the correctness of an arithmetical operation on natural numbers, based on the same principle as casting out nines. The methods of sevens takes ...

Catalan's constant is a constant that commonly appears in estimates of combinatorial functions and in certain classes of sums and definite integrals. It is usually denoted K ...

An axiomatic system is said to be categorical if there is only one essentially distinct representation for it. In particular, the names and types of objects within the system ...