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A line bundle is a special case of a vector bundle in which the fiber is either R, in the case of a real line bundle, or C, in the case of a complex line bundle.

A member of the smallest algebraically closed subfield L of C which is closed under the exponentiation and logarithm operations.

The name Lobachevsky's function is sometimes given to the function Lambda(theta)=1/2Cl_2(2theta), also denoted Pi(theta), where Cl_2(x) is Clausen's integral.

A triangular matrix L of the form L_(ij)={a_(ij) for i>=j; 0 for i<j. (1) Written explicitly, L=[a_(11) 0 ... 0; a_(21) a_(22) ... 0; | | ... 0; a_(n1) a_(n2) ... a_(nn)]. ...

The MacBeath circle, a term coined here for the first time, is the circumcircle of the MacBeath triangle. It has a fairly complicated radius, center function, and circle ...

In abstract topology, a machine is method for producing infinite loop spaces and spectra. In automata theory, an abstract machine that is implemented in hardware is simply ...

An infinite-dimensional differential calculus on the Wiener space, also called stochastic calculus of variations.

For a real number x, the mantissa is defined as the positive fractional part x-|_x_|=frac(x), where |_x_| denotes the floor function. For example, for x=3.14159, the mantissa ...

If x takes only nonnegative values, then P(x>=a)<=(<x>)/a. (1) To prove the theorem, write <x> = int_0^inftyxP(x)dx (2) = int_0^axP(x)dx+int_a^inftyxP(x)dx. (3) Since P(x) is ...

If a matrix group is reducible, then it is completely reducible, i.e., if the matrix group is equivalent to the matrix group in which every matrix has the reduced form ...