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Over a small neighborhood U of a manifold, a vector bundle is spanned by the local sections defined on U. For example, in a coordinate chart U with coordinates (x_1,...,x_n), ...

An unduloid, also called an onduloid, is a surface of revolution with constant nonzero mean curvature. It is a roulette obtained from the path described by the foci of a ...

A theorem, also called a unicity theorem, stating the uniqueness of a mathematical object, which usually means that there is only one object fulfilling given properties, or ...

In machine learning theory, the Vapnik-Chervonenkis dimension or VC-dimension of a concept class C is the cardinality of the largest set S which can be shattered by C. If ...

An ordered vector basisv_1,...,v_n for a finite-dimensional vector space V defines an orientation. Another basis w_i=Av_i gives the same orientation if the matrix A has a ...

Let X=(X,tau) be a topological vector space whose continuous dual X^* separates points (i.e., is T2). The weak topology tau_w on X is defined to be the coarsest/weakest ...

A generalized hypergeometric function _pF_q[alpha_1,alpha_2,...,alpha_p; beta_1,beta_2,...,beta_q;z] is said to be well-poised if p=q+1 and ...

Let B_n(r) be the n-dimensional closed ball of radius r>1 centered at the origin. A function which is defined on B(r) is called an extension to B(r) of a function f defined ...

(d^2u)/(dz^2)+(du)/(dz)+(k/z+(1/4-m^2)/(z^2))u=0. (1) Let u=e^(-z/2)W_(k,m)(z), where W_(k,m)(z) denotes a Whittaker function. Then (1) becomes ...

A sequence of uncorrelated numbers alpha_n developed by Wiener (1926-1927). The numbers are constructed by beginning with {1,-1}, (1) then forming the outer product with ...