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The space E of a fiber bundle given by the map f:E->B, where B is the base space of the fiber bundle.

An l_x table is a tabulation of numbers which is used to calculate life expectancies. x n_x d_x l_x q_x L_x T_x e_x 0 1000 200 1.00 0.20 0.90 2.70 2.70 1 800 100 0.80 0.12 ...

A phenomenon in which a system being forced at an irrational period undergoes rational, periodic motion which persists for a finite range of forcing values. It may occur for ...

The vertical perspective projection is a map projection that corresponds to the appearance of a globe when directly viewed from some distance away with the z-axis of the ...

The conjugate of a quaternion a=a_1+a_2i+a_3j+a_4k is defined by a^_=a_1-a_2i-a_3j-a_4k.

A map T:(M_1,omega_1)->(M_2,omega_2) between the symplectic manifolds (M_1,omega_1) and (M_2,omega_2) which is a diffeomorphism and T^*(omega_2)=omega_1, where T^* is the ...

Several flavors of the open mapping theorem state: 1. A continuous surjective linear mapping between Banach spaces is an open map. 2. A nonconstant analytic function on a ...

A map phi:M->M where M is a manifold is C^r structurally stable if any C^r perturbation is topologically conjugate to phi. Here, C^r perturbation means a function psi such ...

The number of elements of a group in a given conjugacy class.

A relation R on a set S is irreflexive provided that no element is related to itself; in other words, xRx for no x in S.