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In older literature, the term linear connection is occasionally used for an Ehresmann connection or Cartan connection on an arbitrary fiber bundle, [1] to emphasise that these connections are "linear in the horizontal direction" (i.e., the horizontal bundle is a vector subbundle of the tangent bundle of the fiber bundle), even if they are not ...
The following is a list of linear integrated circuits. Many were among the first analog integrated circuits commercially produced; some were groundbreaking innovations, and many are still being used.
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Therefore, an affine connection is associated to a principal connection. It always exists. For any affine connection Γ : Y → J 1 Y, the corresponding linear derivative Γ : Y → J 1 Y of an affine morphism Γ defines a unique linear connection on a vector bundle Y → X. With respect to linear bundle coordinates (x λ, y i) on Y, this ...
A G-connection on E is an Ehresmann connection such that the parallel transport map τ : F x → F x′ is given by a G-transformation of the fibers (over sufficiently nearby points x and x′ in M joined by a curve). [5] Given a principal connection on P, one obtains a G-connection on the associated fiber bundle E = P × G F via pullback.
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The result is a set of non-linear equations that define the configuration parameters of the system for a set of values for the input parameters. Freudenstein introduced a method to use these equations for the design of a planar four-bar linkage to achieve a specified relation between the input parameters and the configuration of the linkage.
The following sets will constitute the basic open subsets of topologies on spaces of linear maps. For any subsets and , let (,):= {: ()}.. The family {(,):,} forms a neighborhood basis [1] at the origin for a unique translation-invariant topology on , where this topology is not necessarily a vector topology (that is, it might not make into a TVS).