Let E → M be a vector bundle of rank k and let F ( E ) be the principal frame bundle of E. Then a ( principal ) connection on F ( E ) induces a connection on E. First note that sections of E are in one-to-one correspondence with right-equivariant maps F ( E ) → R < sup > k </ sup >.

As before, suppose that E is a fibre bundle with structure group G. In the special case when G has a free and transitive left action on F ′, so that F ′ is a principal homogeneous space for the left action of G on itself, then the associated bundle E ′ is called the principal G-bundle associated to the fibre bundle E. If, moreover, the new fibre F ′ is identified with G ( so that F ′ inherits a right action of G as well as a left action ), then the right action of G on F ′ induces a right action of G on E ′.

A solder form on a principal H-bundle P over M is an R < sup > n </ sup >- valued 1-form θ: TP → R < sup > n </ sup > which is horizontal and equivariant so that it induces a bundle homomorphism from TM to the associated bundle P ×< sub > H </ sup > R < sup > n </ sup >.

Since α is a principal connection, it induces a connection on any associated bundle to Q.

Let V a representation of G, and form the vector bundle V = Q ×< sub > G </ sub > V over M. Then the principal G-connection α on Q induces a covariant derivative on V, which is a first order linear differential operator

In particular, on any associated vector bundle the principal connection induces a covariant derivative, an operator that can differentiate sections of that bundle along tangent directions in the base manifold.

For any linear representation W of G there is an associated vector bundle over M, and a principal connection induces a covariant derivative on any such vector bundle.

*( a ) Whoever commits an offense against the United States or aids, abets, counsels, commands, induces or procures its commission, is punishable as a principal.

:( a ) Whoever aids, abets, counsels, commands, induces or procures the commission of an offense, is punishable as a principal.

This transformer induces current in the rotor without a direct electrical connection, thus there are no wires to the rotor limiting its rotation and no need for brushes.

Generalizing all these examples, any ( possibly nonlinear ) connection on M induces a semispray H, and conversely, any semispray H induces a torsion-free nonlinear connection on M. If the original connection is torsion-free it coincides with the connection induced by H, and homogeneous torsion-free connections are in one-to-one correspondence with full sprays.

When a ligand activates the G protein-coupled receptor, it induces a conformational change in the receptor that allows the receptor to function as a guanine nucleotide exchange factor ( GEF ) that exchanges GDP for GTP on the G < sub > α </ sub > subunit.

The diagonal map induces a vector bundle over B called the Whitney sum of these vector bundles and denoted by α ⊕ β.

* If p = 0 in S for some prime number p, then the taking of pth powers induces an endomorphism of G < sub > a </ sub >, and the kernel is the group scheme α < sub > p </ sub >.

The curve α induces a bundle map α < sub >∗</ sub >: TJ → TM so that the following diagram commutes:

* Any endomorphism σ of the field F induces an endomorphism α < sub > σ </ sub > of the group X ( F )

* Any automorphism π of the Dynkin diagram induces an automorphism α < sub > π </ sub > of the group X ( F ).

In a second possible pathway, phosphatidylinositol transfer protein α ( PITP ) binds to phosphorylated DCC which induces phospholipase C ( PLC ) to increase the ratio of cAMP to cGMP.

Moreover, the dominance in parasympathetic action ( with reciprocal inhibition of the sympathetic ) at the hypothalamic level induces, by its peripheral action, the autonomic symptoms of sleep and, by its action on the cortex, a lessening in the reactivity of the sensory and motor apparatus of the somatic nervous system.

The intense vomiting and occasional diarrhea it induces can clear the body of worms and other tropical parasites, and harmala alkaloids themselves have been shown to be anthelmintic Thus, this action is twofold ; a direct action on the parasites by these harmala alkaloids ( particularly harmine in ayahuasca ) works to kill the parasites, and parasites are expelled through the increased intestinal motility that is caused by these alkaloids.

When EM radiation at the frequences for which it is referred to as " radio waves " impinges upon a conductor, it couples to the conductor, travels along it, and induces an electric current on the surface of the conductor by moving the electrons of the conducting material in correlated bunches of charge.

Such generators bear no resemblance to Faraday's homopolar disc generator of 1831, but they still rely on his electromagnetic principle that a conductor linking a changing magnetic field induces a potential difference across its ends.

Other reasons include: a ) changes in plant canopy caused by shifts in plant biomass production associated with moisture regime ; b ) changes in litter cover on the ground caused by changes in both plant residue decomposition rates driven by temperature and moisture dependent soil microbial activity as well as plant biomass production rates ; c ) changes in soil moisture due to shifting precipitation regimes and evapo-transpiration rates, which changes infiltration and runoff ratios ; d ) soil erodibility changes due to decrease in soil organic matter concentrations in soils that lead to a soil structure that is more susceptible to erosion and increased runoff due to increased soil surface sealing and crusting ; e ) a shift of winter precipitation from non-erosive snow to erosive rainfall due to increasing winter temperatures ; f ) melting of permafrost, which induces an erodible soil state from a previously non-erodible one ; and g ) shifts in land use made necessary to accommodate new climatic regimes.

* The action for any group G is defined by for all g in G and all x in X ; that is, the whole group G induces the identity permutation on X.

An example of an inner product which induces an incomplete metric occurs with the space C of continuous complex valued functions on the interval.

The individual magnetic field of adjacent turns induces eddy currents in the wire of the coil, which causes the current in the conductor to be concentrated in a thin strip on the side near the adjacent wire.

If ( V, ‖·‖) is a normed vector space, the norm ‖·‖ induces a metric ( a notion of distance ) and therefore a topology on V. This metric is defined in the natural way: the distance between two vectors u and v is given by ‖ u − v ‖.

Giving ± 1 the discrete topology and ± 1 < sup > F </ sup > the product topology induces the subspace topology on X < sub > F </ sub >.

The group of isometries of space induces a group action on objects in it.

Like above, the group of automorphisms of space induces a group action on objects in it.

The transformer is based on two principles: first, that an electric current can produce a magnetic field ( electromagnetism ) and second that a changing magnetic field within a coil of wire induces a voltage across the ends of the coil ( electromagnetic induction ).

An affine map between two affine spaces is a map that induces a linear transformation on vectors, defined by pairs of points.

Fundamental groups and homology and cohomology groups are not only invariants of the underlying topological space, in the sense that two topological spaces which are homeomorphic have the same associated groups, but their associated morphisms also correspond — a continuous mapping of spaces induces a group homomorphism on the associated groups, and these homomorphisms can be used to show non-existence ( or, much more deeply, existence ) of mappings.

San Andreas quakes induces creep ( movement occurring on earthquake faults ) in the Hayward fault, which runs directly through Oakland, Berkeley, San Jose and other Bay Area cities.

T3 acts directly on cerebral cortex mitochondria and induces release of cytochrome C to induce apoptosis.

In these cases, the highly focused beam of electrons impinges on a sample and induces it to emit light from a localized area.

It induces salivation and a sensation of furriness on the tongue, stimulating the throat, the roof and the back of the mouth ( for review Yamaguchi, 1998 ).

Thus the act of measurement induces a fundamental irreversible change on the density matrix ; this is analogous to the " collapse " of the state vector, or wavefunction collapse.

This point then induces a pseudometric on the space of functions, given by

For vector spaces V, a seminorm p induces a pseudometric on V, as

The signal can be reproduced by running the tape back across the tape head, where the reverse process occurs – the magnetic imprint on the tape induces a small current in the read head which approximates the original signal and is then amplified for playback.

* Theban leader Pelopidas goes on an embassy to the Persian king Artaxerxes II and induces him to propose a settlement of the Greek states ' disputes according to the wishes of the Thebans.