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Namely, it should be represented by a local loop such that begin{aligned} (acdot b cdot b= acdot (bcdot b) end{aligned}whenever both sides are defined.
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First, a local loop is replaced by the corresponding geodesic loop (which, in the analytic case is the same as a right alternative local loop), and then the tangent operations for a geodesic loop are extracted from its canonical connection.
A local loop is called a smooth loop if (U=V=M) in the above definitions.
As a consequence, a monoassociative local loop is sometimes defined as a local loop of a monoassociative quasigroup [1, 8].
One can recover a local loop (F) from the corresponding geodesic loop with the help of the additional operation (varPhi ) defined by begin{aligned} acdot b= atimes varPhi (a,b).
The true analogue of a Lie group in the non-associative Lie theory is not a smooth loop, but, rather, a local loop, or a germ of a local loop (We shall use the term "infinitesimal loops" for germs of local loops).
The invertible elements of a finite-dimensional algebra over the real numbers form a local loop.
An identity satisfied by a local (formal) loop can be lifted to an identity in its algebra of distributions.
This paper presents a theoretical study of an inertial actuator connected to an accelerometer by a local feedback loop for active vibration control on a floating raft.
7 Semiconductor metal composite Ag2S/Ag NPs killed bacteria presumably by a local circuit loop and reactive oxygen species (ROS) produced under UV irradiation.
New wireless technologies might offer a route to customers that by-passes the local loop.
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