Sentence examples for the left division from inspiring English sources

Let (F) be a local loop on (Usubseteq M) and let (Vsubseteq U) be a neighbourhood on which the left division is well-defined.

They are defined by begin{aligned} x/y cdot y = x end{aligned}and begin{aligned} ycdot ybackslash x=x end{aligned}for all (x,yin V), and, for obvious reasons, are called the right and the left division, respectively.

Just as done in [16], we take G k = F ′ ( x k ) and use the left division operation in MATLAB to solve the system of linear equations (2.1) at each iteration.

When the bialgebra in question is a Hopf algebra, the Shestakov Umirbaev operations can be written with the help of the left division: begin{aligned} p(x_1,ldots,x_m y_1,ldots,y_n z)= sum (u_{(1)}v_{(1)})backslash (u_{(2)},v_{(2)},z). end{aligned}This form of the definition may be preferable since it expresses each operation directly via the associator.

The left division was led by Major General Marshall and the central division was under Francis Rawdon-Hastings.

The left division was commanded by Eiliphredas, the dux of Phoenice Libanensis, and included a Hunnic contingent of horse-archers under Apsich.

In general, there is no reason to expect that the right and the left divisions would be expressed as multiplications by an inverse of any kind.

Informally speaking, a non-associative word is an expression formed from several indeterminates by applying the multiplication and the right and the left divisions (In particular, a monomial is a non-associative word formed using multiplication only).

In irreducible Hopf algebras the right and left division are uniquely determined.

In Duitama's data, the rates in upper left division and lower right division are 8.4% and 22.2%, respectively.

Instead of moving beyond the Federals' left and attacking their flank, Longstreet's left division, under McLaws, would face Maj.