Sentence examples for unique multiplication from inspiring English sources

Incidentally, we are using a vector of weighting factors ε instead of a unique multiplication by scalar factor ε. This, however, does not modify derivation nor the final result.

However for any modulus that is a power pn of a prime, it can be shown that there exists a unique multiplication making the group Zpn a ring in a way that makes the nonzero elements of the ring a cyclic (and therefore abelian) group under the multiplication, and hence making the ring a field.

These large, dense bodies grow in the cytoplasm from H6 p.i. to H20 p.i. Electron microscopy allows us to more precisely observe the unique multiplication mode of B. massiliensis.

To assess the functioning of the cell division machinery, RT-PCR assays for the ftsZ, ftsA, and groEL (employed as a control) genes were performed with both B. massiliensis and L. drancourtii, in order to compare B. massiliensis, with its unique multiplication mechanism, to an amoeba-infecting bacterium with a typical division process.

Given the unique cell multiplication mechanism discovered in B. massiliensis (see above), we examined in greater detail the genes implicated in cell division.

Equation (14) illustrates that the definition of K cannot be unique because multiplication of the multipliers α i by any factor λ can be compensated for by the division of every element in k i by λ.

Let v j+1 be the other unit-length eigenvector of (unique up to multiplication by a unit-length scalar).

A Minkowski space possesses a Haar measure  , and this measure is unique up to multiplication of the Lebesgue measure with a positive constant, that is, (2.2).

In particular, they take their maximum and minimum precisely at two antipodal points on the boundary of B. We also prove that, for p close to 2, minimizers are antisymmetric with respect to the hyperplane through the origin perpendicular to the symmetry axis, and that, once the symmetry axis is fixed, they are unique (up to multiplication by a constant).

end{aligned}is unique up to multiplication by a constant, and that there exists (R_{gamma, lambda }(Omega, x_0)in mathbb {R}) and (c_{gamma, lambda }(x_0)>0) such that begin{aligned} G x)=c_{gamma, lambda } (x_0)left( frac{1}{|x-x_0|^{n-2}}+R_{gamma, lambda }(Omega, x_0)right) +o(1 quad hbox { as }xrightarrow x_0.

The final nonzero remainder is the gcd, the Gaussian integer of largest norm that divides both α and β; it is unique up to multiplication by a unit, ±1 or ±i.