In (11), Herstein proved that if R is a prime ring with char R [not equal to] 2 and R admits a

non-zero derivation d such that [d(x), d(y)] = 0 for all x, y [member of] R, then R is commutative.

For a sparse matrix K,

non-zero entries and their respective column indices are stored in two separate arrays, row by row.

For the 18-year-old specimen, all three calibration lines reasonably predict that residual retention is below the level of aboveground contact (4.0 kg/[m.sup.3] or 0.25 pcf) treatment, while the

non-zero intercept line can predict the actual amount of residual preservative.

where a,b are scalars of which b [not equal to] 0 and D is a

non-zero 1-form, then M is called a quasi-Einstein manifold [3].

That is, only a vector with at most two

non-zero integers.

It turns out for reasons that will be seen later that a convenient way to represent the

non-zero finite field elements is through a "polynomial representation".

From the condition as the system (10) to admit

non-zero solutions ([DELTA] = 0) is obtained the natural frequencies equation:

and the

non-zero elements by varying j from 1 to 3 and k varies from 1 to 2 are

Let u be a

non-zero linear functional satisfying the following first-order linear differential equation

Therefore the number of

non-zero non-residues at each column is

And global prosperity will be enhanced wherein everyone will be better off in a

non-zero sum game.

In addition, the power-up state of the analog outputs can be set to independent user-defined values to provide

non-zero voltage settings on application of power.

If we take action now to reduce greenhouse gas emissions, there's a very small (but

non-zero) possibility that it will turn out to have been unnecessary.

A

non-zero value of R due to the [e.sup.-] polarization component, which is perpendicular to the plane spanned by the spin of the decaying neutron and the electron momentum, would signal a violation of time reversal symmetry and thus physics beyond the Standard Model.

(3) A probability or statistical sample is one in which every element of the population has a known,

non-zero, chance of being selected into the sample.