algebraically

First, the well-known national income accounting identity can be manipulated algebraically to yield an identity linking the imbalance between private-sector saving and investment, the country's fiscal balance, and its current account balance.

Their Equation 8 gives a test statistic they deemed "most powerful" against a negative binomial distribution (which describes most aggregated patterns) that is algebraically equivalent to the t-test statistic used for this exercise.

This result can be minimized algebraically by the following steps: Step 1: ABC combines with ABc to produce AB; Step 2: ABC combines with AbC to produce AC; Step 3: ABc combines with aBc to produce Bc; Step 4.

This chapter is written algebraically and almost appears scholastic in its approach.

We can show this algebraically by computing f'(x) = [-4x.sup.3] + 2ux = -2x([2x.sup.2] -u), which will equal zero for at x = 0 and at two other values of x if u is positive.

When X is a non-singular projective variety defined over an algebraically closed field k of characteristic 0 and G is a connected reductive algebraic group over k, moduli spaces of (semi)stable principal G-bundles over X are known to exist and to be quasi-projective schemes (usually singular).

Sharp-eyed readers may note that we haven't assigned a specific numerical value to x (or, as the algebraically disinclined at the Prospect prefer to call it, "the shvitz factor").

Vickie's hubris, you might say, is she's cheerleader-peppy but also algebraically savvy.

We combine these equations algebraically to solve for M and [H.sub.[summation]] in terms of the measured asymptotic rotational velocity and the MOND acceleration.

The equation [T.sub.L] = [[DELTA].sub.p] x [V.sub.m]/2[pi] expresses algebraically the relationship between motor variables.

The concentration of creek 1(S1) can be determined in the same manner or algebraically as: