Even without any calculus, it is straightforward to show

algebraically that f(x,y) [less than or equal to] 1 and that equality occurs at two "peaks" (1,0) and (-1,0).

Let X be a smooth n-dimensional projective variety over an

algebraically closed field k of characteristic zero, let G be a connected reductive algebraic group over k, and let us denote by g its Lie algebra.

The annual revenue [R.sub.k] is expressed

algebraically in terms of the lifetime revenue [W.sub.k] for products launched in year k, and the factors [[alpha].sub.i] for the shape of the revenue wave,

We shall say that the origin of [K.sup.n] is an

algebraically isolated singularity of [phi]([xi]) [member of] K [[[xi].sub.1],..., [[xi].sub.n]], if the origin is the only solution of the system

Rush Hour's computational complexity is greater than that of Blocks World, whose time to a solution increases

algebraically rather than exponentially.

If two of the formula's components are known, the third component can be solved

algebraically. If overall sales of properties with similar wetland ratios have been identified to make a whole-to-whole comparison possible, and sales of all uplands have been identified but no sales of wetlands could be found, then algebra can be used to solve for the residual wetland component.

Accordingly, the gross-up computation should be made

algebraically.

Students are taught to approach the problems in three ways: numerically, graphically and

algebraically.

provides the same answer as the weighted average of relatives price index using base year weights, and it should since the two are

algebraically equivalent.

"Let's Evaluate Performance

Algebraically," by Bernardo, examines the benefits of using stochastically timed process algebras and Petri nets for performance modeling and evaluation.

W, encourages her students to analyze patterns, thus providing the opportunity to think

algebraically. Mrs.

Algebraically, the probability of an Alabama victory is