Then M is a representable even [DELTA]-matroid over any

algebraically closed field of characteristic 0.

T] (the latter graph is equivalent to the directed graph of F with the edge directions reversed); this equivalence again assumes that the numerical values of the nonzeros in F are

algebraically independent.

Property (P3) is particularly helpful to compute

algebraically certain classes of factorizations.

A compass and straight edge construction trisection of a general angle is impossible, proved

algebraically by Wantzell in the 19th century (Weisstein, 2003).

The eleventh edition adds chapters on the role of technology, ratio and proportion, and thinking

algebraically.

The convex hull of all of the spine is not a polytope, but its boundary can be

algebraically described.

Substituting the formulas for the profit streams into the two capitalized values and manipulating

algebraically, we find

of Oregon) acknowledge that much has already been written about the theory of unipotent elements in simple algebraic groups over

algebraically closed or finite fields, and nilpoint elements in the corresponding simple Lie algebras.

It can be shown

algebraically that the lagged dependent variable in Campbell's Model 2 (2012) simply disguises the impact of the president's party on economic performance.

Every high school has a few whizzes who are

algebraically gifted.

Year 5s cannot be expected to reason

algebraically.

Algebraically, solving equations F(x) = 1/3 (2x + 285.

These days Alice's Adventures in Wonderland remains a widely read classic but The Fifth Book of Euclid Treated

Algebraically is sadly forgotten.

Graphically and

algebraically, large mines would undoubtedly receive a much greater reduction under the proposed rule than small mines, not only within each size group that receives the same point assessment, but across the industry.

The approach first constructs a caliber-one LS interpolation operator for a given set of test vectors (representatives of

algebraically smooth error) and then defines the algebraic distance between a fine point and its neighboring points in terms of the values of the local least-squares functionals resulting from the so-defined interpolation.