duality theorem

duality theorem

[dü′al·əd·ē ‚thir·əm]
(mathematics)
A theorem which asserts that for a given n-dimensional space, the (n-p) dimensional homology group is isomorphic to a p-dimensional cohomology group for each p = 0, …, n, provided certain conditions are met.
Let G be either a compact group or a discrete group, let X be its character group, and let G′ be the character group of X ; then there is an isomorphism of G onto G′ so that the groups G and G′ may be identified.
If either of two dual linear-programming problems has a solution, then so does the other.
References in periodicals archive ?
While developing his duality theorem, Poincare already intuited the great potential of a cross-breeding between set-theoretical and combinatorial methods in topological thinking.
Furthermore, if the weak duality Theorem 20 holds for all feasible solutions of the problems (MP) and (MDI), then ([bar.
Terai Alexander duality theorem and Stanley-Reisner rings Surikaisekikenkyusho Kokyu- ruko(1999) no.
Both model (5) and its dual problem are feasible, so by the duality theorem of linear programming they have bounded optimal solutions.
Invoking the Duality Theorem of Linear Programming [22], we arrive at
The graduate textbook illustrates how Cohen-Macaulay rings arise naturally, develops the Hartshorne-Lichtenbaum vanishing theorem, applies two classes of rings to polyhedral geometry, explains Grothendieck's duality theorem, and defines D-modules over rings of differential operators.
Keywords: Evolution equation, Gross Laplacian, potential function, white noise analysis, generalized functions, convolution operator, Laplace transform, duality theorem.
Teo: A converse duality theorem on higher-order dual models in nondifferentiable mathematical programming, Optim.
Chapters discuss duality, linear mappings, matrices, determinant and trace, spectral theory, Euclidean structure, calculus of vector- and matrix-valued functions, matrix inequalities, kinematics and dynamics, convexity, the duality theorem, normed liner spaces, linear mappings between normed linear spaces, positive matrices, and solutions of systems of linear equations.
lambda]]) for (MWD) follows from weak duality theorem.