# 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.
Beginning chapters are devoted to the abstract structure of finite dimensional vector spaces, and subsequent chapters address convexity and the duality theorem as well as describe the basics of normed linear spaces and linear maps between normed spaces.
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