Finally, the duality principle is discussed in some detail between these two sets of conservation equations. In particular, a conservation law called the gauge angular momentum conservation law due to free rotation of anholonomic coordinate frame of a material body in the natural state is believed ...
1.5.5 Duality Principle The duality principle states that any true result involving sets is also true when we replace unions by intersections, intersections by unions, sets by their complements, and if we reverse the inclusion symbols ⊂ and ⊃. For example, if we replace the union in the...
We establish a duality principle for order statistics in the arbitrary case, using which many known dual results on order statistics can be deduced without a formal proof. The literature on order statistics is rich with such dual pairs derived under different assumptions such as continuity, absolute...
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In the setting of an $n$-dimensional Euclidean space, the duality between velocity fields on the class of admissible bodies and Cauchy fluxes is studied using tools from geometric measure theory. A generalized Cauchy flux theory is obtained for sets whose measure theoretic boundaries may be as ...
Natural language syntax exhibitsdiscrete unitswhich lead to adiscreteness-continuity duality(the boundary between syntactic categories can be non-distinct).Footnote3Syntax is driven bycloseness of computation(syntactic objects X and Y form a distinct syntactic object, {X, Y}). Its objects arebounded(...
The different policy options put forward by the EC, the Council and the EP created dualities between related but incompatible frames. Different strategies, e.g. elimination, assimilating, polarisation, reframing or connection, can be utilised to deal with the duality (Dewulf & Bouwen,2012). In ...
In this paper, we investigate the stochastic optimal control problem for the zero-sum stochastic differential game of mean-field type with partial information. We derive a necessary and sufficient maximum principle for that problem by virtue of the duality method and the mean-field backward stochasti...
Allen, G.: Variational inequalities, complementarity problems, and duality theorems. J. Math. Anal. Appl. 58, 1–10 (1977) Article MathSciNet MATH Google Scholar Ansari, Q.H., Lin, Y.C., Yao, J.C.: General KKM theorem with applications to minimax and variational inequalities. J. Op...
48ËChristian Pötzsche and Evamaria RussLet(X,‖·‖)be a Banach space overK∈ {R,C}having the dual spaceX′and〈x,x′〉:=x′(x)stands forthe duality pairing ofx∈Xwithx′∈X′. The open ball inXwith radiusr>0and centerxis denoted asBr(x).For the set of continuousn-li...