# A Course in Combinatorial Optimization by Schrijver A.

By Schrijver A.

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The Complementarity Theory was used in the study of the post-critical equilibrium state of a thin elastic plate by Isac [A 128] and Isac and Th~ra [A 132 - A 133]. The Complementarity Problem was used as mathematical model of maximizing oil production by Meerov, Berschanski and Litvak [A 206], [A 26 - A 27]. The Complementarity Theory is intensively used in Economics [A 29 - A 30], [A 70], [A II0], [A 99], [A 120], [A 131], [A 136], [A 160], [A 202], [A 247], [A 249], [A 250], [A 255], [A 274], [A 303] and ifi study of equilibrium of traffic flow [A 1], [A 190].

The journal bearing problem [A68][A48][AI72]. We describe now the free-boundary A Journal bearing consists surface (the bearing) problem of the flnlte-length of a rotating shaft (the journal) by a thin film of lubricating from a fluid. Journal bearing are among the most used basic engineering annual production journal bearing. separated components; their is in the billions. A journal bearing of general engineering I interest is shown in fig. 2. 7~ ,r~ . . . . . . . . . . . ; B c : L~H6~T Figure 2 One wishes to find the presure distribution of the thin lubricating the gap between the journal and the bearing is very narrow, assumed not to vary across the gap; therefore, problem in the rectangular domain R = ABEF in the 8Z-plane Since the pressure may be the problem becomes X.

Only on the 0 coordinate and can be approximated between by the bearing and the ratio. Fluid Flow through a SemiimpermeableMembrane We say that the boundary ~ of a region ~ ~ R 3 is a semiimpermeable membrane if a fluid may onll flow into the region ~. Consider a region ~ with a semiimpermeable fluid pressure of a fluid flowing boundary. In this case, if p is the > 0; where v is the into the region ~, we have, ~~P - outer normal to the boundary ~ . The fluid outside the region ~ creates a pressure Po(X); x £ ~ .