In this paper we discuss the level set method of Joó and how to use it to give an elementary proof of the well-known Sion’s minimax result. Although this proof technique is initiated by Joó and based on the inter-section of upper level sets and a clever use of the topological notion of...

In this paper we discuss the level set method of Joó and how to use it to give an elementary proof of the well-known Sion’s minimax result. Although this proof technique is initiated by Joó and based on the inter-section of upper level sets and a clever use of the topological notion of...

The numerical prediction of the power performance of a marine current turbine under a free surface is difficult to pursue due to its complex geometry, fluid–structural interactions and ever-changing free surface interface. In this paper, an immersed boundary method is used to couple the...

The present study reports a numerical investigation of water and CO2 (carbon dioxide) flooding at the pore scale of a porous medium. We use high resolution micro-computed tomography (micro-CT) images of Berea sandstone core to obtain the pore geometry. The numerical solution used for the...

Von Neumann proved the minimax theorem (existence of a saddle-point solution to 2 person, zero sum games) in 1928. While his second article on the minimax theorem, stating the proof, has long been translated from German, his first announcement of his result (communicated in French to the Academy...

In 1951, Dantzig showed the equivalence of linear programming problems and two-person zero-sum games. However, in the description of his reduction from linear programs to zero-sum games, he noted that there was one case in which the reduction does not work. This also led to incomplete proofs of...

In this paper, by virtue of the separation theorem of convex sets, we prove a minimax theorem, a cone saddle point theorem and a Ky Fan minimax theorem for a scalar set-valued mapping under nonconvex assumptions of its domains, respectively. As applications, we obtain an existence result for the...

In this paper, we presented new and important existence theorems of solution for quasi-equilibrium problems, and we show the uniqueness of its solution which is also a fixed point of some mapping. We also show that this unique solution can be obtained by Picard’s iteration method. We also get...