We study a simple motion pursuit differential game of many pursuers and many evaders on a nonempty convex subset of R n. In process of the game, all players must not leave the given set. Control functions of players are subjected to integral constraints. Pursuit is said to be completed if the position of each evader y j , j ∈ {1, 2, ...k}, coincides with the position of a pursuer x i , i ∈ {1, ..., m}, at some time t j , that is, x i t j y j t j. We show that if the total resource of the pursuers is greater than that of the evaders, then pursuit can be completed. Moreover, we construct strategies for the pursuers. According to these strategies, we define a finite number of time intervals θ i−1 , θ i and on each interval only one of the pursuers pursues an evader, and other pursuers do not move. We derive inequalities for the resources of these pursuer and evader and, moreover, show that the total resource of the pursuers remains greater than that of the evaders.

We propose a single panel liquid crystal (LC) device that is switchable between reflective and transmissive modes. Operation in the reflective mode can be achieved by applying a vertical field to a dye-doped LC device, whereas the device can be in-plane switched for operation in the transmissive mode. Image inversion that was inevitable in a single panel device using a reflective polarizer is effectively eliminated through the absorption of ambient light by the dye-doped LCs. We believe that the proposed device can be applied to various display systems for outdoor mobile use.

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