The mixed-order eigenvalue problem −δ∆u + ∆u + λu = 0 with δ > 0, modeling small amplitude vibrations of a thin plate, is analyzed in a bounded 2-D domain Ω that contains a single small hole of radius ε centered at some x0 ∈ Ω. Clamped conditions are imposed on the boundary of Ω and on the boundary of the small hole. In the limit ε → 0, and for δ = O(1), the limiting problem for u must satisfy ...

We present an efficient multiobjective mixed binary linear program that automates schematic mapping for network visualization and navigation. Schematic mapping has broad applications in representing transit networks, circuits, disease pathways, project tasks, organograms, and taxonomies. Good schematic maps employ distortion while preserving topology to facilitate access to physical or virtual ...

An instance of a constraint satisfaction problem (CSP) is variable k-consistent if any subinstance with at most k variables has a solution. For a fixed constraint language L, ρk(L) is the largest ratio such that any variable k-consistent instance has a solution that satisfies at least a fraction of ρk(L) of the constraints. We provide an expression for the limit ρ(L) := limk→∞ ρk(L), and show t...

In the facility location problem usually reducing total transferring cost and time are common objectives. Designing of a network with hub facilities can improve network efficiency. In this study a new model is presented for P-hub covering location problem. In the p-hub covering problem it is attempted to locate hubs and allocate customers to established hubs while allocated nodes to hubs are in...

An optimal control problem is studied, in which the state is required to remain in a compact set S. A control feedback law is constructed which, for given ε > 0, produces ε-optimal trajectories that satisfy the state constraint universally with respect to all initial conditions in S. The construction relies upon a constraint removal technique which utilizes geometric properties of inner approxi...

We consider the problem of packing squares with profits into a bounded square region so as to maximize their total profit. More specifically, given a set L of n squares with positive profits, it is required to pack a subset of them into a unit size square region [0;1℄ [0;1℄ so that the total profit of the squares packed is maximized. For any given positive accuracy ε > 0, we present an algorith...