We model the problem of bidding in ad auctions as a penalized multiple choice knapsack problem (PMCKP), a combination of the multiple choice knapsack problem (MCKP) and the penalized knapsack problem (PKP) [1]. We present two versions of PMCKP, GlobalPMCKP and LocalPMCKP, together with a greedy algorithm that solves the linear relaxation of a GlobalPMCKP optimally. We also develop a greedy heur...

We consider the two-dimesional spatially periodic problem for an evolutionary system describing unsteady motions of the fluid with shear-dependent viscosity under general assumptions on the form of nonlinear stress tensors that includes those with pstructure. The global-in-time existence of a weak solution is established. Some models where the nonlinear operator corresponds to the case p = 1 ar...

In a new theory gravity called the dynamic theory, which is derived from thermodymical principles in a five dimensional space, the deflection of a light signal is calculated and compared to that of general relativity. This is achieved by using the dynamic gravity line element which is the usual four dimesional space-time element of Newtonian gravity modified by a negative inverse radial exponet...

We analyze finite volume schemes of arbitrary order r for the one-dimensional singularly perturbed convection-diffusion problem on the Shishkin mesh. We show that the error under the energy norm decays as (Nln(N + 1)), where 2N is the number of subintervals of the primal partition. Furthermore, at the nodal points, the error in function value approximation super-converges with order (Nln(N + 1)...

After the seminal books by Martello and Toth (1990) Kellerer, Pferschy, Pisinger (2004), knapsack problems became a classical rich research area in combinatorial optimization. The purpose of this survey, which is structured two parts, to cover developments that appeared field after publication latter volume. Part I devoted whose goal optimally assign items single knapsack. Besides (binary, subs...

We show that there are 0-1 and unbounded knapsack polytopes with super-polynomial extension complexity. More specifically, for each n ∈ N we exhibit 0-1 and unbounded knapsack polyhedra in dimension n with extension complexity Ω(2 p n).