We design approximation algorithms for Unique Games when the constraint graph admits good low diameter graph decomposition. For the Max-2Link problem in Kr-minor free graphs, when there is an assignment satisfying 1 − ε fraction of constraints, we present an algorithm that produces an assignment satisfying 1−O(rε) fraction of constraints, with the approximation ratio independent of the alphabet...

∂νu = 0, on ∂Ω, where ν denotes a unit vector field normal to ∂Ω and where ε λ ∈ R corresponds to the Lagrange multiplier associated to the constraint V (u) = c0 |Ω|. One can also ignore the volume constraint, in which case a critical point would satisfy equation (1.1) with λ = 0. Since classical methods of the calculus of variation apply, there is no difficulty in finding minimizers of Eε. The...

An exponential wave integrator sine pseudospectral method is presented and analyzed for discretizing the Klein-Gordon-Zakharov (KGZ) system with two dimensionless parameters 0 < ε ≤ 1 and 0 < γ ≤ 1 which are inversely proportional to the plasma frequency and the speed of sound, respectively. The main idea in the numerical method is to apply the sine pseudospectral discretization for spatial der...

Let F : X → X be a C 2 loc map in a Banach space X, and A be its Frèchet derivative at the element w := w ε , which solves the problem (*) ˙ w = −A −1 ε (F (w) + εw), w(0) = w 0 , where A ε := A + εI. Assume that A −1 ε ≤ cε −k , 0 < k ≤ 1, 0 < ε > ε 0. Then (*) has a unique global solution, w(t), there exists w(∞), and (* *) F (w(∞)) + εw(∞) = 0. Thus the DSM (Dynamical Systems Method) is just...

According to the most widely accepted classification the Multiobjective Mathematical Programming (MMP) methods can be classified as a priori, interactive and a posteriori, according to the decision stage in which the decision maker expresses his/her preferences. Although the a priori methods are the most popular, the interactive and the a-posteriori methods convey much more information to the d...

The redundancy allocation problem (RAP) has been studied for many different system structures, objective functions, and distribution assumptions. In this paper, we present a problem formulation and a solution methodology to maximize the system steady-state availability and minimize the system cost for the repairable series-parallel system designs. In the proposed approach, the components’ time-...

An exponential wave integrator sine pseudospectral method is presented and analyzed for discretizing the Klein-Gordon-Zakharov (KGZ) system with two dimensionless parameters 0 < ε ≤ 1 and 0 < γ ≤ 1 which are inversely proportional to the plasma frequency and the speed of sound, respectively. The main idea in the numerical method is to apply the sine pseudospectral discretization for spatial der...

We establish uniform error bounds of a finite difference method for the Klein-Gordon-Zakharov (KGZ) system with a dimensionless parameter ε ∈ (0, 1], which is inversely proportional to the acoustic speed. In the subsonic limit regime, i.e. 0 < ε ≪ 1, the solution propagates highly oscillatory waves in time and/or rapid outgoing initial layers in space due to the singular perturbation in the Zak...

In this paper we study the possibility of generalizing a monocriteria model to a multicriteria partition problem and show the reason why exact algorithms are not efficient in solving the problem. The mathematical model studied is a modified version of a mono-objective model from Mehrotra [1] and applied to the biobjetive case using the ε-constraint method. Research conducted concludes that the ...

We propose a numerical method for computing transport and diffusion on a moving surface. The approach is based on a diffuse interface model in which a bulk diffusion–advection equation is solved on a layer of thickness ε containing the surface. The conserved quantity in the bulk domain is the concentration weighted by a density which vanishes on the boundary of the thin domain. Such a density a...