An algorithm for the quadratic assignment problem using Bender's decomposition

A well known method used for solving quadratic assignment problems proceeds by the construction of an equivalent much larger linear assignment problem with many side constraints. The disadvantage of this method lies in the weakness of the bounds obtained by solving the linear problem. An alternate linearization has been suggested using a general method of Glover. In this paper the mixed integer program obtained by Glover's method is discussed and a solution using Bender's decomposition is proposed.     

A functional method for linear sets

Kronecker sets for approximation by characters are constructed by an application of Baire’s theorem to Banach spaces of differentiable functions.     

Observation of polarization in bottomonium production at square root of s = 38.8 GeV

We present a measurement of the polarization observed for bottomonium states produced in p-Cu collisions at square root of s = 38.8 GeV. The angular distribution of the decay dimuons of the Upsilon(1S) state shows no polarization at small values of the fractional longitudinal momentum x(F) and transverse momentum p(T) but significant positive transverse production polarization for either p(T)>1.8 GeV/c or for x(F)>0.35. The Upsilon(2S+3S) (unresolved) states show a large transverse production polarization at all values of x(F) and p(T) measured. These observations challenge NRQCD calculations of the polarization expected in the hadronic production of bottomonium states.     

Quantifying Fluid Mixing with the Shannon Entropy

Summary: We introduce a methodology to quantify the quality of mixing in various systems, including polymeric ones, by adapting the Shannon information entropy. For illustrative purposes we use particle advection of two species in a two‐dimensional cavity flow. We compute the entropy by using the probability of finding a suitable chosen group/complex of particles of a given species, at a given location. By choosing the size of the group to be in direct proportion to the overall concentration of the components in the mixture we ensure that the entropic measure is maximized for the case of perfect mixing, that is, when at each location the component concentration is equal to the corresponding overall component concentrations. The scale of observation role in evaluating mixing is analyzed using the entropic methodology. We also illustrate the effect of initial conditions on mixing in a laminar system, typical in operations involving polymers.