We present a branch-and-price-and-cut algorithm for solving large-scale instances of the multicommodity capacitated fixed-charge network design problem. The restricted master problem solved at each column generation iteration is obtained directly from the compact arc-based model by considering only a subset of the commodity flow variables. The pricing subproblem corresponds to a Lagrangian rela...

A realistic model of a fixed-charge membrane was constructed to elucidate the principles involved in the Teorell-Meyer-Sievers theory. Polyelectrolyte solutions (polystyrene sulfonic acid or gelatin) were used in a multicompartment cell to serve as the "membrane." The ionic concentration and potential differences between the compartments served as a finite increment approximation to a continuou...

in this paper, we introduce a one-step iterative scheme for finding a common fixed point of a finite family of multivalued quasi-nonexpansive mappings in a real uniformly convex banach space. we establish weak and strong convergence theorems of the propose iterative scheme under some appropriate conditions.

We propose to describe the spin fluctuations in the normal state (spin-pseudogap phase) of underdoped high T(c) cuprates as a manifestation of an algebraic spin liquid. Within the slave boson implementation of spin-charge separation, the normal state is described by massless Dirac fermions, charged bosons, and a gauge field. The gauge interaction, as an exact marginal perturbation, drives the m...

From deep CCD observations of the cluster Abell 2554 we have recovered the cluster’s luminosity distribution over a wide range of magnitude (−24 < MR < −16). We compare the derived A 2554 cluster luminosity function (at redshift 0.1) with that of the local Coma Cluster (A 1656) and the more distant (z = 0.2) cluster A 963. The distribution is remarkably similar for these three clusters of compa...

The present study introduced a novel hierarchical hub set covering problem with capacity constraints. This study showed the significance of fixed charge costs for locating facilities, assigning hub links and designing a productivity network. The proposed model employs mixed integer programming to locate facilities and establish links between nodes according to the travel time between an origin-...

We derive the exact rate of pair production of oppositely charged scalar particles by a smooth potential step φ(x) ∝ tanh kz in three dimensions. As a check we recover from this the known results for an infinitely sharp step as well as for a uniform electric field.