BV Estimates in Optimal Transportation and Applications

In this paper we study the BV regularity for solutions of certain variational problems in Optimal Transportation. We prove that the Wasserstein projection of a measure with BV density on the set of measures with density bounded by a given BV function f is of bounded variation as well and we also provide a precise estimate of its BV norm. Of particular interest is the case f = 1, corresponding to a projection onto a set of densities with an L ^∞ bound, where we prove that the total variation decreases by projection. This estimate and, in particular, its iterations have a natural application to some evolutionary PDEs as, for example, the ones describing a crowd motion. In fact, as an application of our results, we obtain BV estimates for solutions of some non-linear parabolic PDE by means of optimal transportation techniques. We also establish some properties of the Wasserstein projection which are interesting in their own right, and allow, for instance, for the proof of the uniqueness of such a projection in a very general framework.     

Integrated capacity and inventory management with capacity acquisition lead times

We model a make-to-stock production system that utilizes permanent and contingent capacity to meet non-stationary stochastic demand, where a constant lead time is associated with the acquisition of contingent capacity. We determine the structure of the optimal solution concerning both the operational decisions of integrated inventory and flexible capacity management, and the tactical decision of determining the optimal permanent capacity level. Furthermore, we show that the inventory (either before or after production), the pipeline contingent capacity, the contingent capacity to be ordered, and the permanent capacity are economic substitutes. We also show that the stochastic demand variable and the optimal contingent capacity acquisition decisions are economic complements. Finally, we perform numerical experiments to evaluate the value of utilizing contingent capacity and to study the effects of capacity acquisition lead time, providing useful managerial insights.     

On nonlinear cross-diffusion systems: an optimal transport approach

We study a nonlinear, degenerate cross-diffusion model which involves two densities with two different drift velocities. A general framework is introduced based on its gradient flow structure in Wasserstein space to derive a notion of discrete-time solutions. Its continuum limit, due to the possible mixing of the densities, only solves a weaker version of the original system. In one space dimension, we find a stable initial configuration which allows the densities to be segregated. This leads to the evolution of a stable interface between the two densities, and to a stronger convergence result to the continuum limit. In particular derivation of a standard weak solution to the system is available. We also study the incompressible limit of the system, which addresses transport under a height constraint on the total density. In one space dimension we show that the problem leads to a two-phase Hele-Shaw type flow.     

Photophysical and Complexation Properties of Benzenesulfonamide Derivatives with Different Donor and Acceptor Moieties

Pyrrolobenzosulfonamide, indolobenzosulfonamide and carbazolobenzosulfonamide derivatives with different acceptor groups were synthesized and their photophysical properties were compared. The electron donor linking sites are found to influence the emission characteristics of these compounds while acceptor linking sites have no noticeable effects on the spectral properties. P2-A5 which is a C-C linked pyrrole derivative exhibited different spectral properties from the C-N linked pyrrole derivatives. The complexation properties of the molecules were also investigated employing Na (I), Ca (II), Li (I), Mg (II), Zn (II) and Cu (II) ions.     

An Efficient Genetic Algorithm for the p-Median Problem

We propose a new genetic algorithm for a well-known facility location problem. The algorithm is relatively simple and it generates good solutions quickly. Evolution is facilitated by a greedy heuristic. Computational tests with a total of 80 problems from four different sources with 100 to 1,000 nodes indicate that the best solution generated by the algorithm is within 0.1% of the optimum for 85% of the problems. The coding effort and the computational effort required are minimal, making the algorithm a good choice for practical applications requiring quick solutions, or for upper-bound generation to speed up optimal algorithms.     

Evidence for an instability near twice the fermi wave vector in the low electronic density liquid metal Li(NH3)4

We report high-resolution inelastic x-ray scattering measurements in the metallic liquid Li(NH3)4, which to a good approximation can be treated as a dilute alkali metal. We see a well-defined excitation out to large momentum transfers. This excitation shows a strong softening at wave vectors near the first peak in the structure factor, which occurs near twice the Fermi momentum.     

Nuclear resonant magnetometry and its application to Fe/Cr multilayers

We introduce nuclear resonant magnetometry as a means to record the magnetization curve of isotopically enhanced regions of a sample. It is based on nuclear resonant scattering with circularly polarized synchrotron radiation and the use of a nuclear resonant reference sample. We apply this approach to study the interlayer coupling in Fe/Cr(100) multilayers and to obtain a layer-specific magnetization curve. Our measurements provide experimental evidence for the existence of a nontrivial interlayer-coupling angle in Fe/Cr/Fe.     

Rice straw and energy reed fibers reinforced phenol formaldehyde resin polymeric biocomposites

Cellulose - Herein, natural fiber (energy reeds and rice straw) reinforced with phenol formaldehyde (PF) polymeric resin biocomposites are developed and reported in this study. The dimensions of...     

Simultaneous determination of β-lactamic antibiotics by a new high-performance low-pressure chromatographic system using a multisyringe burette coupled to a monolithic column (MSC)

A technique based on multisyringe chromatography (MSC) was developed to determine three beta-lactamic antibiotics. Amoxicillin (AMOXI), ampicillin (AMPI) and cephalexin (CEPHA) were analyzed using a system with a very simple design and very low-cost equipment consisting of a multisyringe module, three low-pressure solenoid valves, a monolithic Chromolith Flash RP-18e column and a diode array spectrophotometric detector monitoring at 250 nm. Mobile phases containing methanol:acetic acid (0.1 M)-sodium acetate (0.1 M), pH 6.2, were tested for various ratios of methanol:acetic acid-sodium acetate, but a ratio of 10:90 gave optimum results with a flow rate of 2 ml min(-1). Validation parameters were evaluated for amoxicillin. The response to amoxicillin was linear over the range 0.04-0.4 mg/mL, with a correlation coefficient of 0.9996; precisions, evaluated as the repeatability for 0.04, 0.16 and 0.4 mg/mL amoxicillin, were 0.6%, 0.1% and 0.6%, respectively. Recovery from a generic formulation of amoxicillin was evaluated. The method showed selectivity in the presence of excipients commonly used in capsules, and satisfactory specificity was observed for amoxicillin and hydrolytic degradation products. The linearity was also evaluated for cephalexin and ampicillin. The conditions selected for MSC separation were compared with those for a HPLC system, and similar results were obtained in terms of chromatographic parameters but a difference in retention times was observed.