Equilibria and dynamics of supply chain network competition with information asymmetry in quality and minimum quality standards

In this paper, we construct a supply chain network model with information asymmetry in product quality. The competing, profit-maximizing firms with, possibly, multiple manufacturing plants, which may be located on-shore or off-shore, are aware of the quality of the product that they produce but consumers, at the demand markets, only know the average quality. Such a framework is relevant to products ranging from certain foods to pharmaceuticals. We propose both an equilibrium model and its dynamic counterpart and demonstrate how minimum quality standards can be incorporated. Qualitative results as well as an algorithm are presented, along with convergence results. The numerical examples, accompanied by sensitivity analysis, reveal interesting results and insights for firms, consumers, as well as policy-makers, who impose the minimum quality standards.     

Soliton propagation in tapered silicon core fibers

Numerical simulations are used to investigate soliton-like propagation in tapered silicon core optical fibers. The simulations are based on a realistic tapered structure with nanoscale core dimensions and a decreasing anomalous dispersion profile to compensate for the effects of linear and nonlinear loss. An intensity misfit parameter is used to establish the optimum taper dimensions that preserve the pulse shape while reducing temporal broadening. Soliton formation from Gaussian input pulses is also observed--further evidence of the potential for tapered silicon fibers to find use in a range of signal processing applications.     

Global periodicity and complete integrability of discrete dynamical systems

Consider the discrete dynamical system generated by a map F. It is said that it is globally periodic if there exists a natural number p such that F ^p (x)=x for all x in the phase space. On the other hand, it is called completely integrable if it has as many functionally independent first integrals as the dimension of the phase space. In this paper, we relate both concepts. We also give a large list of globally periodic dynamical systems together with a complete set of their first integrals, emphasizing the ones coming from difference equations.     

Formation of PAHs and soot platelets: multiconfiguration theoretical study of the key step in the ring closure–radical breeding polyyne‐based mechanism

Polyynes of general formula H? (C?C? )_nH are known to play a significant role in combustion and pyrolysis, possibly being intermediates in the formation of polycyclic aromatic hydrocarbons (PAHs) and soot. They have also been detected in astrophysical investigations. The key step in the polyyne‐based radical breeding mechanism for PAH growth is a cyclization, put forward by Krestinin, which implies disruption of electron couples, plausibly expected to be energy demanding. We explore the electronic features and energy requirements of such a process by quantum mechanical multiconfiguration methods (CASSCF and CASPT2). The features of the wavefunction are analyzed, and the free energy barriers are estimated over a wide range of temperatures, for three molecular models. The initial radical adduct A, generated by H ^. , HC?C ^. (ethynyl), or HC?C? C ^. H₂ ( propargyl ) addition to butadiyne (BD, HC?C? C?CH), undergoes a cyclization with the generation of two new radical centers. However, in most of the cases, one of these new singly occupied sp² orbitals has some overlap with the unpaired electron lobe already existent in A: some sort of bonding builds up and consequently the triradical character cannot be large. Only one model suggests a possible role of the radical breeding mechanism during combustion. Copyright © 2009 John Wiley & Sons, Ltd.     

On generalized Poisson–Nernst–Planck equations with inhomogeneous boundary conditions: a‐priori estimates and stability

In this paper, we consider the strongly nonlinear Nernst–Planck equations coupled with the quasi‐linear Poisson equation under inhomogeneous, moreover, nonlinear boundary conditions. This system describes joint multi‐component electrokinetics in a pore phase. The system is supplemented by the force balance and by the volume and positivity constraints. We establish well‐posedness of the problem in the variational setting. Namely, we prove the existence theorem supported by the energy and the entropy a‐priori estimates, and we provide the Lyapunov stability of the solution as well as its uniqueness in special cases. Copyright © 2016 John Wiley & Sons, Ltd.     

Heuristic solution approaches for the maximum minsum dispersion problem

The Maximum Minsum Dispersion Problem (Max-Minsum DP) is a strongly NP-Hard problem that belongs to the family of equitable dispersion problems. When dealing with dispersion, the operations research literature has focused on optimizing efficiency-based objectives while neglecting, for the most part, measures of equity. The most common efficiency-based functions are the sum of the inter-element distances or the minimum inter-element distance. Equitable dispersion problems, on the other hand, attempt to address the balance between efficiency and equity when selecting a subset of elements from a larger set. The objective of the Max-Minsum DP is to maximize the minimum aggregate dispersion among the chosen elements. We develop tabu search and GRASP solution procedures for this problem and compare them against the best in the literature. We also apply LocalSolver, a commercially available black-box optimizer, to compare our results. Our computational experiments show that we are able to establish new benchmarks in the solution of the Max-Minsum DP.     

Analysis of dissolution profiles of iron,zinc, and manganese from complex dietary supplements by ion chromatography and chemometrics

Four commercially available formulations containing iron, zinc, and manganese were subjected to dissolution profile testing during 60 min and the dissolution was analyzed by ion chromatography. The obtained curves were analyzed directly by principal component analysis (PCA). The main trend (87.1% of variance) was connected with average dissolution percentage over the investigated time. The second component (11.2% of variance) is connected with shape of dissolution profile. All metals behave in the similar way and the differences were connected with excipients. An additional fit was completed on 12 kinetic models: first order kinetics (4 variants), Higuchi (2 variants), Hixson-Crowell (2 variants), Korsemeyer-Peppas, Logistic (2 variants), Peppas-Sahlin, Quadratic (2 variants), Weibull (3 variants), and Zero order kinetics (2 variants). The ranking of the fitting was performed by Akaike information criteria (AIC) values with additional PCA analysis on them, an approach presented in literature for the first time. The main trend (67.4% of variance) was connected with average fit. The second (14.8% of variance) is connected with differences of fitting ability to investigated dissolution curves. This methodology brought an overall look to trends and variances inside obtained data, both the profile shape and fitting ability to particular models.     

Synthesis of deuterium-labelled substrates for the study of oleuropein biosynthesis in Olea europaea callus cultures

We propose the cell culture approach to investigate oleuropein (1) biogenesis in Olea europaea L. We suggest employing olive callus cultures to identify the iridoidic precursor of oleuropein. In fact, we confirmed that callus cells from olive shoot explants are able to produce key secoiridoid as 1. To enable this approach, we synthesised and characterised deuterium-labelled iridoidic precursors belonging both to the loganin and the 8-epiloganin series. These iridoids are [7,8-²H₂]-7-deoxy-8-epi-loganin (2^D), [8,10-²H₂]-8-epi-loganin (4^D) and [7,8-²H₂]-7-deoxy-loganin (3^D).