Dynamic Nonlinear Modelization of Operational Supply Chain Systems

Supply Chain Management (SCM) is an important activity in all producing facilities and in many organizations to enable vendors, manufacturers and suppliers to interact gainfully and plan optimally their flow of goods and services. To realize this, a dynamic modelling approach for characterizing supply chain activities is opportune, so as to plan efficiently the set of activities over a distributed network in a formal and scientific way. The dynamical system will result so complex that it is not generally possible to specify the functional forms and the parameters of interest, relating outputs to inputs, states and stochastic terms by experiential specification methods. Thus the algorithm that will presented is Data Driven, determining simultaneously the functional forms, the parameters and the optimal control policy from the data available for the supply chain. The aim of this paper is to present this methodology, by considering dynamical aspects of the system, the presence of nonlinear relationships and unbiased estimation procedures to quantify these relations, leading to a nonlinear and stochastic dynamical system representation of the SCM problem. Moreover, the convergence of the algorithm will be proved and the satisfaction of the required statistical conditions demonstrated. Thus SCM problems may be formulated as formal scientific procedures, with well defined algorithms and a precise calculation sequence to determine the best alternative to enact. A “Certainty equivalent principle” will be indicated to ensure that the effects of the inevitable uncertainties will not lead to indeterminate results, allowing the formulation of demonstrably asymptotically optimal management plans.     

Heterodinuclear Ln[bond]Na complexes with an asymmetrical macrocyclic compartmental Schiff base

Heterodinuclear lanthanide(III)-sodium(I) complexes [LnNa(L)(Cl)(2)(CH(3)OH)] (Ln=La[bond]Nd, Sm[bond]Lu), where H(2)L is a [1+1] asymmetric compartmental macrocyclic ligand containing a N(3)O(2) Schiff base and a O(3)O(2) crown-ether-like coordination site, have been prepared and characterized by IR, (1)H, (13)C, and (23)Na NMR spectroscopy, mass spectrometry, and electron microscopy. In the solid state, the lanthanide(III) ions coordinate the Schiff-base N(3)O(2) site, and the sodium ion occupies the O(3)O(2) crownlike cavity, as shown by the X-ray crystal structures of the Nd, Eu, Gd, and Yb derivatives. In these complexes, the lanthanide(III) ion is coordinated by two chlorine atoms in the trans position and by three nitrogen and two negatively charged phenol oxygen atoms of the Schiff base, and the ion is heptacoordinated with a pentagonal bipyramidal geometry. The sodium ion is coordinated by three etheric oxygen atoms and the two phenolic oxygens that act as a bridge. A methanol molecule is also coordinated in the apical position of the resulting pentagonal pyramidal polyhedron. A detailed (1)H and (13)C NMR study was carried out in CD(3)OD for both diamagnetic and paramagnetic heterodinuclear complexes [LnNa(L)(Cl)(2)(CH(3)OH)]. The complexes are also isostructural in solution, and their structures parallel those found in the solid state. Moreover, some significative distances determined in the solid state and in solution are comparable. Finally, the potential use of these complexes as molecular probes for the selective recognition of specific metal ions has been tested. In particular, their ability to act as shift reagents and the selectivity of the O(3)O(2) site towards Li(+), Ca(2+), and K(+) were investigated by (23)Na NMR spectroscopy.     

Exciplex Formation in Lipid-bound Escherichia coli Flavohemoglobin

Flavohemoglobins have the particular capability of binding unsaturated and cyclopropanated fatty acids as free acids or phospholipids. Fatty acid binding to the ferric heme results in a weak but direct bonding interaction. Ferrous and ferric protein, in presence or absence of a bound lipid molecule, have been characterized by transient absorption spectroscopy. Measurements have been also carried out both on the ferrous deoxygenated and on the CO bound protein to investigate possible long-range interaction between the lipid acyl chain moiety and the ferrous heme. After excitation of the deoxygenated derivatives the relaxation process reveals a slow dynamics (350 ps) in lipid-bound protein but is not observed in the lipid-free protein. The latter feature and the presence of an extra contribution in the absorption spectrum, indicates that the interaction of iron heme with the acyl chain moiety occurs only in the excited electronic state and not in the ground electronic state. Data analysis highlights the formation of a charge-transfer complex in which the iron ion of the lipid-bound protein in the expanded electronic excited state, possibly represented by a high spin Fe III intermediate, is able to bind to the sixth coordination ligand placed at a distance of at 3.5 Å from the iron. A very small nanosecond geminate rebinding is observed for CO adduct in lipid-free but not in the lipid-bound protein. The presence of the lipid thus appears to inhibit the mobility of CO in the heme pocket.     

Conservative methods for the Toda lattice equations

We are concerned with the numerical integration of the Todalattice equations by using different conservative methods. Numericalexperiments suggest that the global error for isospectral schemesdecreases exponentially with time but it is almost constantfor either symplectic or more general integrators. We providea theoretical explanation for these experimental findings.