Prediction of isocratic nonaqueous reversed-phase high-performance liquid chromatography retention parameters and response factors of triacylglycerols detected by an ultraviolet-diode array-evaporative light-scattering on-line system

Nonaqueous reversed-phase high-performance liquid chromatography of 10 homogeneous triacylglycerol molecular species (TAG), both saturated and unsaturated, is carried out. The eluate from the column is detected by an ultraviolet diode array detector (DAD) on-line with an evaporative light-scattering detector (ELSD). The retention parameters (as selectivities, alpha) for 220 TAGs are determined, and the obtained values are related to the following structural parameters: total carbon number; mono-, di-, and triunsaturated fatty acid residues number/molecule; and monounsaturated fatty acid carbon number. Multiple regression analysis is carried out to obtain a relationship for the prediction of alpha values of any TAG when the same experimental conditions are used. In regard to the quantitative analysis of the separated TAG species, the dependence of response of the two on-line detectors on the aforementioned structural parameters is studied. Three different wavelengths (205, 210, and 215 nm) are considered for TAG detection by DAD; in each case, the obtained multiple regression model shows a good correlation between the dependent variable and predictive values of the TAG species (response factors and considered structural parameters, respectively). The ELSD gives responses exponentially related to injected amounts. Also, in this case, an attempt to relate the response factors of each considered detector to some structural parameters of TAG species is carried out. The results of this study are used to analyze the TAG fraction from an olive oil.     

Formation of Specific Configurations at Stereogenic Nitrogen Centers upon Their Coordination to Zinc and Mercury

The coordination of (R,R)-tetramethylcyclohexane-1,2-diamine derivatives with stereogenic nitrogen centers to zinc and mercury halides is investigated. It is shown that the resulting complexes display one specific configuration at the stereogenic nitrogen centers. This fact is unusual due to the fast inversion of nitrogen centers but highly desirable as the stereoinformation of the ligands is brought closer to the metal centers of the potential catalysts. A combination of NMR studies and quantum chemical calculations gives insight into the selective formation of one specific configuration at the stereogenic nitrogen centers of the zinc complexes.     

Generation of umbilics by magnets and flows

Umbilics in a nematic layer can be seen as topological defects of a complex order parameter. Being analogous to vortex lines in superfluids or superconductors, they are much easier to handle. We describe classroom experiments on controlled generation of umbilics in a nematic layer with homeotropic anchoring conditions submitted to an electric field. For this purpose we submit nematic samples to magnetic fields created by small NdFeB magnets. Umbilics induced by applied fields are unveiled by observation between crossed polarisers in monochromatic or white light. We report also on the winding action of rotating localised magnetic fields and on the winding reversal induced by Poiseuille flows.     

Modeling hop-constrained and diameter-constrained minimum spanning tree problems as Steiner tree problems over layered graphs

The hop-constrained minimum spanning tree problem (HMSTP) is an NP-hard problem arising in the design of centralized telecommunication networks with quality of service constraints. We show that the HMSTP is equivalent to a Steiner tree problem (STP) in an appropriate layered graph. We prove that the directed cut model for the STP defined in the layered graph, dominates the best previously known models for the HMSTP. We also show that the Steiner directed cuts in the extended layered graph space can be viewed as being a stronger version of some previously known HMSTP cuts in the original design space. Moreover, we show that these strengthened cuts can be combined and projected into new families of cuts, including facet defining ones, in the original design space. We also adapt the proposed approach to the diameter-constrained minimum spanning tree problem (DMSTP). Computational results with a branch-and-cut algorithm show that the proposed method is significantly better than previously known methods on both problems.     

The ring-star problem: A new integer programming formulation and a branch-and-cut algorithm

A ring star in a graph is a subgraph that can be decomposed into a cycle (or ring) and a set of edges with exactly one vertex in the cycle. In the minimum ring-star problem (mrsp) the cost of a ring star is given by the sum of the costs of its edges, which vary, depending on whether the edge is part of the ring or not. The goal is to find a ring-star spanning subgraph minimizing the sum of all ring and assignment costs. In this paper we show that the mrsp can be reduced to a minimum (constrained) Steiner arborescence problem on a layered graph. This reduction is used to introduce a new integer programming formulation for the mrsp. We prove that the dual bound generated by the linear relaxation of this formulation always dominates the one provided by an early model from the literature. Based on our new formulation, we developed a branch-and-cut algorithm for the mrsp. On the primal side, we devised a grasp heuristic to generate good upper bounds for the problem. Computational tests with these algorithms were conducted on a benchmark of public domain. In these experiments both our exact and heuristics algorithms had excellent performances, noticeably in dealing with instances whose optimal solution has few vertices in the ring. In addition, we also investigate the minimum spanning caterpillar problem (mscp) which has the same input as the mrsp and admits feasible solutions that can be viewed as ring stars with paths in the place of rings. We present an easy reduction of the mscp to the mrsp, which makes it possible to solve to optimality instances of the former problem too. Experiments carried out with the mscp revealed that our branch-and-cut algorithm is capable to solve to optimality instances with up to 200 vertices in reasonable time.     

Polyhedral results and a Branch-and-cut algorithm for the k-cardinality tree problem

Given an undirected graph $G$ with vertex and edge weights, the $k$ -cardinality tree problem asks for a minimum weight tree of $G$ containing exactly $k$ edges. In this paper we consider a directed graph reformulation of the problem and carry out a polyhedral investigation of the polytope defined by the convex hull of its feasible integral solutions. Three new families of valid inequalities are identified and two of them are proven to be facet implying for that polytope. Additionally, a Branch-and-cut algorithm that separates the new inequalities is implemented and computationally tested. The results obtained indicate that our algorithm outperforms its counterparts from the literature. Such a performance could be attributed, to a large extent, to the use of the new inequalities and also to some pre-processing tests introduced in this study.     

Nuclear forensics: searching for nuclear device debris in trinitite-hosted inclusions

This study documents the 3D morphology of trinitite-hosted metallic inclusions and the first observations of alloys consisting primarily of Pb, Ta, Ga, and W. Scanning electron and backscatter electron imaging, as well as energy dispersive X-ray spectra chemical composition data are reported for heavy metal inclusions in 14 different samples of trinitite. Inclusions consisting of Fe?CTi?CSi are the most abundant and presumably derived predominantly from the explosion tower. Grains of Cu, Pb, Ta?+?Ga?+?W were also observed and are likely derivatives of the trinitite device wiring, tamper, and tamper and core, respectively. Additionally, a Ba-rich grain and multiple zircons (ZrSiO₄) were observed in a large majority of samples. The spherical morphology and the ubiquitous positioning of the heavy metal inclusions on the crater walls of the glassy trinitite surfaces indicate a two-step formation. Stage one involves formation of the glassy trinitite, while the second stage involved the precipitation of the inclusions that were incorporated onto the surface of the trinitite. Furthermore, the precarious positioning of these inclusions further emphasizes the need for analysis using non-destructive techniques prior to methods employing a bulk sample digestion approach.