Nontrivial application of Nielsen theory to differential systems

In reply to a problem of Jean Leray concerning application of the Nielsen theory to differential systems for obtaining multiplicity results, we present a nontrivial example of such an application. The emphasis is on the parameter space in order to ensure that no subdomain becomes subinvariant under the related Hammerstein solution operator. To achieve this goal, we develop a general method applicable also for ordinary differential equations with or without uniqueness as well as for upper-Carathéodory differential inclusions. We are not aware that any alternative approach can be employed, even in the single-valued case.     

A package for symbolic solution of real functional equations of real variables

Summary This paper discusses the problems associated with the symbolic treatment of functional equations and presents a Mathematica package for the solution of real functional equations of real variables. The package includes a minimal basic database which contains a reduced set of functional equations with its four components: equation, domain, class and the corresponding solution. The word minimal is used in the sense that any equation that is solvable by the system using non-searching methods is excluded from the database. The package incorporates a searching algorithm which can solve functional equations independently of their notation and their algebraic representation. Not only general solutions but particular and candidate solutions are dealt with. This implies a careful analysis of domains and classes. The package includes some methods for solving functional equations, which are used when the input functional equations are not found in the database. Some methods have been implemented internally and some are in an external package. Finally, some examples illustrate the use of the package.     

Gold nanoparticles deposited capillaries for in-capillary microextraction capillary zone electrophoresis of monohydroxy-polycyclic aromatic hydrocarbons

This article presents the first application of gold nanoparticles deposited capillaries as pre-concentration devices for in-capillary microextraction CZE and their use for the analysis of monohydroxy-polycyclic aromatic hydrocarbons in synthetic urine samples. The successful separation of 1-hydroxypyrene, 9-hydroxyphenanthrene, 3-hydroxybenzo[a]pyrene (3-OHbap), 4-hydroxybenzo[a]pyrene and 5-hydroxybenzo[a]pyrene under a single set of electrophoretic conditions is demonstrated as well as the feasibility to obtain competitive ultraviolet absorption LOD with commercial instrumentation. Enrichment factors ranging from 87 (9-OHphe) to 100 (3-OHbap) made it possible to obtain LOD ranging from 9 ng/mL (9-OHphe and 3-OHbap) to 14 ng/mL (4-hydroxybenzo[a]pyrene).     

Design of insurance contracts using stochastic programming in forestry planning

This work addresses a tactical planning problem faced by a forestry firm, deciding which timber units to harvest and what roads to build to obtain the greatest possible benefits. We include uncertainty in prices by means of utility theory. This enables solutions to be found that the firm finds preferable to those obtained when risk aversion is ignored and makes it possible to design insurance contracts that benefit the firm while also being attractive to an insurer. Two types of contract are designed; one dependent on the firm’s operating result and the other independent of it. Metrics are then developed to quantify the benefits conferred by a contract, demonstrating that the latter contract type dominates the former. These results are then illustrated by applying them to a simplified planning problem of a forest owned by the Chilean forestry operator Millalemu.     

Determination of polycyclic aromatic hydrocarbons with molecular weight 302 in water samples by solid-phase nano-extraction and laser excited time-resolved Shpol'skii spectroscopy

Monitoring of high-molecular weight polycyclic aromatic hydrocarbons (HMW-PAH) via simple and cost effective methods still remains a challenge. In this article, we combine solid-phase nano-extraction (SPNE) and 4.2 K laser-excited time resolved Shpol'skii spectroscopy (LETRSS) into a valuable alternative for the water analysis of dibenzo[a,l]pyrene, dibenzo[a,h]pyrene, dibenzo[a,i]pyrene and naphtho[2,3-a]pyrene. In comparison to the original SPNE procedure, the present method improves PAH recoveries and reduces extraction time from 30 to 20 min per sample. Quantitative release of HMW-PAH into the Shpol'skii matrix (n-octane) is best accomplished with a mixture of 48 μL of methanol and 2 μL of 1-pentanethiol. Their migration into the 50 μL layer of n-octane provides highly resolved spectra with distinct fluorescence lifetimes for unambiguous isomer determination. Complete analysis takes less than 30 min per sample and consumes only 100 micro-liters of organic solvents. 500 μL of water are sufficient to obtain limits of detection ranging from 16 ng L(-1) (dibenzo[a,l]pyrene) to 55 ng L(-1) (dibenzo[a,i]pyrene), relative standard deviations better than 3% and analytical recoveries above 90%. Although a straightforward comparison to chromatographic methods is not possible because of the lack of analytical figures of merit on HMW-PAH, the excellent precision of measurements, limits of detection and overall recoveries makes SPNE-LETRSS an attractive approach to water analysis of HMW-PAH.     

6-Phosphoryl picolinic acids as europium and terbium sensitizers

Three 6-phosphoryl picolinic acid (6PPA) derivatives were synthesized and used as europium and terbium sensitizers. Two of the three ligands (6-diethoxyphosphoryl picolinic acid (Hdeppa) and 6-monoethoxyphosphoryl picolinic acid (H(2)meppa)) are water-soluble, once complexed to lanthanide ions, while the third (6-dihydroxyphosphoryl picolinic acid (H(3)dhppa)) forms a precipitate. The stability constants of the phosphoryl-based complexes were found to be higher than the carboxylate analogue (dipicolinic acid, H(2)dpa). The main species are the [LnL(3)] complexes under strict stoichiometric conditions, confirmed by (31)P NMR spectroscopy, mass spectrometry and lifetime analyses. The photophysical measurements reveal that the emission intensity of [Eu(deppa)(3)] is maximal at pH 4.8, whereas for [Eu(meppa)(3)](3-), the optimum pH is observed at 9.0. The lifetimes are all in the millisecond range and have confirmed the absence of water molecules in the first coordination sphere. The emissions of the terbium are always brighter than the corresponding europium within this phosphoryl series. The quantum yields of the phosphoryl containing complexes are lower than the carboxylate analogue ([Ln(dpa)(3)](3-)), except for [Tb(deppa)(3)], which exhibits an interesting quantum yield of 40% in aqueous solution.     

On the First Critical Field in Ginzburg–Landau Theory for Thin Shells and Manifolds

In this article, we investigate the response of a thin superconducting shell to an arbitrary external magnetic field. We identify the intensity of the applied field that forces the emergence of vortices in minimizers, the so-called first critical field H _c1 in Ginzburg–Landau theory, for closed simply connected manifolds and arbitrary fields. In the case of a simply connected surface of revolution and vertical and constant field, we further determine the exact number of vortices in the sample as the intensity of the applied field is raised just above H _c1. Finally, we derive via Γ-convergence similar statements for three-dimensional domains of small thickness, where in this setting point vortices are replaced by vortex lines.