Regularity results for evolutionary nonlinear variational and quasi-variational inequalities with applications to dynamic equilibrium problems

The aim of this paper is to obtain the continuity of solutions to time-dependent nonlinear variational and quasi-variational inequalities which express many dynamic equilibrium problems. To prove our results, we make use of Minty’s Lemma and of the notion of the Mosco’s convergence.     

An Efficient Solid-Phase Microextraction–Gas Chromatography–Mass Spectrometry Method for the Analysis of Methyl Farnesoate Released in Growth Medium by Daphnia pulex

Methyl farnesoate (MF), a juvenile hormone, can influence phenotypic traits and stimulates male production in daphnids. MF is produced endogenously in response to stressful conditions, but it is not known whether this hormone can also be released into the environment to mediate stress signaling. In the present study, for the first time, a reliable solid-phase microextraction–gas chromatography–mass spectrometry (SPME-GC-MS) method was developed and validated for the ultra-trace analysis of MF released in growth medium by Daphnia pulex maintained in presence of crowding w/o MK801, a putative upstream inhibitor of MF endogenous production. Two different clonal lineages, I and S clones, which differ in the sensitivity to the stimuli leading to male production, were also compared. A detection limit of 1.3 ng/L was achieved, along with good precision and trueness, thus enabling the quantitation of MF at ultra-trace level. The achieved results demonstrated the release of MF by both clones at the 20 ng/L level in control conditions, whereas a significant decrease in the presence of crowding was assessed. As expected, a further reduction was obtained in the presence of MK801. These findings strengthen the link between environmental stimuli and the MF signaling pathway. Daphnia pulex, by releasing the juvenile hormone MF in the medium, could regulate population dynamics by means of an autoregulatory feedback loop that controls the intra- and extra-individual-level release of MF produced by endogenous biosynthesis.     

Monomeric azaheterofullerene derivatives RC59N: influence of the R moiety on spectroscopic and photophysical properties

We have synthesised nine monomeric azaheterofullerene (AZA) derivatives, RC(59)N, with a wide variety of different side chains R and investigated their spectroscopic and photophysical properties in toluene and o-dichlorobenzene (ODCB). Measurements include their ground-state absorption spectra, molar absorption coefficient (epsilon(G)), fluorescence spectra, fluorescence quantum yields (Phi(F)), singlet-state lifetimes (tau(F)), triplet-state absorption spectra, triplet molar absorption coefficients (epsilon(T)), singlet oxygen (Phi(Delta)), and triplet state (Phi(T)) quantum yields. The replacement of a carbon by a nitrogen atom in the C(60) sphere strongly affects most of the spectroscopic and photophysical properties. The chemical nature of the R moiety has definite effects on these properties in contrast with minor effects on the chemical nature of the addends in [6,6]-ring bridged monoadduct methano[60]fullerene derivatives. These effects concern properties of the ground state, singlet excited state, and triplet states of our nine RC(59)N derivatives and in particular the values of photophysical parameters epsilon(G), epsilon(T), Phi(Delta), and Phi(T), which are significantly lower than those of analogous monoadduct [6,6]-ring bridged methano[60]fullerene derivatives.     

Continuity of solutions for parametric variational inequalities in Banach space

We consider here a type of pseudo-monotone parametric variational inequalities on a class of Banach spaces and show that such problems admit continuous (with respect to the parameter) solutions, as long as generic existence and uniqueness conditions for these solutions are satisfied. In particular, we show that such results are valid on a class of Banach spaces whenever we deal with strong pseudo-monotonicity, while others are valid in Hilbert spaces, whenever strict monotonicity is present. We also provide examples to illustrate the new results.     

Analysis of sterols by high-performance liquid chromatography/mass spectrometry combined with chemometrics

A newly developed high-performance liquid chromatography/mass spectrometry (HPLC/MS) method has been successfully used to analyze plasma concentrations of various phytosterols (cholestanol and beta-sitosterol) and cholesterol metabolites (desmosterol and lathosterol). This was based on an unusual solvent combination of water/methanol vs. methanol/acetone/n-hexane applied on a Purospher Star RP-18e (125 x 2 mm, 3 microm) column, which proved excellent for the separation, identification and quantification of plasma sterols. Simple solid-phase extraction preparation of plasma samples was performed, followed by the developed fast and robust HPLC separation. Results on four groups of people were compared, those with low, normal and high plasma cholesterol levels and those with high cholesterol levels on statin therapy, and the results were evaluated using linear discriminant analysis (LDA). Variable selection for LDA was achieved using backward removal selection. Highly discriminatory variables were the ratios of desmosterol to sitosterol and of lathosterol to total plasma cholesterol. The latter ratio was also excellent for distinguishing subjects on statin therapy. The success rate of classification was 100%. The present pilot study shows the potential of HPLC/MS analysis and chemometrics for studying cholesterol-related disorders and warrants future full-scale medical study.     

On Lagrange duality theory for dynamics vaccination games

The authors study an infinite dimensional duality theory finalized to obtain the existence of a strong duality between a convex optimization problem connected with the management of vaccinations and its Lagrange dual. Specifically, the authors show the solvability of a dual problem using as basic tool an hypothesis known as Assumption S. Roughly speaking, it requires to show that a particular limit is nonnegative. This technique improves the previous strong duality results that need the nonemptyness of the interior of the convex ordering cone. The authors use the duality theory to analyze the dynamic vaccination game in order to obtain the existence of the Lagrange multipliers related to the problem and to better comprehend the meaning of the problem.

     

Almost Exponential Maps and Integrability Results for a Class of Horizontally Regular Vector Fields

We consider a family ${\mathcal{H}}:= \{X_1, \dots, X_m\}$ of C ¹ vector fields in ? ⁿ and we discuss the associated ${\mathcal{H}}$ -orbits. Namely, we assume that our vector fields belong to a horizontal regularity class and we require that a suitable s-involutivity assumption holds. Then we show that any ${\mathcal{H}}$ -orbit ${\mathcal{O}}$ is a C ¹ immersed submanifold and it is an integral submanifold of the distribution generated by the family of all commutators up to length s. Our main tool is a class of almost exponential maps of which we discuss carefully some precise first order expansions.     

Preface to Variational Analysis for Beginners

Set-Valued and Variational Analysis -     

Using several advertising media in a homogeneous market

We propose a variety of models to represent the joint effect of several advertising media on the demand for a product in a homogeneous market, and discuss the associated profit maximization problems. An advertising productivity function represents the combination of several media and, together with demand and advertising cost functions, determines the features of the associated profit problem. We distinguish between additive and nonadditive advertising productivity functions, then between smooth and nonsmooth ones. The demand function may either be linear or not. We observe how different models may exhibit either synergy or interference effects. In some cases we obtain explicit optimal solutions.