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.     

Solid-Phase Synthesis of Fluorescent Probes for Plasma Membrane Labelling

The cellular plasma membrane plays a fundamental role in biological processes, including cell growth, signaling and transport. The labelling of the plasma membrane with targeted fluorescent probes offers a convenient and non-invasive way to image the morphological changes and dynamics of a membrane in real-time and, despite many examples of fluorescent plasma membrane probes, a “universal targeting/anchoring moiety” is still required. In this study, a small number of stearic acid-based probes labelled with 6-carboxyfluorescein was designed and fabricated via solid-phase synthesis in which variations in both charge and hydrophobicity were explored. To ease the synthesis process, a gram-scale synthesis of the Fmoc-Lys(6-carboxyfluoresein diacetate)-OH building block was developed, allowing the discovery of optimal probes that carried a positively charged amino group and a stearic acid tail that exhibited intense plasma membrane brightness and robust retention.     

Development of easy‐to‐use reverse‐phase liquid chromatographic methods for determining PRE‐084, RC‐33 and RC‐34 in biological matrices. The first step for in vivo analysis of sigma1 receptor agonists

Over the years there has been a growing interest in the therapeutic potential for central nervous system pathologies of sigma receptor modulators. The widely studied PRE‐084 and our compounds RC‐33 and RC‐34 are very potent and selective sigma 1 receptor agonists that could represent promising drug candidates for Amyotrophic Lateral Sclerosis (ALS). Herein, we develop and validate robust and easy‐to‐use reverse‐phase chromatographic methods suitable for detecting and quantifying PRE‐084, RC‐33 and RC‐34 in mouse blood, brain and spinal cord. An HPLC/UV/ESI‐MS system was employed for analyzing PRE‐084 and an HPLC/UV‐PDA system for determining RC‐33 and RC‐34. Chromatographic separations were achieved on Waters Symmetry RP₁₈ column (150 × 3.9 mm, 5 µm), eluting with water and acetonitrile (both containing 0.1% formic acid) in gradient conditions. The recovery of PRE‐084, RC‐33 and RC‐34 was >95% in all the considered matrices. Their limits of quantitation and detection were also determined. Validation proved the methods be suitable for separating tested compounds from endogenous interferences, being characterized by good sensitivity, linearity, precision and accuracy. A preliminary central nervous system distribution study showed a high distribution of RC‐33 in brain and spinal cord, with concentration values well above the determined limit of quantitation. The proposed methods will be used in future preclinical investigations. Copyright © 2015 John Wiley & Sons, Ltd.     

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.     

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.     

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.