On an eigenvalue problem related to the critical exponent

In this paper we study the eigenvalue problemwhere is a smooth bounded domain, and u is a positive solution of the problemsuch thatwhere S is the best Sobolev constant for the embedding of H¹₀() into L²*(), We prove several estimates for the eigenvalues _i, of (I), i=2,..,N+2 and some qualitative properties of the corresponding eigenfunctions.Supported by M.I.U.R., project Variational methods and nonlinear differential equations.     

Symmetry of positive solutions of an almost-critical problem in an annulus

We consider the subcritical problem & 0 & \qquad\textrm{in} \; A\\ u & = & 0 & \qquad\textrm{on} \; \delta A\\ \end{array} \right.$$" align="middle" border="0"> where A is an annulus in , , is the critical Sobolev exponent and 0$" align="middle" border="0"> is a small parameter. We prove that solutions of (I) which concentrate at one or two points are axially symmetric.Received: 7 July 2003, Accepted: 10 May 2004, Published online: 16 July 2004Filomena Pacella: Research supported by MIUR, project Variational Methods and Nonlinear Differential Equations.     

The Effects of Cosolvents on the Complexation of α-Cyclodextrin with Alkylated Substances. Calorimetric Studies at 25 °C

The formation of complexes of -cyclodextrin with 1,2-alkanediols, ,-alkanediols and some cycloalkanols has been studied calorimetrically at 25 °C in water, in 7 mol kg^-1 aqueous urea and in 3 mol kg^-1 aqueous glucose. When a complex is formed, calorimetry enables the calculation of both the enthalpy and the association constant, from which the free energy and the entropy of the process can be obtained. The forces involved in the association process are discussed in the light of the signs and values of the thermodynamic parameters obtained. The effect of the variation of the aqueous medium on the hydration of the interacting substances and the consequent changes in the association parameters have been investigated. As respect to water, complexes are less stable in urea and more stable in glucose. The analysis of the data shows that this is the result of a different enthalpy-entropy balance in the two solvent media. Deaquation of the interacting substances plays a major role in determining the stability of the inclusion complexes.     

Phase behavior of C60 by computer simulation using ab‐initio interaction potential

A first‐principles intermolecular potential recently proposed by Pacheco and Ramalho [Phys Rev Lett 1997, 79, 3873–3876] has been used with the Gibbs ensemble and Gibbs–Duhem integration Monte Carlo methods to simulate the vapor–liquid and fluid–solid coexistence properties of C₆₀. The critical properties were calculated by fitting the results to the laws of rectilinear diameters and order parameter scaling. The triple‐point properties were determined from the limiting behavior of the Gibbs ensemble vapor–liquid simulations at the lowest temperature range. A stable liquid phase is predicted for temperatures between 1570±20 and 2006±27 K and densities between 0.444±0.003 and 1.05±0.01 nm^?3. The estimated critical and triple‐point pressures are, respectively, 35±6 and 5±16 bars. We show for the first time, to our knowledge, that it is possible, strictly by computer simulation, to estimate a triple point for C₆₀ in accordance with the predictions of theoretical methods and the basic concepts of thermodynamics. The liquid and fluid radial distribution functions indicate the presence of solid or glasslike features. This may support the suggestion of a more cooperative interaction of clusters in C₆₀. A comparison of our results with the data obtained by other authors is presented and discussed. © 2001 John Wiley & Sons, Inc. Int J Quantum Chem 84: 375–387, 2001     

Structure–Activity Relationship Study of a Potent α-Thrombin Binding Aptamer Incorporating Hexitol Nucleotides

The replacement of one or more nucleotide residues in the potent α-thrombin-binding aptamer NU172 with hexitol-based nucleotides has been devised to study the effect of these substitutions on the physicochemical and functional properties of the anticoagulant agent. The incorporation of single hexitol nucleotides at the T9 and G18 positions of NU172 substantially retained the physicochemical features of the parent oligonucleotide, as a result of the biomimetic properties of the hexitol backbone. Importantly, the NU172- T ^H9 mutant exhibited a higher binding affinity toward human α-thrombin than the native aptamer and an improved stability even after 24 h in 90 % human serum, with a significant increase in the estimated half-life. The anticoagulant activity of the modified oligonucleotide was also found to be slightly preferable to NU172. Overall, these results confirm the potential of hexitol nucleotides as biomimetic agents, while laying the foundations for the development of NU172-inspired α-thrombin-binding aptamers.     

Synthesis,characterization and assessment of the cytotoxic activity of Cu(II), Fe(III) and Mn(III) complexes of camphoric acid‐derived salen ligands

Novel Cu(II), Fe(III) and Mn(III) salen‐type metal complexes from (1R,3S)‐N,N′‐bis[salicylidene]‐1,3‐diamino‐1,2,2‐trimethylcyclopentane were synthesized and screened for their in vitro cytotoxic activity against three human cancer cell lines: melanoma, colorectal and breast. In vitro experiments carried out with the three metal complexes show that the copper complex exhibits the highest cytotoxic activity towards all cell lines studied, presenting IC₅₀ values of 3.32–6.71 μM. A significant improvement in the anti‐proliferative effect, by 20‐fold, is observed with this complex when compared with conventional chemotherapy. The relationship between structure, redox characteristics and biological activity in human cancer cell lines was evaluated for the most efficient Cu(II) complex and associated with theoretical calculations. Copyright © 2015 John Wiley & Sons, Ltd.     

A reduction method for semilinear elliptic equations and solutions concentrating on spheres

We show that any general semilinear elliptic problem with Dirichlet or Neumann boundary conditions in an annulus A⊆R^2m$A\subseteq {\mathbb{R}}^{2m}$, m?2$m?2$, invariant by the action of a certain symmetry group can be reduced to a nonhomogeneous similar problem in an annulus D⊂R^m+1$D\subset {\mathbb{R}}^{m+1}$, invariant by another related symmetry. We apply this result to prove the existence of positive and sign changing solutions of a singularly perturbed elliptic problem in A   which concentrate on one or two (m−1)$(m-1)$ dimensional spheres. We also prove that the Morse indices of these solutions tend to infinity as the parameter of concentration tends to infinity.     

Artificial neural network combined with principal component analysis for resolution of complex pharmaceutical formulations

A chemometric approach based on the combined use of the principal component analysis (PCA) and artificial neural network (ANN) was developed for the multicomponent determination of caffeine (CAF), mepyramine (MEP), phenylpropanolamine (PPA) and pheniramine (PNA) in their pharmaceutical preparations without any chemical separation. The predictive ability of the ANN method was compared with the classical linear regression method Partial Least Squares 2 (PLS2). The UV spectral data between 220 and 300 nm of a training set of sixteen quaternary mixtures were processed by PCA to reduce the dimensions of input data and eliminate the noise coming from instrumentation. Several spectral ranges and different numbers of principal components (PCs) were tested to find the PCA-ANN and PLS2 models reaching the best determination results. A two layer ANN, using the first four PCs, was used with log-sigmoid transfer function in first hidden layer and linear transfer function in output layer. Standard error of prediction (SEP) was adopted to assess the predictive accuracy of the models when subjected to external validation. PCA-ANN showed better prediction ability in the determination of PPA and PNA in synthetic samples with added excipients and pharmaceutical formulations. Since both components are characterized by low absorptivity, the better performance of PCA-ANN was ascribed to the ability in considering all non-linear information from noise or interfering excipients.     

Optimization of the determination of chemical oxygen demand in wastewaters

Chemical oxygen demand (COD) is one of the most relevant chemical parameters for the management of wastewater treatment facilities including the control of the quality of an effluent. The adequacy of decisions based on COD values relies on the quality of the measurements. Cost effective management of the minor sources of uncertainty can be applied to the analytical procedure without affecting measurement quality. This work presents a detailed assessment of the determination of COD values in wastewaters, according to ISO6060:1989 standard, which can support reduction of both measurement uncertainty and cost of analysis. This assessment includes the definition of the measurement traceability chain and the validation of the measurement procedure supported on sound and objective criteria. Detailed models of the measurement performance, including uncertainty, developed from the Differential Approach, were successfully validated by proficiency tests. The assumption of the measurement function linearity of the uncertainty propagation law was tested through the comparison with the numerical Kragten method. The gathered information supported the definition of strategies for measurement uncertainty or cost reduction. The developed models are available as electronic supplementary material, in an MS-Excel file, to be updated with the user's data.     

Blow-up and symmetry of sign-changing solutions to some critical elliptic equations

In this paper we continue the analysis of the blow-up of low energy sign-changing solutions of semi-linear elliptic equations with critical Sobolev exponent, started in [M. Ben Ayed, K. El Mehdi, F. Pacella, Blow-up and nonexistence of sign-changing solutions to the Brezis-Nirenberg problem in dimension three, Ann. Inst. H. Poincaré Anal. Non Linéaire, in press]. In addition we prove axial symmetry results for the same kind of solutions in a ball.