Concentration and energy invariance for a class of fully nonlinear elliptic equations

We study the asymptotic behavior of positive solutions of fully nonlinear elliptic equations in a ball, as the exponent of the power nonlinearity approaches a critical value. We show that solutions concentrate and blow up at the center of the ball, while a suitable associated energy remains invariant.     

Validation of the uncertainty evaluation for the determination of metals in solid samples by atomic spectrometry

 Every analytical result should be expressed with some indication of its quality. The uncertainty as defined by Eurachem ("parameter associated with the result of a measurement that characterises the dispersion of the values that could reasonably be attributed to the, . . ., quantity subjected to measurement") is a good tool to accomplish this goal in quantitative analysis. Eurachem has produced a guide to the estimation of the uncertainty attached to an analytical result. Indeed, the estimation of the total uncertainty by using uncertainty propagation laws is components-dependent. The estimation of some of those components is based on subjective criteria. The identification of the uncertainty sources and of their importance, for the same method, can vary from analyst to analyst. It is important to develop tools which will support each choice and approximation. In this work, the comparison of an estimated uncertainty with an experimentally assessed one, through a variance test, is performed. This approach is applied to the determination by atomic absorption of manganese in digested samples of lettuce leaves. The total uncertainty estimation is calculated assuming 100% digestion efficiency with negligible uncertainty. This assumption was tested. Received: 3 November 1997 · Accepted: 2 January 1998     

On the role of the functional group in determining the strength of hydrophobic interactions in aqueous solutions of α-amino acid derivatives

Calorimetric measurements were carried out at 25°C on binary aqueous solutions containing N-acetyl derivatives of the following -amino acids: glycine, alanine, valine, leucine, norleucine, aspartic acid, glutamic acid, phenylalanine, methionine, asparagine, glutamine, cysteine, histidine, serine. The N-acetyl derivative of the -amino acid proline was also studied. The results obtained have been used to calculate the pairwise enthalpic interaction coefficients and these are compared with results reported in the literature concerning free -amino acids, and their acetylamide derivatives. The coefficients largely increase passing from free amino acids to N-acetyl derivatives. The derivatives of -amino acids bearing unsubstituted alkyl chains present an increased cooperativity of hydrophobic interactions.     

Equilibrium in Saturated Ca(OH)2 Solutions: Parameters and Dissociation Constants

A new computer program has been developed for the calculation of pH, pOH, hydroxide ion concentration m _OH, species distribution coefficients _i, ionic activity coefficients _i ionic strength I, buffer capacity , solubility product K _s0, and the two dissociation constants, K _b1 and K _b2, corresponding, respectively, to first and second dissociation steps of Ca(OH)₂ in aqueous solution. Previously developed methodology, for the calculation of pH, _i, _i I, and parameters of pH buffer solutions, starting from the corresponding acidity constants, has been adapted for the case of aqueous Ca(OH)₂ solutions, for which the pertinent stoichiometric relationships are different from those applicable to mixtures of acids and their salts. The results show that, contrary to what is currently assumed, the first dissociation is far from complete. Values are given for the concentrations and activities of species Ca(OH)₂(aq), Ca(OH)⁺(aq), and Ca²⁺ (aq) in saturated calcium hydroxide solutions at 25°C.     

EFFECT OF THYMINE DIMER INTRODUCTION IN A 21 BASE PAIR OLIGONUCLEOTIDE

Abstract— It is well known that the pyrimidine dimers are the main damage produced by UV radiation on the DNA structure. However, while studies on the photoproduct structure have been carried out extensively, uncertainties still exist on the implication that a single damaging event has on the overall conformation. In particular, the extension of the damage influence on the polynucleotide chain is a matter of debate. This problem is especially important to understanding some steps of the repair mechanisms. In this study we performed a chemical-physical characterization of 21 base pair oligonucleotides containing a single thymine dimer in one strand. Thermodynamic parameters were determined by means of thermal denaturation experiments, and static fluorescence measurements were performed to unequivocally define the primary structure-conformation relationship in this specific case. We used hydroxyl radicals, produced by means of γ-irradiation of the sample solution, to detect fine structure changes. Our data show that the introduction of a single thymine dimer might cause only a slight distortion of the helix geometry, as judged by the evaluation of the enthalpic and the entropic terms and by the small changes observed in the binding of ethidium bromide to DNA. The modifications in the sugar phosphate backbone subsequent to the damaging event are especially evident, near the thymine dimer, toward the 5'-end direction in the strand containing the dimer.     

Meeting the Requirements of the Silver/Silver Chloride Reference Electrode

Potentiometric cells from which the pH values of standard buffer solutions are computed rely on the silver–silver chloride reference electrode which has proved to be convenient, reproducible and reliable. Of the various methods of preparation of silver-silver chloride electrodes only one concerns us here: the thermal–electrolytic type that has been used more extensively than any other form. Once prepared, the electrodes need to be equilibrated before use and between experiments. The equilibration technique must ensure voltage stability and inter-electrode, or bias, potential below 0.1 mV. In potentiometry the stability of a reference electrode is of utmost importance since an offset of 1 mV is equivalent to a deviation of about 0.02 in the pH value.     

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.