Quasilinear elliptic inequalities on complete Riemannian manifolds

We prove maximum and comparison principles for weak distributional solutions of quasilinear, possibly singular or degenerate, elliptic differential inequalities in divergence form on complete Riemannian manifolds. A new definition of ellipticity for nonlinear operators on Riemannian manifolds is introduced, covering the standard important examples. As an application, uniqueness results for some related boundary value problems are presented.     

Procedure for retrieving the optical properties of a two-layered medium from time-resolved reflectance measurements

A procedure for retrieving the optical properties of a two-layered diffusive medium based on an exact analytical solution of the diffusion equation and on relative multidistance time-resolved reflectance measurements is presented. The method overcomes some limitations of previously developed procedures. Five parameters of the medium have been fitted: the absorption and the reduced scattering coefficients of both layers and the thickness of the first layer. The actual values of the parameters are correctly retrieved by the procedure. The inversion procedure does not require an initial guess for the unknown optical properties, but the starting value for the thickness of the first layer needs to be estimated with an error smaller than 50%.     

High-performance liquid chromatography analysis of polyacetylenes and polyenes in Echinacea pallida by using a monolithic reversed-phase silica column

In this study, a RP-HPLC method for the analysis of polyacetylenes and polyenes in Echinacea pallida roots and phytopharmaceuticals was developed. The reference compounds used for quantification were isolated from the plant material and their structures were determined on the basis of the analysis of UV, IR, NMR and MS data. The complete structure elucidation of three compounds, namely 8-hydroxy-tetradec-(9E)-ene-11,13-diyn-2-one (1), tetradec-(8Z)-ene-11,13-diyn-2-one (6) and pentadec-(8Z)-en-2-one (9) is described. In the analysis of the n-hexane extracts of E. pallida roots, the comparison between conventional and monolithic columns showed that the elution order in both cases is identical and the selectivity is equivalent. However, the retention times achieved by the monolithic column are shorter, resulting in a faster separation (20 min). Therefore, the analyses were carried out on a Chromolith Performance RP-18e (100 mm x 4.6 mm i.d.), with a gradient mobile phase composed by H(2)O and ACN at the flow rate of 2 mL/min. The column was thermostatted at 20 degrees C. The photodiode array detector monitored the eluent at 210 nm. The validation procedure confirmed that this technique affords reliable analysis of these components and is appropriate for the quality control of complex matrices, such as E. pallida roots and phytopharmaceuticals.     

Synthesis and host-guest studies of chiral N-linked peptidoresorc[4]arenes

Four cone resorc[4]arene octamethyl ethers (10, 11, ent-10, and ent-11) tetrafunctionalized at the feet with valyl-leucine [LL- (6); DD- (ent-6)] and leucyl-valine [LL- (9); DD- (ent-9)] methyl esters have been synthesized. These compounds, obtained by conjugation of macrocycle tetracarboxylic acid chlorides with the appropriate terminal amino groups of the above dipeptides, are N-linked peptidoresorc[4]arenes. We found that these macrocycles (M) are capable of recognizing the homologue dipeptides as guests (G), both in solution and in the gas phase, by forming relatively stable host-guest complexes ([M.G]), resistant to chromatographic purification but not to heating. Complexation phenomena between M and G in solution were investigated by NMR methods, including NMR DOSY experiments, for the detection of translational diffusion. Heteroassociation constants of 2030 and 186 M(-1) were obtained by the Foster-Fyfe method for the complexes [10.6] and [10.ent-6], respectively, the latter being comparable to the self-association constant of dipeptide itself. Conversely, the structural features of the proton-bound complexes [M.H.Gn]+ (n = 1, 2), generated in the gas phase by electrospray ionization mass spectrometry (ESI-MS), were investigated by collision-induced dissociation (CID) experiments. In both cases, the four N-linked peptidoresorc[4]arenes were shown to act as synthetic receptors and to recognize the homologue dipeptide by means of hydrogen bonds.     

On L^{r} hypoellipticity of solutions with compact support of the Cauchy–Riemann equation

In one complex variable, the existence of a compactly supported solution to the Cauchy–Riemann equation is related to the vanishing of certain integrals of the data; trying to generalize this approach, we find an explicit construction, via convolution, for a compactly supported solution in \(\mathbb C ^n\) , which allows us to estimate the \(L^p\) norm of the solution. We also investigate the possible generalizations of this method to domains of the form \(P\setminus Z\) , where \(P\) is a polydisc and \(Z\) is the zero locus of some holomorphic function.     

Functional MRI changes in the central motor system in myotonic dystrophy type 1

Myotonic dystrophy type 1 (DM1) is a multisystemic disease involving multiple organ systems including central nervous system (CNS) and muscles. Few studies have focused on the central motor system in DM1, pointing to a subclinical abnormality in the CNS. The aim of our study was to investigate patterns of cerebral activation in DM1 during a motor task using functional MRI (fMRI). Fifteen DM1 patients, aged 20 to 59 years, and 15 controls of comparable age were scanned during a self-paced sequential finger-to-thumb opposition task of their dominant right hand. Functional MRI images were analyzed using SPM99. Patients underwent clinical and genetic assessment; all subjects underwent a conventional MR study. Myotonic dystrophy type 1 patients showed greater activation than controls in bilateral sensorimotor areas and inferior parietal lobules, basal ganglia and thalami, in the ipsilateral premotor area, insula and supplementary motor area (corrected P<.05). Analysis of the interaction between disease and age showed that correlation with age was significantly greater in patients than in controls in bilateral sensorimotor areas and in contralateral parietal areas. Other clinical and MR characteristics did not correlate with fMRI. Functional changes in DM1 may represent compensatory mechanisms such as reorganization and redistribution of functional networks to compensate for ultrastructural and neurochemical changes occurring as part of the accelerated aging process.