Time-like minimal submanifolds as singular limits of nonlinear wave equations

We consider the sharp interface limit ?→0⁺ of the semilinear wave equation in R¹⁺ⁿ, where takes values in R^k, k=1,2, and W is a double-well potential if k=1 and vanishes on the unit circle and is positive elsewhere if k=2. For fixed ?>0 we find some special solutions, constructed around minimal surfaces in Rⁿ. In the general case, under some additional assumptions, we show that the solutions converge to a Radon measure supported on a time-like k-codimensional minimal submanifold of the Minkowski space-time. This result holds also after the appearance of singularities, and enforces the observation made by J. Neu that this semilinear equation can be regarded as an approximation of the Born-Infeld equation.     

High-performance liquid chromatography determination of phenyllactic acid in MRS broth

Phenyllactic acid (PLA) is an organic acid produced by some strains of lactic acid bacteria (LAB) and concentrations higher than 7.5 mg/ml inhibit growth of moulds and yeasts. Since PLA can be used to select LAB, a rapid, simple and cheap method for its determination is desirable. Typical methods for its analysis in broth are time-consuming, analytically complicated, and have poor recoveries. Herein we propose a simple and rapid method that does not require extraction, but only microfiltration of broth before injection in HPLC. The improved chromatographic conditions allow separation and quantification of PLA with a recovery of 98.7%. The method is highly reproducible with an intraday repeatability of the total peak area of 2.00%, while an interday repeatability of 2.69%.     

High-throughput analysis of bergamot essential oil by fast solid-phase microextraction-capillary gas chromatography-flame ionization detection

The advantages of using a narrow-bore column in headspace solid-phase microextraction-gas chromatographic (HS-SPME-GC) analysis are investigated. An automated rapid HS-SPME-GC method for the determination of volatile compounds in a complex sample (bergamot essential oil) was developed. A low-capacity (7 microm) SPME fibre was employed, enabling a short equilibration time (15 min). The absorbed volatile compounds were then separated in 12.5 min on a 10 m x 0.1 mm I.D. capillary. The fast GC method was characterized by relatively moderate GC parameters (head pressure: 173 kPa; temperature program rate: 12 degrees C/min). The employment of the low-capacity fibre also suited the reduced sample capacity of the capillary employed, hence column overloading was avoided. Analytical repeatibility was determined in terms of retention times (maximum RSD: 0.32%) and peak areas (maximum RSD: 9.80%). The results obtained were compared to those derived from a conventional HS-SPME-GC (a 30 microm SPME fibre and 0.25 mm I.D. capillary were used) application on the same sample. In this respect, a great reduction of analytical time was obtained both with regard to the conventional SPME equilibration and GC run times, which both required 50 min. Peak resolution was altogether comparable in both applications. Although a slight loss in terms of sensitivity was observed in the rapid approach (generally within the 25-50% range), this did not impair the detection of all peaks of interest. Finally, the selectivities of the 30 and 7 microm fibres were evaluated and, as expected, these were in good agreement.     

Heavy metals in PM10 sampled in the urban area of Campi Salentina (Apulia, southern Italy)

The following paper shows results of PM10 level and Cd, Cr, Cu, Fe, Mn, Ni, Pb, V and Zn concentrations present in this fraction for filters collected in the urban area of Campi Salentina (Apulia, Southern Italy) in 2004 in order to inquire into air quality. PM10 and lead concentrations did not exceed the standard values sanctioned by Italian Legislature with average values equal to 36.54 +/- 14.57 microg x m(-3) and 9.19 +/- 5.24 ng x m(-3) respectively. Significant correlations have been found between the pairs Fe-Mn, Ni-V, Cr-Ni and Cd-Cr. This suggests that these metals have a similar pollution source probably due to metallurgical activity. Multivariate statistical analysis showed that it is possible to distinguish the PM10 samples collected in sampling periods with different meteorological conditions. Indeed, metals concentration increases for samples characterized by scarce rains or by winds prevailing from North or North-West and is reduced due to different meteorological conditions, although there are some exceptions.     

Geometries and properties of excited states in the gas phase and in solution: theory and application of a time-dependent density functional theory polarizable continuum model

In this paper we present the theory and implementation of analytic derivatives of time-dependent density functional theory (TDDFT) excited states energies, both in vacuo and including solvent effects by means of the polarizable continuum model. The method is applied to two case studies: p-nitroaniline and 4-(dimethyl)aminobenzonitrile. For both molecules PCM-TDDFT is shown to be successful in supporting the analysis of experimental data with useful insights for a better understanding of photophysical and photochemical pathways in solution.     

Surface enhanced second harmonic generation from macrocycle, catenane, and rotaxane thin films: experiments and theory

Surface enhanced second harmonic generation (SE SHG) experiments on molecular structures, macrocycles, catenanes, and rotaxanes, deposited as monolayers and multilayers by vacuum sublimation on silver, are reported. The measurements show that the molecules form ordered thin films, where the highest degree of order is observed in the case of macrocycle monolayers and the lowest in the case of rotaxane multilayers. The second harmonic generation activity is interpreted in terms of electric field induced second harmonic (EFISH) generation where the electric field is created by the substrate silver atoms. The measured second order nonlinear optical susceptibility for a rotaxane thin film is compared with that obtained by considering only EFISH contribution to SHG intensity. The electric field on the surface of a silver layer is calculated by using the Delphi4 program for structures obtained with TINKER molecular mechanics/dynamics simulations. An excellent agreement is observed between the calculated and the measured SHG susceptibilities.     

Solid-phase synthesis of cyclic PNA and PNA-DNA chimeras

[structure: see text] A new and versatile on-line automated solid-phase approach to obtain cyclic PNA (I and III) and cyclic PNA-DNA chimeras (II) in highly pure form has been developed. Starting from a Tentagel matrix functionalized with a 3-chloro-4-hydroxyphenylacetic linker, the synthesis of representative, new cyclic molecules by standard peptide and phosphoramidite-based chemistry has been achieved.     

Differentiability properties for a class of non-convex functions

Closed sets K ⊂ satisfying an external sphere condition with uniform radius (called ϕ-convexity or proximal smoothness) are considered. It is shown that for -a.e. x ∊ ∂K the proximal normal cone to K at x has dimension one. Moreover if K is the closure of an open set satisfying a (sharp) nondegeneracy condition, then the De Giorgi reduced boundary is equivalent to ∂ K and the unit proximal normal equals -a.e. the (De Giorgi) external normal. Then lower semicontinuous functions f : with ϕ-convex epigraph are shown, among other results, to be locally BV and twice -a.e. differentiable; furthermore, the lower dimensional rectifiability of the singular set where f is not differentiable is studied. Finally we show that for -a.e. x there exists δ (x) > 0 such that f is semiconvex on B(x,δ(x)). We remark that such functions are neither convex nor locally Lipschitz, in general. Methods of nonsmooth analysis and of geometric measure theory are used. Work partially supported by M.I.U.R., project “Viscosity, metric, and control theoretic methods for nonlinear partial differential equations.”