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.     

Preparation and Flame Retardancy Properties of Novel PA12 and PE/Layered Titanoniobates Nanocomposites

Summary: We report herein a study performed on a layered titanoniobate KTiNbO₅ modified by octadecylamine to evaluate the fire retardancy properties of this novel hybrid nanofiller dispersed in PA12 and LLDPE, by polymer melt intercalation. The nanocomposites have been characterized using Electron Microscopy techniques to evaluate the degree of exfoliation and the morphologies. Thermogravimetric analyses and cone calorimeter tests have been carried out to assess the fire retardant performances.     

Hypergraph decomposition and secret sharing

A secret sharing scheme is a protocol by which a dealer distributes a secret among a set of participants in such a way that only qualified sets of them can reconstruct the value of the secret whereas any non-qualified subset of participants obtain no information at all about the value of the secret. Secret sharing schemes have always played a very important role for cryptographic applications and in the construction of higher level cryptographic primitives and protocols.In this paper we investigate the construction of efficient secret sharing schemes by using a technique called hypergraph decomposition, extending in a non-trivial way the previously studied graph decomposition techniques. A major advantage of hypergraph decomposition is that it applies to any access structure, rather than only structures representable as graphs. As a consequence, the application of this technique allows us to obtain secret sharing schemes for several classes of access structures (such as hyperpaths, hypercycles, hyperstars and acyclic hypergraphs) with improved efficiency over previous results. Specifically, for these access structures, we present secret sharing schemes that achieve optimal information rate. Moreover, with respect to the average information rate, our schemes improve on previously known ones.In the course of the formulation of the hypergraph decomposition technique, we also obtain an elementary characterization of the ideal access structures among the hyperstars, which is of independent interest.     

On-line CE-MS using pressurized liquid junction nanoflow electrospray interface and surface-coated capillaries

A simple and cost-effective laboratory-made liquid junction interface was used for coupling of CE with MS. In this device the capillary column and the spray tip were positioned in the electrode vessel containing appropriate spray liquid. The electrospray potential was applied on the electrode inside the liquid junction. A stable electrospray was produced at nanoliter per minute flow rates generated in the emitter tip without using an external pump. This arrangement provided high durability of the spray tip and independent optimization of the CE separation (use of coated capillaries) and ESI conditions. CE-MS analysis of mixtures of drugs, peptides, tryptic digests of proteins and biological fluids was optimized with respect to the effects of the distance between the separation capillary and electrospray tip and pressure applied on the liquid junction. The sensitivity of the system, in terms of the LOD (base peak monitoring) was below 10 ng/mL for the beta-blocker drugs and below 200 ng/mL for peptide analysis.     

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.     

Condensed 2-pyrrolidinone-1,2-oxazines from lithium enolate of 1-benzyl-5-oxo-3-pyrrolidinecarboxylic acid and β-aryl, β-nitroenamines

The reaction of the lithium enolate of 1-benzyl-5-oxo-3-pyrrolidinecarboxylic acid 3 with a series of β-aryl, β-nitroenamines unexpectedly afforded 6-aryl-2-benzyl-4-oxa-1-oxo-3a-methoxycarbonyl-2,5-diazaindenes 9a-d, whose structure was determined by analytical and NMR spectroscopical analysis. The structure of 9b was further confirmed by X-ray analysis. A reasonable mechanism for their formation is given.     

A Heterotetranuclear [NiIIReIV3] single-molecule magnet

The reaction of [ReIVCl4(ox)]2- and fully solvated Ni2+ ions in a MeCN/i-PrOH mixture affords the heterotetranuclear complex (NBu4)4[Ni{ReCl4(ox)}3] where the rhenium precursor acts as a bidentate ligand toward the nicke(II) ion through the oxalate group. The mixed 3d-5d species exhibits intramolecular ferromagnetic coupling and it behaves like a single-molecule magnet.