Normal Vietoris Implies Compactness: A Short Proof

One of the most celebrated results in the theory of hyperspaces says that if the Vietoris topology on the family of all nonempty closed subsets of a given space is normal, then the space is compact (Ivanova-Keesling-Velichko). The known proofs use cardinality arguments and are long. In this paper we present a short proof using known results concerning Hausdorff uniformities.     

Global weak solutions to the Nordström-Vlasov system

The Nordström-Vlasov system is a Lorentz invariant model for a self-gravitating collisionless gas. We establish suitable a priori bounds on the solutions of this system, which together with energy estimates and the smoothing effect of “momentum averaging” yield the existence of global weak solutions to the corresponding initial value problem. In the process we improve the continuation criterion for classical solutions which was derived recently. The weak solutions are shown to preserve mass.     

Inorganic Sol-Gel Preparation of Medium Sized Microparticles of Li2TiO3 from TiCl4 as Tritium Breeding Material for Fusion Reactors

Microspheres of Li₂TiO₃ were fabricated by a classical, inorganic sol-gel process from commercially available TiCl₄. Elaborated process consists of the following main steps: (1) dissolving of TiCl₄ in concentrated aqueous HCl and addition of LiOH; (2) formation of sol emulsion in 2-ethylhexanol-1 containing the surfactant SPAN-80 (EH); (3) gelation of emulsion drops by extraction of water with partially dehydrated EH; (4) impregnation of gel to Li:Ti molar ratio MR = 2; (5) thermal treatment at 1200°C in order to receive chloride free product. This temperature can be significantly lowered (to 750°C) by dechlorination starting solution TiCl₄ by chemical treatment of the with nitric acid to form of nitrate-stabilized titania sols. Tritium release from sol-gel made Li₂TiO₃ microspheres were found very close to that observed for other traditional materials, however for the first sample process starts slightly earlier.     

A novel strategy to verification of adulteration in alcoholic beverages based on Schlieren effect measurements and chemometric techniques

A novel strategy to evaluation of adulteration in alcoholic beverages based on the measurement of the Schlieren effect using an automated FIA system with photometric detection is proposed. The assay is based on the Schlieren effect produced when beverage samples are injected in a single-line FIA system that uses water as carrier stream and a light-emitting diode-phototransistor photometer controlled by microcomputer as detector. The flow system presents limited mixing conditions which make possible to create gradients of refractive index (Schlieren effect) in the injected sample zone. These gradients are reproducible, characteristic of each alcoholic beverage and undergo specific modifications when adulterations with water or ethanol are imposed. Schlieren effect data of brandies, cachaças, rums, whiskies and vodkas were treated by SIMCA to elaborate class models applied in the evaluation of alcoholic beverages adulteration. Samples of the original matrix of each sort of beverages were adulterated in laboratory by adding water, methanol and ethanol in levels of 5% and 10% (v/v). These samples were used as test set to validate SIMCA class models. The verification of authenticity using Schlieren effect measurements presented good results making possible to identify 100% of the beverages samples adulterated in laboratory and 93% of the actual adulterated alcoholic beverages with confidence levels of 95%. As principal advantage, the automated system does not use reagents to carry out the analysis.     

Immobilized polysiloxanes as stationary phases for high-performance liquid chromatography and solid phase extraction

Polysiloxanes immobilized onto the surfaces of porous silica particles have proven to be good stationary phases for the separation of multiresidues of pesticides and their metabolic/degradation products by reversed-phase high-performance liquid chromatography (RP-HPLC). Similar materials have proven effective for pre-concentration and clean-up procedures using solid phase extraction. The present paper describes the preparation and some applications of several of these packing materials.     

A purely algebraic characterization of the hyperreal numbers

The hyperreal numbers of nonstandard analysis are characterized in purely algebraic terms as homomorphic images of a suitable class of rings of functions.

     

Multicuts in unweighted graphs and digraphs with bounded degree and bounded tree-width

The Multicut problem can be defined as: given a graph G and a collection of pairs of distinct vertices {s_i,t_i} of G, find a minimum set of edges of G whose removal disconnects each s_i from the corresponding t_i. Multicut is known to be NP-hard and Max SNP-hard even when the input graph is restricted to being a tree. The main result of the paper is a polynomial-time approximation scheme (PTAS) for Multicut in unweighted graphs with bounded degree and bounded tree-width. That is, for any ε>0, we present a polynomial-time (1+ε)-approximation algorithm. In the particular case when the input is a bounded-degree tree, we have a linear-time implementation of the algorithm. We also provide some hardness results: we prove that Multicut is still NP-hard for binary trees and that it is Max SNP-hard if we drop any of the three conditions (unweighted, bounded-degree, bounded tree-width). Finally we show that some of these results extend to the vertex version of Multicut and to a directed version of Multicut.     

Assignments of methanol laser lines by frequency measurements and Fourier transform spectroscopy

We have measured the frequencies of four CH₃OH far-infrared laser lines that were previously known only by wavelength measurement. Two of these lines turned out to be doublets, bringing the total number of measured lines to six. We can now confirm the assignments of five of them and definitely disprove the assignments proposed for the sixth.In particular we confirm the assignments for the four strong laser lines at 205 and 208 µm pumped by the 9-P(34) CO₂ laser line. These lines share a common upper level in the first excited CO-stretch state, and terminate in the upper and lower levels of a hybrid state with J=5. Heterodyne frequency measurements and conventional microwave spectroscopy show that both lines are split into two components approximately 3.5 MHz apart. The origin of this further splitting is interpreted as a perturbed K-splitting.Work supported by Consiglio Nazionale delle Ricerche -Italia