Fixed-sign solutions for a system of singular focal boundary value problems

We consider a system of focal boundary value problems where the nonlinearities may be singular in the independent variable and may also be singular in the dependent arguments. Using Schauder fixed point theorem, we establish criteria such that the system of boundary value problems has at least one fixed-sign solution.     

Lagrangian Duality in Set-Valued Optimization

In this paper, we study optimization problems where the objective function and the binding constraints are set-valued maps and the solutions are defined by means of set-relations among all the images sets (Kuroiwa, D. in Takahashi, W., Tanaka, T. (eds.) Nonlinear analysis and convex analysis, pp. 221–228, 1999). We introduce a new dual problem, establish some duality theorems and obtain a Lagrangian multiplier rule of nonlinear type under convexity assumptions. A necessary condition and a sufficient condition for the existence of saddle points are given. The authors thank the two referees for valuable comments and suggestions on early versions of the paper. The research of the first author was partially supported by Ministerio de Educación y Ciencia (Spain) Project MTM2006-02629 and by Junta de Castilla y León (Spain) Project VA027B06.     

Mössbauer studies of the re-entrant spin-glass behaviour of Fe–Al alloys

Fe–Al alloys around the concentration of 30 at. % Al present re-entrant spin-glass behaviour at low temperatures. This behaviour is not completely understood and Mössbauer spectroscopy, combined with other experimental techniques, is useful to describe and explain this behaviour. Results show that the Mössbauer spectra coincide with the magnetic behaviour showed in literature and they can be explained as a magnetic cluster system whose magnetic clusters are getting smaller when the temperature is decreasing. When the temperature is reaching to the spin-glass transition at 92 K the spins in the paramagnetic matrix are moving slower and below this transition the spins are completely frozen.     

Effect of pH and gaseous ammonia flow rate on the composition and structure of ammonium uranate

Ammonium uranate was precipitated from uranyl nitrate solution using gaseous ammonia, then filtered, washed with demineralized water and dried. The influence of pH and ammonia flow rate on their composition and structure were examined by X-ray diffraction analysis, making use of additional information obtained from infrared analysis.     

Preconcentration of trace antimony in tap and sea water on activated alumina. Determination by graphite furnace atomic absorption spectrometry

Summary A method is described for antimony preconcentration based on retention on a column of activated alumina. Recovery is 80% when no pH-control and 4 mol/l HCl as eluent are used. The preconcentration factor is 400. The method was applied to the determination of antimony in spiked tap and sea water. The analytical performance of the method is discussed.     

Smectic liquid-crystalline phases of F(CF2)7(CHOH)(CH2)8H and F(CF2)9(CHOH)(CH2)10H Comparison with other partially fluorinated molecules

Partially fluorinated alcohols F(CF₂)_m(CHOH)(CH₂)_nH (where m = 7, n = 8 and m = 9, n = 10) exhibit highly ordered smectic liquid-crystalline phases, as confirmed by optical microscopy and differential scanning calorimetry. Miscibility studies show that the smectic phases of the two alcohols are not of the same type. The related partially fluorinated ketones F(CF₂)_mCO(CH₂)_nH do not form a detectable mesophase. This is rather surprising since the (more polar) corresponding alcohols and the (less polar) analogous iodides and n-alkanes do. A brief discussion of the results and a comparison among partially fluorinated alkanes with various functional groups are presented.     

Toric cubes

A toric cube is a subset of the standard cube defined by binomial inequalities. These basic semialgebraic sets are precisely the images of standard cubes under monomial maps. We study toric cubes from the perspective of topological combinatorics. Explicit decompositions as CW-complexes are constructed. Their open cells are interiors of toric cubes and their boundaries are subcomplexes. The motivating example of a toric cube is the edge-product space in phylogenetics, and our work generalizes results known for that space.