Weak equilibrium in a spatial model

Spatial models of two-player competition in spaces with more than one dimension almost never have pure-strategy Nash equilibria, and the study of the equilibrium positions, if they exist, yields a disappointing result: the two players must choose the same position to achieve equilibrium. In this work, a discrete game is proposed in which the existence of Nash equilibria is studied using a geometric argument. This includes a definition of equilibrium which is weaker than the classical one to avoid the uniqueness of the equilibrium position. As a result, a “region of equilibrium” appears, which can be located by geometric methods. In this area, the players can move around in an “almost-equilibrium” situation and do not necessarily have to adopt the same position.     

Molybdenum oxide/bipyridine hybrid material {[MoO3(bipy)][MoO3(H2O)]}n as catalyst for the oxidation of secondary amines to nitrones

The inorganic-organic hybrid material {[MoO₃(bipy)][MoO₃(H₂O)]}_n (bipy = 2,2′-bipyridine) can be used as a water-tolerant catalyst for the oxidation of secondary amines under mild conditions using either urea hydrogen peroxide (UHP) or tert-butylhydroperoxide (TBHP) as the oxidant. Under optimized reaction conditions (2 mol % catalyst, 3-4 equiv TBHP, CH₂Cl₂ as the solvent, 40 °C), the corresponding nitrones were obtained with different efficiency depending on the nature of the cyclic or acyclic amine used.     

One-pot synthesis of 2-trifluoromethylchromones

We report a simple and suitable method for the preparation of useful 2-trifluoromethylchromones in one step, in high yields and avoiding the use of solvents. We were able to detect the intermediate of this reaction. Furthermore a mechanism for the formation of the 7-methoxy-3-trifluoroacetyl-2-trifluoromethylchromone through the unexpected double trifluoroacetylation of 4-methoxy-2-hydroxyacetophenone followed by dehydration is also proposed. All compounds are fully identified and characterized by spectroscopic techniques.     

Enantioselective synthesis of tertiary alcohols through a zirconium-catalyzed Friedel-Crafts alkylation of pyrroles with α-ketoesters

Chiral complexes of 1,1'-bi-2-naphthol-based ligands with zirconium tert-butoxide catalyze the Friedel-Crafts alkylation of pyrroles with α-ketoesters to afford tertiary alcohols in good yields and ee up to 98%. The reaction is also of application to 4,7-dihydroindole to give C2-alkylated indoles after oxidation with p-benzoquinone.     

Solid-state dinuclear-to-trinuclear conversion in an oxalato-bridged chromium(III)-cobalt(II) complex as a new route toward single-molecule magnets

A novel bis(oxalato)chromium(III) salt of a ferromagnetically coupled, oxalato-bridged dinuclear chromium(III)-cobalt(II) complex of formula [CrL(ox)(2)CoL'(H(2)O)(2)][CrL(ox)(2)]·4H(2)O (1) has been self-assembled in solution using different aromatic α,α'-diimines as blocking ligands, such as 2,2'-bipyridine (L = bpy) and 2,9-dimethyl-1,10-phenanthroline (L' = Me(2)phen). Thermal dehydration of 1 leads to an intriguing solid-state reaction between the S = 3/2 Cr(III) anions and the S = 3 Cr(III)Co(II) cations to give a ferromagnetically coupled, oxalato-bridged trinuclear chromium(III)-cobalt(II) complex of formula {[CrL(ox)(2)](2)CoL'} (2). Complex 2 possesses a moderately anisotropic S = 9/2 Cr(III)(2)Co(II) ground state, and it exhibits slow magnetic relaxation behavior at very low temperatures (T(B) < 2.0 K).     

Heterogenization of [Ti(η-C5HMe4)Cl3] on to MCM-41 and organomodified MCM-41 to form epoxidation catalyst

This paper describes the heterogenization of a tetramethylmonocyclopentadienyl titanium (IV) trichloride complex, [Ti(η⁵-C₅HMe₄)Cl₃] onto mesoporous MCM-41. Its immobilization has been performed via a straightforward grafting process of the organometallic precursor in the pores of an MCM-41 host material and by reaction with previously organomodified MCM-41 material with a hydroxyl triazine based compound. Applying all-silica MCM-41 hosts, stable and heterogeneous liquid-phase epoxidation catalysts are obtained. Powder X-ray diffraction and nitrogen adsorption-desorption analysis indicated that the structural integrity of the support has been preserved during the titanium complex immobilization. These materials have been also extensively characterized using diffuse reflectance UV-vis, ¹³C and ²⁸Si MAS NMR and FT-IR spectroscopy. With these techniques the strong adsorption of the intact catalytic complex within an all-silica MCM-41 host is demonstrated. These materials have been tested as catalyst for the epoxidation of aliphatic and aromatic alkenes with TBHP as oxidant exhibiting a significant selectivity toward the epoxide with negligible leaching of titanium species. The conversion values are moderated, being the olefin trend reactivity 1-octene > cyclohexene > styrene.     

Depth profile characterization of Zn-TiO2 nanocomposite films by pulsed radiofrequency glow discharge-optical emission spectrometry

In recent years particular effort is being devoted towards the development of radiofrequency (rf) pulsed glow discharges (GDs) coupled to optical emission spectrometry (OES) for depth profile analysis of materials with technological interest. In this work, pulsed rf-GD-OES is investigated for the fast and sensitive depth characterization of Zn-TiO₂ nanocomposite films deposited on conductive substrates (Ti and steel). The first part of this work focuses on assessing the advantages of pulsed GDs, in comparison with the continuous GD, in terms of analytical emission intensities and emission yields. Next, the capability of pulsed rf-GD-OES for determination of thickness and compositional depth profiles is demonstrated by resorting to a simple multi-matrix calibration procedure. A rf forward power of 75 W, a pressure of 600 Pa, 10 kHz pulse frequency and 50% duty cycle were selected as GD operation parameters.Quantitative depth profiles obtained with the GD proposed methodology for Zn-TiO₂ nanocomposite films, prepared by the occlusion electrodeposition method using pulsed reverse current electrolysis, have proved to be in good agreement with results achieved by complementary techniques, including scanning electron microscopy and inductively coupled plasma-mass spectrometry. The work carried out demonstrates that pulsed rf-GD-OES is a promising tool for the fast analytical characterization of nanocomposite films.     

Cold vapor-solid phase microextraction using amalgamation in different Pd-based substrates combined with direct thermal desorption in a modified absorption cell for the determination of Hg by atomic absorption spectrometry

In this work, different Pd-based substrates (i.e. Pd wire, Pd-coated stainless steel wire and Pd-coated SiO₂) are tried for microextraction of Hg prior to its release into a modified quartz T-cell so as to develop a cost-effective, sensitive and easy-to-handle coupling between solid-phase microextraction (SPME) and atomic absorption spectrometry. The new design allows a direct sample injection from the SPME device into a quartz T-cell thus avoiding analyte dilution. Mercury amalgamation onto a Pd wire provided the best performance in respect to sensitivity and fiber lifetime, but Pd wires could not be implemented in the SPME device due to their poor mechanical characteristics. On the contrary, Pd-coated SiO₂ fibers could be easily adapted to the typical sampling device used for SPME. Narrow time-dependent absorption signal profiles that could be integrated within 25 s were obtained. The detection limit was 90 pg mL⁻¹ of Hg, and the repeatability expressed as relative standard deviation was 4.3%.