Application of Hilbert＇s Projective Metric on Symmetric Cones

Let Ω be a symmetric cone. In this note, we introduce Hilbert＇s projective metric on Ω in terms of Jordan algebras and we apply it to prove that, given a linear invertible transformation g such that g（Ω） = Ω and a real number p, ｜p｜ 〉 1, there exists a unique element x ∈ Ω satisfying g（x） = x^p.     

Numerical Modeling of Solitons in a Low Birefringent Optical Fiber

A numerical investigation, based on the split-step Fourier transform algorithm of all optical switching of solitons in a low birefringent optical fiber is presented. The numerical algorithm is described in detail. This revised version was published online in August 2006 with corrections to the Cover Date.     

Microwave-assisted conversion of N-substituted oxazolidin-2,4-diones into α-hydroxyamides

N-Substituted oxazolidin-2,4-diones have been synthesized in a novel one-pot reaction by reacting cyanohydrins stepwise with 1,1′-carbonyldiimidazole and primary amines followed by acidic hydrolysis of the intermediate 4-imino-oxazolidin-2-ones. Their microwave-assisted conversion into α-hydroxyamides was accomplished by treatment with catalytic amounts of sodium methoxide in methanol.     

Kinetics and mechanism of the photolytic CO-substitutions of cyclopentadienyl(dicarbonyl)iron thiocarboxylate complexes,Cp′Fe(CO)2SCOR (Cp′ = C5H5, ButC5H4,1,3-Bu2tC5H3; R = alkyl,aryl)

The kinetics of the photolytic CO-substitution of CpFe(CO)₂SCOR [Cp = C₅H₅, Bu ^t C₅H₄, 1,3-Bu₂ ^t C₅H₃; R = Me, Bu ^t , Ph, 2-(O₂N)C₆H₄, 3-(O₂N)C₆H₄, 4-(O₂N)C₆H₄, 3,5-(O₂N)₂C₆H₃] with PPh₃ were studied in CH₂Cl₂ at 0 °C by i.r. spectroscopy. The reactions yielded exclusively the mono-CO-substituted derivatives, CpFe-(CO)(PPh₃) SCOR, and were found to follow second order kinetics with first order dependence on the concentration of each reactant. The differences in rates are discussed in terms of current knowledge pertaining to such reactions. An associative mechanism is proposed to account for the kinetic data of the reactions described.     

High temperature reactions of titanium(IV) oxide with some alkali persulfates and their decomposition products

The solid state reactions between TiO₂ and Na₂S₂O₈ or K₂S₂O₈ have been investigated using TG, DTG, DTA, IR, and X-ray diffraction studies in the range of 20 to 1000°C.It has been shown that TiO₂ reacts stoichiometrically (1 : 1) with Na₂S₂O₈ in the range of 160 and 220°C forming the complex sodium monoperoxodisulfato—titanium(IV) as characterized by IR and X-ray analysis. The new complex then decomposes into the reactants above 190°C.An exothermic reaction has been observed between TiO₂ and molten K₂S₂O₇ at mole ratio 1:2 respectively and higher, in the range of 280 and 350°C. The IR and X-ray analyses have shown the formation of a complex namely, potassium tetrasulfato titanium(IV) for which the formula and structure have been proposed. This complex decomposes at higher temperatures into K₂SO₄ and a mixed sulfate of potassium and titanium. The mixed sulfate melts at 620°C and decomposes into K₂SO₄, TiO₂, and the gaseous SO₃.On the other hand, Na₂S₂O₈ decomposes in a special mode producing a polymeric product of Na₁₀S₉O₃₂. Decomposition of this species occurs after melting at 560°C into Na₂SO₄ and sulfur oxides. The decomposition reaction has been proved to be catalysed by TiO₂ itself.     

Synthesis and pharmacological activity of 4-(4'-(chlorophenyl)-4-hydroxypiperidine) derivatives

A new series of 4-(4'-chlorophenyl)-4-hydroxypiperidine derivatives (2-5), substituted at nitrogen, were synthesized and tested as potential analgesic compounds as well as evaluated for their effect on hypotensive activity. Results showed that all the derivatives exhibit significant analgesic activity in male Wistar rats at a dose of 50 mg/kg of body weight after intramuscular injection, when tested by thermal stimuli (tail flick test). Pethidine was used as reference drug. Compounds 2, 3 and 5 produced reduction in blood pressure in normotensive rat.     

Electrochemically Induced Iron Release of Adsorbed Horse Spleen Ferritin: Quantitation of Iron Using Long Optical Path Length Thin‐Layer Spectroelectrochemistry

In this work, long optical path length thin‐layer electrochemical cell was constructed using indium‐tin oxide on glass as the electrode material. Iron release from ferritin adsorbed on the electrode was induced by applying a negative potential sweep in the presence of 1,10‐phenanthroline. The usefulness of spectroelectrochemistry as a means of determining the quantity of iron released from an adsorbed layer of ferritin is demonstrated.     

Sol-gel approach to in situ creation of high pH-resistant surface-bonded organic-inorganic hybrid zirconia coating for capillary microextraction (in-tube SPME)

A novel zirconia-based hybrid organic-inorganic sol-gel coating was developed for capillary microextraction (CME) (in-tube SPME). High degree of chemical inertness inherent in zirconia makes it very difficult to covalently bind a suitable organic ligand to its surface. In the present work, this problem was addressed from a sol-gel chemistry point of view. Principles of sol-gel chemistry were employed to chemically bind a hydroxy-terminated silicone polymer (polydimethyldiphenylsiloxane, PDMDPS) to a sol-gel zirconia network in the course of its evolution from a highly reactive alkoxide precursor undergoing controlled hydrolytic polycondensation reactions. A fused silica capillary was filled with a properly designed sol solution to allow for the sol-gel reactions to take place within the capillary for a predetermined period of time (typically 15-30 min). In the course of this process, a layer of the evolving hybrid organic-inorganic sol-gel polymer got chemically anchored to the silanol groups on the capillary inner walls via condensation reaction. At the end of this in-capillary residence time, the unbonded part of the sol solution was expelled from the capillary under helium pressure, leaving behind a chemically bonded sol-gel zirconia-PDMDPS coating on the inner walls. Polycyclic aromatic hydrocarbons, ketones, and aldehydes were efficiently extracted and preconcentrated from dilute aqueous samples using sol-gel zirconia-PDMDPS coated capillaries followed by thermal desorption and GC analysis of the extracted solutes. The newly developed sol-gel hybrid zirconia coatings demonstrated excellent pH stability, and retained the extraction characteristics intact even after continuous rinsing with a 0.1 M NaOH solution for 24 h. To our knowledge, this is the first report on the use of a sol-gel zirconia-based hybrid organic-inorganic coating as an extraction medium in solid phase microextraction (SPME).