Validated Infeasible Interior-Point Predictor–Corrector Methods for Linear Programming

Many problems arising in practical applications lead to linear programming problems. Hence, they are fundamentally tractable. Recent interior-point methods can exploit problem structure to solve such problems very efficiently. Infeasible interior-point predictor–corrector methods using floating-point arithmetic sometimes compute an approximate solution with duality gap less than a given tolerance even when the problem may not have a solution. We present an efficient verification method for solving linear programming problems which computes a guaranteed enclosure of the optimal solution and which verifies the existence of the solution within the computed interval.     

Solvation numbers and hydration constant for thorium(IV) in ethanol-water medium

The solvation number and hydration constant of Th⁴⁺ in ethanol-water medium were determined at 25°C using UV-spectral and electrochemical measurements. A solvate formation equilibrium is demonstrated and characterized. Three molecules of ethanol (S) can bond to the metal cation with strengths comparable to that for H₂O to form ThS₃(H₂O) ₃ ⁴⁺ Formation of thorium monochelate with lawsone (2-hydroxy-1,4-naphthoquinone) eliminates bonding with alcohol molecules. The dissociation constant of the chelating agent_sK_a and the formation contant of the monochelated metal ion_sK _f ^* that are essentially independent of the solution composition are evaluated. Hydration titrations involving thorium-lawsone monochelate are performed and the data obtained from the changes of pH with solvent composition are analyzed. The solution independent constant,_sK _f ^* for thorium-lawsone complex formation in mixed aqueous ethanol is given by $$log_s K_f * = vpK_a + log_s K_h - log[LH] - vpH + 3logv$$ where vpK_a is the dissociation constant of the chelating agent LH in the solvent system of ν volume fraction of water and_sK_h is the solution-independent hydration constant of thorium (IV) in the solvent system. Log-values for the constants_sK_h,_sK _f ^* and_sK _a ^* are found to be 7.8±0.02, 11.38±0.04 and ?0.753, respectively.     

Die Reaktion von Ce(III), Th(IV) und U(VI) mit Chinizaringrün und seinem nichtsulfonierten Grundkörper

The reaction of 1,4-(2-sulpho-4-methylanilino)anthraquinone (quinizarin green,QG) and its non-sulphonated derivative (NSQG) with Ce(III), Th(IV), and U(VI) was investigated. Spectrophotometric and conductometric studies were carried out to investigate the stoichiometry of the complexes formed. The studies revealed the formation of 11 and 12 (ML) complexes. The apparent stability constants of the different complexes were determined. The structure of the ligand in the solid chelates was studied by IR spectrophotometry which showed that the chelate formation takes place through the oxygen of the C=O group and the -imino nitrogen.

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Mit 6 Abbildungen     

Periodic hexagonal mesostructured chalcogenides based on platinum and [SnSe4]4- and [SnTe4]4- precursors. Solvent dependence of nanopore and wall organization

Mesostructured chalcogenide-based materials with long-range order and semiconducting properties can be prepared using suitable molecular building blocks, linkage metal ions and surfactant molecules. In this paper we present surfactant templated, open framework platinum tin selenide and telluride materials assembled using K4SnQ4 (Q = Se, Te) salts and K2PtCl4 as precursors and a study of pore and wall organization. We find that materials prepared in water exhibit disordered pore organization, whereas those prepared in formamide are long-range ordered with hexagonal symmetry. In formamide the [SnQ4]4- anions undergo condensation-oligomerization reactions that produce different chalcogenido molecular species, whereas in water the anions remain intact. In addition to solvent, the pore organization and overall quality of the mesostructured materials strongly depend on the surfactant molecules, i.e., chain length and headgroup size. For example, highly ordered mesostructured platinum tin selenides with hexagonal symmetry were obtained using the hydroxyl-functionalized surfactants CnH2n+1N(CH3)(CH2CH2OH)2Br (n = 16, 18, and 20), but when the headgroup was triethylammonium, hexagonal pore order was achieved only for n = 20 and not for n = 16 and 18. The experimental results imply that in order to achieve highly ordered chalcogenide frameworks a single building anionic block might be insufficient. Finally, we also report the first examples of hexagonal mesostructured Pt/Sn/Te materials based on K4SnTe4 as the precursor. The tellurides behave differently for their selenium analogues and have very low energy band gaps, in the range 0.5-0.7 eV.     

New spectrophotometric method for the determination of trace amounts of palladium

Summary A simple, rapid, selective, and sensitive method for the spectrophotometric determination of palladium is developed based on the reaction of Pd(II) with 1-amino-4-hydroxyanthraquinone (AMHA). The reaction is carried out atpH 3.8 in 50% (v/v) ethanol-water medium. The molar absorptivity of the complexed ligand is 1.1 · 10⁴ l mol^–1 cm^–1 at 620 nm. Calibration plots are linear up to 17 µg Pd cm^–3. The optimum concentration range (Ringbom plot) is between 3–14.5 µg cm^–3. The spectral study of the reaction in solutions containing equimolar concentrations or an excess of one component, in thepH range 0.3–6.5, indicate the possible complex transitions that occur in solution. Complete graphical and logarithmic analysis of the absorbance-pH graphs was performed to demonstrate and characterize the complexation equilibria in solution. Under the optimum conditions, palladium can be determined as the noncharged complex Pd(AMHA)₂ in the presence of a large number of foreign ions. Interferences caused by zirconium(IV) could be masked with fluoride ions.

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Eine neue spektrophotometrische Methode für die Bestimmung von Palladium in Spuren

Zusammenfassung Eine einfache, schnelle und empfindliche Methode für die spektrophotometrische Bestimmung von Palladium wurde auf der Basis der Reaktion von Pd(II) mit 1-Amino-4-hydroxyanthrachinon (AMHA) entwickelt. Die Reaktion wird in 50% (v/v) Ethanol/Wasser beipH 3.8 ausgeführt. Die molare Absorption des komplexierten Liganden beträgt 1.1 · 10⁴ l mol^–1 cm^–1 bei 620 nm. Kalibrierungskurven verlaufen bis zu 17 µg Pd cm^–3 linear. Der optimale Konzentrationsbereich (Ringbom-Plot) liegt zwischen 3 und 14.5 µg cm^–3. Spektroskopische Untersuchungen der Reaktion in Lösungen, entweder mit equimolaren Konzentrationen oder mit einem Überschuß an einer Komponente impH-Bereich 0.3–6.5, lassen Rückschlüsse auf mögliche Komplex-Übergänge in Lösung zu. Es wurde eine vollständige graphische, logarithmische Analyse der Absorptions-pH-Graphen durchgeführt, um die Komplexgleichgewichte in Lösung aufzuklären und zu charakterisieren. Unter den Optimalbedingungen kann Palladium als nichtgeladener Komplex Pd(AMHA)₂ in Gegenwart einer großen Anzahl an Fremd-Ionen bestimmt werden. Schwierigkeiten mit Zirkonium(IV) konnte durch Maskierung mit Fluorid-Ionen umgangen werden.

     

Retracted: Light-Induced Bistability in Iron(III) Spin-Transition Compounds of 5 X-Salicylaldehyde Thiosemicarbazone (X=H,Cl, Br)

The iron(III) spin-crossover compounds [Fe(Hthsa)(thsa)] ⋅ H₂O ( 1 ), [Fe(Hth5Clsa)(th5Clsa)₂] ⋅ H₂O ( 2 ), and [Fe(Hth5Brsa)(th5Brsa)₂] ⋅ H₂O ( 3 ) (H₂thsa=salicylaldehyde thiosemicarbazone, H₂th5Clsa=5-chlorosalicylaldehyde thiosemicarbazone, and H₂th5Brsa=5-bromosalicylaldehyde thiosemicarbazone) have been synthesized and their spin-transition properties investigated by magnetic susceptibility, Mössbauer spectroscopy, and differential scanning calorimetry measurements. The three compounds exhibit an abrupt spin transition with a thermal hysteresis effect. The more polarizable the substituent on the salicylaldehyde moiety, the more complete is the transition at room temperature with an increased degree of cooperativity. The molecular structures of 1 and 2 in the high-spin state are revealed. The occurrence of the light-induced excited-spin-state trapping phenomenon appears to be dependent on the substituent incorporated into the 5-position of the salicylaldehyde subunit. Whereas the compounds with an electron-withdrawing group (-Br or -Cl) exhibit light-induced trapped excited high-spin states with great longevity of metastability, the halogen-free compound does not, even though strong intermolecular interactions (such as hydrogen-bonding networks and π stacking) operate in the system. For compound 2 , the surface level of photoconversion is less than 35 %. In contrast, compound 3 displays full photoexcitation.     

Gas phase interaction of L‐proline with Be2+, Mg2+ and Ca2+ ions: a computational study

Geometry optimisation and metal ion affinities (MIAs) of the binding configurations of Be²⁺, Mg²⁺ and Ca²⁺ to L ‐proline were calculated using the hybrid Density Functional Theory (DFT‐B3LYP) and second order Møllet?Plesset perturbation theory (MP2) methods. Be²⁺ was found to bind preferentially in a charge transfer type arrangement through the carbonyl oxygen (? C?O) and the lone pair of the imino‐group nitrogen atom (? NH? ). On the contrary Mg²⁺ and Ca²⁺ were found to prefer binding in a bi‐dentate manner through the carboxylate group of L ‐proline (OCO) in a zwitterion form. The main types of interactions found to influence the binding preference of M²⁺ ions to L ‐proline were (i) charge transfer in the case of Be²⁺ ions and (ii) electrostatic interactions in the case of Mg²⁺ and Ca²⁺ ions. Inspection of the IR stretching of the N? H and the O? H groups of L ‐proline with M²⁺ ions in a chelating configuration (to both O and N atoms) indicated a considerable shift to higher frequency with decreasing MIA. On the other hand, the MIA for the zwitterion L ‐proline with M²⁺ tracks the reciprocal distance of the M²⁺? OCO bond further confirming that the nature of the bond is mainly electrostatic. Comparison with other molecules containing the carboxylic function is also included in order to gain more insight on the types of interaction of this amino acid with metal ions in general. Copyright © 2007 John Wiley & Sons, Ltd.     

Towards a world‐sheet description of doubled geometry in string theory

Starting from a sigma‐model for a doubled target‐space geometry, we show that the number of target‐space dimensions can be reduced by half through a gauging procedure. We apply this formalism to a class of backgrounds relevant for double field theory, and illustrate how choosing different gaugings leads to string‐theory configurations T‐dual to each other. We furthermore discuss that given a conformal doubled theory, the reduced theories are conformal as well. As an example we consider the three‐dimensional WZW model and show that the only possible reduced backgrounds are the cigar and trumpet CFTs in two dimensions, which are indeed T‐dual to each other.     

Axial anomalies of Lifshitz fermions

We compute the axial anomaly of a Lifshitz fermion theory with anisotropic scaling z = 3 which is minimally coupled to geometry in 3+1 space‐time dimensions. We find that the result is identical to the relativistic case using path integral methods. An independent verification is provided by showing with spectral methods that the η‐invariant of the Dirac and Lifshitz fermion operators in three dimensions are equal. Thus, by the integrated form of the anomaly, the index of the Dirac operator still accounts for the possible breakdown of chiral symmetry in non‐relativistic theories of gravity. We apply this framework to the recently constructed gravitational instanton backgrounds of Hořava–Lifshitz theory and find that the index is non‐zero provided that the space‐time foliation admits leaves with harmonic spinors. Using Hitchin's construction of harmonic spinors on Berger spheres, we obtain explicit results for the index of the fermion operator on all such gravitational instanton backgrounds with SU(2) × U(1) isometry. In contrast to the instantons of Einstein gravity, chiral symmetry breaking becomes possible in the unimodular phase of Hořava–Lifshitz theory arising at λ = 1/3 provided that the volume of space is bounded from below by the ratio of the Ricci to Cotton tensor couplings raised to the third power. Some other aspects of the anomalies in non‐relativistic quantum field theories are also discussed.     

DFT study of carbon monoxide adsorption on α-Al2O3(0001)

The adsorption of CO on α-Al₂O₃(0001) was studied using the DFT-GGA computational method and on α-Al₂O₃ powder experimentally by Infra red spectroscopy. The core and valence level regions of α-Al₂O₃(0001) single crystal surface were also studied experimentally. Ar ions sputtering of the surface results in a slight but reproducible decrease in the XPS O2p lines in the valence band regions due to preferential removal of surface (and near surface) O atoms. Core level XPS O1s and Al2p further confirmed oxygen depletion with an associated surface stoichiometry close to Al₂O_2.9. The adsorption energy of CO was computed and found equal to 0.52 eV for θ = 0.25, it decreased to 0.42 eV at θ = 1. The IR frequency of νCO was also computed and in all cases it was blue shifted with respect to gas phase CO. The shift, Δν, decreased with increasing coverage where it was found equal to 56 cm^? 1 for θ = 0.25 and decreased to 30 cm^? 1 for θ = 1. Structural analyses indicated that the change in the adsorption energy and the associated frequency shift is due to surface relaxation upon adsorption. Experimentally the adsorption of CO gave rise to one main IR peak at 2154 cm^? 1 at 0.3 Torr and above. Two far smaller peaks are also seen at lower pressures of 0.03–0.2 Torr at 2189 and 2178 cm^? 1. The isosteric heat of adsorption was computed for the IR band at 2154 cm^? 1 and was found equal to 0.2 eV which did not change with coverage in the investigated range up to θ = 0.6.