A sharp bound for the Stein-Wainger oscillatory integral

Let denote the space of all real polynomials of degree at most . It is an old result of Stein and Wainger that

for some constant depending only on . On the other hand, Carbery, Wainger and Wright claim that the true order of magnitude of the above principal value integral is . We prove that

     

An inverse-free Newton-Jarratt-type iterative method for solving equations under the gamma condition

A local as well as a semilocal convergence analysis for Newton–Jarratt–type iterative method for solving equations in a Banach space setting is studied here using information only at a point via a gamma-type condition (Argyros in Approximate Solution of Operator Equations with Applications, [2005]; Wang in Chin. Sci. Bull. 42(7):552–555, [1997]). This method has already been examined by us in (Argyros et al. in J. Comput. Appl. Math. 51:103–106, [1994]; Argyros in Comment. Mat. XXIII:97–108, [1994]), where the order of convergence four was established using however information on the domain of the operator. In this study we also establish the same order of convergence under weaker conditions. Moreover we show that all though we use weaker conditions the results obtained here can be used to solve equations in cases where the results in (Argyros et al. in J. Comput. Appl. Math. 51:103–106, [1994]; Argyros in Comment. Mat. XXIII:97–108, [1994]) cannot apply. Our method is inverse free, and therefore cheaper at the second step in contrast with the corresponding two–step Newton methods. Numerical Examples are also provided.     

Synthetic Routes to Imidates and Their Applications in Organic Transformation: Recent Progress

Recent synthetic approaches and diverse applications of imidates are presented in this review. These motifs are successfully used as intermediates in organic transformations, such as the synthesis of N-heterocycles, natural products and metal complexes with a potential catalytic effect. Consequently, many attempts have been made for the development of efficient and facile synthetic methods of imidates in the past few years, as a continuum of previous paths. A wide range of organic compounds can be used as starting materials for these syntheses, including nitriles, isocyanides, amides etc. which through simple and flexible processes are converted to the desired imidates. Herein, an exploration of the recent synthetic routes of imidates and their diverse applications in organic transformations has been categorized and summarized.     

Competitive sorption of Cu(II), Eu(III) and U(VI) ions on TiO2 in aqueous solutions—A potentiometric study

The competitive sorption of Cu(II), Eu(III) and U(VI) ions in aqueous solutions by TiO₂, has been investigated by potentiometry at I = 0.1 M NaClO₄, 25 °C and under atmospheric conditions. For Cu(II) ions the investigation was performed directly by means of a Cu²⁺ ion selective electrode, whereas for the Eu(III) and U(VI) ions indirectly based on competition reactions between the Cu(II) ion and the Eu(III) and U(VI) ions. Numerical analysis of the experimental data supports the formation of inner-sphere surface complexes and allows the evaluation of the formation constant of the (TiO)₂Cu, which is found to amount to log β* = 4.3 ± 0.4. Addition of competing Eu(III) and U(VI) ions in the aqueous system leads to replacement of the Cu(II) by the competitor metal ion. Evaluation of the potentiometric data obtained from competition experiments indicates on an ion exchange mechanism. The formation constant of the Eu(III) and U(VI) species adsorbed on TiO₂ is found to be log β* = 4.4 ± 0.7 and 4.8 ± 0.8, respectively. The relative affinity of the TiO₂ surface for the metal ions under investigation is U(VI) > Eu(III) > Cu(II).     

Study of the resistance of SAMs on aluminium to acidic and basic solutions using dynamic contact angle measurement

We report the development of a method to determine the aqueous stability of self-assembled monolayers (SAMs) using the Wilhelmy plate dynamic contact angle (DCA) experiment. The DCA is measured in solutions over a range of pH values for alkyl carboxylic and alkyl phosphonic acid SAMs formed on magnetron-sputtered aluminum. The change in DCA on repeated immersion is used as a measure of the degradation of the SAMs by hydrolytic attack. The short and intermediate chain length alkyl acids are not stable in water of neutral pH, whereas molecules with the longest alkyl chains show considerably greater stability in neutral and both high and low pH solutions. The packing density inferred from the DCA and the contact angle hysteresis suggests the C18CO2H monolayer to be slightly less well packed than that of the C18P(=O)(OH)2; this is consistent with related friction force microscopy and infrared reflection absorption spectroscopy findings published elsewhere (Foster, T. T.; Alexander, M. R.; Leggett, G. J.; McAlpine, E. Langmuir 2006, 22, 9254-9259). The resistance of the SAMs to acid and alkaline environments is discussed in the context of aluminum oxide solubility, SAM packing density, and the resistance of the interfacial phosphate and carboxylate functionalities to different aqueous conditions.     

Zu den Kristallstrukturen der Übergangsmetall(II)‐Dodekahydro‐closo‐Dodekaborat‐Hydrate Cu(H2O)5,5[B12H12]·2,5 H2O und Zn(H2O)6[B12H12]·6 H2O

On the Crystal Structures of the Transition‐Metal(II) Dodecahydro‐closo‐Dodecaborate Hydrates Cu(H₂O)_5.5[B₁₂H₁₂]·2.5 H₂O and Zn(H₂O)₆[B₁₂H₁₂]·6 H₂O By neutralization of an aqueous solution of the free acid (H₃O)₂[B₁₂H₁₂] with basic copper(II) carbonate or zinc carbonate, blue lath‐shaped single crystals of the octahydrate Cu[B₁₂H₁₂]·8 H₂O (≡ Cu(H₂O)_5.5[B₁₂H₁₂]·2.5 H₂O) and colourless face‐rich single crystals of the dodecahydrate Zn[B₁₂H₁₂]·12 H₂O (≡ Zn(H₂O)₆[B₁₂H₁₂]·6 H₂O) could be isolated after isothermic evaporation. Copper(II) dodecahydro‐closo‐dodecaborate octahydrate crystallizes at room temperature in the monoclinic system with the non‐centrosymmetric space group Pm (Cu(H₂O)_5.5[B₁₂H₁₂]·2.5 H₂O: a = 768.23(5), b = 1434.48(9), c = 777.31(5) pm, β = 90.894(6)°; Z = 2), whereas zinc dodecahydro‐closo‐dodecaborate dodecahydrate crystallizes cubic in the likewise non‐centrosymmetric space group F23 (Zn(H₂O)₆[B₁₂H₁₂]·6 H₂O: a = 1637.43(9) pm; Z = 8). The crystal structure of Cu(H₂O)_5.5[B₁₂H₁₂]·2.5 H₂O can be described as a monoclinic distortion variant of the CsCl‐type arrangement. As characteristic feature the formation of isolated [Cu₂(H₂O)₁₁]⁴⁺ units as a condensate of two corner‐linked Jahn‐Teller distorted [Cu(H₂O)₆]²⁺ octahedra via an oxygen atom of crystal water can be considered. Since “zeolitic” water of hydratation is also present, obviously both classical H–O^δ?···^+δH–O and non‐classical B–H^δ?···^+δH–O hydrogen bonds play a significant role for the stabilization of the structure. A direct coordinative influence of the quasi‐icosahedral [B₁₂H₁₂]^2? anions on the Cu²⁺ cations has not been determined. The zinc compound Zn(H₂O)₆[B₁₂H₁₂]·6 H₂O crystallizes in a NaTl‐type related structure. Two crystallographically different [Zn(H₂O)₆]²⁺ octahedra are present, which only differ in their relative orientation within the packing of the [B₁₂H₁₂]^2? anions. The stabilization of the crystal structure takes place mainly via H–O^δ?···^+δH–O hydrogen bonds, since again the hydrogen atoms of the [B₁₂H₁₂]^2? anions have no direct coordinative influence on the Zn²⁺ cations.     

Das Lanthan‐Dodekahydro‐closo‐Dodekaborat‐Hydrat [La(H2O)9]2[B12H12]3·15 H2O und sein Oxonium‐Chlorid‐Derivat [La(H2O)9](H3O)Cl2[B12H12]·H2O

The Lanthanum Dodecahydro‐closo‐Dodecaborate Hydrate [La(H₂O)₉]₂[B₁₂H₁₂]₃·15 H₂O and its Oxonium‐Chloride Derivative [La(H₂O)₉](H₃O)Cl₂[B₁₂H₁₂]·H₂O By neutralization of an aqueous solution of the free acid (H₃O)₂[B₁₂H₁₂] with basic La₂O₃ and after isothermic evaporation colourless, face‐rich single crystals of a water‐rich lanthanum(III) dodecahydro‐closo‐dodecaborate hydrate [La(H₂O)₉]₂[B₁₂H₁₂]₃·15 H₂O are isolated. The compound crystallizes in the trigonal system with the centrosymmetric space group (a = 1189.95(2), c = 7313.27(9) pm, c/a = 6.146; Z = 6; measuring temperature: 100 K). The crystal structure of [La(H₂O)₉]₂[B₁₂H₁₂]₃·15 H₂O can be characterized by two of each other independent, one into another posed motives of lattice components. The [B₁₂H₁₂]²⁻ anions (d(B–B) = 177–179 pm; d(B–H) = 105–116 pm) are arranged according to the samarium structure, while the La³⁺ cations are arranged according to the copper structure. The lanthanum cations are coordinated in first sphere by nine oxygen atoms from water molecules in form of a threecapped trigonal prism (d(La–O) = 251–262 pm). A coordinative influence of the [B₁₂H₁₂]²⁻ anions on La³⁺ has not been determined. Since “zeolitic” water of hydratation is also present, obviously the classical H–O^δ–···^+δH–O‐hydrogen bonds play a significant role in the stabilization of the crystal structure. During the conversion of an aqueous solution of (H₃O)₂[B₁₂H₁₂] with lanthanum trichloride an anion‐mixed salt with the composition [La(H₂O)₉](H₃O)Cl₂[B₁₂H₁₂]·H₂O is obtained. The compound crystallizes in the hexagonal system with the non‐centrosymmetric space group (a = 808.84(3), c = 2064.51(8) pm, c/a = 2.552; Z = 2; measuring temperature: 293 K). The crystal structure can be characterized as a layer‐like structure, in which [B₁₂H₁₂]²⁻ anions and H₃O⁺ cations alternate with layers of [La(H₂O)₉]³⁺ cations (d(La–O) = 252–260 pm) and Cl⁻ anions along [001]. The [B₁₂H₁₂]²⁻ (d(B–B) = 176–179 pm; d(B–H) = 104–113 pm) and Cl⁻ anions exhibit no coordinative influence on La³⁺. Hydrogen bonds are formed between the H₃O⁺ cations and [B₁₂H₁₂]²⁻ anions, also between the water molecules of [La(H₂O)₉]³⁺ and Cl⁻ anions, which contribute to the stabilization of the crystal structure.     

Zeolite NaY-promoted cyclization of farnesal: a short route to nanaimoal

The sesquiterpene nanaimoal was synthesized in 21% overall yield and in a biomimetic manner. As a key step, the acid-catalyzed cyclization of farnesal under zeolite NaY confinement conditions was used. The intrazeolite cyclization of farnesal affords as major product a double-bond isomer of nanaimoal, via a novel diastereoselective tandem 1,5-diene cyclization/Prins-type reaction.     

Synthesis of (+)-zerumin B using a regioselective singlet oxygen furan oxidation

A short and efficient synthesis of the antitumor diterpenoid (+)-zerumin B has been accomplished starting from (+)-sclareolide. At the heart of the synthetic strategy lies the regioselective formation of the alpha-substituted gamma-hydroxybutenolide moiety of zerumin B. This was achieved by means of a [1,4] O-->C triisopropylsilyl migration followed by singlet oxygen (1 O 2) oxidation of the resulting 2-triisopropylsilyl-3-(alpha-hydroxy)alkylfuran.     

HPLC determination of cefotaxime and cephalexine residues in milk and cephalexine in veterinary formulation

An HPLC method was developed and validated for the determination of the cephalosporins cefotaxime and cephalexine in skimmed bovine milk. The analytical column, Kromasil C₁₈ (250 mm × 4.0 mm, 5 μm) was operated at ambient temperature. Mobile phase consisted of CH₃OH-acetate buffer (pH = 4.0) and it was delivered isocratically at a flow rate of 1.0 mL · min⁻¹. Total analysis time was less than 5 min. Caffeine was used as internal standard (5 ng · μL⁻¹). UV detection was performed at 265 nm. Method validation was performed by means of intra-day (n = 5) and inter-day accuracy and precision (n = 8), sensitivity and linearity. Limits of detection (LOD) and limits of quantification (LOQ) were 0.1 and 0.3 ng · μL⁻¹, respectively. The method was applied to the analysis of a veterinary drug (CEPOREX) containing cephalexine. The results were quite accurate with the relative error varying from −8.0 to −3.5%. Solid-phase extraction was applied to remove all matrix interference from milk samples. High extraction recoveries (average 84–121%) were achieved by using Abselut NEXUS cartridges with acetonitrile as eluent and a rinsing step with water and n-butanol. A pre-concentration step was necessary in a 1/10 level to reach the EU MRL concentration level (100 μg · kg⁻¹). RSD values were less than 7% for both cephalosporins. Correspondence: Ioannis N. Papadoyannis, Laboratory of Analytical Chemistry, Department of Chemistry, Aristotle University of Thessaloniki, GR-54124 Thessaloniki, Greece