Boundary conditions of Sturm-Liouville operators with mixed spectra

We study bounds on averages of spectral functions corresponding to Sturm-Liouville operators on the half line for different boundary conditions. As a consequence constraints are obtained which imply existence of singular spectrum embedded in a.c. spectrum for sets of boundary conditions with positive measure and potentials vanishing in an interval [0,N]. These constraints are related to estimates on the measure of sets where the spectral density is positive.     

A two-dimensional Minkowski ?(x) function

A function from a triangle to itself is defined that has both interesting number theoretic and analytic properties. This function is shown to be a natural generalization of the classical Minkowski ?(x) function. It is shown there exists a natural class of pairs of cubic irrational numbers in the same cubic number field that are mapped to pairs of rational numbers, in analog to ?(x) mapping quadratic irrationals on the unit interval to rational numbers on the unit interval. It is also shown that this new function satisfies an analog to the fact that ?(x), while increasing and continuous, has derivative zero almost everywhere.     

Transformations of <Emphasis Type="Italic">N</Emphasis>-ethylamines into amide derivatives under the action of sulfur monochloride

Tertiary N-ethylamines were converted into amide derivatives by reactions with sulfur monochloride and DABCO at 0 °C. Depending on the nature of the substituents in the amine, the reaction can be accompanied by unexpected transformations. Published in Russian in Izvestiya Akademii Nauk. Seriya Khimicheskaya, No. 6, pp. 1135–1140, June, 2007.     

Gold ultra-microelectrode arrays: application to the steady-state voltammetry of hydroxide ion in aqueous solution.

Gold ultra-microelectrode arrays are used to explore the electrochemical oxidation of hydroxide ions and are shown to be analytical useful. Two types of ultra-microelectrode arrays are used; the first consist of 256 individual electrodes of 5 microm in radius, 170 of which are electrochemically active in a cubic arrangement which are separated from their nearest neighbour by a distance of 100 microm. The second array compromises 2597 electrodes of 2.5 microm in radius and of which 1550 of which are electrochemically active in a hexagonal arrangement separated by the nearest neighbour by 55 microm. Well defined voltammetric waves are found with peak currents proportional to the concentration of hydroxide ions in the range 50 microM to 1 mM. Detection limits of 20 microM using the 170 ultra-microelectrode and 10 microM with the 1550 ultra-microelectrode array are shown to be possible but with a higher sensitivity of 4 mA M(-1) observed using the 1550 ultra-microelectrode array compared to 1.2 mA M(-1) with the 170 ultra-microelectrode array.     

Influence of the conditions of manufacture of nanomeric zirconium dioxide,stabilized with yttrium oxide,on its catalytic properties in the oxidation of CO

The morphological and catalytic properties of samples of nanomeric zirconium dioxide, stabilized with yttrium oxide, manufactured via the effect of a UHF field during the process of drying precipitated zirconium hydroxide and calcination at temperatures from 300 to 1000 °C, were studied. It was shown that the highest activity in the oxidation of CO occurred with 40 nm particles of zirconium dioxide prepared at 1000 °C. __________ Translated from Teoreticheskaya i éksperimental’naya Khimiya, Vol. 43, No. 2, pp. 96–101, March–April, 2007.     

Application of Horner–Emmons Olefination to the Crown-Ether Derivatives

An effective synthetic approach to the preparation of a new crown-ether vinylogs involving the Horner–Emmons olefination of carbonyl precursors with the use of C₂- and C₅-phosphonates was proposed. The effects of the conjugation chain length and the nature of the terminal polar functions in the phosphonate reagent on the yield and process stereoselectivity were discussed.     

Platinum metallodrug-protein binding studies by capillary electrophoresis-inductively coupled plasma-mass spectrometry: characterization of interactions between Pt(II) complexes and human serum albumin

Characterizing how platinum metallocomplexes bind to human serum albumin (HSA) is essential in evaluating anticancer drug candidates. Using cisplatin as a reference complex, the application of capillary electrophoresis (CE) to reliably assess drug/HSA interactions was validated. Since this complex is small compared to the size of the protein, the binding response could only be recognized when applying CE coupled to a (platinum) metal-specific mode of detection, namely inductively coupled plasma-mass spectrometry (ICP-MS). This coupling allowed for confirmation of a specific affinity of cisplatin and novel Pt complexes to HSA, measurement of the kinetics of binding reactions, and determination of the number of drug molecules attached to the protein. As the cisplatin/HSA molar ratio increased, the reaction rate became faster with a maximum on the kinetic curve appearing at about 50 h of incubation at 20 times excess of cisplatin. The reaction was characterized as a pseudo-first order reaction with the rate constant k = 0.003 min(-1) at 37 degrees C. When incubated with a 20-fold excess of cisplatin, HSA bound up to 10 mol of Pt per mol of the protein. This is indicative for a strong metal-protein coordination occurring at several HSA sites other than the only protein cysteine residue. Structural analogs of cisplatin, bearing aminoalcohol ligands, showed comparable protein binding reactivity and stoichiometry but a common equilibrium was not reached even after one week of incubation. Also apparent was a two-step mechanism of the binding reaction. Results demonstrated the suitability of CE-ICP-MS as a rapid assay for high-throughput studying of drug/HSA interactions.     

Synthesis and Inclusion Properties of the Host Compound 1,3-Dihydro-1,1,3,3-tetraphenylisobenzofuran. X-Ray Crystal Structures of the Free Host and of an Inclusion Compound with 1,4-Dioxane

A novel host molecule, 1, suitable for crystalline lattice-type inclusion, has been synthesized, and its cocrystal formation ability has been investigated. Host 1 proved to be of potential use for organic solvent separation and retrieval, and a promising auxiliary for solidification of certain odorous substances. The crystal structures of the solvent-free host 1, and its complex with 1,4-dioxane (1 : 1), have been determined by single crystal X-ray diffraction. The structure of 1 (guest-free) is triclinic, P , with a = 9.452(2), b = 10.359(3), c = 13.116(3) Å, = 101.80(2), = 106.53(1) and = 104.32(1)°. The spacious, propeller-like molecules are held together by weak van der Waals' forces. The dioxane inclusion compound is monoclinic, P21/a, with a = 15.050(1), b = 8.641(1) and c = 20.658(1) Å, and = 94.56(1)°, and contains two crystallographically independent guest molecules, both located around symmetry centres. The molecular packing seems to be governed by C—H···O type bonds (C···O = 3.31 and 3.48 Å) from the host to the dioxane oxygens.     

Synthesis of Cationic Cholesterol Derivatives with Succinyl Spacer Group

Syntheses of N,N,N-trimethyl[2-(3-cholesteryloxy)syccinyloxyethyl]ammonium iodide, N,N-dimethyl-N-2-hydroxyethyl[2-(3-cholesteryloxy)syccinyloxyethyl]ammonium iodide, and N-[(3-cholesteryloxy)syccinyl]piperazine were performed. The compounds synthesized in a liposomal form may be used for delivery of genetical material into cells.