Stationary Distribution Function Estimation for Ergodic Diffusion Process

The problem of nonparametric stationary distribution function estimation by the observations of an ergodic diffusion process is considered. The local asymptotic minimax lower bound on the risk of all the estimators is found and it is proved that the empirical distribution function is asymptotically efficient in the sense of this bound.     

Optimization of the synthesis of non-symmetrical alkyl dimethyl sulfonium halides

This work is aimed at the optimization of the yield and purity of non-symmetrical trialkyl sulfonium halide salts. The effects of parameters such as solvent, temperature and concentration were studied. The products were carefully analyzed and the crystal structure of [{n-CH₃(CH₂)₁₅}(CH₃)₂S]Br determined. The overall aim of the present study is future syntheses of low-dimensional magnetic materials.     

Multiplicity of zeros and discrete orthogonal polynomials

We consider a problem of bounding the maximal possible multiplicity of a zero of some expansions Σ a_iF_i(x), at a certain point c, depending on the chosen family {imi}. The most important example is a polynomial with c = 1. It is shown that this question naturally leads to discrete orthogonal polynomials. Using this connection we derive some new bounds, in particular on the multiplicity of the zero at one of a polynomial with a prescribed norm. 30C15, 33C47     

Mechanistic characterization of aerobic alcohol oxidation catalyzed by Pd(OAc)(2)/pyridine including identification of the catalyst resting state and the origin of nonlinear [catalyst] dependence

The Pd(OAc)(2)/pyridine catalyst system is one of the most convenient and versatile catalyst systems for selective aerobic oxidation of organic substrates. This report describes the catalytic mechanism of Pd(OAc)(2)/pyridine-mediated oxidation of benzyl alcohol, which has been studied by gas-uptake kinetic methods and (1)H NMR spectroscopy. The data reveal that turnover-limiting substrate oxidation by palladium(II) proceeds by a four-step pathway involving (1) formation of an adduct between the alcohol substrate and the square-planar palladium(II) complex, (2) proton-coupled ligand substitution to generate a palladium-alkoxide species, (3) reversible dissociation of pyridine from palladium(II) to create a three-coordinate intermediate, and (4) irreversible beta-hydride elimination to produce benzaldehyde. The catalyst resting state, characterized by (1)H NMR spectroscopy, consists of an equilibrium mixture of (py)(2)Pd(OAc)(2), 1, and the alcohol adduct of this complex, 1xRCH(2)OH. These in situ spectroscopic data provide direct support for the mechanism proposed from kinetic studies. The catalyst displays higher turnover frequency at lower catalyst loading, as revealed by a nonlinear dependence of the rate on [catalyst]. This phenomenon arises from a competition between forward and reverse reaction steps that exhibit unimolecular and bimolecular dependences on [catalyst]. Finally, overoxidation of benzyl alcohol to benzoic acid, even at low levels, contributes to catalyst deactivation by formation of a less active palladium benzoate complex.     

Spectrophotometric determination of gadolinium(III) with 2-(5-bromo-2-pyridylazo)-5-diethylaminophenol (5-Br-PADAP)

Reaction between gadolinium(III) and 2-(5-bromo-2-pyridylazo)-5-diethylaminophenol (5- Br-PADAP) was studied for delineating optimal conditions for complexation. This reagent can be used for the spectrophotometric determination of Gd(III) in concentrations ranging from 0.04 to 1.2 ppm (a = 1.76(+/- 0.03) x 10(5) (1.(-1) mole(-1). cm). The reaction takes place at a pH between 9.2 and 11.6. In the presence of Triton X-100 this complex is soluble in water. In order to overcome difficulties caused by the presence of other lanthanides, an ion exchange chromatographic technique was used.     

Tensor products of coherent configurations

A Cartesian decomposition of a coherent configuration ✗ is defined as a special set of its parabolics that form a Cartesian decomposition of the underlying set. It turns out that every tensor decomposition of ✗ comes from a certain Cartesian decomposition. It is proved that if the coherent configuration ✗ is thick, then there is a unique maximal Cartesian decomposition of ✗; i.e., there is exactly one internal tensor decomposition of ✗ into indecomposable components. In particular, this implies an analog of the Krull–Schmidt theorem for the thick coherent configurations. A polynomial-time algorithm for finding the maximal Cartesian decomposition of a thick coherent configuration is constructed.     

Sensitive spectrophotometric determination of vanadium with hydrogen peroxide and 2-(5-chloro-2-pyridylazo)-5-dimethylaminophenol after extraction with N-benzoyl-N-phenylhydroxylamine

A selective and precise spectrophotometric determination of vanadium(V) is performed after preceding extraction with N-benzoyl-N-phenylhydroxylamine (BPHA). The color is developed in a water-ethanol solution with hydrogen peroxide and 2-(5-chloro-2-pyridylazo)-5-dimethylaminophenol (5-Cl-DMPAP). The molar absorptivity at 588 nm is (6.57 ± 0.05) × 10⁴ L mol^–1 cm^–1 at pH 2.1. The method permits the determination of vanadium (V) at trace levels in the presence of large amounts of other ions. It is applied to the determination of vanadium in aluminium (analytical reagent grade) and in human hair. High accuracy and precision is obtained.     

Spectrophotometr1c determination of cadmium with 2-(5-chloro-2-pyridylazo)-5-dimethylaminophenol

The reaction between cadmium and 2-(5-chloro-2-pyridylazo)-5-dimethylaminophenol (5-Cl DMPAP) in aqueous alcohol media at pH 8.8-10.7 results in an intense violet colour which is stable for at least 8 hr. The composition is 2:1 reagent:metal and the formation constant (5.29 +/- 0.01) x 10(18). Beer's law is obeyed up to 1.34 ppm of cadmium at 550 nm. The optimal concentration range (Ringbom) is between 0.16 and 0.72 ppm. The apparent molar absorptivity at 550 nm is (1.20 +/- 0.01) x 10(5) l.mole(-1). cm(-1), making the sensitivity one of the highest known. The interference due to copper(III), iron(III), cobalt(II), nickel(II), gold(III), zinc(II) and manganese(II) can be suppressed.     

Pentacoordinate spirosilicate anion, bis(2,2′-biphenyldiyl)methylsilicate, synthesized by the lithium cleavage of dimethoxyethane

The reaction of spirobisilafluorene (1) with lithium in dimethoxyethane produces lithium 1-methyl-spirobisilafluorenide (2), a stable pentacoordinate silicon compound with five carbon ligands, and lithium 2-methoxyethoxide, which was identified by trapping with Ph₃SiCl to give Ph₃Si-OCH2CH2OCH3 (4). The X-ray crystal structure of 2 shows that the geometry at silicon is an idealized trigonal bipyramid, slightly distorted toward a square pyramid. Methanolysis of 2 cleaves a Si-aryl bond producing a methyl biphenylsilafluorene, 3. Crystal structures are reported for 3 and 4.     

Simultaneous spectrophotometric determination of La, Ho, Mn 5-Br-PADAP complexes using multivariate calibration with partial least-squares (PLS) data evaluation

A simple and fast analytical pocedure is proposed for the simultaneous spectrophotometric determination of lanthanum, holmium and manganese in synthetic ceramics, (La(0.8-x) Hox Sr0.2 MnO3), by using the partial least-squares (PLS) method. As chromogenic agent 5-Br-PADAP [2-(5-bromo-2-pyridylazo)-5-diethylaminophenol] was used, which form colored complexes with the three elements studied. To avoid metal hydrolysis, a mixture of ethanol and Triton X-100 at pH 9.5 was used for all experiments. A set of 17 calibration solutions measured throughout the 400-700 nm wavelength range was used in the calibration step. The concentration range for Mn(II) was 1-12 x 10(-6) mol L-1, while the range for the rare earth elements La(III) and Ho(III) was 2-8 x 10(-6) mol L-1. In order to demonstrate the applicability of the proposed method, a set of artificial samples containing the three analytes in variable proportions was prepared and analyzed. The analytical results obtained were quite acceptable with relative errors not greater than 7% in most cases.