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Oxidative dehydrogenation of crotonaldehyde overK2HPMo12O40catalyst

Summary The oxidative dehydrogenation of crotonaldehyde to furan and maleic anhydride was carried out over K₂HPMo₁₂O₄₀catalyst. A positive effect of water vapor on furan formation is explained by ability of the catalyst to isomerize 2E- to 2Z-crotonaldehyde.</o:p>     

A criterion for the uniform distribution of sequences in compact metric spaces

LetX be a compact metric space, le μ be a non-negative normalized Borel measure onX and letf be a measurable bounded real-valued function defined onX such thatf is μ-almost everywhere continuous and different from zero. It is proved that a sequence (x _n ),n=1,2, … of points inX is μ-uniformly distributed if and only if for every Borel setE?X with μ(Bd(E))=0 we have \(\mathop {\lim }\limits_{N \to \infty } \frac{1}{N}\sum\limits_{n = 1}^N {f(x_n )} 1_E (x_n ) = \int\limits_E {f(x)d\mu (x)} ,\) where 1 _E denotes the characteristic function ofE andbdE the boundary ofE. Furthermore some quantitative aspects and generalizations of this theorem are discussed.     

On uniform distribution of double sequences

In this paper a new notion of uniform distribution of double sequences is introduced. In the most elementary case a double sequence (x_mn)_{m, nN} is called uniformly distributed in this sense if all finite matrices of equal size appear with the same frequency as submatrices of the infinite matrix (x_mn). Some special double sequences with such a distribution property are studied and metric theorems are proved.     

On the mechanism of propylene oxidation over gallium-molybdenum oxide catalysts

The products of selective oxidation are shown to be formed via a stepwise mechanism with participation of surface allylic complexes. A successive transformation of -allyl to -allyl and further to acrolein is possible. The products of complete oxidation may be formed through surface carbonate-carboxylate complexes via either a stepwise mechanism involving the catalyst's oxygen, or a concerted mechanism with the participation of molecular oxygen.

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Synthesis, Characterization, and Physical Properties of Two Trinuclear, Mixed-Valence Species of Type [μ3-OMnIIMnIII 2(O2CCF3)6(R)3] (R=H2O, CH3COOH)

The preparation and characterization of two new mixed-valence, trinuclear species, [Mn₃O(O₂CCF₃)₆(H₂O)₃]CF₃COOH4/3H₂O (1) and [Mn₃O(O₂CCF₃)₆(CH₃COOH)₃] (2), is reported. Compound 1 crystallizes in the triclinic space group, P¯1 (No. 2), with the parameters, a=12.3131(9) Å, b=12.4427(9) Å, c=12.965(1) Å, =72.593(4)°, =73.453(5)°, =68.345(4)°, V=1727.2(2) ų, and Z=2. A total of 14060 reflections were collected in the range 1.6827.52°. The final weighted and non-weighted agreement indices, R1=0.0589 and wR2=0.1445 were based on a total of 6953 unique reflections with an R _int value of 0.0542. Compound 2 crystallizes in the monoclinic space group, P2₁/n (No. 14), with the parameters, a=12.876(3) Å, b=12.212(4) Å, c=17.732(4) Å, =100.40(3)°, V=3640.4(1) ų, and Z=4. A total of 32197 reflections were collected in the range 1.7227.13°. The final weighted and non-weighted agreement factors, R1=0.0647 and wR2=0.1609 were based on a total of 8018 unique reflections with an R _int value of 0.0462. An investigation of the physical properties revealed that both compounds display an intermediate ground state of S=3/2 as a consequence of intramolecular antiferromagnetic coupling. The magnetic data for compound 1 was best fit to the parameters g=2.09, J=–5.5 cm^–1, J=–3.4 cm^–1, and D _Mn(III)=–4.5 cm^–1; the data for compound 2 was best fit to the parameters g=2.10, J=–2.9 cm^–1, J=–5.5 cm^–1, and D _Mn(III)=–4.5 cm^–1.     

Enhanced ethanol sensing properties of WO3 modified TiO2 nanorods

Pristine and WO₃ decorated TiO₂ nanorods (NRs) were synthesised to investigate n-n-type heterojunction gas sensing properties. TiO₂ NRs were fabricated via hydrothermal method on fluorine-doped tin oxide coated glass (FTO) substrates. Then, tungsten was sputtered on the TiO₂ NRs and thermally oxidised to obtain WO₃ nanoparticles. The heterostructure was characterised by X-ray diffraction (XRD), scanning electron microscopy (SEM), and energy-dispersive X-ray (EDX) spectroscopy. Fabricated sensor devices were exposed to VOCs such as toluene, xylene, acetone and ethanol, and humidity at different operation temperatures. Experimental results demonstrated that the heterostructure has better sensor response toward ethanol at 200 °C. Enhanced sensing properties are attributed to the heterojunction formation by decorating TiO₂ NRs with WO₃.     

Metric Theorems for Distribution Measures of Pseudorandom Sequences

 We improve a recent result of Mauduit and Sárk?zy (2000) on the well-distribution measure of pseudorandom sequences and complement another of their results on the correlation measure.     

On quantitative aspects of the unit sum number problem

We investigate the function u _K,S (n; q) which counts the number of representations of algebraic integers α with |N_{K/\mathbb Q}(a)| ￡ q{|N_{K/{\mathbb Q}}(\alpha)| \leq q} for some real positive q that can be written as sums of exactly n S-units of the number field K.