Sustainable feasibility of waste printer ink to magnetically separable iron oxide–doped nanocarbons for styrene oxidation

A simpler cost-effective method for the isolation of magnetically separable ‘self-doped iron oxide nanocarbons’ (FeO-NC) from waste printer ink (used as a carbon source material which is available free of cost) is discussed here. The process involves carbonization of waste printer ink in a muffle furnace at ~600 °C to obtain FeO-NC. The as-prepared FeO-NC has been investigated as an efficient heterogeneous catalyst for the long-known important organic reaction involving transformation of styrene to benzaldehyde in a quantitative yield (~70%). Importantly, FeO-NC were magnetically separable along with good recyclability, which supports the sustainability of reported process.     

Titania deposited on soft magnetic activated carbon as a magnetically separable photocatalyst with enhanced activity

Magnetically separable composite photocatalysts, TiO₂ deposited on soft magnetic ferrite activated carbon (TFAC), were prepared by sol-gel and dip-coating technique. The prepared composites were characterized by X-ray diffraction (XRD), field emission scanning electron microscopy (FESEM), Fourier transform infrared spectra (FTIR), optical absorption spectroscopy, vibrating sample magnetometer (VSM) and nitrogen adsorption. These photocatalysts exhibited enhanced photocatalytic activity compared to Degussa P25 for the degradation of methyl orange (MO) in aqueous solution. The kinetics of MO degradation was well fitted to the Langmuir-Hinshelwood model. The samples showed good magnetic response and could be completely recovered by an external magnet. Furthermore, the photocatalysts could maintain high photocatalytic activity after five cycles, and the degradation rate of MO was still close to 90%.     

Subdirectly irreducible separable dynamic algebras

A characterization of the subdirectly irreducible separable dynamic algebras is presented. The notions develo‐ ped for this study were also suitable to describe the previously found class of simple separable dynamic algebras (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

On the residual properties of Baumslag–Solitar groups

A survey of results on the residual properties of Baumslag–Solitar groups that have been obtained to date. Some unpublished results are included and for certain results new proofs are given     

Neither first countable nor Cech-complete spaces are maximal Tychonoff connected

A connected Tychonoff space is called maximal Tychonoff connected if there is no strictly finer Tychonoff connected topology on . We show that if is a connected Tychonoff space and locally separable spaces, locally \v{C}ech-complete spaces, first countable spaces, then is not maximal Tychonoff connected. This result is new even in the cases where is compact or metrizable.

     

Homogeneity in powers of subspaces of the real line

Working in ZFC, we prove that for every zero-dimensional subspace of the real line, the Tychonoff power is homogeneous ( denotes the nonnegative integers). It then follows as a corollary that is homogeneous whenever is a separable zero-dimensional metrizable space. The question of homogeneity in powers of this type was first raised by Ben Fitzpatrick, and was subsequently popularized by Gary Gruenhage and Hao-xuan Zhou.

     

Convergence in the pth-mean and some Weak Laws of Large Numbers for weighted sums of random elements in separable normed linear spaces

Theorem. Let X_n, n ≥ 1, be a sequence of tight random elements taking values in a separable Banach space B such that |X_n|, n ≥ 1, is uniformly integrable. Let a_nk, n ≥ 1, k ≥ 1, be a double array of real numbers satisfying Σ_{k ≥ 1} |a_nk| ≤ Γ for every n ≥ 1 for some positive constant Γ. Then Σ_{k ≥ 1}a_nkX_k, n ≥ 1, converges to 0 in probability if and only if Σ_{k ≥ 1}a_nkf(X_k), n ≥ 1, converges to 0 in probability for every f in the dual space B¹.     

The Urysohn space embeds in Banach spaces in just one way

In a Master's thesis in 1985 and a subsequent paper published in 1992, the author discovered that the universal separable metric space (up to isometry) discovered by Urysohn in 1925 has a uniquely determined linear closure (up to linear isometry) when isometrically embedded in a Banach space so as to include the zero of the Banach space. The proof of this result is given in this note and the current status of some related questions is discussed.     

用可分命题简化证明实数系中定理

修改了连续归纳法,利用修改后的连续归纳法证明了一个关于可分命题的重要定理,利用该定理简化证明实数系中若干定理.