Synthesis of 2-(5-aryl-4-methyl-2-oxo-1,2-dihydro- 3<Emphasis Type="Italic">H</Emphasis>-pyrrol-3-ylidene)malononitriles

4-Oxoalkane-1,1,2,2-tetracarbonitriles in the presence of an equimolar amount of morpholine were converted to previously unknown 2-(5-aryl-4-methyl-2-oxo-1,2-dihydro-3H-pyrrol-3-ylidene)malononitriles.     

Hypergraph list coloring and Euclidean Ramsey theory

A hypergraph is simple if it has no two edges sharing more than a single vertex. It is s‐list colorable (or s‐choosable) if for any assignment of a list of s colors to each of its vertices, there is a vertex coloring assigning to each vertex a color from its list, so that no edge is monochromatic. We prove that for every positive integer r, there is a function d_r(s) such that no r‐uniform simple hypergraph with average degree at least d_r(s) is s‐list‐colorable. This extends a similar result for graphs, due to the first author, but does not give as good estimates of d_r(s) as are known for d₂(s), since our proof only shows that for each fixed r ≥ 2, d_r(s) ≤ 2 We use the result to prove that for any finite set of points X in the plane, and for any finite integer s, one can assign a list of s distinct colors to each point of the plane so that any coloring of the plane that colors each point by a color from its list contains a monochromatic isometric copy of X. © 2011 Wiley Periodicals, Inc. Random Struct. Alg., 2011     

Anodic TiO2 Nanotube Layers for Wastewater and Air Treatments: Assessment of Performance Using Sulfamethoxazole Degradation and N2O Reduction

The preparation of anodic TiO₂ nanotube layers has been performed using electrochemical anodization of Ti foil for 4 h at different voltages (from 0 V to 80 V). In addition, a TiO₂ thin layer has been also prepared using the sol–gel method. All the photocatalysts have been characterized by XRD, SEM, and DRS to investigate the crystalline phase composition, the surface morphology, and the optical properties, respectively. The performance of the photocatalyst has been assessed in versatile photocatalytic reactions including the reduction of N₂O gas and the oxidation of aqueous sulfamethoxazole. Due to their high specific surface area and excellent charge carriers transport, anodic TiO₂ nanotube layers have exhibited the highest N₂O conversion rate (up to 10% after 22 h) and the highest degradation extent of sulfamethoxazole (about 65% after 4 h) under UVA light. The degradation mechanism of sulfamethoxazole has been investigated by analyzing its transformation products by LC-MS and the predominant role of hydroxyl radicals has been confirmed. Finally, the efficiency of the anodic TiO₂ nanotube layer has been tested in real wastewater reaching up to 45% of sulfamethoxazole degradation after 4 h.     

Dual-State Emission of 2-(Butylamino)Cinchomeronic Dinitrile Derivatives

New representatives of 2-(butylamino)cinchomeronic dinitrile derivatives were synthesized as promising fluorophores showing dual-state emission. To characterize the influence of the length (from methyl to butyl) and the structure (both linear and branched) of the alkyl substituent at the amino nitrogen atom, the spectral fluorescence properties of all synthesized compounds were carefully studied both in solution and in solid state. The highest photoluminescence quantum yield values of 63% were noted for solutions of 2-(butylamino)-6-phenylpyridine-3,4-dicarbonitrile in DCM and 2-(butylamino)-5-methyl-6-phenylpyridine-3,4-dicarbonitrile in toluene.     

Distribution of Platinum and Palladium between Dissolved,Nanoparticulate, and Microparticulate Fractions of Road Dust

Ageing processes of vehicle catalytic converters inevitably lead to the release of Pt and Pd into the environment, road dust being the main sink. Though Pt and Pd are contained in catalytic converters in nanoparticulate metallic form, under environmental conditions, they can be transformed into toxic dissolved species. In the present work, the distribution of Pt and Pd between dissolved, nanoparticulate, and microparticulate fractions of Moscow road dust is assessed. The total concentrations of Pt and Pd in dust vary in the ranges 9–142 ng (mean 35) and 155–456 (mean 235) ng g⁻¹, respectively. The nanoparticulate and dissolved species of Pt and Pd in dust were studied using single particle inductively coupled plasma mass spectrometry. The median sizes of nanoparticulate Pt and Pd were 7 and 13 nm, respectively. The nanoparticulate fraction of Pt and Pd in Moscow dust is only about 1.6–1.8%. The average contents of dissolved fraction of Pt and Pd are 10.4% and 4.1%, respectively. The major fractions of Pt and Pd (88–94%) in road dust are associated with microparticles. Although the microparticulate fractions of Pt and Pd are relatively stable, they may become dissolved under changing environmental conditions and, hence, transformed into toxic species.     

Stability in the Erdős–Gallai Theorem on cycles and paths,II

The Erd?s–Gallai Theorem states that for $k\ge 3$, any $n$-vertex graph with no cycle of length at least $k$ has at most $\frac{1}{2}(k?1)(n?1)$ edges. A stronger version of the Erd?s–Gallai Theorem was given by Kopylov: If $G$ is a 2-connected $n$-vertex graph with no cycle of length at least $k$, then $e\left(G\right)\le max\{h(n,k,2),h(n,k,?\frac{k?1}{2}?)\}$, where $h(n,k,a)?\left(\genfrac{}{}{0ex}{}{k?a}{2}\right)+a(n?k+a)$. Furthermore, Kopylov presented the two possible extremal graphs, one with $h(n,k,2)$ edges and one with $h(n,k,?\frac{k?1}{2}?)$ edges.In this paper, we complete a stability theorem which strengthens Kopylov’s result. In particular, we show that for $k\ge 3$ odd and all $n\ge k$, every $n$-vertex 2-connected graph $G$ with no cycle of length at least $k$ is a subgraph of one of the two extremal graphs or $e\left(G\right)\le max\{h(n,k,3),h(n,k,\frac{k?3}{2})\}$. The upper bound for $e\left(G\right)$ here is tight.     

A Novel Synthetic Approach to Phosphorylated Peptidomimetics

It has been shown that the derivatives of diethyl 5‐amino‐2‐phthalimidoalkyl‐1,3‐oxazol‐4‐ylphosphonates can be employed in the synthesis of phosphorylated peptidomimetics containing the phosphonoglycine residue. The reaction of diethyl 5‐alkylamino‐2‐aminoalkyl‐1,3‐oxazol‐4‐ylphosphonates with unsaturated azlactones was utilized to obtain phosphorylated peptidomimetics with dehydroamino acid moieties. The double bond in the latter was reduced with zinc in acetic acid to provide the corresponding saturated peptidomimetics containing a diethoxyphosphoryl group in the side chain.