Jessen–Wintner type random variables and fractal properties of their distributions

Formulas are given for the Lebesgue measure and the Hausdorff–Besicovitch dimension of the minimal closed set S_ξ supporting the distribution of the random variable ξ = 2^–k τ_k, where τ_k are independent random variables taking the values 0, 1, 2 with probabilities p _0k , p _1k , p _2k , respectively. A classification of the distributions of the r.v. ξ via the metric‐topological properties of S_ξ is given. Necessary and sufficient conditions for superfractality and anomalous fractality of S_ξ are found. It is also proven that for any real number a ₀ ∈ [0, 1] there exists a distribution of the r.v. ξ such that the Hausdorff–Besicovitch dimension of S_ξ is equal to a ₀. The results are applied to the study of the metric‐topological properties of the convolutions of random variables with independent binary digits, i.e., random variables ξⁱ = , where η_k are independent random variables taking the values 0 and 1. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Trianionic 1,3,2-Dioxaborine-Containing Polymethines: Bright Near-Infrared Fluorophores

Trianionic polymethines of the A′-π-A-π-A-π-A′ type comprising dioxaborine rings (A) and different electron-accepting end groups (A′) have been synthesized. The obtained dyes absorb and emit light in the near-infrared region with remarkably high molar attenuation coefficients (ϵ up to 495 000 M⁻¹ cm⁻¹ in DMF) and fluorescence quantum yields (Φ_f up to 0.73 in DMF). Thus, the novel trianionic dyes stand among the brightest individual fluorophores known to date – with a magnitude of fluorescence brightness (ϵ⋅Φ_f) of 313 000 M⁻¹ cm⁻¹ in DMF. The synthesized dyes demonstrate a minor negative solvatochromism and small Stokes shifts. X-ray data reveal the nearly planar geometry of the trianionic chromophore. All the obtained compounds are stable in the solid state and in a solution, although the relative stability is much higher in polar aprotic than in protic solvents.     

A four-step domino Knoevenagel–hetero-Diels–Alder reaction

A new, catalyst-free, domino Knoevenagel–hetero-Diels–Alder elimination oxidation reaction is reported. 5-Aryl-2H,6H-chromeno[4′,3′:4,5]thiopyrano[2,3-d][1,3]thiazol-2-ones are formed in moderate to good yields via reaction of 2-(3-aryl-3-chloro-2-propenyloxy)benzaldehydes with 4-thioxo-1,3-thiazolidin-2-one.     

A new domino-Knoevenagel-hetero-Diels-Alder reaction

Various novel 3,5a,6,11b-tetrahydro-2H,5H-chromeno[4′,3′:4,5]thiopyrano[2,3-d][1,3]thiazol-2-ones were synthesized in 60-80% yields via domino-Knoevenagel-hetero-Diels-Alder reactions of 4-thioxo-1,3-thiazolidin-2-one with 3,7-dimethyl-6-octenal, 2-allyloxybenzaldehydes and 2-formylphenyl (E)-3-aryl-2-propenoates with base catalysis. The possibility of stereo- and regioselective cycloaddition was investigated.     

Template-derived mesoporous carbons with highly dispersed transition metals as media for the reactive adsorption of dibenzothiophene

Mesoporous carbons with highly dispersed copper, cobalt, and iron were obtained from an organic polymer within amorphous silica powder, alumina, and zeolite 13X. The materials were characterized using the adsorption of nitrogen, potentiometric titration, and elemental analysis. The small metal content (less than 1%) and its chelation in the precursor polymers ensure a high dispersion of metallic centers. The materials obtained are mainly mesoporous but differ significantly in their porosity and surface chemistry, which is linked to the effect of template constraints and chemistry and the kind of metal and is related to the differences in the carbonization mechanism. On the carbon obtained, the adsorption of dibenzothiophene (DBT) from hexane was carried out. The high capacities (up to 130 mg S/g) obtained were linked to the high volume of mesopores and specific interactions of DBT with surface acidic groups and strong interactions of metals with dibenzothiophene via S-M sigma bonds or, in the case of copper, via interaction of metals with disturbed pi electrons of aromatic rings of DBT.     

Charge Transfer Salt with Substituted Lindquist Polyoxometalate: Synthesis, Crystal Structure, and Physical Properties of α-(BEDT-TTF)6(VW5O19)⋅DMF⋅2H2O

A new charge transfer salt based on bis(ethylenedithio)tetrathiafulvalene (BEDT-TTF) and the vanadium substituted Lindquist anion [VW₅O₁₉]^3– was synthesized and characterized by X-ray and spectroscopic analysis. Monoclinic, C2, F _w =3789.2, a=41.5019(5), b=11.2600(2), c=12.7514(2) Å, =101.877(5)°, Z=2, R=0.060, based on 12095 reflections with I>2(I). The structure consists of alternating organic and inorganic layers. The inorganic layer is generated by [VW₅O₁₉]^3– anions, dimethylformamide (DMF) and water molecules. The organic layer, which is generated by three different BEDT-TTF units, belongs to the -type of packing and consists of trimerized chains parallel to the c direction. The compound is a semi-conductor with _{300 K} =1.1 Scm^–1 and E _a =0.1 eV. Polarized reflectance spectra of single crystals were measured over the spectral range from 650 to 25000 cm^–1. FT-NIR Raman spectra of powdered crystals dispersed in KBr pellets were also recorded. Vibrational and electronic features are discussed.     

Adsorption of ammonia on graphite oxide/Al13 composites

Graphite oxide/Al₁₃ composites were prepared using graphite oxide and commercial solution of Chlorhydrol^®. Although surfactant was used to disperse of graphene-like layers, they were restacked together upon addition of Al₁₃ Keggin polycations. The crust of inorganic phase was deposited on the outer surface of GO platelets. The resulting materials were used as adsorbents of ammonia in dry or wet conditions either in an as received form or prehumidified for 2 h before the breakthrough test. It was shown that water in the system decreases the amount adsorbed, likely as a result of the competition with ammonia for adsorption centers. The highest and strongest adsorption was found in the dry conditions where interlayer space was partially available and the acidic centers of an inorganic phase played an enhancing role in the retention of ammonia.