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.     

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)     

On the loss process in a batch arrival queue

In this paper, we investigate the loss process in a finite-buffer queue with batch arrivals and total rejection discipline. In such a model, if the buffer has insufficient capacity to accept all the customers included in an arriving batch, the whole batch is blocked and lost. This scheme is especially useful in performance evaluation of buffering processes in IP (internet protocol) networks. The main result of this paper is a closed-form formula for the joint distribution of the length of the first lost series of batches and the time of the first loss. Moreover, the limiting distribution (as the buffer size grows to infinity) is shown.     

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.     

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.