A variant of Davenport’s constant

Let p be a prime number. Let G be a finite abelian p-group of exponent n (written additively) and A be a non-empty subset of ]n[≔ {1, 2,…, n} such that elements of A are incongruent modulo p and non-zero modulo p. Let k ≥ D(G/|A| be any integer where D(G) denotes the well-known Davenport’s constant. In this article, we prove that for any sequence g ₁, g ₂,…, g _k (not necessarily distinct) in G, one can always extract a subsequence with 1 ≤ ℓ ≤ k such that

Transformation of proton-conducting Perovskite-type into fluorite-type fast oxide ion electrolytes using a CO2 capture technique and their electrical properties

Fast oxide ion conducting Ce 1- x M x O 2-delta (M = In, Sm; x = 0.1, 0.2) and Ce 0.8Sm 0.05Ca 0.15O 1.825 were prepared from the corresponding perovskite-like structured materials with nominal chemical composition of BaCe 1- x M x O 3-delta and BaCe 0.8Sm 0.05Ca 0.15O 2.825, respectively, by reacting with CO 2 at 800 degrees C for 12 h. Powder X-ray diffraction (PXRD) analysis showed the formation of fluorite-type CeO 2 and BaCO 3 just after reaction with CO 2. The amount of CO 2 gained per ceramic gram was found to be consistent with the Ba content. The CO 2 reacted samples were washed with dilute HCl and water, and the resultant solid product was characterized structurally and electrically employing various solid-state characterization methods, including PXRD, and alternating current (ac) impedance spectroscopy. The lattice constant of presently prepared Ce 1- x M x O 2-delta and Ce 0.8Sm 0.05Ca 0. 15O 1.825 by a CO 2 capture technique follows the expected ionic radii trend. For example, In-doped Ce 0.9In 0.1O 1.95 (In (3+) (VIII) = 0.92 A) sample showed a fluorite-type cell constant of 5.398(1) A, which is lower than the parent CeO 2 (5.411 A, Ce (4+) (VIII) = 0.97 A). Our attempt to prepare single-phase In-doped CeO 2 samples at 800, 1000, and 1500 degrees C using the ceramic method was unsuccessful. However, we were able to prepare single-phase Ce 0.9In 0.1O 1.95 and Ce 0.8In 0.2O 1.9 by the CO 2 capture method from the corresponding barium perovskites. The PXRD studies showed that the In-doped samples are thermodynamically unstable above 800 degrees C. The ac electrical conductivity studies using Pt electrodes showed the presence of bulk, grain-boundary, and electrode contributions over the investigated temperature range in the frequency range of 10 (-2)-10 (7) Hz. The bulk ionic conductivity and activation energy for the electrical conductivity of presently prepared Sm- and (Sm + Ca)-doped CeO 2 samples shows conductivities similar to those of materials prepared by the ceramic method reported in the literature. For instance, the conductivity of Ce 0.8Sm 0.2O 1.9 using the CO 2 capture technique was determined to be 4.1 x 10 (-3) S/cm, and the conductivity of the same sample prepared using the ceramic method was 3.9 x 10 (-3) S/cm at 500 degrees C. The apparent activation energy of the area-specific polarization resistance for the symmetric cell (Sm,Sr)CoO 3- x |Ce 0.8Sm 0.2O 1.9|(Sm,Sr)CoO 3- x was determined to be 1 eV in air.     

Bio-inspired phosphole-lipids: from highly fluorescent organogels to mechanically responsive FRET

Sensitive gels: the amphiphilic features of phosphole-lipids lead to intriguing self-assembly properties and the formation of highly fluorescent organogels. Moreover, the dynamic structural features of the system make it possible to amplify the mechanochromic emission shifts (100 nm) in a donor-acceptor system through thermally and mechanically responsive fluorescence resonance energy transfer (FRET).     

Anthraquinone derivatives as electron-acceptors with liquid crystalline properties

Dialkoxy derivatives of anthraquinone (AQ), dicyano-anthraquinone (DCAQ) and tetracyanoanthraquinone (TCAQ) were synthesized and their associated electrochemical, optical and self-assembling properties were investigated as candidates for n-type materials. AQ shows UV absorption features, whereas both DCAQ and TCAQ exhibit bathochromic and hyperchromic electronic transitions into the visible region. The electron accepting strength of the three compounds was established by cyclic voltammetry as -1.52 V, -1.3 V and -0.9 V vs. ferrocene/ferricenium for AQ, DCAQ and TCAQ, respectively. All three quinones displayed quasireversible, two sequential one-electron transfer redox reactions. DFT calculations of DCAQ and TCAQ demonstrate structural changes upon reduction, which is supported by spectroelectrochemical experiments. Furthermore, the structural changes result in different absorption profiles and show potential as electrochromic materials. Finally, both AQ and DCAQ show liquid crystalline phases and importantly, DCAQ exhibits both a smectic liquid crystalline and a soft crystal phase between -6 °C and 85 °C, which offers promise as a self-assembling n-type material.     

On zero-sum sequences of prescribed length

Summary. Let k ≥ 1 be any integer. Let G be a finite abelian group of exponent n. Let s_k(G) be the smallest positive integer t such that every sequence S in G of length at least t has a zero-sum subsequence of length kn. We study this constant for groups when d = 3 or 4. In particular, we prove, as a main result, that for every k ≥ 4, and for every prime p ≥ 5.     

含NS和NNSS供电子原子的钌(Ⅲ)席夫碱配合物:催化性能和抗微生物活性

通过[RuX₃(EPh₃)₃] 或 [RuBr₃(PPh₃)₂(MeOH)] (式中X=Cl或Br; E=P或As)与适当的席夫碱以1∶1的物质的量的比反应合成了[RuX₂(L′)(EPh₃)₂]或[RuX(LL′)(PPh₃)](式中L′=席夫碱配体1，即[S-benzyl     

Antibacterial activity of ruthenium(II) carbonyl complexes containing tetradentate Schiff bases

Several new hexa-coordinated ruthenium(II) complexes of the type [Ru(CO)(LL)(B)] (where, LL = anthacac, anthdibm, 2-amtpacac or 2-amtpdibm; B = PPh₃ or py or pip or morph) have been prepared by reacting [RuHCl(CO)(PPh₃)₃] or [RuHCl(CO)(PPh₃)₂(B)] with tetradentate Schiff bases such as bis(anthranilic acid)acetylacetimine (H₂-anthacac), bis(anthranilic acid) dibenzoylmethimine (H₂-anthdibm), bis(2-aminothiophenol) acetylacetimine (H₂-2-amptacac) or bis(2-aminothiophenol) dibenzoylmethimine (H₂-2-amtpdibm). The complexes have been characterised by elemental analyses and spectral (i.r., electronic spectra, ¹H- and ³¹P-n.m.r.) data. An octahedral structure has been tentatively proposed for the complexes, which were also tested for their antibacterial properties.     

Effect of sintering on the ionic conductivity of garnet-related structure Li5La3Nb2O12 and In- and K-doped Li5La3Nb2O12

Garnet-structure related metal oxides with the nominal chemical composition of Li₅La₃Nb₂O₁₂, In-substituted Li_5.5La₃Nb_1.75In_0.25O₁₂ and K-substituted Li_5.5La_2.75K_0.25Nb₂O₁₂ were prepared by solid-state reactions at 900, 950, and 1000 °C using appropriate amounts of corresponding metal oxides, nitrates and carbonates. The powder XRD data reveal that the In- and K-doped compounds are isostructural with the parent compound Li₅La₃Nb₂O₁₂. The variation in the cubic lattice parameter was found to change with the size of the dopant ions, for example, substitution of larger In³⁺(r_CN6: 0.79 Å) for smaller Nb⁵⁺ (r_CN6: 0.64 Å) shows an increase in the lattice parameter from 12.8005(9) to 12.826(1) Å at 1000 °C. Samples prepared at higher temperatures (950, 1000 °C) show mainly bulk lithium ion conductivity in contrast to those synthesized at lower temperatures (900 °C). The activation energies for the ionic conductivities are comparable for all samples. Partial substitution of K⁺ for La³⁺ and In³⁺ for Nb⁵⁺ in Li₅La₃Nb₂O₁₂ exhibits slightly higher ionic conductivity than that of the parent compound over the investigated temperature regime 25-300 °C. Among the compounds investigated, the In-substituted Li_5.5La₃Nb_1.75In_0.25O₁₂ exhibits the highest bulk lithium ion conductivity of 1.8×10⁻⁴ S/cm at 50 °C with an activation energy of 0.51 eV. The diffusivity (“component diffusion coefficient”) obtained from the AC conductivity and powder XRD data falls in the range 10⁻¹⁰-10⁻⁷ cm²/s over the temperature regime 50-200 °C, which is extraordinarily high and comparable with liquids. Substitution of Al, Co, and Ni for Nb in Li₅La₃Nb₂O₁₂ was found to be unsuccessful under the investigated conditions.     

Tridentate Schiff base complexes of ruthenium(III) containing ONS/ONO donor atoms and their biocidal activities

New ruthenium(III) complexes of the [RuY(LL)(E)₂] type (Y = Cl or Br; LL = tridentate Schiff bases; E = PPh₃ or AsPh₃) have been synthesised by reacting [RuX₃(EPh₃)₃] (X = Cl, E = P; X = Cl or Br, E = As) or [RuBr₃(EPh₃)₂(MeOH)] with Schiff bases having the donor groups (O, N, X) viz., salicylaldehydethiosemicarbazone (X = S), salicylaldehydesemicarbazone (X = O), o-hydroxyacetophenonethiosemicarbazone (X = S) and o-hydroxyacetophenonesemicarbazone (X = O). The new complexes were characterised by elemental analysis, spectral (i.r., electronic spectra, e.p.r.), magnetic moment and cyclic voltammetry data. Biocidal activity studies were also carried out for the new complexes.     

Fluorescence enhancement of N2O2-type dipyrrin ligand in two step responding to zinc(II) ion

Fluorescence imaging is well-suited for the live imaging of biological Zn(II), which has no facile spectroscopic or magnetic signature. The successful application of this methodology requires the development of robust Zn(II) imaging agents that display high sensitivity, selectivity and temporal fidelity. In this study, a N₂O₂-type dipyrrin based bimolecular zinc(II) complex was produced and shown to have sharper, blue-shifted and more enhanced fluorescence emission. An approximate three-fold fluorescence enhancement was achieved within the micromolar concentration range, which is an important parameter for Zn(II) detection in vivo. The increase in emission intensity was due to the dominant role of aryl-ring rotation in governing the excited state dynamics and fluorescence properties of the dipyrrin dye. Fluorescence titration showed that the ligand complex exhibited very strong zinc(II) binding affinity when compared to that in the binuclear chloro complex. The fluorescence emission changes in the dipyrrin dye to zinc(II) ion could be observed not only using instruments but also by the naked-eye (violet→sky blue).