FRET based selective and ratiometric ‘naked-eye’ detection of CN in aqueous solution on fluorescein–Zn–naphthalene ensemble platform

We have developed a FRET-based ratiometric fluorescent probe for the detection of CN⁻ using a fluorescein–Zn–naphthalene ensemble (NFH·Zn²⁺). The sensing mechanism was ascribed by displacement approach. The chemosensor exhibits high selectivity and sensibility for CN⁻. The speculation was supported by fluorescence emission spectra, UV–vis spectrum, ¹H NMR titration experiments, and mass spectra. The interconversion of probe NFH and NFH·Zn²⁺ via the complexation/decomplexation by the modulation of Zn²⁺/CN⁻ mimics INHIBIT gate. In addition, it also shows an excellent performance in ‘dip stick’ method.     

On Kre?n's formula

Kre?n's formula provides a parametrization of the generalized resolvents and Štraus extensions of a closed symmetric operator with equal possibly infinite defect numbers in a Hilbert space in terms of Nevanlinna families in a parameter space. The aim of this note is to give a simple complete analytical proof of Kre?n's formula.     

On non-strong jumping numbers and density structures of hypergraphs

Estimating Turán densities of hypergraphs is believed to be one of the most challenging problems in extremal set theory. The concept of ‘jump’ concerns the distribution of Turán densities. A number α∈[0,1) is a jump for r-uniform graphs if there exists a constant c>0 such that for any family F of r-uniform graphs, if the Turán density of F is greater than α, then the Turán density of F is at least α+c. A fundamental result in extremal graph theory due to Erd?s and Stone implies that every number in [0,1) is a jump for graphs. Erd?s also showed that every number in [0,r!/r^r) is a jump for r-uniform hypergraphs. Furthermore, Frankl and Rödl showed the existence of non-jumps for hypergraphs. Recently, more non-jumps were found in [r!/r^r,1) for r-uniform hypergraphs. But there are still a lot of unknowns regarding jumps for hypergraphs. In this paper, we propose a new but related concept-strong-jump and describe several sequences of non-strong-jumps. It might help us to understand the distribution of Turán densities for hypergraphs better by finding more non-strong-jumps.     

Madelung fluid description of the generalized derivative nonlinear Schrödinger equation: Special solutions and their stability

Theoretical and Mathematical Physics - A correspondence between the families of generalized nonlinear Schrödinger (NLS) equations and generalized KdV equations was recently found using a...     

On Kähler-Norden manifolds

This paper is concerned with the problem of the geometry of Norden manifolds. Some properties of Riemannian curvature tensors and curvature scalars of Kähler-Norden manifolds using the theory of Tachibana operators is presented.     

Photophysical properties of novel fluorescent poly(oxyethylene phosphate) tris(β-diketonate) europium (III) complexes

In the present study, photophysical properties of fluorescent poly(oxyethylene phosphate) tris(β-diketonate) europium (III) complexes have been studied by means of stationary and time-resolved fluorescence spectroscopy (in ethanol at room temperature). The luminescent quantum yields and efficiency for the energy transfer from β-diketonate ligands to Eu(III) ion have been determined for the studied complexes by using diffusion-enhanced fluorescence resonance energy transfer. Obtained results show effect of the polymer ligands upon photophysical properties of the complexes and a relation has been established with length of the oxyethylene spacer between two phosphonate groups. The Förster radiuses of the synthesized compounds with SulfoRhodamine 101 as acceptor have been calculated. Measured distances between molecules of the donors and acceptor at identical acceptor/donor molar ratios have been illustrated the difference in structure of the ternary and polymer complexes in solution even at low concentration.     

Detecting unalloyed tin in LiSn2(PO4)3-based anodes with Mössbauer spectroscopy

The first discharge of the Li⁺ ion anode material LiSn₂(PO₄)₃ was investigated with Mössbauer spectroscopy and electrochemical techniques. Mössbauer spectroscopy provided insight into the structure of the tin atoms of the fully discharged anode materials. Spectra consist of overlapping peaks, which are assigned to noncrystalline β-Sn and Li–Sn alloy domains. An analysis of the relative intensities of the Mössbauer spectra shows the relative abundance of β-Sn increases at the expense of the Li–Sn alloy as the discharge rate increases. Cell polarization occurs at higher discharge rates, leading to inefficient electrode utilization and poor cycling performance. Sluggish Li⁺ ion diffusion through the amorphous Li₃PO₄ network that is formed early in the discharge process might be responsible for the poor electrochemical performance and the accumulation of unalloyed tin.     

Tafel slopes from first principles

Tafel slopes for multistep electrochemical reactions are derived from first principles. The derivation takes place in two stages. First, Dirac’s perturbation theory is used to solve the Schrödinger equation. Second, current–voltage curves are obtained by integrating the single-state results over the full density of states in electrolyte solutions. Thermal equilibrium is assumed throughout. Somewhat surprisingly, it is found that the symmetry factor that appears in the Butler–Volmer equation is different from the symmetry factor that appears in electron transfer theory, and a conversion formula is given. Finally, the Tafel slopes are compiled in a convenient look-up table.