Staudinger’s phosphazene as an efficient esterifying reagent

A new application of Staudinger’s phosphazene as an efficient esterifying reagent is reported. Staudinger’s phosphazene formed in situ by the reaction of organic mono-azide with triphenylphosphine, which is trapped by carboxylic acid, to afford amide exclusively. In contrast, interestingly the same phosphazene behaves in a different way as an efficient esterifying reagent, affording ester under a solvent-free microwave-assisted protocol wherein alcohol is added as the another component in addition to the other reactants. This discovery adds yet another new application of Staudinger’s phosphazene to synthetic chemistry.     

Generalization of some polynomial inequalities not vanishing in a disk

If $P(z) = \sum\limits_{\nu = 0}^n {c_\nu z^\nu } $ is a polynomial of degree n, then for |β| ≤ 1, it was proved in [4] that $\left| {zP'(z) + n\frac{\beta } {2}P(z)} \right| \leqslant n\left| {1 + \frac{\beta } {2}} \right|\mathop {\max }\limits_{|z| = 1} |P(z)|,|z| = 1 $ In this paper, first we generalize the above result for the s ^th derivative of polynomials and next we improve the above inequality for polynomials with restricted zeros.     

Transmission gaps in one-dimensional Fibonacci quasiperiodic structure containing epsilon-negative materials

We investigate the transmission properties of one-dimensional Fibonacci quasiperiodic structure consisting of dispersive and lossless epsilon-negative (ENG) materials. It is found that for both TE and TM polarizations with normal and oblique incidences, there exist transmission gaps which are invariant with a change of scale and sensitive to incident angles. Analytical methods based on transfer matrices and effective medium theory have been used to explain the properties of transmission gaps.     

Transmission properties of a double-periodic quasi-crystal containing single-negative materials

The transmission properties of a double-periodic quasi-crystal containing single-negative materials are investigated with the transfer matrix method and effective medium theory. It is shown that the double-periodic quasi-crystal has a single-negative band gap between the zeros of average permittivity and average permeability of the effective medium. These zeros are affected only by the filling factor of the structure, and are independent from the order of the double-periodic quasi-crystal. Moreover, we show that the periodic structure created by repeating the double-periodic quasi-crystal has some omnidirectional band gaps at the single-negative frequency region. The number of such omnidirectional band gap increases by increasing the order of double-periodic quasi-crystal. Then, the structure can be used as a multichannel filter.     

Band structure of two-dimensional square lattice photonic crystals of circular dispersive metamaterial rods

By virtue of the efficiency of the Dirichlet-to-Neumann map method, the details of the band structure of a two-dimensional square lattice photonic crystal composed of dispersive metamaterial circular rods in air background has been studied. We show that there are two flat bands at the band structure of the system for both H-polarization and E-polarization. These flat bands are created around the magnetic resonance frequency, surface plasmon frequency and magnetic surface plasmon frequency. We realized that the modes with frequencies lying above the resonance frequency behave like resonant cavity modes created in a single metallic cylindrical waveguide. While, due to the relatively large and imaginary refractive index of the metamaterial rods at the frequencies lying below the resonance frequency, the modes are localized modes with negligible penetration into the rods. Moreover, the modes are localized at the interface of the cylindrical metamaterial rods and the air background for the frequencies around the surface plasmon frequency and the magnetic surface plasmon frequency.