Construction and studies of a new class of reciprocal trees: interknitting of the Pascal's triangle

A method of construction of a new class of trees with reciprocal pairs of eigenvalues (λ, 1/λ) has been developed. They are derived from star graphs and can be symbolized as K _{1, n ?1} + n(p) + mK ₂ (1 ≤ m ≤ n ? 1 except for n = 1). The trees are minimally Kekulenoid and hence contain reciprocal pairs of eigenvalues in their eigenspectra. The characteristic polynomial coefficients of these trees with given values of n and m are shown to be obtainable by appropriate use of the Pascal's triangle. A general formula for this purpose has been developed. An analytical formula for the Wiener indices of such trees in terms of m and n has been derived and some consequences of this formula are presented. The relevance of these trees to real molecular structures is discussed. The trees have been shown to be useful in observing the subspectrallity of two series of IPR fullerenes of formulae C_{50+10 n} and C_{60+12 n} (n is a positive integer).     

Magnetoelectric response and dielectric property of multiferroic Co0.65Zn0.35Fe2O4–PbZr0.52Ti0.48O3 nanocomposites

The effect of nanometric grain size modulation on the behavior of different kinds of chemically synthesized multiferroic ferrite–ferroelectric nanocomposites with cobalt zinc ferrite (Co_0.65Zn_0.35Fe₂O₄) as a ferrimagnetic component and lead zirconate titanate (PbZr_0.52Ti_0.48O₃) as a ferroelectric component have been investigated in detail. Formation of two distinct pure phases of as-prepared nanocomposites was confirmed from recorded X-ray diffraction patterns at room temperature. The backscattered mode of a field emission scanning electron microscope micrograph has been used to study the microstructure, average grain size, and distribution of the two individual phases in the composites. Magnetization vs. magnetic field measurements clearly show the room temperature good hysteretic ferrimagnetic behavior of the composites having coercivity of 83–124 Oe and spontaneous magnetization of 20–24 emu/g. The dielectric constant is found to increase with increasing grain size of the nanocomposites from 124 to 687 at a frequency of 1 kHz. Investigation of temperature-dependent dielectric constant behavior reveals that the paraelectric–ferroelectric transition temperature decreases from 364 to 351 °C with decreasing particle size. A complex impedance spectroscopy study was carried out in the frequency range of 50 Hz–1 MHz and in the temperature range of 27–400 °C. The contribution of both grains and grain boundaries in the electrical properties of the composites has been confirmed from the complex impedance spectroscopy data. The activation energies estimated from the complex impedance spectroscopy and the ac conductivity spectrum are found to be nearly the same for the nanocomposites. The polarization vs. electric field measurement exhibits a typical ferroelectric hysteresis loop at room temperature and provides conclusive evidence of the presence of spontaneous polarization in the composites, confirming the presence of excellent ferroelectricity in the nanocomposites. At room temperature the multiferroic behavior of the composites is also confirmed from detailed magnetoelectric (ME) response studies. The optimal ME response is observed to be 0.6 % for higher temperature sintered composites.     

Intermediate coupling model description of55Fe and57Fe

The properties of the negative parity states of⁵⁵Fe and⁵⁷Fe are investigated in the framework of the intermediate coupling model. In the model, a neutron or a quasineutron is coupled to anharmonic vibrations of the core. Anharmonicities of the vibrations are estimated through the observed properties of the core. Energy levels, spectroscopic factors and electromagnetic properties have been calculated. The results of the present calculations are also compared with available experimental results and other theoretical results. The model reasonably accounts for many of the properties of the low-lying states.     

Time Resolved Fluorescence and Energy Transfer Analysis of Nd<Superscript>3+</Superscript>–Yb<Superscript>3+</Superscript>–Er<Superscript>3+</Superscript> Triply-Doped Ba–Al-Metaphosphate Glasses for an Eye Safe Emission (1.54 μm)

This paper reports on the preparation and systematic analysis of energy transfer mechanisms in Nd³⁺–Yb³⁺–Er³⁺ co-doped new series of barium-alumino-metaphosphate glasses. The time resolved fluorescence of Nd³⁺ in triply doped Ba–Al-metaphosphate glasses have revealed that, Yb³⁺ ions could function as quite efficient bridge for an energy transfer between Nd³⁺ and Er³⁺ ions. As a result, a fourfold emission enhancement at 1.54 μm of Er³⁺ ions has been achieved through an excitation of ⁴F_5/2 level of Nd³⁺ at 806 nm for the glass having 3 mol% Yb³⁺ with an energy transfer efficiency reaching up to 94%. Decay of donor (Nd³⁺) ion fluorescence has been analyzed based on theoretical models such as direct energy transfer model (Inokuti–Hirayama) and migration assisted energy transfer models (Burshtein’s hopping and Yokota–Tanimoto’s diffusion). The corresponding energy transfer parameters have been evaluated and discussed. Primarily, electrostatic dipole–dipole (s ~ 6) interactions are found to be responsible for the occurrence of energy transfer process in theses glasses.     

Studies on binary mixtures of 4-pentyloxy-4′-cyanobiphenyl with three 4, 4′-di(alkoxy)azoxybenzenes

Eighteen binary mixtures of 4-pentyloxy-4′-cyanobiphenyl (5OCB) and 4, 4′-di(alkoxy)azoxybenzenes (nOAB) with n = 5, 6, and 7 at different concentrations have been studied in detail. Over a wide concentration range, induced SmA phase was observed in all the mixtures except in one. In most of the mixtures, the refractive indices no, ne, and Δn lie between the values of pure components. The optical birefringence of the mixtures is found to decrease non-additively with concentration. The molecular polarizability anisotropy and the orientational order parameter <P₂> of the mixtures were calculated. Nature of variation of polarizability anisotropy with concentration is similar to that of Δn. In allmixtures <P₂> is more in smectic phase than in nematic phase and it also shows non-additive behaviour. Observed <P₂> values of the mixtures were compared with McMillan’s and Maier-Saupe theoretical values and good agreement is found in some mixtures. The transition temperatures obtained by fitting <P₂> data to McMillan’s theory agree with the observed values within a few degrees. Ratio of elastic constants K₃₃ and K₁₁ is determined for mixtures having nematic phase and found to diverge at T_NA transition point.     

Cyclic oligofurans: one-pot synthesis of 30pi and 40pi expanded porphyrinoids

Acid-catalyzed condensation of furan and pentafluorobenzaldehyde yielded conjugated macrocycles with six and eight furan rings. They represent systems similar to annulenes with 30pi and 40pi electrons. From their structural analyses, it was found that furan rings in both the molecules were inverted in an alternative fashion and displayed nontwisted conformations. [structure: see text].