Excitation of defect modes from the extended photonicband-gap structures of 1D photonic lattices

This paper stuides numerically the model equation in a one dimensional defective photonic lattice by modifying the potential function to a periodic function. It is found that defect modes (DMs) can be regarded as Bloch modes which are excited from the extended photonic band-gap structure at Bloch wave-numbers with k x = 0. The DMs for both positive and negative defects are considered in this method.     

Magnetoacoustic waves with effect of arbitrary degree of temperature and spin degeneracy in electron-positron-ion plasmas

The linear properties of magnetosonic waves are studied in nearly degenerate and nearly non-degenerate quantum plasmas composed of electrons, positrons and ions in the presence of spin- effect. Using the fluid equations, a generalized dispersion relation for perpendicular and oblique propagation is derived. It is found that degree of temperature and spin degeneracy modify the dispersive properties of the given modes. The results of analysis are beneficial for understanding the collective phenomena in dense quantum astrophysical plasmas.     

Smectogenic properties of N,N'-bis[(2-hydroxy-4-alkoxyphenyl)methylene]benzene-1,4-diamine liquid crystals with double lateral H-bonds

A series of eight liquid crystalline compounds, N,N'-bis[(2-hydroxy-4-alkoxyphenyl)methylene]benzene-1,4-diamines, has been synthesized and characterized. These homologous compounds differ in the length of terminal alkyl group C _n H_2n+1 wherein n is an even number ranging from 4 to 18. The spectroscopic techniques, FTIR, ¹H NMR and ¹³C NMR, were employed to characterize the molecular structure. The transition temperatures of all the title compounds and their mesophases were studied by differential scanning calorimetry and polarizing microscopy. All the compounds were smectogenic, exhibiting both tilted and non-tilted molecular orientation in their smectic phases. Further investigation to ascertain the anisotropic nature of subphases within the smectogenic region was carried out using X-ray diffraction.     

First observation of K X-rays from pp atoms

K and L series X-rays have been observed from p$\text{p}$ atoms formed in hydrogen gas at NTP in association with annihilations into neutral particles. The total K X-ray yield is (6.5 ± 3.2) × 10^?3 per stopped antiproton. A model-dependent fit of the K X-ray spectrum gives a K_α energy of 8.9±0.3 keV, corresponding to a strong interaction shift of (?0.5±0.3) keV.     

Fractional photon model of three-photon mixing in the non-linear interaction process

In this paper, a fractional photon model is proposed by considering the photon-exchange interaction in the reverse process of the non-linear three-photon mixing interaction. The phase matching condition for various types of uniaxial crystals can be simplified and classified by this model with the consideration of the unequal fractional photon-exchange of the two generated waves in the reverse manner. This also leads to the explanation of observing the phase mismatch and output bandwidth of the resonant and non-resonant waves in a cavity. Finally, a quantitative approach to this model, with experimental results, is also demonstrated.     

A study of tautomerism in diazonium coupling products of 4-hydroxycoumarin

The spectra (¹H nmr, ir and uv) of a series of 3-arylazo-4-hydroxycoumarins 1a-m indicate that such compounds exist predominantly in the keto hydrazone form 1A both in solid state and in solution. The acid dissociation constants of the series studied were determined spectrophotometrically in 80 vol% ethanol-water mixture at 27° and ionic strength of 0.1. The results of the correlations of these constants by Hammett and Yukawa-Tsuno equations exclude the presence of the hydroxyazo form 1B in equilibrium with 1A in agreement with the spectral data. Also, the HMO method has been used to study tautomerism in such compounds. The results are also in full agreement with both the spectral and linear free energy correlations, the hydrazone form 1A being the most stable. It is further shown that both the intermolecular and intramolecular hydrogen bonding favor the hydrazone tautomer.     

Modelling the CPI using a lognormal diffusion process and implications on forecasting inflation

The Maximum Likelihood estimator is used within a lognormaldiffusion process and closed form analytical solutions are obtained.The monthly CPI forecasts are estimated for the period between1970 and 2002. The quarterly estimates of inflation rates areobtained from monthly forecasts rather than from quarterly data.This has significantly improved the estimates of inflation rates.The model also produced a superior fit as compared to randomwalk and GARCH(p,q)-M models. The adopted approach is foundto be simple, economical and generally suitable for modellingstochastic processes that reflect aggregation over time stemmingfrom many factors, and in which the transition path betweenconsecutive states is relatively smooth.     

A simple multi-scroll hyperchaotic system

We propose a simple autonomous hyperchaotic system that can generate multi-scroll attractors. The proposed system has a canonical structure, one control parameter, and a switching-type nonlinearity. If multiple breakpoints are added to the system nonlinearity, multi-scroll behavior can be obtained. We numerically demonstrate hyperchaotic behavior of the proposed system, under different nonlinearities, as its control parameter is changed. Furthermore, we study hyperchaos in the proposed system when it assumes a fractional order, and demonstrate that hyperchaotic behavior can be obtained in systems less than fourth order. Throughout the study, hyperchaos is verified by examining the Lyapunov spectrum, where the presence of multiple positive Lyapunov exponents in the spectrum is indicative of hyperchaos.     

Weighted ebyev-Ostrowski type inequalities

In account of the famous ebyev inequality,a rich theory has appeared in the literature.We establish some new weighted ebyev type integral inequalitíes.Our proofs are of independent interest and provide new estimates on these types of inequalities.