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.     

Existence of solutions for generalized implicit vector variational-like inequalities

In this paper, we introduce a new class of generalized implicit vector variational-like inequalities in Hausdorff topological vector spaces and Banach spaces which contain implicit vector equilibrium problems, implicit vector variational inequalities and implicit vector complementarity problems as special cases. We derive some new results by using the KKM–Fan theorem, under compact and noncompact assumptions on underlying convex sets.     

Lifetime measurements and decay of superdeformed bands in Hg isotopes

The lifetimes of states in Superdeformed (SD) bands in ^192,194Hg have been measured using the Doppler shift attenuation method. Intrinsic quadrupole moments have been extracted for band 1 of ¹⁹²Hg and for bands 1, 2, and 3 of ¹⁹⁴Hg. It was found that the quadrupole moments for the “identical” SD bands in these nuclei are the same. In the same experiment, one-step transitions linking SD states to yrast and near yrast states for bands 1 and 3 of ¹⁹⁴Hg have been identified. From this observation, excitation energies, spins and probable parities have been assigned to SD states in these bands.     

Natural radioactivity in marble stones- Jordan

Natural radioactivity has been measured in marble stone samples collected from Dabaa'h, Ajloun and Azrak areas using a gamma spectroscopy technique. The measured ²²⁶Ra activities in the stones collected from Dabaa'h quarries varied from 264.9 Bq kg⁻¹ to 369.5 Bq kg⁻¹. In samples from Ajloun and Azrak the maximum values of ²²⁶Ra were 28.3 Bq kg⁻¹ and 23.41 Bq kg⁻¹, respectively. The measured values of ²³²Th were less than 17.89 Bq kg⁻¹. The average values of the radium equivalent activities as well as external and internal hazard indices were also calculated. It was observed that for marble stones from Dabaa'h area, estimated average value of the external hazard index is 0.873 and that of internal hazard index is 1.71.     

Hyperfine structure and isotope shift of the neutron-rich barium isotopes139–146Ba and148Ba

The hyperfme structure and isotope shift in the 6s ² S _1/2?6p ²P_3/2 line of Ba II (455.4 nm) have been measured by collinear fast-beam laser spectroscopy for the neutron-rich isotopes^139–146Ba and¹⁴⁸Ba. Nuclear moments and mean square charge radii of these isotopes have been recalculated. The isotope shift of the isotope¹⁴⁸Ba (T_1/2=0.64 s) could be studied for the first time, yieldingδ〈r²〉^138,148=1.245(3) fm².     

Schiff base tantalum(V) complexes

Summary Complexes of pentachlorotantalum with the Schiff bases: bis(vanillin)benzidine, bis(vanillin)-o-dianisidine, bis(acetylacetone)benzidine, bis(p-dimethylaminobenzaldehyde)-o-dianisidine, bis(anisaldehyde)-1, 3-propanediamine and bis(p-dimethylaminobenzaldehyde)-o-phenylenediamine have been prepared and characterized by molar conductance, decomposition temperature, elemental and t.g. analyses and i.r. spectral measurements. The conductances reveal that pentachlorotantalum (1 mole) interacts with all the ligands (1 mole), all five chloride ions thus forming simple adducts. A comparative study of the i.r. spectra of the parent ligands and their complexes allows the coordination sites to be ascertained. The studies show that tantalum(V) chloride prefers to form complexes of high coordination number.