Hierarchy of rational order families of chaotic maps with an invariant measure

We introduce an interesting hierarchy of rational order chaotic maps that possess an invariant measure. In contrast to the previously introduced hierarchy of chaotic maps [1–5], with merely entropy production, the rational order chaotic maps can simultaneously produce and consume entropy. We compute the Kolmogorov-Sinai entropy of these maps analytically and also their Lyapunov exponent numerically, where the obtained numerical results support the analytical calculations.     

Pattern structures fabricated on ZnS–SiO2/AgO x /ZnS–SiO2 thin film structure by laser direct writing technology

In this work, we used the multilayered ZnS–SiO₂/AgO _x /ZnS–SiO₂ films as the laser direct writing materials, and pattern structures with different shapes and sizes were directly written with green laser (λ=488 nm). Compared with traditional photoresist materials, the pattern structures can be directly formed in this film structures without developing and etching procedures and also can be directly written by very low laser power. By tuning the laser parameters precisely, pattern structures with different sizes and shapes could be obtained as well. The analysis indicates that the formation mechanism of the pattern structure is mainly due to the volume expansion caused by AgO _x decomposition into silver particles and oxygen. The oxygen applies pressure to the ZnS–SiO₂ layer and makes a hollow shell under the film. The aspect ratios of the patterns rapidly increase from the minimum of 0.012 in laser power of 3.0 mW to the maximum of 0.201 in laser power of 5.0 mW. The thermal stability of the patterns was also qualitatively studied.     

Propagation properties of Airy–Gaussian beams

The propagation of the Airy–Gaussian beams is studied in strongly nonlocal nonlinear media analytically and numerically. The linear momentum of the analytical Airy–Gaussian beam solution of the Snyder–Mitchell model is not conservational, which is the reason that results in the disagreement between the analytical Airy–Gaussian beam solution and the numerical simulations of the nonlocal nonlinear Schr?dinger equation in the case of strong nonlocality. The quasi-Airy–Gaussian soliton in the Gaussian-shaped response material can be obtained when the parameter χ ₀ is large enough, and the patterns of Airy–Gaussian beams are variable periodically in liquid crystal material during propagation.     

Calculation of energy characteristics for Si<Subscript>1–<Emphasis Type="Italic">x</Emphasis></Subscript>Ge<Subscript><Emphasis Type="Italic">x</Emphasis></Subscript>–Si structures with single quantum wells

Energy characteristics of Si_1–x Ge _x –Si quantum-size structures with single quantum wells were calculated numerically based on a four-band k·p method. Analytical expressions for the Luttinger parameters are obtained as functions of the component composition of Si_1–x Ge _x compounds. Analytical expressions for the energy ħω of optical band-to-band transitions are obtained in an effective mass approximation and agree well with numerical calculations by the k·p method. This allows one to determine accurately a range of changes while varying the component compositions and thickness of the active and barrier layers.     

Charging of a conducting sphere moving in a weakly ionized gas under an arbitrarily oriented external uniform electric field

A charging conducting sphere moving in a weakly ionized gas is investigated. An external uniform electric field is applied with arbitrary orientation relative to the gas flow. The ion current is obtained analytically and investigated numerically in ballistic assumption. It is shown that charging regimes depend not only on the net charge of the sphere but also on the gas flow type, and the parameter ξ_± – the ratio of ion drift velocity far from the sphere to the gas velocity. The cases |ξ_±|<1 and |ξ_±|>1 yield two different charging regimes for Stokes and potential flows. For the potential flow, the ion current has been found analytically in continuous ξ_±-parameter space. The stationary charge of an isolated sphere is also calculated numerically as a function of α. It achieves maximum magnitudes in direct (α=0) and back (α=π) flows respectively.     

Multiple-valued steady states and their stability in a saturable-absorber laser

We present the results of a theoretical consideration of steady states in a saturable-absorber laser for different frequencies of transition in the active medium, the absorber, and the cavity. The conditions for the coexistence of several (up to five) stationary values of intensity are obtained. The stability of such states is analytically studied, and the possible regimes of generation and switching for the parameters corresponding to solid-state lasers with a saturable absorber are shown. Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 67, No. 3, pp. 322–326, May–June, 2000.     

Alpha radioactivity for proton-rich even Pb isotopes

Half-lives for alpha radioactivity from proton-rich even Pb isotopes in the range A = 182–202 have been calculated using the unified fission-like approach. The geometrical shape of the potential barrier is parametrized in terms of a highly versatile, asymmetric and analytically solvable form of potential based on Ginnochio’s potential. Good agreement with the experimental data has been obtained with the variation of just one parameter. Half-lives of three unknown alpha emitters in the neutron-deficient Pb chain (¹⁹⁸Pb, ²⁰⁰Pb and ²⁰⁴Pb) have been predicted. The exact expression for the transmission coefficient has been compared with those obtained from WKB approximation method for symmetric Eckart potential.      

Harmonic Averages and New Explicit Constants for Invariant Densities of Piecewise Expanding Maps of the Interval

The statistical behavior of families of maps is important in studying the stability properties of chaotic maps. For a piecewise expanding map τ whose slope >2 in magnitude, much is known about the stability of the associated invariant density. However, when the map has slope magnitude ≤2 many different behaviors can occur as shown in (Keller in Monatsh. Math. 94(4): 313–333, 1982) for W maps. The main results of this note use a harmonic average of slopes condition to obtain new explicit constants for the upper and lower bounds of the invariant probability density function associated with the map, as well as a bound for the speed of convergence to the density. Since these constants are determined explicitly the results can be extended to families of approximating maps.     

The energy eigenvalues of the Kratzer potential in the presence of a magnetic field

Two dimensional solution of the Schr?dinger equation for the Kratzer potential with and without the presence of a constant magnetic field is investigated within the framework of the asymptotic iteration method. The energy eigenvalues are analytically obtained for the absence of the magnetic field case. However, in the presence of a constant magnetic field, the energy eigenvalues are calculated numerically using the same method. The results obtained by using different Larmor frequencies and potential parameters are compared with the results of the absence of the magnetic field case (ω _L = 0). Effect of the magnetic field on the energy eigenvalues of the Kratzer potential is precisely presented.     

On the Formation of Nanostructures from Stilbazolium-like Dyes

Nanostructures with well-defined shape and highly monodisperse size were fabricated from model stilbazolium-like dyes with specific molecular structural and conformational characteristics. With the help of absorption and fluorescence optical spectroscopy, the correlated spectroscopy (COSY) and two- dimensional nuclear Overhauser effect spectroscopy (2D NOESY) techniques, along with X-ray diffraction (XRD) measurement, distinctively different aggregation processes of the model molecules are demonstrated. For model dye molecule with linear donor–π system–acceptor (D–π–A) structure, strong D–A pair, and planar conformation, specific intermolecular interaction was identified and special crystal structures as well as spectral properties were observed. For model dye molecules bearing nonlinear D–π–A–π–D structure, weak D–A pair but actual amphiphilic characteristics, a special aggregation process was confirmed and a focused size distribution of the produced nanostructures was obtained.     

Stimulated scattering and wavefront conjugation in an inhomogeneous plasma

In the context of the problem of stimulated scattering we discuss the mechanism of wavefront conjugation in an inhomogeneous plasma proposed relatively recently, associated with a difference in suppression of scattering (due to inhomogeneities) for the inverted and uninverted components. We analyze the solutions of the integro-differential equations describing this process both numerically and analytically for different sound attenuation lengths (v ⁻¹). It is shown that for this effect to exist it is necessary that n not be too small. We also consider extinction of the inverted wave in terms of this mechanism. Zh. éksp. Teor. Fiz. 113, 168–180 (January 1998)     

Fano resonances in stubbed quantum waveguides with impurities

We consider T–shaped, two–dimensional quantum waveguides containing attractive or repulsive impurities with a smooth, realistic shape, and study how the resonance behavior of the total conductance depends upon the strength of the defect potential and the geometry of the device. The resonance parameters are determined locating the relevant S–matrix poles in the Riemann energy surface. The total scattering operator is obtained from the S–matrices of the various constituent segments of the device through the –product composition rule. This allows for a numerically stable evaluation of the scattering matrix and of the resonance parameters.     

Self-Imaging Effect Based on Airy Beams with Quadratic Phase Modulation

The self-imaging effect based on Airy beams with quadratic phase modulation (QPM) in 1 + 1 and 2 + 1 dimensions is studied both numerically and analytically. It is demonstrated that, in spite of spatial spectral shape being kept invariant, both the intensity pattern and the accelerating trajectory of this self-imaging effect depend considerably on the QPM. When the QPM parameter is negative, the self-imaging accelerating wave exhibits deceleration and then acceleration, and the self-imaging scope can be expanded. In the opposite case, the self-imaging extent would be narrowed and the self-imaging accelerating wave will only accelerate during propagation. Numerical simulations agree with the theoretical results very well. This study shows the possibility of controlling the self-imaging effect based on 1D and circular Airy beams, by purposely choosing appropriate QPM parameters.     

Ferromagnetic resonance in multilayer [Fe/Cr]n structures with noncollinear magnetic ordering

The excitation spectrum in an [Fe/Cr]n multilayer structure with non-collinear magnetic ordering was studied by the ferromagnetic resonance (FMR) method in the frequency interval 9.5–37 GHz at room temperature. Besides an acoustic branch, several additional modes were observed under parallel excitation of resonance. The FMR spectrum was calculated analytically in a biquadratic exchange model, neglecting in-plane anisotropy, for an infinite number of layers in the structure and numerically for a finite number of layers contained in real samples. It was shown that the observed modes correspond to excitation of standing spin waves with wave vectors perpendicular to the film plane. Pis’ma Zh. éksp. Teor. Fiz. 67, No. 9, 690–695 (10 May 1998)     

The characterization of electroplex generated from the interface between 2-(4-trifluoromethyl-2-hydroxyphenyl)benzothiazole] zinc and N,N′-diphenyl-N,N′- bis(1-naphthyl)-(1,1′-biphenyl)-4,4′-diamine

The electroplex between (2-(4-trifluoromethyl-2-hydroxyphenyl)benzothiazole) zinc [Zn(4-TfmBTZ)₂] as an electron-acceptor and N,N′-diphenyl-N,N′-bis(1-naphthyl)-(1,1′-biphenyl)-4,4′-diamine (NPB) as an electron-donor was characterized by bilayer, blend, and multilayer quantum-well (MQW) device, respectively. The blend composition and quantum-well number are effective parameters for tuning electroluminescence color. White light with high color purity and color rendering index (CRI) was observed from these devices based on Zn(4-TfmBTZ)₂/NPB. Moreover, the blend and MQW devices all exhibit high operation stability, hence excellent color stability. For the device with 5 mol% NPB in blend layer, its Commission International Del’Eclairage (CIE) coordinate region is x=0.28–0.31, y=0.33–0.35 and CRI is 83.3–91.2 at 5–9 V. For MQW structure device with NPB of 60 nm thickness, its CIE coordinate region is x=0.29–0.32, y=0.31–0.34 and CRI=87.9–92.5 at 10–15 V. Such high color stability and purity and CRI, being close to ideal white light, are of current important for white OLED.     

Analysis of shape isomer yields of <Superscript><Emphasis Type="Bold">237</Emphasis></Superscript>Pu in the framework of dynamical–statistical model

Data on shape isomer yield for α + ²³⁵U reaction at E_a ^lab =   E_\alpha ^{\rm lab} =\,\,20–29 MeV are analysed in the framework of a combined dynamical–statistical model. From this analysis, information on the double humped fission barrier parameters for some Pu isotopes has been obtained and it is shown that the depth of the second potential well should be less than the results of statistical model calculations.     

Sub-poissonian light in third-harmonic generation: Quantum predictions via classical trajectories

Sub-Poissonian light in the third-harmonic generation process is studied numerically and analytically. Special regime exhibiting the time-stable maximum sub-Poissonian behaviour with the Fano factorF ≈ 0.81 is found and analyzed. Theoretical prediction of the Fano factor and explanation of the extraordinary time stability of the sub-Poissonian behaviour are given using the semiclassical method of classical trajectories.     

Water vapor overtones pressure line broadening and shifting measurements

By using a spectrometer having as source a commercial etherostructure Al _x Ga_{1 − x} As diode laser operating in “free-running mode”, line shape parameters of some water vapor ro-vibrational overtones at 820–830 nm have been measured at room temperature. These weak absorption lines have been detected by using the wavelength modulation spectroscopy technique with second-harmonic detection. The broadening and shifting coefficients have been obtained by fitting the collected second-harmonic absorption features while varying the pressure of different foreign gases.     

Spectrofluorimetric Determination of Oxamniquine in Dosage Forms and Spiked Human Plasma through Derivatization with 1-dimethylaminonaphthalene-5-sulphonyl chloride

A sensitive, simple and selective spectrofluorimetric method was developed for the determination of oxamniquine (OXM) in pharmaceutical formulations and biological fluids. The method is based on the reaction between the drug and 1-dimethylaminonaphthalene-5-sulphonyl chloride (dansyl chloride) in presence of 0.5 M sodium carbonate (pH 10) to yield a highly fluorescent derivative that is measured at 445 nm after excitation at 335 nm. The different experimental parameters affecting the development and stability of the reaction product were carefully studied and optimized. The fluorescence concentration plot was rectilinear over the range of 0.02–0.2 μg ml⁻¹ with a lower detection limit (LOD) of 0.007 μg ml⁻¹ and limit of quantitation (LOQ) of 0.02 μg ml⁻¹. The proposed method was successfully applied to the analysis of commercial capsules. The results obtained were in good agreement with those obtained using the official spectrophotometric method. Furthermore, the method was applied for the determination of oxamniquine in spiked human plasma, the mean % recovery (n = 4) is 97.77 ± 1.19. A proposal of the reaction pathway was presented.     

Soliton-magnon scattering in a two-dimensional isotropic magnetic material

We use the generalized σ-model to analytically study the solution of the problem of magnon scattering in two-dimensional isotropic ferromagnets and antiferromagnets in the presence of a Belavin-Polyakov soliton. We obtain the exact analytical solution to this problem for the partial mode with the azimuthal quantum number m=1. The scattering amplitude for other values of m (i.e., values not equal to unity) are studied analytically in the long-and short-wavelength approximations and also numerically for an arbitrary value of the wave number. We establish the general laws governing the soliton-magnon interaction. For a magnetic material of finite dimensions we calculate the frequencies of the magnon modes. We also use the data on local modes to derive the equations of motion of the soliton. Finally, we calculate the low-temperature (long-wavelength) asymptotic behavior of the magnon density of states due to the soliton-magnon interaction. Zh. éksp. Teor. Fiz. 116, 1091–1114 (September 1999)