Third-order optical harmonic coefficients of atomic hydrogen at low frequencies

The analytical expression is derived for the third-order optical harmonic coefficients χ⁽³⁾₁₁₁₁ (ω, ω, ω) = χ⁽³⁾₂₂₂₂ (ω, ω, ω) = χ⁽³⁾₃₃₃₃ (ω, ω, ω) of the atomic hydrogen at very low frequencies ω → 0.     

New extragradient methods for solving variational inequality problems and fixed point problems

In this paper, we introduce two new iterative algorithms for finding a common element of the set of fixed points of a quasi-nonexpansive mapping and the set of solutions of the variational inequality problem with a monotone and Lipschitz continuous mapping in real Hilbert spaces, by combining a modified Tseng’s extragradient scheme with the Mann approximation method. We prove weak and strong convergence theorems for the sequences generated by these iterative algorithms. The main advantages of our algorithms are that the construction of solution approximations and the proof of convergence of the algorithms are performed without the prior knowledge of the Lipschitz constant of cost operators. Finally, we provide numerical experiments to show the efficiency and advantage of the proposed algorithms.     

A remark on semi-stable fibrations over P 1 in positive characteristic

We prove a lower bound for the number of singular fibres of a non-isotrivial semi-stable family of curves over the projective line, in positive characteristic. The result is the same obtained previously by Beauville in characteristic zero, namely that the number is at least 4. Furthermore some consequences are discussed in the case that the number is exactly 4.     

Stability radii for some propagation models

The simple idea of Hinrichsen & Pritchard who defined thestructured stability radius has proved to be unexpectedly fruitful,generating a large amount of work and making interesting connections.The aim of this paper is twofold: to study stability radii forsome specific propagation models and to make connections withresults on Popov-type frequency-domain stability inequalities.     

Hypersingular integral operators along surfaces

In this note, we estimate the boundedness for singular integral operators along curves and surfaces with highly singular kernels.     

Preparation, structural analysis and dielectric properties of Bi x La1−x FeO3 perovskite

Rare earth element substituted bismuth ferrites (BiFeO₃) are of enormous importance as magnetoelectric materials. The polycrystalline samples of Bi _x La_1−x FeO₃ (x=0, 0.2, 0.4, 0.6, 0.8) were prepared by solid-state reaction using standard ceramic method. The single-phase formation of these compounds was confirmed by X-ray diffraction (XRD) studies. The samples with x=0, 0.2, 0.4, 0.6 are found to be orthorhombic while the sample with x=0.8 is triclinic. The dielectric constant (ε′) and dissipation factor (tan δ) were measured in the frequency range 100 Hz to 1 MHz at room temperature and as a function of temperature at certain fixed frequencies (1 kHz, 10 kHz, 100 kHz, 1 MHz). All the samples showed dielectric dispersion. The dielectric constant with temperature shows a broad peak; the peak temperature shifts with frequency which reflects the relaxor-type behavior. The peak above 600 K in the measured temperature range corresponds to antiferromagnetic ordering temperature (Néel temperature). The broadness of the peak changes with composition. The ac conductivity as well as ε′ are found to be maximum for the sample x=0.2 at room temperature.     

Magnetoelectric effect in cobalt ferrite-barium titanate composites and their electrical properties

CoFe₂O₄-BaTiO₃ composites were prepared using conventional ceramic double sintering process with various compositions. Presence of two phases in the composites was confirmed using X-ray diffraction. The dc resistivity and thermoemf as a function of temperature in the temperature range 300 K to 600 K were measured. Variation of dielectric constant (ɛ′) with frequency in the range 100 Hz to 1 MHz and also with temperature at a fixed frequency of 1 kHz was studied. The ac conductivity was derived from dielectric constant (ɛ′) and loss tangent (tan δ). The nature of conduction is discussed on the basis of small polaron hopping model. The static value of magnetoelectric conversion factor has been studied as a function of magnetic field.     

Interband electronic Raman scattering of polarized light in cubic semiconductors with degenerate valence bands

The cross-sections are calculated for the Raman scattering processes with polarized light in cubic semiconductors whose valence band top is fourfold degenerate γ₈. The exciton effect is taken into account.