Bifurcation of periodic solutions to variational inequalities in R κ based on Alexander-Yorke theorem

Variational inequalities are studied, where K is a closed convex cone in , 3, B is a × matrix, G is a small perturbation, a real parameter. The assumptions guaranteeing a Hopf bifurcation at some ₀ for the corresponding equation are considered and it is proved that then, in some situations, also a bifurcation of periodic solutions to our inequality occurs at some _{I 0}. Bifurcating solutions are obtained by the limiting process along branches of solutions to penalty problems starting at ₀ constructed on the basis of the Alexander-Yorke theorem as global bifurcation branches of a certain enlarged system.     

Optical constants of thin oxide films on titanium

Thin oxide films on titanium formed by heating were studied by the ellipsometric method. To obtain the complex refractive index and film thicknesses, the ellipsometric measurements were performed by means of the immersing method: each sample was measured first in air and then in a liquid of known refractive index (in our case CCl₄). The optical constants and the oxide film thickness were computed by means of a computer from two pairs of ellipsometric values. To state the optical constants of clean titanium surface the graphic-computational method was proposed and applied. The measurements were carried out at two wavelengths on oxide films grown in air and dry oxygen by thermal oxidation at temperatures from 150 to 700 °C. It has been shown that when increasing the film thickness the refractive index of the film decreases, whereas the absorption coefficient is independent on the film thickness. Optical constants of oxide films growing in dry oxygen are smaller than those growing in air.     

The K-Quotient

The Rayleigh Quotient and a recently proposed Timoshenko Quotient [1] are upper bounds to the fundamental eigenvalue of a discrete dynamic system. The closeness of these upper bounds to the fundamental eigenvalue depends on the closeness of the trial vectors to the eigenmode used in the calculation. In the present paper, a new quotient is presented. This quotient does not require the closeness of the trial vector to the eigenmode and its accuracy is improvable by raising the numerical value of the parameter p.     

d-d excitations in manganites probed by resonant inelastic x-ray scattering

We report a study of electronic excitations in manganites exhibiting a range of ground states, using resonant inelastic x-ray scattering (RIXS) at the Mn K edge. Excitations with temperature dependent changes correlated with the magnetism were observed as high as 10 eV. By calculating Wannier functions, and finite-q response functions, we associate this dependence with intersite d-d excitations. The calculated dynamical structure factor is found to be similar to the RIXS spectra.     

Deeply penetrating photoacoustic tomography in biological tissues enhanced with an optical contrast agent

Photoacoustic tomography (PAT) in a circular scanning configuration was developed to image deeply embedded optical heterogeneity in biological tissues. While the optical penetration was maximized with near-infrared laser pulses of 800-nm wavelength, the optical contrast was enhanced by Indocyanine Green (ICG) dye whose absorption peak matched the laser wavelength. This optimized PAT was able to image objects embedded at depths of as much as 5.2 cm, 6.2 times the 1/e optical penetration depth, in chicken breast muscle at a resolution of <780 microm and a sensitivity of <7 pmol of ICG in blood. The resolution was found to deteriorate slowly with increasing imaging depth. The effects of detection bandwidth on the quality of images acquired simultaneously by four different ultrasonic transducers are described.     

Waveform preservation of the backscattered stimulated Brillouin scattering wave by using a prepulse injection

We have found that it is possible to preserve the temporal waveform of the reflected wave generated from stimulated Brillouin scattering (SBS) by using a prepulse technique. The waveform of the SBS wave usually shows a steep rising edge in the ordinary SBS process. It has been found that the waveform of the reflected wave depends on both the prepulse energy and the time delay between the main pulse and the prepulses. A prepulse energy of 5 mJ and a time delay of 5 ns have been measured to be the optimum values under the experimental conditions. This prepulse method is useful in developing a multistage system employing several SBS cells in series for high-power laser applications.     

Spin and orbital magnetic moments of Fe3O4

We present measurements of the spin and orbital magnetic moments of Fe3O4 by using SQUID and magnetic circular dichroism in soft x-ray absorption. The measurements show that Fe3O4 has a noninteger spin moment, in contrast to its predicted half-metallic feature. Fe3O4 also exhibits a large unquenched orbital moment. Calculations using the local density approximation including the Hubbard U method and the configuration interaction cluster-model suggest that strong correlations and spin-orbit interaction of the 3d electrons result in the noninteger spin and large orbital moments of Fe3O4.     

Structure,transport and magnetic properties of the double perovskite (Ca<Subscript>2-2x</Subscript>Sr<Subscript>2x</Subscript>)FeMoO<Subscript>6</Subscript>

In this paper we report the results of a detailed investigation of the double perovskite (Ca_2-2xSr_2x)FeMoO₆ system. Chemical size effects on structural, electrical, and magnetic properties caused by the substitution of isovalent, larger Sr ions into the smaller Ca sites, resulting in (Ca_2-2xSr_2x)FeMoO₆, have been examined. The compounds crystallize in the monoclinic space group P2₁/n for 0.0x<0.2, the orthorhombic space group Pbnm for 0.2x<0.4, and the tetragonal space group I4/m and I4/mmm for x0.4. Examination of the resistivity of all compounds reveals a metallic behavior which is well described by a Tⁿ dependence except for x=1.0. These n values change from 1 to 2 as T decreases lower than T_c. This is indicative of a variation in the transport mechanism at T_c. The ferrimagnetic transition temperature T_c increases with increasing x from 318 (x=0.0) to 393 K (x=1.0). For all samples, the saturation magnetization at 82 K obeys M_s3.5_B/(formula unit), compared to a theoretical spin-only moment of 4_B/(formula unit) for a perfectly ordered compound. PACS 74.25.Fy; 74.25.Ha