Difference of Mutant Knot Invariants and Their Differential Expansion

JETP Letters - We evaluate the differences of HOMFLY-PT invariants for pairs of mutant knots colored with representations of SL(N), which are large enough to distinguish between them. These mutant...     

Dissipative dynamics of fission in the framework of asymptotic expansion of Fokker-Planck equation

The dynamics of fission has been formulated by generalising the asymptotic expansion of the Fokker-Planck equation in terms of the strength of the fluctuations where the diffusion coefficients depend on the stochastic variables explicitly. The prescission neutron multiplicities and mean kinetic energies of the evaporated neutrons have been calculated and compared with the respective experimental data over a wide range of excitation energy and compound nuclear mass. The mean and the variance of the total kinetic energies of the fission fragments have been calculated and compared with the experimental values. Received: 8 September 1999 / Revised version: 22 November 1999     

Derivations with power central values on Lie ideals in prime rings

Let R be a prime ring of char R ≠ 2 with a nonzero derivation d and let U be its noncentral Lie ideal. If for some fixed integers n ₁ ⩾ 0, n ₂ ⩾ 0, n ₃ ⩾ 0, (u ⁿ¹ [d(u), u]u ⁿ²) ⁿ³ ∈ Z(R) for all u ∈ U, then R satisfies S ₄, the standard identity in four variables.     

Imaging characteristics of a birefringent lens under broadband illumination

This paper reports the imaging characteristics of an optical system consisting of a lens made of a uniaxial birefringent crystal sandwiched between two linear polarizers under polychromatic input illumination. The optic axis of the birefringent crystal is perpendicular to the lens axis and for an initial investigation, the spectral profile of the input beam is considered to be uniform for all wavelengths. The study reveals that if the variation of the birefringence parameters of the device with the wavelength is less, a larger bandwidth may be used without considerably deviating from the imaging characteristics under strictly monochromatic illumination. The nonlinear variation of birefringence with wavelength results in an asymmetric axial irradiance distribution. This obviates an optimal operating wavelength as well as a proper choice of the lens material. It is found that no appreciable change in image quality under diffraction-limited condition results for an input beam having 632 nm operating wavelength and 60 nm bandwidth. Therefore, it may be feasible to use this system with a white light source in conjunction with a wavelength-selective filter.     

Stress relaxation in a perfect nanocrystal by coherent ejection of lattice layers

We show that a small crystal trapped within a potential well and in contact with its own fluid responds to large compressive stresses by a novel mechanism--the transfer of complete lattice layers across the solid-fluid interface. Further, when the solid is impacted by a momentum impulse set up in the fluid, a coherently ejected lattice layer carries away a definite quantity of energy and momentum, resulting in a sharp peak in the calculated phonon absorption spectrum. Apart from its relevance to studies of stability and failure of small sized solids, such coherent nanospallation may be used to make atomic wires or monolayer films.     

New Characterization of Stochastic Resonance in Bistable Square Potential Well

The features of first passage time density function is analysed theoretically in a symmetric double square well system modulated periodically with a signal of arbitrary amplitude and frequency. Resonance is demonstrated as a maximum synchronization between periodic signal and noise. Resonance is characterized as a linear relation between noise strength at resonance and frequency. This characterization is shown to hold good for amplitude lesser or greater than the depth of the unmodulated potential well. The mean first passage time of the process at resonance is also shown to decrease linearly with the strength of the noise for high amplitude of the signal while it increases linearly with inverse of the noise strength for low amplitude.     

Raman and Photoluminescence Spectroscopic Detection of Surface‐Bound Li+O2− Defect Sites in Li‐Doped ZnO Nanocrystals Derived from Molecular Precursors

We present a detailed study of Raman spectroscopy and photoluminescence measurements on Li‐doped ZnO nanocrystals with varying lithium concentrations. The samples were prepared starting from molecular precursors at low temperature. The Raman spectra revealed several sharp lines in the range of 100–200 cm^?1, which are attributed to acoustical phonons. In the high‐energy range two peaks were observed at 735 cm^?1 and 1090 cm^?1. Excitation‐dependent Raman spectroscopy of the 1090 cm^?1 mode revealed resonance enhancement at excitation energies around 2.2 eV. This energy coincides with an emission band in the photoluminescence spectra. The emission is attributed to the deep lithium acceptor and intrinsic point defects such as oxygen vacancies. Based on the combined Raman and PL results, we introduce a model of surface‐bound LiO₂ defect sites, that is, the presence of Li⁺O₂^? superoxide. Accordingly, the observed Raman peaks at 735 cm^?1 and 1090 cm^?1 are assigned to Li? O and O? O vibrations of LiO₂.     

Determinations of low atomic number elements in real uranium oxide samples using vacuum chamber total reflection x‐ray fluorescence

Conditions for the total reflection x‐ray fluorescence (TXRF) analysis of real uranium samples for low atomic number elements using vacuum chamber TXRF spectrometer were optimized. It was observed that for analysis of low atomic number elements, almost complete removal of uranium matrix is required. Two certified reference materials of uranium containing trace elements in different concentrations were dissolved in minimum amount of high purity nitric acid. The uranium matrix from these solutions was separated by solvent extraction using tri‐n‐butyl phosphate as extracting reagent. Low atomic number elements in TXRF spectrum of the aqueous phase could be seen only after six tri‐n‐butyl phosphate equilibrations in extraction. The TXRF determinations of the certified low atomic number elements Mg and Al were made in these aqueous solutions after addition of Sc as an internal standard. The TXRF determined values for Mg were in good agreement with the certified values, whereas TXRF determined Al values differed from the certified values appreciably, probably due to the interference of Al Kα peak with escape peak of U Mα and the neighboring Si Kα peak. Copyright © 2013 John Wiley & Sons, Ltd.