Optical implementation of scale invariant fractional Fourier transform of continuously variable orders with a two-lens system

A simple two ordinary lens system is proposed to realize the fractional Fourier transform (FRT) of continuously variable order while keeping the scaling factors of both the input and output functions as the same constant independent of the geometric parameters of the system and the FRT orders. It can remove the necessity and inconvenience of using input masks of different scales or any other special devices, and then is helpful to those who want to observe the FRT but have no specific facilities.     

Measuring persistence in a stationary time series using the complex network theory

A growing interest exists currently in the analysis of time series by the complex network theory. Here we present a simple and quick way for mapping time series to complex networks. Using a simple rule allows us to transform time series into a textual sequence then we divide it into words with fixed size. Distinct words are nodes of the network, and we have complete control on the network scale by adjusting the word size. Two nodes are linked if their associated words co-occur in sequence. We show that the network topological measures quantify the persistence and the long range correlations in fractional Brownian processes. For a particular word size we assume some relations between the topological measures and the Hurst exponent which characterised the persistence in fractional Brownian processes.     

Magnetoquantum de Haas-van Alphen oscillations in spin-split two-dimensional Fermi liquid

Theory of magnetoquantum oscillations with spin-split structure in strongly anisotropic (two-dimensional (2D)) metal is developed in the formalism of level approach. Parametric method for exact calculation of oscillations wave forms and amplitudes, developed earlier for spin degenerate levels is generalized on a 2D electron system with spin-split levels. General results are proved: 1) proportionality relation between magnetization and chemical potential oscillations accounting for spin-split energy levels and magnetic field unperturbed levels (states of reservoir), 2) basic equation for chemical potential oscillations invariant to various models of 2D and 1D energy bands (intersecting or overlapping) and localized states. Equilibrium transfer of carriers between overlapping 2D and 1D bands, characterizing the band structure of organic quasi 2D metals, is considered. Transfer parameter, calculated in this model to be of the order of unity, confirms the fact that the wave form of oscillations in organic metals should be quasisymmetric up to ultralow temperature. Presented theory accounts for spin-split magnetization oscillations at magnetic field directions tilted relative to the anisotropic axis of a metal. Theoretical results are compared with available experimental data on organic quasi-2D metal α-(BEDT-TTF)₂KHg(SNC)₄ explaining the appearance of clear split structure under the kink magnetic field and absence above by the corresponding change in the electron g-factor rather than cyclotron mass. Received 20 December 2000 and Received in final form 13 July 2001     

Optical asymmetric watermarking using modified wavelet fusion and diffractive imaging

In most of the existing image encryption algorithms the generated keys are in the form of a noise like distribution with a uniform distributed histogram. However, the noise like distribution is an apparent sign indicating the presence of the keys. If the keys are to be transferred through some communication channels, then this may lead to a security problem. This is because; the noise like features may easily catch people׳s attention and bring more attacks. To address this problem it is required to transfer the keys to some other meaningful images to disguise the attackers. The watermarking schemes are complementary to image encryption schemes. In most of the iterative encryption schemes, support constraints play an important role of the keys in order to decrypt the meaningful data. In this article, we have transferred the support constraints which are generated by axial translation of CCD camera using amplitude-, and phase- truncation approach, into different meaningful images. This has been done by developing modified fusion technique in wavelet transform domain. The second issue is, in case, the meaningful images are caught by the attacker then how to solve the copyright protection. To resolve this issue, watermark detection plays a crucial role. For this purpose, it is necessary to recover the original image using the retrieved watermarks/support constraints. To address this issue, four asymmetric keys have been generated corresponding to each watermarked image to retrieve the watermarks. For decryption, an iterative phase retrieval algorithm is applied to extract the plain-texts from corresponding retrieved watermarks.     

Optimized t-expansion method for the Rabi Hamiltonian

A polemic arose recently about the applicability of the t-expansion method to the calculation of the ground state energy E₀ of the Rabi model. For specific choices of the trial function and very large number of involved connected moments, the t-expansion results are rather poor and exhibit considerable oscillations. In this Letter, we formulate the t-expansion method for trial functions containing two free parameters which capture two exactly solvable limits of the Rabi Hamiltonian. At each order of the t-series, E₀ is assumed to be stationary with respect to the free parameters. A high accuracy of E₀ estimates is achieved for small numbers (5 or 6) of involved connected moments, the relative error being smaller than ¹⁰−4 (0.01%) within the whole parameter space of the Rabi Hamiltonian. A special symmetrization of the trial function enables us to calculate also the first excited energy E₁, with the relative error smaller than ¹⁰−2 (1%).     

Theoretical calculation of electron impact widths and shifts of XeII lines

Summary The shifts and widths of prominent XeII transitions are calculated in the semi-empirical approach; a very good agreement with experimental values is obtained. The oscillator strengths were calculated using complete intermediate coefficients after energy matrix diagonalization. The author of this paper has agreed to not receive the proofs for correction.     

Generating synthetic time series from Bak-Sneppen co-evolution model mixtures

The Bak-Sneppen model of co-evolution is used to derive synthetic time series with a priori specified fractal dimension (or Hurst exponent) through a mixing of processes in various lattice dimensions. Both theoretical and numerical analyses concern the avalanches at the critical threshold and provide a model for time series reconstruction that can be tested as an alternative to the classical fractional Brownian motion (fBm) because of differences in properties. New results on critical threshold and avalanche structure are obtained up to Euclidean dimension d=6. The method involves a lattice-based structure and therefore is suitable for the application of parallel computing.     

Fractional Fourier transform of an elliptical dark-hollow beam

The fractional Fourier transform (FRT) of an elliptical dark-hollow beam (EDHB) is studied in detail. Based on the definition of FRT in the rectangular coordinate system, analytical formulae are derived for the FRT of an EDHB with the help of a tensor method. The properties of an EDHB in the FRT plane are illustrated numerically by use of the derived formulae. The results show that the properties of the EDHB in the FRT plane are closely related to the parameters of the beam and to the fractional order. The derived formula provides a convenient way for analyzing and calculating the FRT of an EDHB.     

The AΠu state of : Electric properties, fine and hyperfine coupling constants, and magnetic moments (g-factors). A theoretical study

Several properties are calculated for A²Π_u of —the majority for the first time—including electric and magnetic moments, and fine/hyperfine structure (fs/hfs) parameters. The new results are compared with our previous ones for X² and B² of [P.J. Bruna, F. Grein, J. Mol. Spectrosc. 227 (2004) 67–80]. The electric quadrupole Θ and hexadecapole Φ moments, polarizability α, and hfs constants a, b, c, d, eQq₀, eQq₂ are evaluated at the density functional theory (DFT) level [B3LYP/aug-cc-pVQZ]. The fs constants (spin–orbit coupling A_Π, Λ-doubling p, q, spin-rotation γ_Π), and magnetic moments (g-factors) are obtained via 2nd-order sum-over-states expansions, using wavefunctions and matrix elements obtained with a multireference configuration interaction (MRDCI) method, and the Breit–Pauli Hamiltonian. At equilibrium, 2nd-order properties of A²Π_u are dominated by its coupling with B². For the A state, two independent components are reported for traceless tensor properties (multipoles Θ and Φ; hfs parameters c/d and q₀/q₂) and three for traced properties (polarizability α and g-factors), i.e., one more component than for axially symmetric Σ states. The currently available experimental data on — limited to A_Π, p, and q—are well reproduced by our theoretical results.