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In Fourier transform profilometry (FTP), we must restrain spectrum overlapping caused by the nonlinearity of the charge coupled device (CCD) and increase the measurement accuracy of the object shape. Firstly, the causes of producing higher-order spectrum components and inducing spectrum overlapping are analysed theoretically, and a simple physical explanation and analytical deduction are given. Secondly, aiming to suppress spectrum overlapping and improve measurement accuracy, the influence of spatial carrier frequency of projection grating on them is analysed. A method of increasing the spatial carrier frequency of projection grating to restrain or reduce the spectrum overlapping significantly is proposed. We then analyze the mechanism of how the spectrum overlapping is reduced. Finally, the simulation results and experimental measurements verify the correction of the proposed theory and method. [ABSTRACT FROM AUTHOR]

The angular distribution of CH3I is investigated experimentally using a single Fourier transform-limited laser pulse and a pulse train, where a 90-fs 800-nm linearly polarized laser field with a moderate intensity of 2.8×1013 W/cm2 is used. The dynamic alignment is demonstrated in a single pulse experiment. Moreover, a pulse train is used to optimize the molecular alignment, and the alignment degree is almost identical to that with the single pulse. The results are analysed by using chirped femtosecond laser pulses, and it demonstrates that the structure of pulse train rather than its effective duration is crucial to the molecular alignment. [ABSTRACT FROM AUTHOR]

Photoacoustic computed tomography (PACT), also known as optoacoustic tomography, is an emerging imaging modality that has great potential for a wide range of biomedical imaging applications. In this note, we derive a hybrid reconstruction formula that is mathematically exact and operates on a data function that is expressed in the temporal frequency and spatial domains. This formula explicitly reveals new insights into how the spatial frequency components of the sought-after object function are determined by the temporal frequency components of the data functionmeasured with a circular or spherical measurement geometry in two- and three-dimensional implementations of PACT, respectively. The structure of the reconstruction formula is surprisingly simple compared with existing Fourier-domain reconstruction formulae. It also yields a straightforward numerical implementation that is robust and two orders ofmagnitude more computationally efficient than filtered backprojection algorithms. [ABSTRACT FROM AUTHOR]

Linear response laws and causality (the effect cannot precede the cause) are of fundamental importance in physics. In the context of classical electrodynamics, students often have a difficult time grasping these concepts because the physics is obscured by the intermingling of the time and frequency domains. In this paper, we analyse the linear response laws and causality in the time and frequency domains with the aim of pedagogical clarity. We will show that it is easy to violate causality in the frequency domain by making a vanishing absorption approximation. Furthermore, we will show that there can be subtle differences between Fourier transformingMaxwell equations and using a monochromatic source function. We discuss how these concepts can be obscured and offer some suggestions to improve the situation. [ABSTRACT FROM AUTHOR]

Directly driven ablative Rayleigh-Taylor (R-T) instability of modulated CH targets was studied using the faceon X-ray radiography on the Shen-Guang II device. We obtained temporal evolution images of the R-T instability perturbation. The R-T instability growth factor has been obtained by using the methods of fast Fourier transform and seeking the difference of light intensity between the peak and the valley of the targets. Through comparison with the the theoretical simulation, we found that the experimental data had a good agreement with the theoretical simulation results before 1.8 ns, and was lower than the theoretical simulation results after that. [ABSTRACT FROM AUTHOR]

The reflecting of a single attosecond pulse from a periodic Mo/Si multilayer was investigated. By changing the number of bi-layers, the periodic multilayer showed greatly different spectral and temporal responses of the attosecond pulse reflection, which has been discussed in detail in this paper. The capability of attosecond pulse reflection of the periodic multilayers with different bi-layer numbers has been evaluated using suitable temporal parameters. In addition, the condition for obtaining high-efficiency reflected pulses has been analyzed by comparing the pulse responses of the periodic multilayer with different layers. The transfer-matrix method together with the fast Fourier transform has been used in our simulation. [ABSTRACT FROM AUTHOR]

The generator coordinatemethod in the Gaussian overlap approximation (GOA) is applied to a description of the nuclear quadrupole collective states. The full five-dimensional quadrupole tensor is used as a set of the generator coordinates. The integral Hill-Wheeler equation is reduced to a differential equation by using the Fourier transforms of the overlap and energy kernels. The differential Bohr Hamiltonian obtained this way is compared with that derived by the usual approach to the collective Hamiltonian in the GOA which does contain an additional approximation. The method of calculating the quantities which determine the Bohr Hamiltonian from the set of deformation-dependent intrinsic states is demonstrated. In particular, it appears that the moments of inertia at the quadrupole rotations are of the Yoccoz type. [ABSTRACT FROM AUTHOR]

Propagation into the far field changes initialwaves into their Fourier transforms. This implies that the Riemann zeros could be observed experimentally in the radiation pattern generated by an initial wave whose Fourier transform is proportional to the Riemann zeta function on the critical line. Two such waves are examined, generating the Riemann &b.Xi;(t) function (pattern 1) and the function ζ (1/2 + it)/(1/2 + it) (pattern 2). For pattern 1, the radiation side lobes are probably too weak to allow detection of the zeros, but for pattern 2 the lobes are stronger, suggesting a feasible experiment. [ABSTRACT FROM AUTHOR]

We provide (partial) reconstruction formulas and discrete Fourier transforms for wavefunctions in standard Fock-Bargmann (holomorphic) phase-number representation from a finite number N of phase samples {&thetas;k = 2πk/N}N-1 k=0 for a given mean number p of particles. The resulting coherent state subsystem S = {|zk = p1/2 ei&thetas;k 〉} is complete (a frame) for truncated Hilbert spaces (finite number of particles) and reconstruction formulas are exact. For an unbounded number of particles, S is 'almost complete' (a pseudo-frame) and partial reconstruction formulas are provided along with a study of the accuracy of the approximation, which tends to be exact when p < N and/or N →∞. [ABSTRACT FROM AUTHOR]

We consider the Fourier transform of tubular volume densities, with arbitrary axial geometry and (possibly) twisted internal structure. This density can be used to represent, among others, magnetic flux or the electron density of biopolymer molecules. We consider tubes of both finite radii and unrestricted radius. When there is overlap of the tube structure the net density is calculated using the super-position principle. The Fourier transform of this density is composed of two expressions, one for which the radius of the tube is less than the curvature of the axis and one for which the radius is greater (which must have density overlap). This expression can accommodate an asymmetric density distribution and a tube structure which has non-uniform twisting. In addition we give several simpler expressions for isotropic densities, densities of finite radius, densities which decay at a rate sufficient to minimize local overlap and finally individual surfaces of the tube manifold. These simplified cases can often be expressed as arclength integrals and can be evaluated using a system of first-order ODEs. [ABSTRACT FROM AUTHOR]

This paper presents the first observation of geodesic acoustic modes (GAMs) on Tore Supra plasmas. Using the Doppler backscattering system, the oscillations of the plasma flow velocity, localized between r/a = 0.85 and r/a = 0.95, and with a frequency, typically around 10 kHz, have been observed at the plasma edge in numerous discharges. When the additional heating power is varied, the frequency is found to scale with Cs/R. The MUltiple SIgnal Classification (MUSIC) algorithm is employed to access the temporal evolution of the perpendicular velocity of density fluctuations. The method is presented in some detail, and is validated and compared against standard methods, such as the conventional fast Fourier transform method, using a synthetic signal. It stands out as a powerful data analysis method to follow the Doppler frequency with a high temporal resolution, which is important in order to extract the dynamics of GAMs. [ABSTRACT FROM AUTHOR]

We present spatially resolved observations of the canonical transition disk object TW Hya at 8.74 µm, 11.66 µm, and 18.30 µm, obtained with the T-ReCS instrument on the Gemini telescope. These observations are a result of a novel observing mode at Gemini that enables speckle imaging. Using this technique, we image our target with short enough exposure times to achieve diffraction limited images. We use Fourier techniques to reduce our data, which allows high-precision calibration of the instrumental point-spread function. Our observations span two epochs and we present evidence for temporal variability at 11.66 µm in the disk of TW Hya. We show that previous models of TW Hya's disk from the literature are incompatible with our observations and construct a model to explain the discrepancies. We detect marginal asymmetry in our data, most significantly at the shortest wavelengths. To explain our data, we require a model that includes an optically thin inner disk extending from 0.02 to 3.9AU, an optically thick ring representing the outer disk wall at 3.9AU and extending to 4.6AU, and a hotter-than-disk-equilibrium source of emission located at ~3.5AU. [ABSTRACT FROM AUTHOR]

Recently, there have been significant new insights concerning the conditions under which closed systems equilibrate locally. The question of whether subsystems thermalize-if the equilibrium state is independent of the initial state-is, however, much harder to answer in general. Here, we consider a setting in which thermalization can be addressed: a quantum quench under a Hamiltonian whose spectrum is fixed and whose basis is drawn from the Haar measure. If the Fourier transform of the spectral density is small, almost all bases lead to local equilibration to the thermal state with infinite temperature. This allows us to show that, under almost all Hamiltonians that are unitarily equivalent to a local Hamiltonian, it takes an algebraically small time for subsystems to thermalize. [ABSTRACT FROM AUTHOR]

Direct visualization of electronic-structure symmetry within each crystalline unit cell is a new technique for complex electronic matter research (Lawler et al 2010 Nature 466 347-51, Schmidt et al 2011 New J. Phys. 13 065014, Fujita K et al 2012 J. Phys. Soc. Japan 81 011005). By studying the Bragg peaks in Fourier transforms of electronic structure images and particularly by resolving both the real and imaginary components of the Bragg amplitudes, distinct types of intra-unit-cell symmetry breaking can be studied. However, establishing the precise symmetry point of each unit cell in real space is crucial in defining the phase for such a Bragg-peak Fourier analysis. Exemplary of this challenge is the high-temperature superconductor Bi2Sr2CaCu2O8+δ for which the surface Bi atom locations are observable, while it is the invisible Cu atoms that define the relevant CuO2 unit-cell symmetry point. Here we demonstrate, by imaging with picometer precision the electronic impurity states at individual Zn atoms substituted at Cu sites, that the phase established using the Bi lattice produces a ~2%(2π) error relative to the actual Cu lattice. Such a phase assignment error would not diminish reliability in the determination of intra-unitcell rotational symmetry breaking at the CuO2 plane (Lawler et al 2010 Nature 466 347-51, Schmidt et al 2011 New J. Phys. 13 065014, Fujita K et al 2012 J. Phys. Soc. Japan 81 011005). Moreover, this type of impurity atom substitution at the relevant symmetry site can be of general utility in phase determination for the Bragg-peak Fourier analysis of intra-unit-cell symmetry. [ABSTRACT FROM AUTHOR]

Using the Weyl quantization scheme and based on the Fourier slice transformation (FST) of the Wigner operator, we construct a new expansion formula of the density operator ρ, with the expansion coefficient being the FST of ρ's classical Weyl correspondence, and the latter the Fourier transformation of ρ's quantum tomogram. The coordinate- momentum intermediate representation is used as the Radon transformation of the Wigner operator. [ABSTRACT FROM AUTHOR]

A methodology is presented to obtain the basis of qudits which are admissible to quantum Fourier transform (QFT) in the sense that the set of such kets are related by the QFT in the same way as the kets of the computational basis. We first study this method for qubits to characterize the ensemble that works for the Hadamard transformation (QFT for two dimension). In this regard we identify certain incompleteness in the result of Maitra and Parashar (Int. J. Quantum Inform. 4 (2006) 653). Next we characterize the ensemble of qutrits for which QFT is possible. Further, some theoretical results related to higher dimensions are also discussed. Considering the unitary matrix n related to QFT, the issue boils down to the problem of characterizing matrices that commute with n [ABSTRACT FROM AUTHOR]

Experiments to study inward heat transport phenomena have been performed in the Tore Supra tokamak with off-axis electron cyclotron resonance heating (ECRH). Both power balance and perturbation transport analysis have been done for low-frequency (1 Hz) ECRH modulation experiments. Heat diffusivity and heat pinch have been separately determined by fitting the experimental data of the amplitude and phase of the Fourier transform of the modulated temperature with a linear transport model including convection term. Comparison with the critical gradient model has shown that the heat pinch previously obtained could include a pseudo-pinch due to the non-linearity of the diffusivity and an additional non-diffusive heat pinch. The pinch effect is reduced for higher densities. [ABSTRACT FROM AUTHOR]

We investigate the Ramsey fringes of a single electron spin of the nitrogen-vacancy center in diamond with different microwave radiation frequency detunings. The fast Fourier transform demonstrates that the Ramsey fringes consist of three components caused by hyperfine interaction with 14 N nuclear spin, and the Ramsey fringes cannot be well explained without the phase term of the three components, which has not been mentioned before. Each phase is determined by the microwave frequency detuning and the resonant Rabi frequency as well as the π/2 pulse. [ABSTRACT FROM AUTHOR]

The vortex effects of high temperature superconducting (HTS) microstrip resonators have been studied using the theoretical approach developed by Coffey and Clem (CC). A rectangular HTS strip resonator printed on sapphire substrate and subjected to a static magnetic field is considered, where the HTS strip is in the mixed state. An impedance type Green's function is derived which connects the strip current to the electric field around the resonator, in the Fourier transformed domain. Galerkin's procedure is used in the spectral domain to determine the resonant frequency and the unloaded Q value, both of which are computed for different applied fields, reduced temperatures and superconducting strip thicknesses. The results reveal considerable influence of applied field on resonant frequency and quality factor due to vortex motion, which should be considered when designing resonators which operate under external magnetic field. [ABSTRACT FROM AUTHOR]

We study the use of a pair of qubits as a decoherence probe of a nontrivial environment. This dual-probe configuration is modelled by three twolevel systems (TLSs), which are coupled in a chain in which the middle system represents an environmental TLS. This TLS resides within the environment of the qubits and therefore its coupling to perturbing fluctuations (i.e. its decoherence) is assumed much stronger than the decoherence acting on the probe qubits. We study the evolution of such a tripartite system including the appearance of a decoherence-free state (dark state) and non-Markovian behaviour. We find that all parameters of this TLS can be obtained from measurements of one of the probe qubits. Furthermore, we show the advantages of two qubits in probing environments and the new dynamics imposed by a TLS that couples to two qubits at once. [ABSTRACT FROM AUTHOR]

We present the numerical calculations of spin wave dispersions in magnetic nanostructures. The dispersion is obtained by processing the space-time data calculated using the finite difference method based micromagnetic simulations. Various issues related to the calculation of the two-dimensional fast Fourier transform and methods to obtain high-quality dispersion curves are discussed. The spatial profile of the spin wave modes is also presented. The method is validated by applying it to various nanomagnetic systems including magnetic nanostripes, magnetic nanowires and confined thin film elements. Further, we calculate the magnonic dispersions in simple 1D and 2D magnonic crystals based on magnetic anti-dot arrays. [ABSTRACT FROM AUTHOR]

A new kind of four-mode continuous variable coherent-entangled state is proposed in the Fock space by using the technique of integration within an ordered product, which exhibits both the properties of a coherent state and an entangled state, and spans a complete and orthonormal representation. The conjugate state of the four-mode continuous variable coherent-entangled state is derived by using the Fourier transformation. Moreover, a simple experimental protocol of generating a four-mode continuous variable coherent-entangled state is proposed by using beam splitters. As applications of this four-mode continuous variable coherent-entangled state, a four-mode entangled state and a four-mode squeezing-Fresnel operator are constructed. [ABSTRACT FROM AUTHOR]

We demonstrate an x-ray imaging method that combines Fourier transform holography with tomography ('tomoholography') for threedimensional (3D) microscopic imaging. A 3D image of a diatom shell with a spatial resolution of 140 nm is presented. The experiment is realized by using a small gold sphere as the reference wave source for holographic imaging. This setup allows us to rotate the sample and to collect a number of 2D projections for tomography. [ABSTRACT FROM AUTHOR]

We present here an overview of the Fourier-transform scanning tunnelling spectroscopy technique (FT-STS). This technique allows one to probe the electronic properties of a two-dimensional system by analysing the standing waves formed in the vicinity of defects. We review both the experimental and theoretical aspects of this approach, basing our analysis on some of our previous results, as well as on other results described in the literature. We explain how the topology of the constant-energy maps can be deduced from the FT of dI /dV map images which exhibit standing waves patterns. We show that not only the position of the features observed in the FT maps but also their shape can be explained using different theoretical models of different levels of approximation. Thus, starting with the classical and well known expression of the Lindhard susceptibility which describes the screening of electron in a free electron gas, we show that from the momentum dependence of the susceptibility we can deduce the topology of the constant-energy maps in a joint-density-of-states approximation (JDOS). We describe how some of the specific features predicted by the JDOS are (or are not) observed experimentally in the FT maps. The role of the phase factors which are neglected in the rough JDOS approximation is described using the stationary-phase conditions. We present also the technique of the T -matrix approximation, which accurately takes into account these phase factors. This technique has been successfully applied to normal metals, as well as to systems with more complicated constant-energy contours. We present results recently obtained on graphene systems which demonstrate the power of this technique, and the usefulness of local measurements for determining the band structure, the map of the Fermi energy and the constant-energy maps. [ABSTRACT FROM AUTHOR]

Time-frequency analysis of heart rate variability (HRV) provides relevant clinical information. However, time-frequency analysis is very sensitive to artefacts. Artefacts that are present in heart rate recordings may be corrected, but this reduces the variability in the signal and therefore adversely affects the accuracy of calculated spectral estimates. To overcome this limitation of traditional techniques for time-frequency analysis, a new continuous wavelet transform (CWT)-based method was developed in which parts of the scalogram that have been affected by artefact correction are excluded from power calculations. The method was evaluated by simulating artefact correction on HRV data that were originally free of artefacts. Commonly used spectral HRV parameters were calculated by the developed method and by the short-time Fourier transform (STFT), which was used as a reference. Except for the powers in the very low-frequency and low-frequency (LF) bands, powers calculated by the STFT proved to be extremely sensitive to artefact correction. The CWT-based calculations in the high-frequency and very high-frequency bands corresponded well with their theoretical values. The standard deviations of these powers, however, increase with the number of corrected artefacts which is the result of the non-stationarity of the R-R interval series that were analysed. The powers calculated in the LF band turned out to be slightly sensitive to artefact correction, but the results were acceptable up to 20% artefact correction. Therefore, the CWT-based method provides a valuable alternative for the analysis of HRV data that cannot be guaranteed to be free of artefacts. [ABSTRACT FROM AUTHOR]

We trace with analytical methods and in a model parameter-independent manner the independent bits of Fisher information of each of the moments of the lognormal distribution as a now standard prescription for the distribution of the cosmological matter density field as it departs from Gaussian initial conditions. We show that, when entering the regime of large fluctuations, only a tiny, dramatically decaying fraction of the total information content remains accessible through the extraction of the full series of moments of the field. This is due to the known peculiarity of highly tailed distributions that they cannot be uniquely recovered given the values of all of their moments. Under this lognormal assumption, cosmological probes such as the correlation function hierarchy or, equivalently, their Fourier transforms, are rendered fundamentally limited once the field becomes nonlinear, for any parameter of interest. We show that the fraction of the information accessible from two-point correlations decays to zero following the inverse squared variance of the field. We discuss what general properties of a random field's probability density function are making the correlation function hierarchy an efficient or inefficient, complete or incomplete, set of probes of any model parameter. [ABSTRACT FROM AUTHOR]

We determine the magnetic helicity, along with the magnetic energy, at high latitudes using data from the Ulysses mission. The data set spans the time period from 1993 to 1996. The basic assumption of the analysis is that the solar wind is homogeneous. Because the solar wind speed is high, we follow the approach first pioneered by Matthaeus et al. by which, under the assumption of spatial homogeneity, one can use Fourier transforms of the magnetic field time series to construct one-dimensional spectra of the magnetic energy and magnetic helicity under the assumption that the Taylor frozen-in-flow hypothesis is valid. That is a well-satisfied assumption for the data used in this study. The magnetic helicity derives from the skew-symmetric terms of the three-dimensional magnetic correlation tensor, while the symmetric terms of the tensor are used to determine the magnetic energy spectrum. Our results show a sign change of magnetic helicity at wavenumber k ≈ 2 AU-1 (or frequency v ≈ 2 μHz) at distances below 2.8 AU and at k ≈ 30 AU-1 (or v ≈ 25 μHz) at larger distances. At small scales the magnetic helicity is positive at northern heliographic latitudes and negative at southern latitudes. The positive magnetic helicity at small scales is argued to be the result of turbulent diffusion reversing the sign relative to what is seen at small scales at the solar surface. Furthermore, the magnetic helicity declines toward solar minimum in 1996. The magnetic helicity flux integrated separately over one hemisphere amounts to about 1045 Mx2 cycle-1 at large scales and to a three times lower value at smaller scales. [ABSTRACT FROM AUTHOR]

In this article, we show the implementation of a computer-based digital storage oscilloscope (DSO) and function generator (FG) using the computer's soundcard for off-campus acoustic experiments. The microphone input is used for the DSO, and a speaker jack is used as the FG. In an effort to reduce the cost of implementing the experiment, we examine software available for free, online. A small number of applications were compared in terms of their interface and functionality, for both the DSO and the FG. The software was then used to investigate standing waves in pipes using the computer-based DSO. Standing wave theory taught in high school and in first year physics is based on a one-dimensional model. With the use of the DSO's fast Fourier transform function, the experimental uncertainly alone was not sufficient to account for the difference observed between the measure and the calculated frequencies. Hence the original experiment was expanded upon to include the end correction effect. The DSO was also used for other simple acoustics experiments, in areas such as the physics of music. [ABSTRACT FROM AUTHOR]

The Ernst equation for Fourier transform nuclear magnetic resonance (MR) describes the spoiled steady-state signal created by periodic partial excitation. In MR imaging (MRI), it is commonly applied to spoiled gradient-echo acquisition in the steady state, created by a small flip angle a at a repetition time TR much shorter than the longitudinal relaxation time T1. We describe two parameter transformations of a and TR/T1, which render the Ernst equation as a low-order rational function. Computer algebra can be readily applied for analytically solving protocol optimization, as shown for the dual flip angle experiment. These transformations are based on the half-angle tangent substitution and its hyperbolic analogue. They are monotonic and approach identity for small a and small TR/T1 with a third-order error. Thus, the exact algebraization can be readily applied to fast gradient echo MRI to yield a rational approximation in a and TR/T1. This reveals a fundamental relationship between the square of the flip angle and TR/T1 which characterizes the Ernst angle, constant degree of T1-weighting and the influence of the local radio-frequency field. [ABSTRACT FROM AUTHOR]

Non-equilibrium dynamics of a Lieb-Liniger system in the presence of the hard-wall potential is studied. We demonstrate that a time-dependent wave function, which describes quantum dynamics of a Lieb-Liniger wave packet consisting of N particles, can be found by solving an N-dimensional Fourier transform; this follows from the symmetry properties of the many-body eigenstates in the presence of the hard-wall potential. The presented formalism is employed to numerically calculate reflection of a few-body wave packet from the hard wall for various interaction strengths and incident momenta. [ABSTRACT FROM AUTHOR]

We analyse two-mirror resonators in terms of their fractional Fourier transform (FRFT) properties. We use the basic ABCD ray transfer matrix method to show how the resonator can be regarded as the cascade of two propagation-lens-propagation FRFT systems. Then, we present a connection between the geometric properties of the resonator (the g parameters) and those of the equivalent FRFT systems (the FRFT order and scaling parameters). Expressions connecting Gaussian beam q-transformation with FRFT parameters are derived. In particular, we show that the beam waist of the resonator's mode is located at the plane leading to two FRFT subsystems with equal scaling parameter which, moreover, coincides with the mode Rayleigh range. Finally we analyse the resonator's stability diagram in terms of the fractional orders of each FRFT subsystem, and the round trip propagation. The presented analysis represents an interesting link between two topics (optical resonators and Fourier optics) usually covered in optics and photonics courses at university level, which can be useful to teach and connect the principles of these subjects. [ABSTRACT FROM AUTHOR]

In this paper the relations between two spreads, between two group delays, and between one spread and one group delay in fractional Fourier transform (FRFT) domains, are presented and three theorems on the uncertainty principle in FRFT domains are also developed. Theorem 1 gives the bounds of two spreads in two FRFT domains. Theorem 2 shows the uncertainty relation between two group delays in two FRFT domains. Theorem 3 presents the crossed uncertainty relation between one group delay and one spread in two FRFT domains. The novelty of their results lies in connecting the products of different physical measures and giving their physical interpretations. The existing uncertainty principle in the FRFT domain is only a special case of theorem 1, and the conventional uncertainty principle in time-frequency domains is a special case of their results. Therefore, three theorems develop the relations of two spreads in time-frequency domains into the relations between two spreads, between two group delays, and between one spread and one group delay in FRFT domains. [ABSTRACT FROM AUTHOR]

We consider the Fisher-KPP equation with a non-local saturation effect defined through an interaction kernel ph(x) and investigate the possible differences with the standard Fisher-KPP equation. Our first concern is the existence of steady states. We prove that if the Fourier transform \hat\phi(\xi) is positive or if the length s of the non-local interaction is short enough, then the only steady states are u [?] 0 and u [?] 1. Next, we study existence of the travelling waves. We prove that this equation admits travelling wave solutions that connect u = 0 to an unknown positive steady state u[?](x), for all speeds c [?] c*. The travelling wave connects to the standard state u[?](x) [?] 1 under the aforementioned conditions: \hat\phi(\xi)>0 or s is sufficiently small. However, the wave is not monotonic for s large. [ABSTRACT FROM AUTHOR]

This paper addresses the problem of estimating lower atmospheric refractivity under the nonstandard propagation conditions frequently encountered in low altitude maritime radar applications. The vertical structure of the refractive environment is modeled by using a five-parameter model, and the horizontal structure is modeled as range-independent. The electromagnetic propagation in the troposphere is simulated by using a split-step fast Fourier transform based on parabolic approximation to the wave equation. A global search marked as a modified genetic algorithm (MGA) for the 5 environmental parameters is performed by using a genetic algorithm (GA) integrated with a simulated annealing technique. The retrieved results from simulated runs demonstrate the ability of this method to make atmospheric refractivity estimations. A comparison with the classical GA and the Bayesian Markov Chain Monte Carlo (Bayesian-MCMC) technique shows that the MGA can not only shorten the inverse time but also improve the inverse precision. For real data cases, the inversion values do not match the reference data very well. The inverted profile, however, can be used to synoptically describe the real refractive structure. [ABSTRACT FROM AUTHOR]

In this paper, we study the optical properties of single defects emitting in the near infrared (NIR) in nanodiamonds at liquid helium temperature. The nanodiamonds are synthesized using a microwave chemical vapor deposition method followed by nickel implantation and annealing. We show that single defects exhibit several striking features at cryogenic temperature: the photoluminescence is strongly concentrated into a sharp zerophonon line (ZPL) in the NIR, the radiative lifetime is in the nanosecond range and the emission is linearly polarized. The spectral stability of the defects is then investigated. An optical resonance linewidth of 4 GHz is measured using resonant excitation on the ZPL. Although Fourier-transform-limited emission is not achieved, our results show that it might be possible to use consecutive photons emitted in the NIR by single defects in diamond nanocrystals to perform two photon interference experiments, which are at the heart of linear quantum computing protocols. [ABSTRACT FROM AUTHOR]

We consider quantum learning machines-quantum computers that modify themselves in order to improve their performance in some way-that are trained to perform certain classical task, i.e. to execute a function that takes classical bits as input and returns classical bits as output. This allows a fair comparison between learning efficiency of quantum and classical learning machines in terms of the number of iterations required for completion of learning. We find an explicit example of the task for which numerical simulations show that quantum learning is faster than its classical counterpart. The task is extraction of the kth root of NOT (NOT = logical negation), with k = 2m and mϵℕ. The reason for this speed-up is that the classical machine requires memory of size log k = m to accomplish the learning, while the memory of a single qubit is sufficient for the quantum machine for any k. [ABSTRACT FROM AUTHOR]

The influence of the coordination on the Kondo temperature of a magnetic impurity at a noble metal surface and the line shape observed in low temperature scanning tunneling spectroscopy (STS) is investigated for single cobalt atoms adsorbed on and embedded in copper surfaces. Surprisingly, the Kondo temperature for substitutional cobalt atoms is almost the same as that of adatoms on the Cu(100) surface. This is in stark contrast to the behaviour observed at the Cu(111) surface. DFT calculations reveal that in the case of Cu(100) the coupling of the spin of the cobalt atom to the conduction band is not substantially increased by the incorporation of the cobalt atom. At the same time the observed line shape differs strongly from what is observed on adatom systems. [ABSTRACT FROM AUTHOR]

In this work, we propose an efficient method of reducing the computational effort of variational calculation with a Hylleraas-like trial wavefunction. The method consists of introducing integral transforms for the terms as rk12 exp ([?]lr12) which provide the calculation of the expectation value of energy and the relevant matrix elements to be done analytically over single-electron coordinates instead of Hylleraas coordinates. We have used this method to calculate the ground state energy of a two-electron system in a spherical dot and a disk-like quantum dot separately. Under parabolic confinement potential and within effective mass approximation size and shape effects of quantum dots on the ground state energy of two electrons have been investigated. The calculation shows that our results even with a small number of basis states are in good agreement with previous theoretical results. [ABSTRACT FROM AUTHOR]

This paper introduces Lorentz beams to describe certain laser sources that produce highly divergent fields. The fractional Fourier transform (FRFT) is applied to treat the propagation of Lorentz beams. Based on the definition of convolution and the convolution theorem of the Fourier transform, an analytical expression for a Lorentz beam passing through a FRFT system has been derived. By using the derived formula, the properties of a Lorentz beam in the FRFT plane are illustrated numerically. [ABSTRACT FROM AUTHOR]

Previous works have resulted in some practical achievements for mechanomyogram (MMG) to control powered prostheses. This work presents the investigation of classifying the hand motion using MMG signals for multifunctional prosthetic control. MMG is thought to reflect the intrinsic mechanical activity of muscle from the lateral oscillations of fibers during contraction. However, external mechanical noise sources such as a movement artifact are known to cause considerable interference to MMG, compromising the classification accuracy. To solve this noise problem, we proposed a new scheme to extract robust MMG features by the integration of the wavelet packet transform (WPT), singular value decomposition (SVD) and a feature selection technique based on distance evaluation criteria for the classification of hand motions. The WPT was first adopted to provide an effective time-frequency representation of non-stationary MMG signals. Then, the SVD and the distance evaluation technique were utilized to extract and select the optimal feature representing the hand motion patterns from the MMG time-frequency representation matrix. Experimental results of 12 subjects showed that four different motions of the forearm and hand could be reliably differentiated using the proposed method when two channels of MMG signals were used. Compared with three previously reported time-frequency decomposition methods, i.e. short-time Fourier transform, stationary wavelet transform and S-transform, the proposed classification system gave the highest average classification accuracy up to 89.7%. The results indicated that MMG could potentially serve as an alternative source of electromyogram for multifunctional prosthetic control using the proposed classification method. [ABSTRACT FROM AUTHOR]

We have derived an analytic geometric transfer function (GTF) for a convergent slit-slat collimator that treats the parallel slit-slat collimator as a special case. The effective point spread function (EPSF) is then derived from the GTF through the Fourier transform. The results of these derivations give an accurate description of the complete geometric response for a slit-slat collimator that includes the effects of the shape and orientation of the slit and slats. We have also derived exact and approximate sensitivity formulae and spatial resolution formulae using the EPSF. [ABSTRACT FROM AUTHOR]

An analytical model of acoustic field excited by a pulsed-laser line source on a coated cylinder is presented. Surface wave dispersive behaviours for a cylinder with a slow coating are analysed and compared with that of a bare cylinder. Based on this analysis, the laser-generated transient response of the perturbed Rayleigh wave and the higher modes of steel cylinder with a zinc coating are calculated from the model using residue theory and FFT technique. The theoretical result from the superposed waveform of the perturbed Rayleigh wave and higher modes agree well with the waveform obtained in experiment. The results show that the model and numerical method provide a useful technique for quantitatively characterizing coating parameters of coated cylinder by the laser generated surface waves. [ABSTRACT FROM AUTHOR]

Passive Fourier transform infrared (FTIR) remote sensing measurement of chemical gas cloud is a vital technology. It takes an important part in many fields for the detection of released gases. The principle of concentration measurement is based on the Beer-Lambert law. Unlike the active measurement, for the passive remote sensing, in most cases, the difference between the temperature of the gas cloud and the brightness temperature of the background is usually a few kelvins. The gas cloud emission is almost equal to the background emission, thereby the emission of the gas cloud cannot be ignored. The concentration retrieval algorithm is quite different from the active measurement. In this paper, the concentration retrieval algorithm for the passive FTIR remote measurement of gas cloud is presented in detail, which involves radiative transfer model, radiometric calibration, absorption coefficient calculation, et al. The background spectrum has a broad feature, which is a slowly varying function of frequency. In this paper, the background spectrum is fitted with a polynomial by using the Levenberg-Marquardt method which is a kind of nonlinear least squares fitting algorithm. No background spectra are required. Thus, this method allows mobile, real-time and fast measurements of gas clouds. [ABSTRACT FROM AUTHOR]

This paper reports that an analytic method is used to calculate the load responses of the two-wire transmission line excited by a plane-wave directly in the time domain. By the frequency-domain Baum-Liu-Tesche (BLT) equation, the time-domain analytic solutions are obtained and expressed in an infinite geometric series. Moreover, it is shown that there exist only finite nonzero terms in the infinite geometric series if the time variate is at a finite interval. In other word, the time-domain analytic solutions are expanded in a finite geometric series indeed if the time variate is at a finite interval. The computed results are subsequently compared with transient responses obtained by using the frequency-domain BLT equation via a fast Fourier transform, and the agreement is excellent. [ABSTRACT FROM AUTHOR]

The discrete Fourier transform (DFT) is the base of modern signal processing. 1-dimensional fast Fourier transform (ID FFT) and 2D FFT have time complexity O (N log N) and O (N2 log N) respectively. Since 1965, there has been no more essential breakthrough for the design of fast DFT algorithm. DFT has two properties. One property is that DFT is energy conservation transform. The other property is that many DFT coefficients are close to zero. The basic idea of this paper is that the generalized Grover's iteration can perform the computation of DFT which acts on the entangled states to search the big DFT coefficients until these big coefficients contain nearly all energy. One-dimensional quantum DFT (ID QDFT) and two-dimensional quantum DFT (2D QDFT) are presented in this paper. The quantum algorithm for convolution estimation is also presented in this paper. Compared with FFT, ID and 2D QDFT have time complexity O([?]N) and O (N) respectively. QDFT and quantum convolution demonstrate that quantum computation to process classical signal is possible. [ABSTRACT FROM AUTHOR]

The aim of this study was to assess the validity of an artificial neural network based on flow-related spectral entropy as a diagnostic test for obstructive sleep apnoea and Cheyne-Stokes respiration. A data set of 37 subjects was used for spectral analysis of the airflow by performing a fast Fourier transform. The examined intervals were divided into epochs of 3 min. Spectral entropy S was applied as a measure for the spread of the related power spectrum. The spectrum was divided into several frequency areas with various subsets of spectral entropy. We studied 11 subjects with obstructive apnoeas (n = 267 epochs), 10 subjects with obstructive hypopnoeas (n = 80 epochs), 11 subjects with Cheyne-Stokes respiration (n = 253 epochs) and 5 subjects with normal breathing in non-REM sleep (n = 174 epochs). Based on spectral entropy an artificial neural network was built, and we obtained a sensitivity of 90.2% and a specificity of 90.9% for distinguishing between obstructive apnoeas and Cheyne-Stokes respiration, and a sensitivity of 91.3% and a specificity of 94.6% for discriminating between obstructive hypopnoeas and normal breathing in non-REM sleep. This resulted in an accuracy of 91.5% for identifying flow patterns of obstructive sleep apnoea, Cheyne-Stokes respiration and normal breathing in non-REM sleep. It is concluded that the use of an artificial neural network relying on spectral analysis of the airflow could be a useful method as a diagnostic test for obstructive sleep apnoea and Cheyne-Stokes respiration. [ABSTRACT FROM AUTHOR]

Discretization of the Lippmann-Schwinger integral equation with complex conjugate gradient method and fast Fourier transform (CCGM-FFT) is solved, which can reduce the memory storage and the CPU time compared with the traditional method, MOM. Thus objects with large size and multiple scattering objects could be simulated with CCGM-FFT. The total intensity and the distribution of each field component of the dielectric and metallic objects under the excitation of the TE/TM-polarized wave are calculated with photon scanning tunnelling microscopy (PSTM) at the constant height. The simulating results are analysed and explained reasonably. The results show that the polarization plays an important role for imaging of PSTM. [ABSTRACT FROM AUTHOR]

This paper is a further work of the authors' paper published previously (Liao T H and Gao Q 2005 Chin. Phys. Lett. 22 2316). The amplitudes of fractional Fourier transform of Cantor sets are analysed from the viewpoint of multifractal by wavelet transform maxima method (WTMM). An integral operation is carried out before the application of WTMM, such that the function obtained can be considered as the perturbed devil staircase. Also, wavelets with large number of vanishing moments are used, which makes the complete singularity spectrum more accessible. The validity of multifractal formalism is guaranteed by restricting parameter q to a proper range, so that the phenomenon of multifractal phase transition can be explained reasonably. Particularly, the method of determining the range of parameter q in the above paper is developed to be more operational and rigorous. [ABSTRACT FROM AUTHOR]

We study the transport property passing through a weakly open equilateral triangular billiards by using the semiclassical method. We extend the Green function and the transport matrix theory to include the multiple scattering effect at the boundary and the diffractions of the pair of the lead apertures. For analysing the structure of semiclassical pseudo path kinks, the geometric and the special dynamical symmetries of the system are simultaneously taken into account. The conductance is calculated by Landauer formula as a function of the electron's Fermi wave number. Its Fourier transformation, the quantum path-length spectrum, is qualitatively in accordance with the results of the classical trajectories, which indicates that such approach provides an obvious improvement of the semiclassical description. [ABSTRACT FROM AUTHOR]

Making use of the molecular closed-orbit theory and a new model potential for the Rydberg molecule, we have calculated the recurrence spectra of He2+ molecular ion in a magnetic field for different quantum defects. The Fourier transform spectra of He2+ molecular ion may be used to perform a direct comparison between peaks in the spectra and the scaled action values of closed orbits of the excited electron in external fields. We find that the spectral modulations can be analysed in terms of the scattering of the excited electron on the molecular core. Unlike the case of the Rydberg atom where the elastic scattering is predominant, modulations produced by inelastic scattering are also vital to the photoabsorption spectrum of the Rydberg molecule. Our results are in good agreement with the quantum results, which suggests that our method is correct. [ABSTRACT FROM AUTHOR]