Fourier series and orthogonal polynomials
Jackson, Dunham
2004-01-01
This text for undergraduate and graduate students illustrates the fundamental simplicity of the properties of orthogonal functions and their developments in related series. Starting with a definition and explanation of the elements of Fourier series, the text follows with examinations of Legendre polynomials and Bessel functions. Boundary value problems consider Fourier series in conjunction with Laplace's equation in an infinite strip and in a rectangle, with a vibrating string, in three dimensions, in a sphere, and in other circumstances. An overview of Pearson frequency functions is followe
Liflyand, E.
2012-01-01
We study an extension to Fourier transforms of the old problem on absolute convergence of the re-expansion in the sine (cosine) Fourier series of an absolutely convergent cosine (sine) Fourier series. The results are obtained by revealing certain relations between the Fourier transforms and their Hilbert transforms.
A summation procedure for expansions in orthogonal polynomials
International Nuclear Information System (INIS)
Garibotti, C.R.; Grinstein, F.F.
1977-01-01
Approximants to functions defined by formal series expansions in orthogonal polynomials are introduced. They are shown to be convergent even out of the elliptical domain where the original expansion converges
Transfer Function Identification Using Orthogonal Fourier Transform Modeling Functions
Morelli, Eugene A.
2013-01-01
A method for transfer function identification, including both model structure determination and parameter estimation, was developed and demonstrated. The approach uses orthogonal modeling functions generated from frequency domain data obtained by Fourier transformation of time series data. The method was applied to simulation data to identify continuous-time transfer function models and unsteady aerodynamic models. Model fit error, estimated model parameters, and the associated uncertainties were used to show the effectiveness of the method for identifying accurate transfer function models from noisy data.
Orthogonal Expansions for VIX Options Under Affine Jump Diffusions
DEFF Research Database (Denmark)
Barletta, Andrea; Nicolato, Elisa
2017-01-01
In this work we derive new closed–form pricing formulas for VIX options in the jump-diffusion SVJJ model proposed by Duffie et al. (2000). Our approach is based on the classic methodology of approximating a density function with an orthogonal expansion of polynomials weighted by a kernel. Orthogo......In this work we derive new closed–form pricing formulas for VIX options in the jump-diffusion SVJJ model proposed by Duffie et al. (2000). Our approach is based on the classic methodology of approximating a density function with an orthogonal expansion of polynomials weighted by a kernel...
On the Equisummability of Hermite and Fourier Expansions
Indian Academy of Sciences (India)
We prove an equisummability result for the Fourier expansions and Hermite expansions as well as special Hermite expansions. We also prove the uniform boundedness of the Bochner-Riesz means associated to the Hermite expansions for polyradial functions.
Orthogonal expansions related to compact Gelfand pairs
DEFF Research Database (Denmark)
Berg, Christian; Peron, Ana P.; Porcu, Emilio
2017-01-01
. The functions of this class are the functions having a uniformly convergent expansion ∑ϕεZB(ϕ)(u)ϕ(x) for xεG,uεL, where the sum is over the space Z of positive definite spherical functions ϕ:G→C for the Gelfand pair, and (B(ϕ))ϕεZ is a family of continuous positive definite functions on L such that ∑ϕε......For a locally compact group G, let P(G) denote the set of continuous positive definite functions f:G→C. Given a compact Gelfand pair (G,K) and a locally compact group L, we characterize the class PK#(G,L) of functions fεP(G×L) which are bi-invariant in the G-variable with respect to K......(d)) and (U(q),U(q-1)) as well as for the product of these Gelfand pairs.The result generalizes recent theorems of Berg-Porcu (2016) and Guella-Menegatto (2016)....
International Nuclear Information System (INIS)
Li Shun; Zhang Sijiong
2014-01-01
A numerical model is presented to simulate the influence function of deformable mirror actuators. The numerical model is formed by Bessel Fourier orthogonal functions, which are constituted of Bessel orthogonal functions and a Fourier basis. A detailed comparison is presented between the new Bessel Fourier model, the Zernike model, the Gaussian influence function and the modified Gaussian influence function. Numerical experiments indicate that the new numerical model is easy to use and more accurate compared with other numerical models. The new numerical model can be used for describing deformable mirror performances and numerical simulations of adaptive optics systems. (research papers)
On the non-orthogonal sampling scheme for Gabor's signal expansion
Bastiaans, M.J.; Leest, van A.J.; Veen, J.P.
2000-01-01
Gabor's signal expansion and the Gabor transform are formulated on a non-orthogonal time-frequency lattice instead of on the traditional rectangular lattice [1,2]. The reason for doing so is that a non-orthogonal sampling geometry might be better adapted to the form of the window functions (in the
On the equisummability of Hermite and Fourier expansions
Indian Academy of Sciences (India)
is the Fourier transform on Rn. Let ب ; 2 Nn be the n-dimensional Hermite functions which are eigenfunctions of the Hermite operator H ¼ ہء jxj. 2 with the eigenvalue. ً2j j nق where j j ¼ 1 ءءء n. Let Pk be the orthogonal projection of L 2ًRnق onto the kth eigenspace spanned by ب ; j j ¼ k. More precisely,. Pk fًxق ¼. X j j¼k. Z.
Fourier expansions and multivariable Bessel functions concerning radiation programmes
International Nuclear Information System (INIS)
Dattoli, G.; Richetta, M.; Torre, A.; Chiccoli, C.; Lorenzutta, S.; Maino, G.
1996-01-01
The link between generalized Bessel functions and other special functions is investigated using the Fourier series and the generalized Jacobi-Anger expansion. A new class of multivariable Hermite polynomials is then introduced and their relevance to physical problems discussed. As an example of the power of the method, applied to radiation physics, we analyse the role played by multi-variable Bessel functions in the description of radiation emitted by a charge constrained to a nonlinear oscillation. (author)
Orthogonality-condition model for bound states with a separable expansion of the potential
International Nuclear Information System (INIS)
Pal, K.F.
1984-01-01
A very efficient solution of the equation of Saito's orthogonality-condition model (OCM) is reported for bound states by means of a separable expansion of the potential (PSE method). Some simplifications of the published formulae of the PSE method is derived, which facilitate its application to the OCM and may be useful in solving the Schroedinger equation as well. (author)
Gabor's signal expansion based on a non-orthogonal sampling geometry
Bastiaans, M.J.; Caulfield, H. J.
2002-01-01
Gabor’s signal expansion and the Gabor transform are formulated on a nonorthogonal time-frequency lattice instead of on the traditional rectangular lattice. The reason for doing so is that a non-orthogonal sampling geometry might be better adapted to the form of the window functions (in the
Cong, Lin-xiao; Huang, Min; Cai, Qi-sheng
2017-10-01
In this paper, a multi-line interferogram stitching method based on orthogonal shear using the Wollaston prism(WP) was proposed with a 2D projection interferogram recorded through the rotation of CCD, making the spectral resolution of Fourier-Transform spectrometer(FTS) of a limited spatial size increase by at least three times. The fringes on multi-lines were linked with the pixels of equal optical path difference (OPD). Ideally, the error of sampled phase within one pixel was less than half the wavelength, ensuring consecutive values in the over-sampled dimension while aliasing in another. In the simulation, with the calibration of 1.064μm, spectral lines at 1.31μm and 1.56μm of equal intensity were tested and observed. The result showed a bias of 0.13% at 1.31μm and 1.15% at 1.56μm in amplitude, and the FWHM at 1.31μm reduced from 25nm to 8nm after the sample points increased from 320 to 960. In the comparison of reflectance spectrum of carnauba wax within near infrared(NIR) band, the absorption peak at 1.2μm was more obvious and zoom of the band 1.38 1.43μm closer to the reference, although some fluctuation was in the short-wavelength region arousing the spectral crosstalk. In conclusion, with orthogonal shear based on the rotation of the CCD relative to the axis of WP, the spectral resolution of static FTS was enhanced by the projection of fringes to the grid coordinates and stitching the interferograms into a larger OPD, which showed the advantages of cost and miniaturization in the space-constrained NIR applications.
The investigation of the non-orthogonal basis expansion method for a three-fermion system
International Nuclear Information System (INIS)
Baoqiu Chen; Kentucky Univ., Lexington, KY
1992-01-01
In this paper, the non-orthogonal basis expansion method has been extended to solve a three-fermion system. The radial wavefunction of such a system is expanded in terms of a non-orthogonal Gaussian basis. All matrix elements of the Hamiltonian, including the central, tensor and spin-orbit potentials are derived in analytical forms. The new method simplifies the three-body system calculations, which are usually rather tedious by other methods. The method can be used to calculate energies for both the ground state and low excited states and has been used further to investigate the other nuclear properties of a three-body system such as Λ 3 H. (Author)
Quadrature formulas for Fourier coefficients
Bojanov, Borislav; Petrova, Guergana
2009-01-01
We consider quadrature formulas of high degree of precision for the computation of the Fourier coefficients in expansions of functions with respect to a system of orthogonal polynomials. In particular, we show the uniqueness of a multiple node
Design of Extended Depth-of-Focus Laser Beams Using Orthogonal Beam Expansions
Directory of Open Access Journals (Sweden)
Leonard Bergstein
2005-06-01
Full Text Available Laser beams with extended depth of focus have many practical applications, such as scanning printed bar codes. Previous work has concentrated on synthesizing such beams by approximating the nondiffracting Bessel beam solution to the wave equation. In this paper, we introduce an alternate novel synthesis method that is based on maintaining a minimum MTF value (contrast over the largest possible distance. To achieve this, the coefficients of an orthogonal beam expansion are sequentially optimized to this criterion. One of the main advantages of this method is that it can be easily generalized to noncircularly symmetrical beams by the appropriate choice of the beam expansion basis functions. This approach is found to be very useful for applications that involve scanning of the laser beam.
DEFF Research Database (Denmark)
2017-01-01
Systems, methods, apparatuses, and computer program products for generating sequences for zero-tail discrete fourier transform (DFT)-spread-orthogonal frequency division multiplexing (OFDM) (ZT DFT-s-OFDM) reference signals. One method includes adding a zero vector to an input sequence...... of each of the elements, converting the sequence to time domain, generating a zero-padded sequence by forcing a zero head and tail of the sequence, and repeating the steps until a final sequence with zero-tail and flat frequency response is obtained....
Teaching Graphical Simulations of Fourier Series Expansion of Some Periodic Waves Using Spreadsheets
Singh, Iqbal; Kaur, Bikramjeet
2018-01-01
The present article demonstrates a way of programming using an Excel spreadsheet to teach Fourier series expansion in school/colleges without the knowledge of any typical programming language. By using this, a student learns to approximate partial sum of the n terms of Fourier series for some periodic signals such as square wave, saw tooth wave,…
Teaching graphical simulations of Fourier series expansion of some periodic waves using spreadsheets
Singh, Iqbal; Kaur, Bikramjeet
2018-05-01
The present article demonstrates a way of programming using an Excel spreadsheet to teach Fourier series expansion in school/colleges without the knowledge of any typical programming language. By using this, a student learns to approximate partial sum of the n terms of Fourier series for some periodic signals such as square wave, saw tooth wave, half wave rectifier and full wave rectifier signals.
CMB in a box: Causal structure and the Fourier-Bessel expansion
International Nuclear Information System (INIS)
Abramo, L. Raul; Reimberg, Paulo H.; Xavier, Henrique S.
2010-01-01
This paper makes two points. First, we show that the line-of-sight solution to cosmic microwave anisotropies in Fourier space, even though formally defined for arbitrarily large wavelengths, leads to position-space solutions which only depend on the sources of anisotropies inside the past light cone of the observer. This foretold manifestation of causality in position (real) space happens order by order in a series expansion in powers of the visibility γ=e -μ , where μ is the optical depth to Thomson scattering. We show that the contributions of order γ N to the cosmic microwave background (CMB) anisotropies are regulated by spacetime window functions which have support only inside the past light cone of the point of observation. Second, we show that the Fourier-Bessel expansion of the physical fields (including the temperature and polarization momenta) is an alternative to the usual Fourier basis as a framework to compute the anisotropies. The viability of the Fourier-Bessel series for treating the CMB is a consequence of the fact that the visibility function becomes exponentially small at redshifts z>>10 3 , effectively cutting off the past light cone and introducing a finite radius inside which initial conditions can affect physical observables measured at our position x-vector=0 and time t 0 . Hence, for each multipole l there is a discrete tower of momenta k il (not a continuum) which can affect physical observables, with the smallest momenta being k 1l ∼l. The Fourier-Bessel modes take into account precisely the information from the sources of anisotropies that propagates from the initial value surface to the point of observation - no more, no less. We also show that the physical observables (the temperature and polarization maps), and hence the angular power spectra, are unaffected by that choice of basis. This implies that the Fourier-Bessel expansion is the optimal scheme with which one can compute CMB anisotropies.
Quadrature formulas for Fourier coefficients
Bojanov, Borislav
2009-09-01
We consider quadrature formulas of high degree of precision for the computation of the Fourier coefficients in expansions of functions with respect to a system of orthogonal polynomials. In particular, we show the uniqueness of a multiple node formula for the Fourier-Tchebycheff coefficients given by Micchelli and Sharma and construct new Gaussian formulas for the Fourier coefficients of a function, based on the values of the function and its derivatives. © 2009 Elsevier B.V. All rights reserved.
Directory of Open Access Journals (Sweden)
Agata Bezubik
2006-03-01
Full Text Available This paper presents recent results obtained by the authors (partly in collaboration with A. Dabrowska concerning expansions of zonal functions on Euclidean spheres into spherical harmonics and some applications of such expansions for problems involving Fourier transforms of functions with rotational symmetry. The method used to derive the expansion formula is based entirely on differential methods and completely avoids the use of various integral identities commonly used in this context. Some new identities for the Fourier transform are derived and as a byproduct seemingly new recurrence relations for the classical Bessel functions are obtained.
Dong, Shuo; Kettenbach, Joachim; Hinterleitner, Isabella; Bergmann, Helmar; Birkfellner, Wolfgang
2008-01-01
Current merit functions for 2D/3D registration usually rely on comparing pixels or small regions of images using some sort of statistical measure. Problems connected to this paradigm the sometimes problematic behaviour of the method if noise or artefacts (for instance a guide wire) are present on the projective image. We present a merit function for 2D/3D registration which utilizes the decomposition of the X-ray and the DRR under comparison into orthogonal Zernike moments; the quality of the match is assessed by an iterative comparison of expansion coefficients. Results in a imaging study on a physical phantom show that--compared to standard cross--correlation the Zernike moment based merit function shows better robustness if histogram content in images under comparison is different, and that time expenses are comparable if the merit function is constructed out of a few significant moments only.
Grimm, C. A.
This document contains two units that examine integral transforms and series expansions. In the first module, the user is expected to learn how to use the unified method presented to obtain Laplace transforms, Fourier transforms, complex Fourier series, real Fourier series, and half-range sine series for given piecewise continuous functions. In…
Hornikx, Maarten; Dragna, Didier
2015-07-01
The Fourier pseudospectral time-domain method is an efficient wave-based method to model sound propagation in inhomogeneous media. One of the limitations of the method for atmospheric sound propagation purposes is its restriction to a Cartesian grid, confining it to staircase-like geometries. A transform from the physical coordinate system to the curvilinear coordinate system has been applied to solve more arbitrary geometries. For applicability of this method near the boundaries, the acoustic velocity variables are solved for their curvilinear components. The performance of the curvilinear Fourier pseudospectral method is investigated in free field and for outdoor sound propagation over an impedance strip for various types of shapes. Accuracy is shown to be related to the maximum grid stretching ratio and deformation of the boundary shape and computational efficiency is reduced relative to the smallest grid cell in the physical domain. The applicability of the curvilinear Fourier pseudospectral time-domain method is demonstrated by investigating the effect of sound propagation over a hill in a nocturnal boundary layer. With the proposed method, accurate and efficient results for sound propagation over smoothly varying ground surfaces with high impedances can be obtained.
Zhang, B.; Oosterlee, C.W.
2013-01-01
We propose an efficient pricing method for arithmetic and geometric Asian options under exponential Lévy processes based on Fourier cosine expansions and Clenshaw–Curtis quadrature. The pricing method is developed for both European style and American-style Asian options and for discretely and
CSIR Research Space (South Africa)
Shatalov, MY
2006-01-01
Full Text Available -scale structure to guarantee the numerical accuracy of solution. In the present paper the authors propose to use a novel method of solution of the Helmholtz integral equation, which is based on expansion of the integrands in double Fourier series. The main...
A non-hydrostatic flat-bottom ocean model entirely based on Fourier expansion
Wirth, A.
2005-01-01
We show how to implement free-slip and no-slip boundary conditions in a three dimensional Boussinesq flat-bottom ocean model based on Fourier expansion. Our method is inspired by the immersed or virtual boundary technique in which the effect of boundaries on the flow field is modeled by a virtual force field. Our method, however, explicitly depletes the velocity on the boundary induced by the pressure, while at the same time respecting the incompressibility of the flow field. Spurious spatial oscillations remain at a negligible level in the simulated flow field when using our technique and no filtering of the flow field is necessary. We furthermore show that by using the method presented here the residual velocities at the boundaries are easily reduced to a negligible value. This stands in contradistinction to previous calculations using the immersed or virtual boundary technique. The efficiency is demonstrated by simulating a Rayleigh impulsive flow, for which the time evolution of the simulated flow is compared to an analytic solution, and a three dimensional Boussinesq simulation of ocean convection. The second instance is taken form a well studied oceanographic context: A free slip boundary condition is applied on the upper surface, the modeled sea surface, and a no-slip boundary condition to the lower boundary, the modeled ocean floor. Convergence properties of the method are investigated by solving a two dimensional stationary problem at different spatial resolutions. The work presented here is restricted to a flat ocean floor. Extensions of our method to ocean models with a realistic topography are discussed.
Fukushima, Toshio
2018-02-01
In order to accelerate the spherical harmonic synthesis and/or analysis of arbitrary function on the unit sphere, we developed a pair of procedures to transform between a truncated spherical harmonic expansion and the corresponding two-dimensional Fourier series. First, we obtained an analytic expression of the sine/cosine series coefficient of the 4 π fully normalized associated Legendre function in terms of the rectangle values of the Wigner d function. Then, we elaborated the existing method to transform the coefficients of the surface spherical harmonic expansion to those of the double Fourier series so as to be capable with arbitrary high degree and order. Next, we created a new method to transform inversely a given double Fourier series to the corresponding surface spherical harmonic expansion. The key of the new method is a couple of new recurrence formulas to compute the inverse transformation coefficients: a decreasing-order, fixed-degree, and fixed-wavenumber three-term formula for general terms, and an increasing-degree-and-order and fixed-wavenumber two-term formula for diagonal terms. Meanwhile, the two seed values are analytically prepared. Both of the forward and inverse transformation procedures are confirmed to be sufficiently accurate and applicable to an extremely high degree/order/wavenumber as 2^{30} {≈ } 10^9. The developed procedures will be useful not only in the synthesis and analysis of the spherical harmonic expansion of arbitrary high degree and order, but also in the evaluation of the derivatives and integrals of the spherical harmonic expansion.
Passos, Cláudia P; Cardoso, Susana M; Barros, António S; Silva, Carlos M; Coimbra, Manuel A
2010-02-28
Fourier transform infrared (FTIR) spectroscopy has being emphasised as a widespread technique in the quick assess of food components. In this work, procyanidins were extracted with methanol and acetone/water from the seeds of white and red grape varieties. A fractionation by graded methanol/chloroform precipitations allowed to obtain 26 samples that were characterised using thiolysis as pre-treatment followed by HPLC-UV and MS detection. The average degree of polymerisation (DPn) of the procyanidins in the samples ranged from 2 to 11 flavan-3-ol residues. FTIR spectroscopy within the wavenumbers region of 1800-700 cm(-1) allowed to build a partial least squares (PLS1) regression model with 8 latent variables (LVs) for the estimation of the DPn, giving a RMSECV of 11.7%, with a R(2) of 0.91 and a RMSEP of 2.58. The application of orthogonal projection to latent structures (O-PLS1) clarifies the interpretation of the regression model vectors. Moreover, the O-PLS procedure has removed 88% of non-correlated variations with the DPn, allowing to relate the increase of the absorbance peaks at 1203 and 1099 cm(-1) with the increase of the DPn due to the higher proportion of substitutions in the aromatic ring of the polymerised procyanidin molecules. Copyright 2009 Elsevier B.V. All rights reserved.
Tolstov, Georgi P
1962-01-01
Richard A. Silverman's series of translations of outstanding Russian textbooks and monographs is well-known to people in the fields of mathematics, physics, and engineering. The present book is another excellent text from this series, a valuable addition to the English-language literature on Fourier series.This edition is organized into nine well-defined chapters: Trigonometric Fourier Series, Orthogonal Systems, Convergence of Trigonometric Fourier Series, Trigonometric Series with Decreasing Coefficients, Operations on Fourier Series, Summation of Trigonometric Fourier Series, Double Fourie
Narea, J. Freddy; Muñoz, Aarón A.; Castro, Jorge; Muñoz, Rafael A.; Villalba, Caroleny E.; Martinez, María. F.; Bravo, Kelly D.
2013-11-01
Human skin has been studied in numerous investigations, given the interest in knowing information about physiology, morphology and chemical composition. These parameters can be determined using non invasively optical techniques in vivo, such as the diffuse reflectance spectroscopy. The human skin color is determined by many factors, but primarily by the amount and distribution of the pigment melanin. The melanin is produced by the melanocytes in the basal layer of the epidermis. This research characterize the spectral response of the human skin using the coefficients of Fourier series expansion. Simulating the radiative transfer equation for the Monte Carlo method to vary the concentration of the melanocytes (fme) in a simplified model of human skin. It fits relating the Fourier series coefficient a0 with fme. Therefore it is possible to recover the skin biophysical parameter.
International Nuclear Information System (INIS)
Cohl, H S; Kalnins, E G
2012-01-01
Due to the isotropy of d-dimensional hyperbolic space, there exists a spherically symmetric fundamental solution for its corresponding Laplace–Beltrami operator. The R-radius hyperboloid model of hyperbolic geometry with R > 0 represents a Riemannian manifold with negative-constant sectional curvature. We obtain a spherically symmetric fundamental solution of Laplace’s equation on this manifold in terms of its geodesic radius. We give several matching expressions for this fundamental solution including a definite integral over reciprocal powers of the hyperbolic sine, finite summation expressions over hyperbolic functions, Gauss hypergeometric functions and in terms of the associated Legendre function of the second kind with order and degree given by d/2 − 1 with real argument greater than unity. We also demonstrate uniqueness for a fundamental solution of Laplace’s equation on this manifold in terms of a vanishing decay at infinity. In rotationally invariant coordinate systems, we compute the azimuthal Fourier coefficients for a fundamental solution of Laplace’s equation on the R-radius hyperboloid. For d ⩾ 2, we compute the Gegenbauer polynomial expansion in geodesic polar coordinates for a fundamental solution of Laplace’s equation on this negative-constant curvature Riemannian manifold. In three dimensions, an addition theorem for the azimuthal Fourier coefficients of a fundamental solution for Laplace’s equation is obtained through comparison with its corresponding Gegenbauer expansion. (paper)
Muñoz Morales, Aarón A; Vázquez Y Montiel, Sergio
2012-10-01
The determination of optical parameters of biological tissues is essential for the application of optical techniques in the diagnosis and treatment of diseases. Diffuse Reflection Spectroscopy is a widely used technique to analyze the optical characteristics of biological tissues. In this paper we show that by using diffuse reflectance spectra and a new mathematical model we can retrieve the optical parameters by applying an adjustment of the data with nonlinear least squares. In our model we represent the spectra using a Fourier series expansion finding mathematical relations between the polynomial coefficients and the optical parameters. In this first paper we use spectra generated by the Monte Carlo Multilayered Technique to simulate the propagation of photons in turbid media. Using these spectra we determine the behavior of Fourier series coefficients when varying the optical parameters of the medium under study. With this procedure we find mathematical relations between Fourier series coefficients and optical parameters. Finally, the results show that our method can retrieve the optical parameters of biological tissues with accuracy that is adequate for medical applications.
Revisiting the Fourier expansion of Mie scattering matrices in generalized spherical functions
International Nuclear Information System (INIS)
Sanghavi, Suniti
2014-01-01
Mie computations of the scattering properties of large particles are a time consuming step in the radiative transfer modeling of aerosol and clouds. Currently, there exist two methods based on the use of spherical functions for computing the Fourier moments of the phase matrix of a given spherical particle or particulate polydispersion: The first, developed over the years before being presented in a convenient form by Siewert [31], required an intermediate computation of the phase matrix over which numerical integration was performed to deliver the required Fourier components. The second, suggested by Domke [9], promised a direct computation of the Fourier moments using Wigner 3-j symbols. While the former was relatively easy to implement and is thus the most commonly used to date, its numerical implementation using an arbitrary user choice of angular quadrature (NAI-1) can produce inaccurate results. Numerical integration using quadrature points as recommended by de Rooij and van der Stap [5] (NAI-2) delivers accurate results with high computational efficiency. Domke's method enables a direct computation of the exact number of required Fourier components. However, the original manuscript contained several misprints, many of which were subsequently corrected by de Rooij and van der Stap [5]. Unfortunately, the main recurrence relationship used in Domke [9] remained uncorrected. In this paper, the corrected relationship is presented along with other minor corrections. de Rooij and van der Stap [5] had found the straightforward application of Domke's method viable only for size parameters smaller than ∼120 due to issues involving computer storage. A means of implementing the corrected Domke formalism using precomputed tabulations of Wigner 3-j symbols (PCW) is presented here, making it more computationally economical and applicable over much broader particle size ranges. The accuracy of PCW is only limited by machine precision. For a single particle, NAI-2 is found
Siminos, Evangelos; Bénisti, Didier; Gremillet, Laurent
2011-05-01
We study the stability of spatially periodic, nonlinear Vlasov-Poisson equilibria as an eigenproblem in a Fourier-Hermite basis (in the space and velocity variables, respectively) of finite dimension, N. When the advection term in the Vlasov equation is dominant, the convergence with N of the eigenvalues is rather slow, limiting the applicability of the method. We use the method of spectral deformation introduced by Crawford and Hislop [Ann. Phys. (NY) 189, 265 (1989)] to selectively damp the continuum of neutral modes associated with the advection term, thus accelerating convergence. We validate and benchmark the performance of our method by reproducing the kinetic dispersion relation results for linear (spatially homogeneous) equilibria. Finally, we study the stability of a periodic Bernstein-Greene-Kruskal mode with multiple phase-space vortices, compare our results with numerical simulations of the Vlasov-Poisson system, and show that the initial unstable equilibrium may evolve to different asymptotic states depending on the way it was perturbed. © 2011 American Physical Society
Directory of Open Access Journals (Sweden)
Jiran L.
2016-06-01
Full Text Available Thick-walled tubes made from isotropic and anisotropic materials are subjected to an internal pressure while the semi-analytical method is employed to investigate their elastic deformations. The contribution and novelty of this method is that it works universally for different loads, different boundary conditions, and different geometry of analyzed structures. Moreover, even when composite material is considered, the method requires no simplistic assumptions. The method uses a curvilinear tensor calculus and it works with the analytical expression of the total potential energy while the unknown displacement functions are approximated by using appropriate series expansion. Fourier and Taylor series expansion are involved into analysis in which they are tested and compared. The main potential of the proposed method is in analyses of wound composite structures when a simple description of the geometry is made in a curvilinear coordinate system while material properties are described in their inherent Cartesian coordinate system. Validations of the introduced semi-analytical method are performed by comparing results with those obtained from three-dimensional finite element analysis (FEA. Calculations with Fourier series expansion show noticeable disagreement with results from the finite element model because Fourier series expansion is not able to capture the course of radial deformation. Therefore, it can be used only for rough estimations of a shape after deformation. On the other hand, the semi-analytical method with Fourier Taylor series expansion works very well for both types of material. Its predictions of deformations are reliable and widely exploitable.
Directory of Open Access Journals (Sweden)
Youngsun Kim
2017-05-01
Full Text Available The most common structure used for current transformers (CTs consists of secondary windings around a ferromagnetic core past the primary current being measured. A CT used as a surge protection device (SPD may experience large inrushes of current, like surges. However, when a large current flows into the primary winding, measuring the magnitude of the current is difficult because the ferromagnetic core becomes magnetically saturated. Several approaches to reduce the saturation effect are described in the literature. A Rogowski coil is representative of several devices that measure large currents. It is an electrical device that measures alternating current (AC or high-frequency current. However, such devices are very expensive in application. In addition, the volume of a CT must be increased to measure sufficiently large currents, but for installation spaces that are too small, other methods must be used. To solve this problem, it is necessary to analyze the magnetic field and electromotive force (EMF characteristics when designing a CT. Thus, we proposed an analysis method for the CT under an inrush current using the time-domain finite element method (TDFEM. The input source current of a surge waveform is expanded by a Fourier series to obtain an instantaneous value. An FEM model of the device is derived in a two-dimensional system and coupled with EMF circuits. The time-derivative term in the differential equation is solved in each time step by the finite difference method. It is concluded that the proposed algorithm is useful for analyzing CT characteristics, including the field distribution. Consequently, the proposed algorithm yields a reference for obtaining the effects of design parameters and magnetic materials for special shapes and sizes before the CT is designed and manufactured.
Kim, Youngsun
2017-05-01
The most common structure used for current transformers (CTs) consists of secondary windings around a ferromagnetic core past the primary current being measured. A CT used as a surge protection device (SPD) may experience large inrushes of current, like surges. However, when a large current flows into the primary winding, measuring the magnitude of the current is difficult because the ferromagnetic core becomes magnetically saturated. Several approaches to reduce the saturation effect are described in the literature. A Rogowski coil is representative of several devices that measure large currents. It is an electrical device that measures alternating current (AC) or high-frequency current. However, such devices are very expensive in application. In addition, the volume of a CT must be increased to measure sufficiently large currents, but for installation spaces that are too small, other methods must be used. To solve this problem, it is necessary to analyze the magnetic field and electromotive force (EMF) characteristics when designing a CT. Thus, we proposed an analysis method for the CT under an inrush current using the time-domain finite element method (TDFEM). The input source current of a surge waveform is expanded by a Fourier series to obtain an instantaneous value. An FEM model of the device is derived in a two-dimensional system and coupled with EMF circuits. The time-derivative term in the differential equation is solved in each time step by the finite difference method. It is concluded that the proposed algorithm is useful for analyzing CT characteristics, including the field distribution. Consequently, the proposed algorithm yields a reference for obtaining the effects of design parameters and magnetic materials for special shapes and sizes before the CT is designed and manufactured.
Zhang, B.; Oosterlee, C.W.
2011-01-01
We propose an efficient pricing method for arithmetic, and geometric, Asian options under Levy processes, based on Fourier cosine expansions and Clenshaw–Curtis quadrature. The pricing method is developed for both European–style and American–style Asian options, and for discretely and continuously
Fourier analysis and its applications
Folland, Gerald B
2009-01-01
This book presents the theory and applications of Fourier series and integrals, eigenfunction expansions, and related topics, on a level suitable for advanced undergraduates. It includes material on Bessel functions, orthogonal polynomials, and Laplace transforms, and it concludes with chapters on generalized functions and Green's functions for ordinary and partial differential equations. The book deals almost exclusively with aspects of these subjects that are useful in physics and engineering, and includes a wide variety of applications. On the theoretical side, it uses ideas from modern ana
Hornikx, M.C.J.; Dragna, D.
2015-01-01
The Fourier pseudospectral time-domain method is an efficient wave-based method to model sound propagation in inhomogeneous media. One of the limitations of the method for atmospheric sound propagation purposes is its restriction to a Cartesian grid, confining it to staircase-like geometries. A
Freud, Géza
1971-01-01
Orthogonal Polynomials contains an up-to-date survey of the general theory of orthogonal polynomials. It deals with the problem of polynomials and reveals that the sequence of these polynomials forms an orthogonal system with respect to a non-negative m-distribution defined on the real numerical axis. Comprised of five chapters, the book begins with the fundamental properties of orthogonal polynomials. After discussing the momentum problem, it then explains the quadrature procedure, the convergence theory, and G. Szegő's theory. This book is useful for those who intend to use it as referenc
International Nuclear Information System (INIS)
Sadeghi, Y.
2006-01-01
Computer Programs are important tools in physics. Analysis of the experimental data and the control of complex handle physical phenomenon and the solution of numerical problem in physics help scientist to the behavior and simulate the process. In this paper, calculation of several Fourier series gives us a visual and analytic impression of data analyses from Fourier series. One of important aspect in data analyses is to find optimum method for de-noising. Wavelets are mathematical functions that cut up data into different frequency components, and then study each component with a resolution corresponding to its scale. They have advantages over usual traditional methods in analyzing physical situations where the signal contains discontinuities and sharp spikes. Transformed data by wavelets in frequency space has time information and can clearly show the exact location in time of the discontinuity. This aspect makes wavelets an excellent tool in the field of data analysis. In this paper, we show how Fourier series and wavelets can analyses data in Damavand tokamak. ?
Yamasaki, K.; Fujisawa, A.; Nagashima, Y.
2017-09-01
It is a critical issue to find the best set of fitting function bases in mode structural analysis of two dimensional images like plasma emission profiles. The paper proposes a method to optimize a set of the bases in the case of Fourier-Bessel function series, using their orthonormal property, for more efficient and precise analysis. The method is applied on a tomography image of plasma emission obtained with the Maximum-likelihood expectation maximization method in a linear cylindrical device. The result demonstrates the excellency of the method that realizes the smaller residual error and minimum Akaike information criterion using smaller number of fitting function bases.
On Orthogonal Decomposition of a Sobolev Space
Lakew, Dejenie A.
2016-01-01
The theme of this short article is to investigate an orthogonal decomposition of a Sobolev space and look at some properties of the inner product therein and the distance defined from the inner product. We also determine the dimension of the orthogonal difference space and show the expansion of spaces as their regularity increases.
Generalizations of orthogonal polynomials
Bultheel, A.; Cuyt, A.; van Assche, W.; van Barel, M.; Verdonk, B.
2005-07-01
We give a survey of recent generalizations of orthogonal polynomials. That includes multidimensional (matrix and vector orthogonal polynomials) and multivariate versions, multipole (orthogonal rational functions) variants, and extensions of the orthogonality conditions (multiple orthogonality). Most of these generalizations are inspired by the applications in which they are applied. We also give a glimpse of these applications, which are usually generalizations of applications where classical orthogonal polynomials also play a fundamental role: moment problems, numerical quadrature, rational approximation, linear algebra, recurrence relations, and random matrices.
The finite Fourier transform of classical polynomials
Dixit, Atul; Jiu, Lin; Moll, Victor H.; Vignat, Christophe
2014-01-01
The finite Fourier transform of a family of orthogonal polynomials $A_{n}(x)$, is the usual transform of the polynomial extended by $0$ outside their natural domain. Explicit expressions are given for the Legendre, Jacobi, Gegenbauer and Chebyshev families.
International Nuclear Information System (INIS)
Boyd, John P.; Rangan, C.; Bucksbaum, P.H.
2003-01-01
The Fourier-sine-with-mapping pseudospectral algorithm of Fattal et al. [Phys. Rev. E 53 (1996) 1217] has been applied in several quantum physics problems. Here, we compare it with pseudospectral methods using Laguerre functions and rational Chebyshev functions. We show that Laguerre and Chebyshev expansions are better suited for solving problems in the interval r in R set of [0,∞] (for example, the Coulomb-Schroedinger equation), than the Fourier-sine-mapping scheme. All three methods give similar accuracy for the hydrogen atom when the scaling parameter L is optimum, but the Laguerre and Chebyshev methods are less sensitive to variations in L. We introduce a new variant of rational Chebyshev functions which has a more uniform spacing of grid points for large r, and gives somewhat better results than the rational Chebyshev functions of Boyd [J. Comp. Phys. 70 (1987) 63
Tunable fractional-order Fourier transformer
International Nuclear Information System (INIS)
Malyutin, A A
2006-01-01
A fractional two-dimensional Fourier transformer whose orders are tuned by means of optical quadrupoles is described. It is shown that in the optical scheme considered, the Fourier-transform order a element of [0,1] in one of the mutually orthogonal planes corresponds to the transform order (2-a) in another plane, i.e., to inversion and inverse Fourier transform of the order a. (laser modes and beams)
Many-body orthogonal polynomial systems
International Nuclear Information System (INIS)
Witte, N.S.
1997-03-01
The fundamental methods employed in the moment problem, involving orthogonal polynomial systems, the Lanczos algorithm, continued fraction analysis and Pade approximants has been combined with a cumulant approach and applied to the extensive many-body problem in physics. This has yielded many new exact results for many-body systems in the thermodynamic limit - for the ground state energy, for excited state gaps, for arbitrary ground state avenges - and are of a nonperturbative nature. These results flow from a confluence property of the three-term recurrence coefficients arising and define a general class of many-body orthogonal polynomials. These theorems constitute an analytical solution to the Lanczos algorithm in that they are expressed in terms of the three-term recurrence coefficients α and β. These results can also be applied approximately for non-solvable models in the form of an expansion, in a descending series of the system size. The zeroth order order this expansion is just the manifestation of the central limit theorem in which a Gaussian measure and hermite polynomials arise. The first order represents the first non-trivial order, in which classical distribution functions like the binomial distributions arise and the associated class of orthogonal polynomials are Meixner polynomials. Amongst examples of systems which have infinite order in the expansion are q-orthogonal polynomials where q depends on the system size in a particular way. (author)
Hoch, Jeffrey C.
2017-10-01
Non-Fourier methods of spectrum analysis are gaining traction in NMR spectroscopy, driven by their utility for processing nonuniformly sampled data. These methods afford new opportunities for optimizing experiment time, resolution, and sensitivity of multidimensional NMR experiments, but they also pose significant challenges not encountered with the discrete Fourier transform. A brief history of non-Fourier methods in NMR serves to place different approaches in context. Non-Fourier methods reflect broader trends in the growing importance of computation in NMR, and offer insights for future software development.
Hoch, Jeffrey C
2017-10-01
Non-Fourier methods of spectrum analysis are gaining traction in NMR spectroscopy, driven by their utility for processing nonuniformly sampled data. These methods afford new opportunities for optimizing experiment time, resolution, and sensitivity of multidimensional NMR experiments, but they also pose significant challenges not encountered with the discrete Fourier transform. A brief history of non-Fourier methods in NMR serves to place different approaches in context. Non-Fourier methods reflect broader trends in the growing importance of computation in NMR, and offer insights for future software development. Copyright © 2017 Elsevier Inc. All rights reserved.
Simultaneous orthogonal plane imaging.
Mickevicius, Nikolai J; Paulson, Eric S
2017-11-01
Intrafraction motion can result in a smearing of planned external beam radiation therapy dose distributions, resulting in an uncertainty in dose actually deposited in tissue. The purpose of this paper is to present a pulse sequence that is capable of imaging a moving target at a high frame rate in two orthogonal planes simultaneously for MR-guided radiotherapy. By balancing the zero gradient moment on all axes, slices in two orthogonal planes may be spatially encoded simultaneously. The orthogonal slice groups may be acquired with equal or nonequal echo times. A Cartesian spoiled gradient echo simultaneous orthogonal plane imaging (SOPI) sequence was tested in phantom and in vivo. Multiplexed SOPI acquisitions were performed in which two parallel slices were imaged along two orthogonal axes simultaneously. An autocalibrating phase-constrained 2D-SENSE-GRAPPA (generalized autocalibrating partially parallel acquisition) algorithm was implemented to reconstruct the multiplexed data. SOPI images without intraslice motion artifacts were reconstructed at a maximum frame rate of 8.16 Hz. The 2D-SENSE-GRAPPA reconstruction separated the parallel slices aliased along each orthogonal axis. The high spatiotemporal resolution provided by SOPI has the potential to be beneficial for intrafraction motion management during MR-guided radiation therapy or other MRI-guided interventions. Magn Reson Med 78:1700-1710, 2017. © 2016 International Society for Magnetic Resonance in Medicine. © 2016 International Society for Magnetic Resonance in Medicine.
Orthogonality and Dimensionality
Directory of Open Access Journals (Sweden)
Olivier Brunet
2013-12-01
Full Text Available In this article, we present what we believe to be a simple way to motivate the use of Hilbert spaces in quantum mechanics. To achieve this, we study the way the notion of dimension can, at a very primitive level, be defined as the cardinality of a maximal collection of mutually orthogonal elements (which, for instance, can be seen as spatial directions. Following this idea, we develop a formalism based on two basic ingredients, namely an orthogonality relation and matroids which are a very generic algebraic structure permitting to define a notion of dimension. Having obtained what we call orthomatroids, we then show that, in high enough dimension, the basic constituants of orthomatroids (more precisely the simple and irreducible ones are isomorphic to generalized Hilbert lattices, so that their presence is a direct consequence of an orthogonality-based characterization of dimension.
Orthogonalization of correlated states
International Nuclear Information System (INIS)
Fantoni, S.; Pandharipande, V.R.
1988-01-01
A scheme for orthogonalizing correlated states while preserving the diagonal matrix elements of the Hamiltonian is developed. Conventional perturbation theory can be used with the orthonormal correlated basis obtained from this scheme. Advantages of using orthonormal correlated states in calculations of the response function and correlation energy are discussed
Orthogonal serialisation for Haskell
DEFF Research Database (Denmark)
Berthold, Jost
2010-01-01
support for parallel Haskell on distributed memory platforms. This serialisation has highly desirable and so-far unrivalled properties: it is truly orthogonal to evaluation and also does not require any type class mechanisms. Especially, (almost) any kind of value can be serialised, including functions...
Orthogonal bases of radial functions for charge density refinements
International Nuclear Information System (INIS)
Restori, R.
1990-01-01
Charge density determination from X-ray measurements necessitates the evaluation of the Fourier-Bessel transforms of the radial functions used to expand the charge density. Analytical expressions are given here for four sets of orthogonal functions which can substitute for the 'traditional exponential functions' set in least-squares refinements. (orig.)
Indian Academy of Sciences (India)
polynomials are dense in the class of continuous functions! The body of literature dealing with Fourier series has reached epic proportions over the last two centuries. We have only given the readers an outline of the topic in this article. For the full length episode we refer the reader to the monumental treatise of. A Zygmund.
Indian Academy of Sciences (India)
The theory of Fourier series deals with periodic functions. By a periodic ..... including Dirichlet, Riemann and Cantor occupied themselves with the problem of ... to converge only on a set which is negligible in a certain sense (Le. of measure ...
Mason, A M
2018-01-01
In this paper the authors apply to the zeros of families of L-functions with orthogonal or symplectic symmetry the method that Conrey and Snaith (Correlations of eigenvalues and Riemann zeros, 2008) used to calculate the n-correlation of the zeros of the Riemann zeta function. This method uses the Ratios Conjectures (Conrey, Farmer, and Zimbauer, 2008) for averages of ratios of zeta or L-functions. Katz and Sarnak (Zeroes of zeta functions and symmetry, 1999) conjecture that the zero statistics of families of L-functions have an underlying symmetry relating to one of the classical compact groups U(N), O(N) and USp(2N). Here the authors complete the work already done with U(N) (Conrey and Snaith, Correlations of eigenvalues and Riemann zeros, 2008) to show how new methods for calculating the n-level densities of eigenangles of random orthogonal or symplectic matrices can be used to create explicit conjectures for the n-level densities of zeros of L-functions with orthogonal or symplectic symmetry, including al...
CSIR Research Space (South Africa)
Fedotov, I
2006-07-01
Full Text Available The Combined Helmholtz Integral Equation – Fourier series Formulation (CHIEFF) is based on representation of a velocity potential in terms of Fourier series and finding the Fourier coefficients of this expansion. The solution could be substantially...
App. 1. Fourier series and Fourier transform
International Nuclear Information System (INIS)
Anon.
1977-01-01
Definitions, formulas and practical properties in quantum mechanics are presented: Fourier series (development of periodic function, Bessel-Parseval equality); Fourier transform (Parseval-Plancherel formula, Fourier transform in three-dimensional space) [fr
Properties of the Magnitude Terms of Orthogonal Scaling Functions.
Tay, Peter C; Havlicek, Joseph P; Acton, Scott T; Hossack, John A
2010-09-01
The spectrum of the convolution of two continuous functions can be determined as the continuous Fourier transform of the cross-correlation function. The same can be said about the spectrum of the convolution of two infinite discrete sequences, which can be determined as the discrete time Fourier transform of the cross-correlation function of the two sequences. In current digital signal processing, the spectrum of the contiuous Fourier transform and the discrete time Fourier transform are approximately determined by numerical integration or by densely taking the discrete Fourier transform. It has been shown that all three transforms share many analogous properties. In this paper we will show another useful property of determining the spectrum terms of the convolution of two finite length sequences by determining the discrete Fourier transform of the modified cross-correlation function. In addition, two properties of the magnitude terms of orthogonal wavelet scaling functions are developed. These properties are used as constraints for an exhaustive search to determine an robust lower bound on conjoint localization of orthogonal scaling functions.
Reducing Approximation Error in the Fourier Flexible Functional Form
Directory of Open Access Journals (Sweden)
Tristan D. Skolrud
2017-12-01
Full Text Available The Fourier Flexible form provides a global approximation to an unknown data generating process. In terms of limiting function specification error, this form is preferable to functional forms based on second-order Taylor series expansions. The Fourier Flexible form is a truncated Fourier series expansion appended to a second-order expansion in logarithms. By replacing the logarithmic expansion with a Box-Cox transformation, we show that the Fourier Flexible form can reduce approximation error by 25% on average in the tails of the data distribution. The new functional form allows for nested testing of a larger set of commonly implemented functional forms.
Boundary value problems and Fourier expansions
MacCluer, Charles R
2004-01-01
Based on modern Sobolev methods, this text for advanced undergraduates and graduate students is highly physical in its orientation. It integrates numerical methods and symbolic manipulation into an elegant viewpoint that is consonant with implementation by digital computer. The first five sections form an informal introduction that develops students' physical and mathematical intuition. The following section introduces Hilbert space in its natural environment, and the next six sections pose and solve the standard problems. The final seven sections feature concise introductions to selected topi
Introduction to partial differential equations from Fourier series to boundary-value problems
Broman, Arne
2010-01-01
This well-written, advanced-level text introduces students to Fourier analysis and some of its applications. The self-contained treatment covers Fourier series, orthogonal systems, Fourier and Laplace transforms, Bessel functions, and partial differential equations of the first and second orders. Over 260 exercises with solutions reinforce students' grasp of the material. 1970 edition.
Theoretical Models for Orthogonal Cutting
DEFF Research Database (Denmark)
De Chiffre, Leonardo
This review of simple models for orthogonal cutting was extracted from: “L. De Chiffre: Metal Cutting Mechanics and Applications, D.Sc. Thesis, Technical University of Denmark, 1990.”......This review of simple models for orthogonal cutting was extracted from: “L. De Chiffre: Metal Cutting Mechanics and Applications, D.Sc. Thesis, Technical University of Denmark, 1990.”...
Alexandrov, Mikhail D.; Cairns, Brian; Mishchenko, Michael I.
2012-01-01
We present a novel technique for remote sensing of cloud droplet size distributions. Polarized reflectances in the scattering angle range between 135deg and 165deg exhibit a sharply defined rainbow structure, the shape of which is determined mostly by single scattering properties of cloud particles, and therefore, can be modeled using the Mie theory. Fitting the observed rainbow with such a model (computed for a parameterized family of particle size distributions) has been used for cloud droplet size retrievals. We discovered that the relationship between the rainbow structures and the corresponding particle size distributions is deeper than it had been commonly understood. In fact, the Mie theory-derived polarized reflectance as a function of reduced scattering angle (in the rainbow angular range) and the (monodisperse) particle radius appears to be a proxy to a kernel of an integral transform (similar to the sine Fourier transform on the positive semi-axis). This approach, called the rainbow Fourier transform (RFT), allows us to accurately retrieve the shape of the droplet size distribution by the application of the corresponding inverse transform to the observed polarized rainbow. While the basis functions of the proxy-transform are not exactly orthogonal in the finite angular range, this procedure needs to be complemented by a simple regression technique, which removes the retrieval artifacts. This non-parametric approach does not require any a priori knowledge of the droplet size distribution functional shape and is computationally fast (no look-up tables, no fitting, computations are the same as for the forward modeling).
An introduction to orthogonal polynomials
Chihara, Theodore S
1978-01-01
Assuming no further prerequisites than a first undergraduate course in real analysis, this concise introduction covers general elementary theory related to orthogonal polynomials. It includes necessary background material of the type not usually found in the standard mathematics curriculum. Suitable for advanced undergraduate and graduate courses, it is also appropriate for independent study. Topics include the representation theorem and distribution functions, continued fractions and chain sequences, the recurrence formula and properties of orthogonal polynomials, special functions, and some
Scattering theory and orthogonal polynomials
International Nuclear Information System (INIS)
Geronimo, J.S.
1977-01-01
The application of the techniques of scattering theory to the study of polynomials orthogonal on the unit circle and a finite segment of the real line is considered. The starting point is the recurrence relations satisfied by the polynomials instead of the orthogonality condition. A set of two two terms recurrence relations for polynomials orthogonal on the real line is presented and used. These recurrence relations play roles analogous to those satisfied by polynomials orthogonal on unit circle. With these recurrence formulas a Wronskian theorem is proved and the Christoffel-Darboux formula is derived. In scattering theory a fundamental role is played by the Jost function. An analogy is deferred of this function and its analytic properties and the locations of its zeros investigated. The role of the analog Jost function in various properties of these orthogonal polynomials is investigated. The techniques of inverse scattering theory are also used. The discrete analogues of the Gelfand-Levitan and Marchenko equations are derived and solved. These techniques are used to calculate asymptotic formulas for the orthogonal polynomials. Finally Szego's theorem on toeplitz and Hankel determinants is proved using the recurrence formulas and some properties of the Jost function. The techniques of inverse scattering theory are used to calculate the correction terms
Hyperbolic Cross Truncations for Stochastic Fourier Cosine Series
Zhang, Zhihua
2014-01-01
Based on our decomposition of stochastic processes and our asymptotic representations of Fourier cosine coefficients, we deduce an asymptotic formula of approximation errors of hyperbolic cross truncations for bivariate stochastic Fourier cosine series. Moreover we propose a kind of Fourier cosine expansions with polynomials factors such that the corresponding Fourier cosine coefficients decay very fast. Although our research is in the setting of stochastic processes, our results are also new for deterministic functions. PMID:25147842
(Anti)symmetric multivariate exponential functions and corresponding Fourier transforms
International Nuclear Information System (INIS)
Klimyk, A U; Patera, J
2007-01-01
We define and study symmetrized and antisymmetrized multivariate exponential functions. They are defined as determinants and antideterminants of matrices whose entries are exponential functions of one variable. These functions are eigenfunctions of the Laplace operator on the corresponding fundamental domains satisfying certain boundary conditions. To symmetric and antisymmetric multivariate exponential functions there correspond Fourier transforms. There are three types of such Fourier transforms: expansions into the corresponding Fourier series, integral Fourier transforms and multivariate finite Fourier transforms. Eigenfunctions of the integral Fourier transforms are found
Bolthausen, Erwin; Van Der Hofstad, Remco; Kozma, Gady
2018-01-01
We show Green's function asymptotic upper bound for the two-point function of weakly self-Avoiding walk in d >4, revisiting a classic problem. Our proof relies on Banach algebras to analyse the lace-expansion fixed point equation and is simpler than previous approaches in that it avoids Fourier
On some orthogonality properties of Maxwell's multipole vectors
International Nuclear Information System (INIS)
Gramada, Apostol
2007-01-01
We determine the location of the expansion points with respect to which the two Maxwell's multipole vectors of the quadrupole moment and the dipole vector of a distribution of charge form an orthogonal trihedron. We find that with respect to these 'orthogonality centres' both the dipole and the quadrupole moments are each characterized by a single real parameter. We further show that the orthogonality centres coincide with the stationary points of the magnitude of the quadrupole moment and, therefore, they can be seen as an extension of the concept of centre of the dipole moment of a neutral system introduced previously in the literature. The nature of the stationary points then provides the means for the classification of a distribution of charge in two different categories
Higher spin currents in orthogonal Wolf space
International Nuclear Information System (INIS)
Ahn, Changhyun; Paeng, Jinsub
2015-01-01
For the N=4 superconformal coset theory by ((SO(N+4))/(SO(N)×SU(2)))×U(1) (that contains an orthogonal Wolf space) with N = 4, the N=2 WZW affine current algebra is obtained. The 16 generators (or 11 generators) of the large N=4 linear (or nonlinear) superconformal algebra are described by these WZW affine currents explicitly. Along the line of large N=4 holography, the extra 16 currents with spins (2,(5/2),(5/2),3), ((5/2),3,3,(7/2)), ((5/2),3,3,(7/2)), and (3,(7/2),(7/2),4) are obtained in terms of the WZW affine currents. The lowest spin of this N=4 multiplet is two rather than one, which is for a unitary Wolf space. The operator product expansions between the above 11 currents and these extra 16 higher spin currents are found explicitly. (paper)
Fourier Series Formalization in ACL2(r
Directory of Open Access Journals (Sweden)
Cuong K. Chau
2015-09-01
Full Text Available We formalize some basic properties of Fourier series in the logic of ACL2(r, which is a variant of ACL2 that supports reasoning about the real and complex numbers by way of non-standard analysis. More specifically, we extend a framework for formally evaluating definite integrals of real-valued, continuous functions using the Second Fundamental Theorem of Calculus. Our extended framework is also applied to functions containing free arguments. Using this framework, we are able to prove the orthogonality relationships between trigonometric functions, which are the essential properties in Fourier series analysis. The sum rule for definite integrals of indexed sums is also formalized by applying the extended framework along with the First Fundamental Theorem of Calculus and the sum rule for differentiation. The Fourier coefficient formulas of periodic functions are then formalized from the orthogonality relations and the sum rule for integration. Consequently, the uniqueness of Fourier sums is a straightforward corollary. We also present our formalization of the sum rule for definite integrals of infinite series in ACL2(r. Part of this task is to prove the Dini Uniform Convergence Theorem and the continuity of a limit function under certain conditions. A key technique in our proofs of these theorems is to apply the overspill principle from non-standard analysis.
NIEMELÄ, EERO
2008-01-01
Tutkielman aiheena on Fourier-muunnoksen esittely. Tarkoituksena on erityisesti johdatella lukija Fourier-sarjan ja -muunnoksen käsitteisiin. Fourier-muunnosten teoria kuuluu yleisempään Fourier-analyysin aihepiiriin. Fourier-analyysin keskiössä on tulos, jonka mukaan tietyt ehdot täyttävää funktiota voidaan approksimoida mielivaltaisen tarkasti niin sanotun Fourier-sarjan avulla. Osoitamme, että 2\\pi-jaksollisen funktion Lebesgue-neliöintegroituvuus takaa suppenevan Fourier-sarjakehitelm...
Orthogonal Polynomials and Special Functions
Assche, Walter
2003-01-01
The set of lectures from the Summer School held in Leuven in 2002 provide an up-to-date account of recent developments in orthogonal polynomials and special functions, in particular for algorithms for computer algebra packages, 3nj-symbols in representation theory of Lie groups, enumeration, multivariable special functions and Dunkl operators, asymptotics via the Riemann-Hilbert method, exponential asymptotics and the Stokes phenomenon. The volume aims at graduate students and post-docs working in the field of orthogonal polynomials and special functions, and in related fields interacting with orthogonal polynomials, such as combinatorics, computer algebra, asymptotics, representation theory, harmonic analysis, differential equations, physics. The lectures are self-contained requiring only a basic knowledge of analysis and algebra, and each includes many exercises.
Symmetric functions and orthogonal polynomials
Macdonald, I G
1997-01-01
One of the most classical areas of algebra, the theory of symmetric functions and orthogonal polynomials has long been known to be connected to combinatorics, representation theory, and other branches of mathematics. Written by perhaps the most famous author on the topic, this volume explains some of the current developments regarding these connections. It is based on lectures presented by the author at Rutgers University. Specifically, he gives recent results on orthogonal polynomials associated with affine Hecke algebras, surveying the proofs of certain famous combinatorial conjectures.
Alternating multivariate trigonometric functions and corresponding Fourier transforms
International Nuclear Information System (INIS)
Klimyk, A U; Patera, J
2008-01-01
We define and study multivariate sine and cosine functions, symmetric with respect to the alternating group A n , which is a subgroup of the permutation (symmetric) group S n . These functions are eigenfunctions of the Laplace operator. They determine Fourier-type transforms. There exist three types of such transforms: expansions into corresponding sine-Fourier and cosine-Fourier series, integral sine-Fourier and cosine-Fourier transforms, and multivariate finite sine and cosine transforms. In all these transforms, alternating multivariate sine and cosine functions are used as a kernel
Julia Sets of Orthogonal Polynomials
DEFF Research Database (Denmark)
Christiansen, Jacob Stordal; Henriksen, Christian; Petersen, Henrik Laurberg
2018-01-01
For a probability measure with compact and non-polar support in the complex plane we relate dynamical properties of the associated sequence of orthogonal polynomials fPng to properties of the support. More precisely we relate the Julia set of Pn to the outer boundary of the support, the lled Julia...... set to the polynomial convex hull K of the support, and the Green's function associated with Pn to the Green's function for the complement of K....
International Nuclear Information System (INIS)
Hallenga, K.
1991-01-01
This paper discusses the concept of Fourier transformation one of the many precious legacies of the French mathematician Jean Baptiste Joseph Fourier, essential for understanding the link between continuous-wave (CW) and Fourier transform (FT) NMR. Although in modern FT NMR the methods used to obtain a frequency spectrum from the time-domain signal may vary greatly, from the efficient Cooley-Tukey algorithm to very elaborate iterative least-square methods based other maximum entropy method or on linear prediction, the principles for Fourier transformation are unchanged and give invaluable insight into the interconnection of many pairs of physical entities called Fourier pairs
Chromatic Derivatives, Chromatic Expansions and Associated Spaces
Ignjatovic, Aleksandar
2009-01-01
This paper presents the basic properties of chromatic derivatives and chromatic expansions and provides an appropriate motivation for introducing these notions. Chromatic derivatives are special, numerically robust linear differential operators which correspond to certain families of orthogonal polynomials. Chromatic expansions are series of the corresponding special functions, which possess the best features of both the Taylor and the Shannon expansions. This makes chromatic derivatives and ...
Orthogonality preserving infinite dimensional quadratic stochastic operators
International Nuclear Information System (INIS)
Akın, Hasan; Mukhamedov, Farrukh
2015-01-01
In the present paper, we consider a notion of orthogonal preserving nonlinear operators. We introduce π-Volterra quadratic operators finite and infinite dimensional settings. It is proved that any orthogonal preserving quadratic operator on finite dimensional simplex is π-Volterra quadratic operator. In infinite dimensional setting, we describe all π-Volterra operators in terms orthogonal preserving operators
Principles of Fourier analysis
Howell, Kenneth B
2001-01-01
Fourier analysis is one of the most useful and widely employed sets of tools for the engineer, the scientist, and the applied mathematician. As such, students and practitioners in these disciplines need a practical and mathematically solid introduction to its principles. They need straightforward verifications of its results and formulas, and they need clear indications of the limitations of those results and formulas.Principles of Fourier Analysis furnishes all this and more. It provides a comprehensive overview of the mathematical theory of Fourier analysis, including the development of Fourier series, "classical" Fourier transforms, generalized Fourier transforms and analysis, and the discrete theory. Much of the author''s development is strikingly different from typical presentations. His approach to defining the classical Fourier transform results in a much cleaner, more coherent theory that leads naturally to a starting point for the generalized theory. He also introduces a new generalized theory based ...
Jos, Sujit; Kumar, Preetam; Chakrabarti, Saswat
Orthogonal and quasi-orthogonal codes are integral part of any DS-CDMA based cellular systems. Orthogonal codes are ideal for use in perfectly synchronous scenario like downlink cellular communication. Quasi-orthogonal codes are preferred over orthogonal codes in the uplink communication where perfect synchronization cannot be achieved. In this paper, we attempt to compare orthogonal and quasi-orthogonal codes in presence of timing synchronization error. This will give insight into the synchronization demands in DS-CDMA systems employing the two classes of sequences. The synchronization error considered is smaller than chip duration. Monte-Carlo simulations have been carried out to verify the analytical and numerical results.
Orthogonal Multiwavelet Frames in L2Rd
Directory of Open Access Journals (Sweden)
Liu Zhanwei
2012-01-01
Full Text Available We characterize the orthogonal frames and orthogonal multiwavelet frames in L2Rd with matrix dilations of the form (Df(x=detAf(Ax, where A is an arbitrary expanding d×d matrix with integer coefficients. Firstly, through two arbitrarily multiwavelet frames, we give a simple construction of a pair of orthogonal multiwavelet frames. Then, by using the unitary extension principle, we present an algorithm for the construction of arbitrarily many orthogonal multiwavelet tight frames. Finally, we give a general construction algorithm for orthogonal multiwavelet tight frames from a scaling function.
Expansions for model-independent analyses of inelastic electron scattering
International Nuclear Information System (INIS)
Jackson, D.F.; Hilton, J.M.; Roberts, A.C.M.
1977-01-01
It is noted that the commonly-used Fourier-Bessel expansion for the transition density for inelastic electron scattering depends sensitively on an arbitrary parameter and is not realistic at large distances. Alternative expansions are suggested. (author)
Orthogonal polynomials and random matrices
Deift, Percy
2000-01-01
This volume expands on a set of lectures held at the Courant Institute on Riemann-Hilbert problems, orthogonal polynomials, and random matrix theory. The goal of the course was to prove universality for a variety of statistical quantities arising in the theory of random matrix models. The central question was the following: Why do very general ensembles of random n {\\times} n matrices exhibit universal behavior as n {\\rightarrow} {\\infty}? The main ingredient in the proof is the steepest descent method for oscillatory Riemann-Hilbert problems.
Towards orthogonal Haskell data serialisation
DEFF Research Database (Denmark)
Berthold, Jost
2010-01-01
This paper investigates a novel approach to serialisation of Haskell data structures with a high degree of flexibility, based on runtime support for parallel Haskell on distributed memory platforms. This serialisation has highly desirable and so-far unrivalled properties: it is truly orthogonal...... to evaluation and does not require any type class mechanisms. Especially, (almost) any kind of value can be serialised, including functions and IO actions. We outline the runtime support on which our serialisation is based, and present different versions of the wrapper code in Haskell which can ensure type...
Introduction to Real Orthogonal Polynomials
1992-06-01
uses Green’s functions. As motivation , consider the Dirichlet problem for the unit circle in the plane, which involves finding a harmonic function u(r...xv ; a, b ; q) - TO [q-N ab+’q ; q, xq b. Orthogoy RMotion O0 (bq :q)x p.(q* ; a, b ; q) pg(q’ ; a, b ; q) (q "q), (aq)x (q ; q), (I -abq) (bq ; q... motivation and justi- fication for continued study of the intrinsic structure of orthogonal polynomials. 99 LIST OF REFERENCES 1. Deyer, W. M., ed., CRC
Fractional finite Fourier transform.
Khare, Kedar; George, Nicholas
2004-07-01
We show that a fractional version of the finite Fourier transform may be defined by using prolate spheroidal wave functions of order zero. The transform is linear and additive in its index and asymptotically goes over to Namias's definition of the fractional Fourier transform. As a special case of this definition, it is shown that the finite Fourier transform may be inverted by using information over a finite range of frequencies in Fourier space, the inversion being sensitive to noise. Numerical illustrations for both forward (fractional) and inverse finite transforms are provided.
Fourier Series Optimization Opportunity
Winkel, Brian
2008-01-01
This note discusses the introduction of Fourier series as an immediate application of optimization of a function of more than one variable. Specifically, it is shown how the study of Fourier series can be motivated to enrich a multivariable calculus class. This is done through discovery learning and use of technology wherein students build the…
Sterken, C.
2003-03-01
This paper gives a short account of some key elements in the life of Jean Baptiste Joseph Fourier (1768-1830), specifically his relation to Napoleon Bonaparte. The mathematical approach to Fourier series and the original scepticism by French mathematicians are briefly illustrated.
Generalized Fourier transforms classes
DEFF Research Database (Denmark)
Berntsen, Svend; Møller, Steen
2002-01-01
The Fourier class of integral transforms with kernels $B(\\omega r)$ has by definition inverse transforms with kernel $B(-\\omega r)$. The space of such transforms is explicitly constructed. A slightly more general class of generalized Fourier transforms are introduced. From the general theory...
Directory of Open Access Journals (Sweden)
Osilenker Boris Petrovich
2013-08-01
Full Text Available The article has findings on convergence and additivity (uniform and almost universal of Fourier series in respect of loaded orthonormalized polynomials. The findings are applied to the Fourier series in respect of loaded Jacobi polynomials. The objective of research into loaded systems of mathematical physics was formulated in the classical book by R. Courant and D. Hilbert “Methods of Mathematical Physics”. Many researchers drive attention to polynomial systems, as they are used in the study of the Sturm–Liouville problem with a parameter in the boundary conditions, loaded integral equations and Schrodinger point potentials.As for applied problems, they are immediately related to important and frequent types of problems concerning concentrated loads, including oscillations of a heterogeneous loaded rod, torsional oscillations of a rod having pulleys at the ends, propagation of heat inside the rod having concentrated heat sources at the ends, etc.Анонсирован ряд результатов о сходимости и суммируемости (равномерно и почти всюду рядов Фурье по нагруженным ортонормированным полиномам. Полученные результаты прилагаются к рядам Фурье по нагруженным полиномам Якоби.
International Nuclear Information System (INIS)
Kobayashi, Keisuke; Ishibashi, Hideo
1978-01-01
A two-dimensional neutron diffusion equation for a triangular region is shown to be solved by the finite Fourier transformation. An application of the Fourier transformation to the diffusion equation for triangular region yields equations whose unknowns are the expansion coefficients of the neutron flux and current in Fourier series or Legendre polynomials expansions only at the region boundary. Some numerical calculations have revealed that the present technique gives accurate results. It is shown also that the solution using the expansion in Legendre polynomials converges with relatively few terms even if the solution in Fourier series exhibits the Gibbs' phenomenon. (auth.)
Directory of Open Access Journals (Sweden)
Moret Nicola
2010-01-01
Full Text Available Abstract We address the efficient realization of a filtered multitone (FMT modulation system and its orthogonal design. FMT modulation can be viewed as a Discrete Fourier Transform (DFT modulated filter bank (FB. It generalizes the popular orthogonal frequency division multiplexing (OFDM scheme by deploying frequency confined subchannel pulses. We compare three realizations that have been described by Cvetković and Vetterli (1998, and Weiss and Stewart (2000, and Tonello (2006. A detailed derivation of them is performed in the time-domain via the exploitation of different FB polyphase decompositions. We then consider the design of an orthogonal FMT system and we exploit the third realization which allows simplifying the orthogonal FB design and obtaining a block diagonal system matrix with independent subblocks. A numerical method is then presented to obtain an orthogonal FB with well frequency confined subchannel pulses for arbitrarily large number of subchannels. Several examples of pulses with minimal length are reported and their performance is evaluated in typical multipath fading channels. Finally, we compare the orthogonal FMT system with a cyclically prefixed OFDM system in the IEEE 802.11 wireless LAN channel. In this scenario, FMT with minimal length pulses and single tap subchannel equalization outperforms the OFDM system in achievable rate.
Directory of Open Access Journals (Sweden)
Andrea M. Tonello
2010-01-01
Full Text Available We address the efficient realization of a filtered multitone (FMT modulation system and its orthogonal design. FMT modulation can be viewed as a Discrete Fourier Transform (DFT modulated filter bank (FB. It generalizes the popular orthogonal frequency division multiplexing (OFDM scheme by deploying frequency confined subchannel pulses. We compare three realizations that have been described by Cvetković and Vetterli (1998, and Weiss and Stewart (2000, and Tonello (2006. A detailed derivation of them is performed in the time-domain via the exploitation of different FB polyphase decompositions. We then consider the design of an orthogonal FMT system and we exploit the third realization which allows simplifying the orthogonal FB design and obtaining a block diagonal system matrix with independent subblocks. A numerical method is then presented to obtain an orthogonal FB with well frequency confined subchannel pulses for arbitrarily large number of subchannels. Several examples of pulses with minimal length are reported and their performance is evaluated in typical multipath fading channels. Finally, we compare the orthogonal FMT system with a cyclically prefixed OFDM system in the IEEE 802.11 wireless LAN channel. In this scenario, FMT with minimal length pulses and single tap subchannel equalization outperforms the OFDM system in achievable rate.
Moret, Nicola; Tonello, Andrea M.
2010-12-01
We address the efficient realization of a filtered multitone (FMT) modulation system and its orthogonal design. FMT modulation can be viewed as a Discrete Fourier Transform (DFT) modulated filter bank (FB). It generalizes the popular orthogonal frequency division multiplexing (OFDM) scheme by deploying frequency confined subchannel pulses. We compare three realizations that have been described by Cvetković and Vetterli (1998), and Weiss and Stewart (2000), and Tonello (2006). A detailed derivation of them is performed in the time-domain via the exploitation of different FB polyphase decompositions. We then consider the design of an orthogonal FMT system and we exploit the third realization which allows simplifying the orthogonal FB design and obtaining a block diagonal system matrix with independent subblocks. A numerical method is then presented to obtain an orthogonal FB with well frequency confined subchannel pulses for arbitrarily large number of subchannels. Several examples of pulses with minimal length are reported and their performance is evaluated in typical multipath fading channels. Finally, we compare the orthogonal FMT system with a cyclically prefixed OFDM system in the IEEE 802.11 wireless LAN channel. In this scenario, FMT with minimal length pulses and single tap subchannel equalization outperforms the OFDM system in achievable rate.
Fourier analysis an introduction
Stein, Elias M
2003-01-01
This first volume, a three-part introduction to the subject, is intended for students with a beginning knowledge of mathematical analysis who are motivated to discover the ideas that shape Fourier analysis. It begins with the simple conviction that Fourier arrived at in the early nineteenth century when studying problems in the physical sciences--that an arbitrary function can be written as an infinite sum of the most basic trigonometric functions.The first part implements this idea in terms of notions of convergence and summability of Fourier series, while highlighting applications such as th
Debnath, Lokenath
2012-01-01
This article deals with a brief biographical sketch of Joseph Fourier, his first celebrated work on analytical theory of heat, his first great discovery of Fourier series and Fourier transforms. Included is a historical development of Fourier series and Fourier transforms with their properties, importance and applications. Special emphasis is made…
Digital Fourier analysis fundamentals
Kido, Ken'iti
2015-01-01
This textbook is a thorough, accessible introduction to digital Fourier analysis for undergraduate students in the sciences. Beginning with the principles of sine/cosine decomposition, the reader walks through the principles of discrete Fourier analysis before reaching the cornerstone of signal processing: the Fast Fourier Transform. Saturated with clear, coherent illustrations, "Digital Fourier Analysis - Fundamentals" includes practice problems and thorough Appendices for the advanced reader. As a special feature, the book includes interactive applets (available online) that mirror the illustrations. These user-friendly applets animate concepts interactively, allowing the user to experiment with the underlying mathematics. For example, a real sine signal can be treated as a sum of clockwise and counter-clockwise rotating vectors. The applet illustration included with the book animates the rotating vectors and the resulting sine signal. By changing parameters such as amplitude and frequency, the reader ca...
Fourier Transform Mass Spectrometry
Scigelova, Michaela; Hornshaw, Martin; Giannakopulos, Anastassios; Makarov, Alexander
2011-01-01
This article provides an introduction to Fourier transform-based mass spectrometry. The key performance characteristics of Fourier transform-based mass spectrometry, mass accuracy and resolution, are presented in the view of how they impact the interpretation of measurements in proteomic applications. The theory and principles of operation of two types of mass analyzer, Fourier transform ion cyclotron resonance and Orbitrap, are described. Major benefits as well as limitations of Fourier transform-based mass spectrometry technology are discussed in the context of practical sample analysis, and illustrated with examples included as figures in this text and in the accompanying slide set. Comparisons highlighting the performance differences between the two mass analyzers are made where deemed useful in assisting the user with choosing the most appropriate technology for an application. Recent developments of these high-performing mass spectrometers are mentioned to provide a future outlook. PMID:21742802
Generalized Fourier transforms classes
DEFF Research Database (Denmark)
Berntsen, Svend; Møller, Steen
2002-01-01
The Fourier class of integral transforms with kernels $B(\\omega r)$ has by definition inverse transforms with kernel $B(-\\omega r)$. The space of such transforms is explicitly constructed. A slightly more general class of generalized Fourier transforms are introduced. From the general theory foll...... follows that integral transform with kernels which are products of a Bessel and a Hankel function or which is of a certain general hypergeometric type have inverse transforms of the same structure....
Generalized fiber Fourier optics.
Cincotti, Gabriella
2011-06-15
A twofold generalization of the optical schemes that perform the discrete Fourier transform (DFT) is given: new passive planar architectures are presented where the 2 × 2 3 dB couplers are replaced by M × M hybrids, reducing the number of required connections and phase shifters. Furthermore, the planar implementation of the discrete fractional Fourier transform (DFrFT) is also described, with a waveguide grating router (WGR) configuration and a properly modified slab coupler.
Directory of Open Access Journals (Sweden)
Harold Exton
1996-05-01
Full Text Available A special case of the biconfluent Heun equation which is not reducible to a form of a hypergeometric equation is solved by means of a Laplace transform. The solutions are double series which exhibit a type of orthogonality comparable in some respects to that of Fourier-Bessel type.
Orthogonal sparse linear discriminant analysis
Liu, Zhonghua; Liu, Gang; Pu, Jiexin; Wang, Xiaohong; Wang, Haijun
2018-03-01
Linear discriminant analysis (LDA) is a linear feature extraction approach, and it has received much attention. On the basis of LDA, researchers have done a lot of research work on it, and many variant versions of LDA were proposed. However, the inherent problem of LDA cannot be solved very well by the variant methods. The major disadvantages of the classical LDA are as follows. First, it is sensitive to outliers and noises. Second, only the global discriminant structure is preserved, while the local discriminant information is ignored. In this paper, we present a new orthogonal sparse linear discriminant analysis (OSLDA) algorithm. The k nearest neighbour graph is first constructed to preserve the locality discriminant information of sample points. Then, L2,1-norm constraint on the projection matrix is used to act as loss function, which can make the proposed method robust to outliers in data points. Extensive experiments have been performed on several standard public image databases, and the experiment results demonstrate the performance of the proposed OSLDA algorithm.
Fourier transformation for engineering and natural science
International Nuclear Information System (INIS)
Klingen, B.
2001-01-01
The following topics are covered: functions, Dirac delta function, Fourier operators, Fourier integrals, Fourier transformation and periodic functions, discrete Fourier transformations and discrete filters, applications. (WL)
Orthogonal polynomials in transport theories
International Nuclear Information System (INIS)
Dehesa, J.S.
1981-01-01
The asymptotical (k→infinity) behaviour of zeros of the polynomials gsub(k)sup((m)(ν)) encountered in the treatment of direct and inverse problems of scattering in neutron transport as well as radiative transfer theories is investigated in terms of the amplitude antiwsub(k) of the kth Legendre polynomial needed in the expansion of the scattering function. The parameters antiwsub(k) describe the anisotropy of scattering of the medium considered. In particular, it is shown that the asymptotical density of zeros of the polynomials gsub(k)sup(m)(ν) is an inverted semicircle for the anisotropic non-multiplying scattering medium
Power system frequency estimation based on an orthogonal decomposition method
Lee, Chih-Hung; Tsai, Men-Shen
2018-06-01
In recent years, several frequency estimation techniques have been proposed by which to estimate the frequency variations in power systems. In order to properly identify power quality issues under asynchronously-sampled signals that are contaminated with noise, flicker, and harmonic and inter-harmonic components, a good frequency estimator that is able to estimate the frequency as well as the rate of frequency changes precisely is needed. However, accurately estimating the fundamental frequency becomes a very difficult task without a priori information about the sampling frequency. In this paper, a better frequency evaluation scheme for power systems is proposed. This method employs a reconstruction technique in combination with orthogonal filters, which may maintain the required frequency characteristics of the orthogonal filters and improve the overall efficiency of power system monitoring through two-stage sliding discrete Fourier transforms. The results showed that this method can accurately estimate the power system frequency under different conditions, including asynchronously sampled signals contaminated by noise, flicker, and harmonic and inter-harmonic components. The proposed approach also provides high computational efficiency.
[Orthogonal Vector Projection Algorithm for Spectral Unmixing].
Song, Mei-ping; Xu, Xing-wei; Chang, Chein-I; An, Ju-bai; Yao, Li
2015-12-01
Spectrum unmixing is an important part of hyperspectral technologies, which is essential for material quantity analysis in hyperspectral imagery. Most linear unmixing algorithms require computations of matrix multiplication and matrix inversion or matrix determination. These are difficult for programming, especially hard for realization on hardware. At the same time, the computation costs of the algorithms increase significantly as the number of endmembers grows. Here, based on the traditional algorithm Orthogonal Subspace Projection, a new method called. Orthogonal Vector Projection is prompted using orthogonal principle. It simplifies this process by avoiding matrix multiplication and inversion. It firstly computes the final orthogonal vector via Gram-Schmidt process for each endmember spectrum. And then, these orthogonal vectors are used as projection vector for the pixel signature. The unconstrained abundance can be obtained directly by projecting the signature to the projection vectors, and computing the ratio of projected vector length and orthogonal vector length. Compared to the Orthogonal Subspace Projection and Least Squares Error algorithms, this method does not need matrix inversion, which is much computation costing and hard to implement on hardware. It just completes the orthogonalization process by repeated vector operations, easy for application on both parallel computation and hardware. The reasonability of the algorithm is proved by its relationship with Orthogonal Sub-space Projection and Least Squares Error algorithms. And its computational complexity is also compared with the other two algorithms', which is the lowest one. At last, the experimental results on synthetic image and real image are also provided, giving another evidence for effectiveness of the method.
On orthogonality preserving quadratic stochastic operators
Energy Technology Data Exchange (ETDEWEB)
Mukhamedov, Farrukh; Taha, Muhammad Hafizuddin Mohd [Department of Computational and Theoretical Sciences, Faculty of Science International Islamic University Malaysia, P.O. Box 141, 25710 Kuantan, Pahang Malaysia (Malaysia)
2015-05-15
A quadratic stochastic operator (in short QSO) is usually used to present the time evolution of differing species in biology. Some quadratic stochastic operators have been studied by Lotka and Volterra. In the present paper, we first give a simple characterization of Volterra QSO in terms of absolutely continuity of discrete measures. Further, we introduce a notion of orthogonal preserving QSO, and describe such kind of operators defined on two dimensional simplex. It turns out that orthogonal preserving QSOs are permutations of Volterra QSO. The associativity of genetic algebras generated by orthogonal preserving QSO is studied too.
On orthogonality preserving quadratic stochastic operators
International Nuclear Information System (INIS)
Mukhamedov, Farrukh; Taha, Muhammad Hafizuddin Mohd
2015-01-01
A quadratic stochastic operator (in short QSO) is usually used to present the time evolution of differing species in biology. Some quadratic stochastic operators have been studied by Lotka and Volterra. In the present paper, we first give a simple characterization of Volterra QSO in terms of absolutely continuity of discrete measures. Further, we introduce a notion of orthogonal preserving QSO, and describe such kind of operators defined on two dimensional simplex. It turns out that orthogonal preserving QSOs are permutations of Volterra QSO. The associativity of genetic algebras generated by orthogonal preserving QSO is studied too
The Role of Orthogonal Polynomials in Tailoring Spherical Distributions to Kurtosis Requirements
Directory of Open Access Journals (Sweden)
Luca Bagnato
2016-08-01
Full Text Available This paper carries out an investigation of the orthogonal-polynomial approach to reshaping symmetric distributions to fit in with data requirements so as to cover the multivariate case. With this objective in mind, reference is made to the class of spherical distributions, given that they provide a natural multivariate generalization of univariate even densities. After showing how to tailor a spherical distribution via orthogonal polynomials to better comply with kurtosis requirements, we provide operational conditions for the positiveness of the resulting multivariate Gram–Charlier-like expansion, together with its kurtosis range. Finally, the approach proposed here is applied to some selected spherical distributions.
Is Fourier analysis performed by the visual system or by the visual investigator.
Ochs, A L
1979-01-01
A numerical Fourier transform was made of the pincushion grid illusion and the spectral components orthogonal to the illusory lines were isolated. Their inverse transform creates a picture of the illusion. The spatial-frequency response of cortical, simple receptive field neurons similarly filters the grid. A complete set of these neurons thus approximates a two-dimensional Fourier analyzer. One cannot conclude, however, that the brain actually uses frequency-domain information to interpret visual images.
International Nuclear Information System (INIS)
Yun, Y.
2015-01-01
Thermal expansion of fuel pellet is an important property which limits the lifetime of the fuels in reactors, because it affects both the pellet and cladding mechanical interaction and the gap conductivity. By fitting a number of available measured data, recommended equations have been presented and successfully used to estimate thermal expansion coefficient of the nuclear fuel pellet. However, due to large scatter of the measured data, non-consensus data have been omitted in formulating the equations. Also, the equation is strongly governed by the lack of appropriate experimental data. For those reasons, it is important to develop theoretical methodologies to better describe thermal expansion behaviour of nuclear fuel. In particular, first-principles and molecular dynamics simulations have been certainly contributed to predict reliable thermal expansion without fitting the measured data. Furthermore, the two theoretical techniques have improved on understanding the change of fuel dimension by describing the atomic-scale processes associated with lattice expansion in the fuels. (author)
Fourier plane imaging microscopy
Energy Technology Data Exchange (ETDEWEB)
Dominguez, Daniel, E-mail: daniel.dominguez@ttu.edu; Peralta, Luis Grave de [Department of Physics, Texas Tech University, Lubbock, Texas 79409 (United States); Nano Tech Center, Texas Tech University, Lubbock, Texas 79409 (United States); Alharbi, Nouf; Alhusain, Mdhaoui [Department of Physics, Texas Tech University, Lubbock, Texas 79409 (United States); Bernussi, Ayrton A. [Nano Tech Center, Texas Tech University, Lubbock, Texas 79409 (United States); Department of Electrical and Computer Engineering, Texas Tech University, Lubbock, Texas 79409 (United States)
2014-09-14
We show how the image of an unresolved photonic crystal can be reconstructed using a single Fourier plane (FP) image obtained with a second camera that was added to a traditional compound microscope. We discuss how Fourier plane imaging microscopy is an application of a remarkable property of the obtained FP images: they contain more information about the photonic crystals than the images recorded by the camera commonly placed at the real plane of the microscope. We argue that the experimental results support the hypothesis that surface waves, contributing to enhanced resolution abilities, were optically excited in the studied photonic crystals.
Definite Integrals using Orthogonality and Integral Transforms
Directory of Open Access Journals (Sweden)
Howard S. Cohl
2012-10-01
Full Text Available We obtain definite integrals for products of associated Legendre functions with Bessel functions, associated Legendre functions, and Chebyshev polynomials of the first kind using orthogonality and integral transforms.
Sign patterns of J-orthogonal matrices
Czech Academy of Sciences Publication Activity Database
Hall, F.J.; Li, Z.; Parnass, C.; Rozložník, Miroslav
2017-01-01
Roč. 5, č. 1 (2017), s. 225-241 ISSN 2300-7451 Institutional support: RVO:67985840 Keywords : G-matrix * J-orthogonal matrix * sign pattern matrix * sign patterns that allow J-orthogonality Subject RIV: BA - General Mathematics OBOR OECD: Applied mathematics https://www.degruyter.com/view/j/spma.2017.5.issue-1/spma-2017-0016/spma-2017-0016.xml?format=INT
Sign patterns of J-orthogonal matrices
Czech Academy of Sciences Publication Activity Database
Hall, F.J.; Li, Z.; Parnass, C.; Rozložník, Miroslav
2017-01-01
Roč. 5, č. 1 (2017), s. 225-241 ISSN 2300-7451 Institutional support: RVO:67985840 Keywords : G-matrix * J-orthogonal matrix * sign pattern matrix * sign patterns that allow J-orthogonality Subject RIV: BA - General Mathematics OBOR OECD: Applied mathematics https://www.degruyter.com/view/j/spma.2017.5.issue-1/spma-2017-0016/spma-2017-0016. xml ?format=INT
The morphing of geographical features by Fourier transformation.
Li, Jingzhong; Liu, Pengcheng; Yu, Wenhao; Cheng, Xiaoqiang
2018-01-01
This paper presents a morphing model of vector geographical data based on Fourier transformation. This model involves three main steps. They are conversion from vector data to Fourier series, generation of intermediate function by combination of the two Fourier series concerning a large scale and a small scale, and reverse conversion from combination function to vector data. By mirror processing, the model can also be used for morphing of linear features. Experimental results show that this method is sensitive to scale variations and it can be used for vector map features' continuous scale transformation. The efficiency of this model is linearly related to the point number of shape boundary and the interceptive value n of Fourier expansion. The effect of morphing by Fourier transformation is plausible and the efficiency of the algorithm is acceptable.
From Fourier Transforms to Singular Eigenfunctions for Multigroup Transport
International Nuclear Information System (INIS)
Ganapol, B.D.
2001-01-01
A new Fourier transform approach to the solution of the multigroup transport equation with anisotropic scattering and isotropic source is presented. Through routine analytical continuation, the inversion contour is shifted from the real line to produce contributions from the poles and cuts in the complex plane. The integrand along the branch cut is then recast in terms of matrix continuum singular eigenfunctions, demonstrating equivalence of Fourier transform inversion and the singular eigenfunction expansion. The significance of this paper is that it represents the initial step in revealing the intimate connection between the Fourier transform and singular eigenfunction approaches as well as serves as a basis for a numerical algorithm
Fourier Transform Mass Spectrometry.
Gross, Michael L.; Rempel, Don L.
1984-01-01
Discusses the nature of Fourier transform mass spectrometry and its unique combination of high mass resolution, high upper mass limit, and multichannel advantage. Examines its operation, capabilities and limitations, applications (ion storage, ion manipulation, ion chemistry), and future applications and developments. (JN)
Approximating the Analytic Fourier Transform with the Discrete Fourier Transform
Axelrod, Jeremy
2015-01-01
The Fourier transform is approximated over a finite domain using a Riemann sum. This Riemann sum is then expressed in terms of the discrete Fourier transform, which allows the sum to be computed with a fast Fourier transform algorithm more rapidly than via a direct matrix multiplication. Advantages and limitations of using this method to approximate the Fourier transform are discussed, and prototypical MATLAB codes implementing the method are presented.
Interlacing of zeros of quasi-orthogonal meixner polynomials | Driver ...
African Journals Online (AJOL)
... interlacing of zeros of quasi-orthogonal Meixner polynomials Mn(x;β; c) with the zeros of their nearest orthogonal counterparts Mt(x;β + k; c), l; n ∈ ℕ, k ∈ {1; 2}; is also discussed. Mathematics Subject Classication (2010): 33C45, 42C05. Key words: Discrete orthogonal polynomials, quasi-orthogonal polynomials, Meixner
Grafakos, Loukas
2014-01-01
The main goal of this text is to present the theoretical foundation of the field of Fourier analysis on Euclidean spaces. It covers classical topics such as interpolation, Fourier series, the Fourier transform, maximal functions, singular integrals, and Littlewood–Paley theory. The primary readership is intended to be graduate students in mathematics with the prerequisite including satisfactory completion of courses in real and complex variables. The coverage of topics and exposition style are designed to leave no gaps in understanding and stimulate further study. This third edition includes new Sections 3.5, 4.4, 4.5 as well as a new chapter on “Weighted Inequalities,” which has been moved from GTM 250, 2nd Edition. Appendices I and B.9 are also new to this edition. Countless corrections and improvements have been made to the material from the second edition. Additions and improvements include: more examples and applications, new and more relevant hints for the existing exercises, new exercises, and...
Fourier techniques and applications
1985-01-01
The first systematic methods of Fourier analysis date from the early eighteenth century with the work of Joseph Fourier on the problem of the flow of heat. (A brief history is contained in the first paper.) Given the initial tempera ture at all points of a region, the problem was to determine the changes in the temperature distribution over time. Understanding and predicting these changes was important in such areas as the handling of metals and the determination of geological and atmospheric temperatures. Briefly, Fourier noticed that the solution of the heat diffusion problem was simple if the initial temperature dis tribution was sinusoidal. He then asserted that any distri bution can be decomposed into a sum of sinusoids, these being the harmonics of the original function. This meant that the general solution could now be obtained by summing the solu tions of the component sinusoidal problems. This remarkable ability of the series of sinusoids to describe all "reasonable" functions, the sine qua n...
Directory of Open Access Journals (Sweden)
Masjed-Jamei Mohammad
2005-01-01
Full Text Available From the main equation ( a x 2 +bx+c y ″ n ( x +( dx+e y ′ n ( x −n( ( n−1 a+d y n ( x =0 , n∈ ℤ + , six finite and infinite classes of orthogonal polynomials can be extracted. In this work, first we have a survey on these classes, particularly on finite classes, and their corresponding rational orthogonal polynomials, which are generated by Mobius transform x=p z −1 +q , p≠0 , q∈ℝ . Some new integral relations are also given in this section for the Jacobi, Laguerre, and Bessel orthogonal polynomials. Then we show that the rational orthogonal polynomials can be a very suitable tool to compute the inverse Laplace transform directly, with no additional calculation for finding their roots. In this way, by applying infinite and finite rational classical orthogonal polynomials, we give three basic expansions of six ones as a sample for computation of inverse Laplace transform.
Fourier transforms principles and applications
Hansen, Eric W
2014-01-01
Fourier Transforms: Principles and Applications explains transform methods and their applications to electrical systems from circuits, antennas, and signal processors-ably guiding readers from vector space concepts through the Discrete Fourier Transform (DFT), Fourier series, and Fourier transform to other related transform methods. Featuring chapter end summaries of key results, over two hundred examples and four hundred homework problems, and a Solutions Manual this book is perfect for graduate students in signal processing and communications as well as practicing engineers.
Orthogonality catastrophe and fractional exclusion statistics
Ares, Filiberto; Gupta, Kumar S.; de Queiroz, Amilcar R.
2018-02-01
We show that the N -particle Sutherland model with inverse-square and harmonic interactions exhibits orthogonality catastrophe. For a fixed value of the harmonic coupling, the overlap of the N -body ground state wave functions with two different values of the inverse-square interaction term goes to zero in the thermodynamic limit. When the two values of the inverse-square coupling differ by an infinitesimal amount, the wave function overlap shows an exponential suppression. This is qualitatively different from the usual power law suppression observed in the Anderson's orthogonality catastrophe. We also obtain an analytic expression for the wave function overlaps for an arbitrary set of couplings, whose properties are analyzed numerically. The quasiparticles constituting the ground state wave functions of the Sutherland model are known to obey fractional exclusion statistics. Our analysis indicates that the orthogonality catastrophe may be valid in systems with more general kinds of statistics than just the fermionic type.
Orthogonal Coupling in Cavity BPM with Slots
Lipka, D; Siemens, M; Vilcins, S; Caspers, Friedhelm; Stadler, M; Treyer, DM; Maesaka, H; Shintake, T
2009-01-01
XFELs require high precision orbit control in their long undulator sections. Due to the pulsed operation of drive linacs the high precision has to be reached by single bunch measurements. So far only cavity BPMs achieve the required performance and will be used at the European XFEL, one between each of the up to 116 undulators. Coupling between the orthogonal planes limits the performance of beam position measurements. A first prototype build at DESY shows a coupling between orthogonal planes of about -20 dB, but the requirement is lower than -40 dB (1%). The next generation cavity BPM was build with tighter tolerances and mechanical changes, the orthogonal coupling is measured to be lower than -43 dB. This report discusses the various observations, measurements and improvements which were done.
On the Fourier integral theorem
Koekoek, J.
1987-01-01
Introduction. In traditional proofs of convergence of Fourier series and of the Fourier integraI theorem basic tools are the theory of Dirichlet integraIs and the Riemann-Lebesgue lemma. Recently CHERNOFF [I) and REoIlEFFER (2) gave new proofs of convergenceof Fourier series which make no use of the
Riemannian geometry in an orthogonal frame
Cartan, Elie Joseph
2001-01-01
Foreword by S S Chern. In 1926-27, Cartan gave a series of lectures in which he introduced exterior forms at the very beginning and used extensively orthogonal frames throughout to investigate the geometry of Riemannian manifolds. In this course he solved a series of problems in Euclidean and non-Euclidean spaces, as well as a series of variational problems on geodesics. In 1960, Sergei P Finikov translated from French into Russian his notes of these Cartan's lectures and published them as a book entitled Riemannian Geometry in an Orthogonal Frame. This book has many innovations, such as the n
Differential recurrence formulae for orthogonal polynomials
Directory of Open Access Journals (Sweden)
Anton L. W. von Bachhaus
1995-11-01
Full Text Available Part I - By combining a general 2nd-order linear homogeneous ordinary differential equation with the three-term recurrence relation possessed by all orthogonal polynomials, it is shown that sequences of orthogonal polynomials which satisfy a differential equation of the above mentioned type necessarily have a differentiation formula of the type: gn(xY'n(x=fn(xYn(x+Yn-1(x. Part II - A recurrence formula of the form: rn(xY'n(x+sn(xY'n+1(x+tn(xY'n-1(x=0, is derived using the result of Part I.
International Nuclear Information System (INIS)
Knoll, J.
1985-10-01
A quantum dynamical model is suggested which describes the expansion and disassembly phase of highly excited compounds formed in energetic heavy-ion collisions. First applications in two space and one time dimensional model world are discussed and qualitatively compared to standard freeze-out concepts. (orig.)
Indian Academy of Sciences (India)
of a system under investigation is to model the system in terms of some ... The organization of the paper is as follows: In §2, a brief account of the (G /G)- expansion ...... It is interesting to note that from the general results, one can easily recover.
Fourier transforms in spectroscopy
Kauppinen, Jyrki
2000-01-01
This modern approach to the subject is clearly and logically structured, and gives readers an understanding of the essence of Fourier transforms and their applications. All important aspects are included with respect to their use with optical spectroscopic data. Based on popular lectures, the authors provide the mathematical fundamentals and numerical applications which are essential in practical use. The main part of the book is dedicated to applications of FT in signal processing and spectroscopy, with IR and NIR, NMR and mass spectrometry dealt with both from a theoretical and practical poi
Feldkhun, Daniel (Inventor); Wagner, Kelvin H. (Inventor)
2013-01-01
Methods and systems are disclosed of sensing an object. A first radiation is spatially modulated to generate a structured second radiation. The object is illuminated with the structured second radiation such that the object produces a third radiation in response. Apart from any spatially dependent delay, a time variation of the third radiation is spatially independent. With a single-element detector, a portion of the third radiation is detected from locations on the object simultaneously. At least one characteristic of a sinusoidal spatial Fourier-transform component of the object is estimated from a time-varying signal from the detected portion of the third radiation.
Nonclassical Orthogonal Polynomials and Corresponding Quadratures
Fukuda, H; Alt, E O; Matveenko, A V
2004-01-01
We construct nonclassical orthogonal polynomials and calculate abscissas and weights of Gaussian quadrature for arbitrary weight and interval. The program is written by Mathematica and it works if moment integrals are given analytically. The result is a FORTRAN subroutine ready to utilize the quadrature.
A new description of orthogonal bases
Coecke, Bob; Pavlovic, Dusko; Vicary, Jamie
2012-01-01
We show that an orthogonal basis for a finite-dimensional Hilbert space can be equivalently characterised as a commutative †-Frobenius monoid in the category FdHilb, which has finite-dimensional Hilbert spaces as objects and continuous linear maps as morphisms, and tensor product for the monoidal
A class of orthogonal nonrecursive binomial filters.
Haddad, R. A.
1971-01-01
The time- and frequency-domain properties of the orthogonal binomial sequences are presented. It is shown that these sequences, or digital filters based on them, can be generated using adders and delay elements only. The frequency-domain behavior of these nonrecursive binomial filters suggests a number of applications as low-pass Gaussian filters or as inexpensive bandpass filters.
Local copying of orthogonal entangled quantum states
International Nuclear Information System (INIS)
Anselmi, Fabio; Chefles, Anthony; Plenio, Martin B
2004-01-01
In classical information theory one can, in principle, produce a perfect copy of any input state. In quantum information theory, the no cloning theorem prohibits exact copying of non-orthogonal states. Moreover, if we wish to copy multiparticle entangled states and can perform only local operations and classical communication (LOCC), then further restrictions apply. We investigate the problem of copying orthogonal, entangled quantum states with an entangled blank state under the restriction to LOCC. Throughout, the subsystems have finite dimension D. We show that if all of the states to be copied are non-maximally entangled, then novel LOCC copying procedures based on entanglement catalysis are possible. We then study in detail the LOCC copying problem where both the blank state and at least one of the states to be copied are maximally entangled. For this to be possible, we find that all the states to be copied must be maximally entangled. We obtain a necessary and sufficient condition for LOCC copying under these conditions. For two orthogonal, maximally entangled states, we provide the general solution to this condition. We use it to show that for D = 2, 3, any pair of orthogonal, maximally entangled states can be locally copied using a maximally entangled blank state. However, we also show that for any D which is not prime, one can construct pairs of such states for which this is impossible
On the windowed Fourier transform as an interpolation of the Gabor transform
Bastiaans, M.J.; Prochßzka, A.; Uhlør, J.; Sovka, P.
1997-01-01
The windowed Fourier transform and its sampled version - the Gabor transform - are introduced. With the help of Gabor's signal expansion, an interpolation function is derived with which the windowed Fourier transform can be constructed from the Gabor transform. Using the Zak transform, it is shown
Study on MHD instabilities in the CECI plasma device using Fourier probes
International Nuclear Information System (INIS)
Rosal, A.C.; Aso, Y.; Ueda, M.
1991-01-01
A magnetic diagnostics called Fourier analyser aiming to study MHD instabilities by Fourier series expansion of poloidal magnetic field for m ≤ 3 modes was developed and tested. The diagnostics will be used in the RFP (reversed field pinch) type toroidal plasma device. (M.C.K.)
Fast Fourier transform telescope
International Nuclear Information System (INIS)
Tegmark, Max; Zaldarriaga, Matias
2009-01-01
We propose an all-digital telescope for 21 cm tomography, which combines key advantages of both single dishes and interferometers. The electric field is digitized by antennas on a rectangular grid, after which a series of fast Fourier transforms recovers simultaneous multifrequency images of up to half the sky. Thanks to Moore's law, the bandwidth up to which this is feasible has now reached about 1 GHz, and will likely continue doubling every couple of years. The main advantages over a single dish telescope are cost and orders of magnitude larger field-of-view, translating into dramatically better sensitivity for large-area surveys. The key advantages over traditional interferometers are cost (the correlator computational cost for an N-element array scales as Nlog 2 N rather than N 2 ) and a compact synthesized beam. We argue that 21 cm tomography could be an ideal first application of a very large fast Fourier transform telescope, which would provide both massive sensitivity improvements per dollar and mitigate the off-beam point source foreground problem with its clean beam. Another potentially interesting application is cosmic microwave background polarization.
Matrix-Vector Based Fast Fourier Transformations on SDR Architectures
Directory of Open Access Journals (Sweden)
Y. He
2008-05-01
Full Text Available Today Discrete Fourier Transforms (DFTs are applied in various radio standards based on OFDM (Orthogonal Frequency Division Multiplex. It is important to gain a fast computational speed for the DFT, which is usually achieved by using specialized Fast Fourier Transform (FFT engines. However, in face of the Software Defined Radio (SDR development, more general (parallel processor architectures are often desirable, which are not tailored to FFT computations. Therefore, alternative approaches are required to reduce the complexity of the DFT. Starting from a matrix-vector based description of the FFT idea, we will present different factorizations of the DFT matrix, which allow a reduction of the complexity that lies between the original DFT and the minimum FFT complexity. The computational complexities of these factorizations and their suitability for implementation on different processor architectures are investigated.
Fourier Transform Spectrometer System
Campbell, Joel F. (Inventor)
2014-01-01
A Fourier transform spectrometer (FTS) data acquisition system includes an FTS spectrometer that receives a spectral signal and a laser signal. The system further includes a wideband detector, which is in communication with the FTS spectrometer and receives the spectral signal and laser signal from the FTS spectrometer. The wideband detector produces a composite signal comprising the laser signal and the spectral signal. The system further comprises a converter in communication with the wideband detector to receive and digitize the composite signal. The system further includes a signal processing unit that receives the composite signal from the converter. The signal processing unit further filters the laser signal and the spectral signal from the composite signal and demodulates the laser signal, to produce velocity corrected spectral data.
Gauthier, Robert C.; Alzahrani, Mohammed A.; Jafari, Seyed Hamed
2015-02-01
The plane wave expansion (PWM) technique applied to Maxwell's wave equations provides researchers with a supply of information regarding the optical properties of dielectric structures. The technique is well suited for structures that display a linear periodicity. When the focus is directed towards optical resonators and structures that lack linear periodicity the eigen-process can easily exceed computational resources and time constraints. In the case of dielectric structures which display cylindrical or spherical symmetry, a coordinate system specific set of basis functions have been employed to cast Maxwell's wave equations into an eigen-matrix formulation from which the resonator states associated with the dielectric profile can be obtained. As for PWM, the inverse of the dielectric and field components are expanded in the basis functions (Fourier-Fourier-Bessel, FFB, in cylindrical and Fourier- Bessel-Legendre, BLF, in spherical) and orthogonality is employed to form the matrix expressions. The theoretical development details will be presented indicating how certain mathematical complications in the process have been overcome and how the eigen-matrix can be tuned to a specific mode type. The similarities and differences in PWM, FFB and BLF are presented. In the case of structures possessing axial cylindrical symmetry, the inclusion of the z axis component of propagation constant makes the technique applicable to photonic crystal fibers and other waveguide structures. Computational results will be presented for a number of different dielectric geometries including Bragg ring resonators, cylindrical space slot channel waveguides and bottle resonators. Steps to further enhance the computation process will be reported.
Some Improved Nonperturbative Bounds for Fermionic Expansions
Energy Technology Data Exchange (ETDEWEB)
Lohmann, Martin, E-mail: marlohmann@gmail.com [Universita di Roma Tre, Dipartimento di Matematica (Italy)
2016-06-15
We reconsider the Gram-Hadamard bound as it is used in constructive quantum field theory and many body physics to prove convergence of Fermionic perturbative expansions. Our approach uses a recursion for the amplitudes of the expansion, discovered in a model problem by Djokic (2013). It explains the standard way to bound the expansion from a new point of view, and for some of the amplitudes provides new bounds, which avoid the use of Fourier transform, and are therefore superior to the standard bounds for models like the cold interacting Fermi gas.
The Fractional Orthogonal Difference with Applications
Directory of Open Access Journals (Sweden)
Enno Diekema
2015-06-01
Full Text Available This paper is a follow-up of a previous paper of the author published in Mathematics journal in 2015, which treats the so-called continuous fractional orthogonal derivative. In this paper, we treat the discrete case using the fractional orthogonal difference. The theory is illustrated with an application of a fractional differentiating filter. In particular, graphs are presented of the absolutel value of the modulus of the frequency response. These make clear that for a good insight into the behavior of a fractional differentiating filter, one has to look for the modulus of its frequency response in a log-log plot, rather than for plots in the time domain.
HOLA: Human-like Orthogonal Network Layout.
Kieffer, Steve; Dwyer, Tim; Marriott, Kim; Wybrow, Michael
2016-01-01
Over the last 50 years a wide variety of automatic network layout algorithms have been developed. Some are fast heuristic techniques suitable for networks with hundreds of thousands of nodes while others are multi-stage frameworks for higher-quality layout of smaller networks. However, despite decades of research currently no algorithm produces layout of comparable quality to that of a human. We give a new "human-centred" methodology for automatic network layout algorithm design that is intended to overcome this deficiency. User studies are first used to identify the aesthetic criteria algorithms should encode, then an algorithm is developed that is informed by these criteria and finally, a follow-up study evaluates the algorithm output. We have used this new methodology to develop an automatic orthogonal network layout method, HOLA, that achieves measurably better (by user study) layout than the best available orthogonal layout algorithm and which produces layouts of comparable quality to those produced by hand.
Effective Results Analysis for the Similar Software Products’ Orthogonality
Directory of Open Access Journals (Sweden)
Ion Ivan
2009-10-01
Full Text Available It is defined the concept of similar software. There are established conditions of archiving the software components. It is carried out the orthogonality evaluation and the correlation between the orthogonality and the complexity of the homogenous software components is analyzed. Shall proceed to build groups of similar software products, belonging to the orthogonality intervals. There are presented in graphical form the results of the analysis. There are detailed aspects of the functioning of the software product allocated for the orthogonality.
Fourier-Hermite communications; where Fourier meets Hermite
Korevaar, C.W.; Kokkeler, Andre B.J.; de Boer, Pieter-Tjerk; Smit, Gerardus Johannes Maria
A new signal set, based on the Fourier and Hermite signal bases, is introduced. It combines properties of the Fourier basis signals with the perfect time-frequency localization of the Hermite functions. The signal set is characterized by both a high spectral efficiency and good time-frequency
Characterizing locally distinguishable orthogonal product states
Feng, Yuan; Shi, Yaoyun
2007-01-01
Bennett et al. \\cite{BDF+99} identified a set of orthogonal {\\em product} states in the $3\\otimes 3$ Hilbert space such that reliably distinguishing those states requires non-local quantum operations. While more examples have been found for this counter-intuitive ``nonlocality without entanglement'' phenomenon, a complete and computationally verifiable characterization for all such sets of states remains unknown. In this Letter, we give such a characterization for the $3\\otimes 3$ space.
Rotation of 2D orthogonal polynomials
Czech Academy of Sciences Publication Activity Database
Yang, B.; Flusser, Jan; Kautský, J.
2018-01-01
Roč. 102, č. 1 (2018), s. 44-49 ISSN 0167-8655 R&D Projects: GA ČR GA15-16928S Institutional support: RVO:67985556 Keywords : Rotation invariants * Orthogonal polynomials * Recurrent relation * Hermite-like polynomials * Hermite moments Subject RIV: JD - Computer Applications, Robotics Impact factor: 1.995, year: 2016 http://library.utia.cas.cz/separaty/2017/ZOI/flusser-0483250.pdf
Biogeography-Based Optimization with Orthogonal Crossover
Directory of Open Access Journals (Sweden)
Quanxi Feng
2013-01-01
Full Text Available Biogeography-based optimization (BBO is a new biogeography inspired, population-based algorithm, which mainly uses migration operator to share information among solutions. Similar to crossover operator in genetic algorithm, migration operator is a probabilistic operator and only generates the vertex of a hyperrectangle defined by the emigration and immigration vectors. Therefore, the exploration ability of BBO may be limited. Orthogonal crossover operator with quantization technique (QOX is based on orthogonal design and can generate representative solution in solution space. In this paper, a BBO variant is presented through embedding the QOX operator in BBO algorithm. Additionally, a modified migration equation is used to improve the population diversity. Several experiments are conducted on 23 benchmark functions. Experimental results show that the proposed algorithm is capable of locating the optimal or closed-to-optimal solution. Comparisons with other variants of BBO algorithms and state-of-the-art orthogonal-based evolutionary algorithms demonstrate that our proposed algorithm possesses faster global convergence rate, high-precision solution, and stronger robustness. Finally, the analysis result of the performance of QOX indicates that QOX plays a key role in the proposed algorithm.
Non-Orthogonal Opportunistic Beamforming: Performance Analysis and Implementation
Xia, Minghua; Wu, Yik-Chung; Aissa, Sonia
2012-01-01
be successfully served within a single transmission, non-orthogonal OBF can be applied to obtain lower worst-case delay among the users. On the other hand, if user traffic is heavy, non-orthogonal OBF is inferior to orthogonal OBF in terms of sum-rate and packet
A Dynamic BI–Orthogonal Field Equation Approach to Efficient Bayesian Inversion
Directory of Open Access Journals (Sweden)
Tagade Piyush M.
2017-06-01
Full Text Available This paper proposes a novel computationally efficient stochastic spectral projection based approach to Bayesian inversion of a computer simulator with high dimensional parametric and model structure uncertainty. The proposed method is based on the decomposition of the solution into its mean and a random field using a generic Karhunen-Loève expansion. The random field is represented as a convolution of separable Hilbert spaces in stochastic and spatial dimensions that are spectrally represented using respective orthogonal bases. In particular, the present paper investigates generalized polynomial chaos bases for the stochastic dimension and eigenfunction bases for the spatial dimension. Dynamic orthogonality is used to derive closed-form equations for the time evolution of mean, spatial and the stochastic fields. The resultant system of equations consists of a partial differential equation (PDE that defines the dynamic evolution of the mean, a set of PDEs to define the time evolution of eigenfunction bases, while a set of ordinary differential equations (ODEs define dynamics of the stochastic field. This system of dynamic evolution equations efficiently propagates the prior parametric uncertainty to the system response. The resulting bi-orthogonal expansion of the system response is used to reformulate the Bayesian inference for efficient exploration of the posterior distribution. The efficacy of the proposed method is investigated for calibration of a 2D transient diffusion simulator with an uncertain source location and diffusivity. The computational efficiency of the method is demonstrated against a Monte Carlo method and a generalized polynomial chaos approach.
International Nuclear Information System (INIS)
Kobayashi, Keisuke
1975-01-01
A method of solution is presented for a monoenergetic diffusion equation in two-dimensional hexagonal cells by a finite Fourier transformation. Up to the present, the solution by the finite Fourier transformation has been developed for x-y, r-z and x-y-z geometries, and the flux and current at the boundary are obtained in terms of Fourier series. It is shown here that the method can be applied to hexagonal cells and the expansion of boundary values in a Legendre polynomials gives numerically a higher accuracy than is obtained by a Fourier series. (orig.) [de
On fractional Fourier transform moments
Alieva, T.; Bastiaans, M.J.
2000-01-01
Based on the relation between the ambiguity function represented in a quasi-polar coordinate system and the fractional power spectra, the fractional Fourier transform moments are introduced. Important equalities for the global second-order fractional Fourier transform moments are derived and their
Grafakos, Loukas
2014-01-01
This text is addressed to graduate students in mathematics and to interested researchers who wish to acquire an in depth understanding of Euclidean Harmonic analysis. The text covers modern topics and techniques in function spaces, atomic decompositions, singular integrals of nonconvolution type, and the boundedness and convergence of Fourier series and integrals. The exposition and style are designed to stimulate further study and promote research. Historical information and references are included at the end of each chapter. This third edition includes a new chapter entitled "Multilinear Harmonic Analysis" which focuses on topics related to multilinear operators and their applications. Sections 1.1 and 1.2 are also new in this edition. Numerous corrections have been made to the text from the previous editions and several improvements have been incorporated, such as the adoption of clear and elegant statements. A few more exercises have been added with relevant hints when necessary. Reviews fr...
Hypergeometric series recurrence relations and some new orthogonal functions
International Nuclear Information System (INIS)
Wilson, J.A.
1978-01-01
A set of hypergeometric orthogonal polynomials, a set of biorthogonal rational functions generalizing them, and some new three-term relations for hypergeometric series containing properties of these functions are exhibited. The orthogonal polynomials depend on four free parameters, and their orthogonality relations include as special or limiting cases the orthogonalities for the classical polynomials, the Hahn and dual Hahn polynomials, Pollaczek's polynomials orthogonal on an infinite interval, and the 6-j symbols of angular momentum in quantum mechanics. Their properties include a second-order difference equation and a Rodrigues-type formula involving a divided difference operator
Fast algorithm of adaptive Fourier series
Gao, You; Ku, Min; Qian, Tao
2018-05-01
Adaptive Fourier decomposition (AFD, precisely 1-D AFD or Core-AFD) was originated for the goal of positive frequency representations of signals. It achieved the goal and at the same time offered fast decompositions of signals. There then arose several types of AFDs. AFD merged with the greedy algorithm idea, and in particular, motivated the so-called pre-orthogonal greedy algorithm (Pre-OGA) that was proven to be the most efficient greedy algorithm. The cost of the advantages of the AFD type decompositions is, however, the high computational complexity due to the involvement of maximal selections of the dictionary parameters. The present paper offers one formulation of the 1-D AFD algorithm by building the FFT algorithm into it. Accordingly, the algorithm complexity is reduced, from the original $\\mathcal{O}(M N^2)$ to $\\mathcal{O}(M N\\log_2 N)$, where $N$ denotes the number of the discretization points on the unit circle and $M$ denotes the number of points in $[0,1)$. This greatly enhances the applicability of AFD. Experiments are carried out to show the high efficiency of the proposed algorithm.
Orthogonal and symplectic Yangians and Yang–Baxter R-operators
International Nuclear Information System (INIS)
Isaev, A.P.; Karakhanyan, D.; Kirschner, R.
2016-01-01
Yang–Baxter R operators symmetric with respect to the orthogonal and symplectic algebras are considered in an uniform way. Explicit forms for the spinorial and metaplectic R operators are obtained. L operators, obeying the RLL relation with the orthogonal or symplectic fundamental R matrix, are considered in the interesting cases, where their expansion in inverse powers of the spectral parameter is truncated. Unlike the case of special linear algebra symmetry the truncation results in additional conditions on the Lie algebra generators of which the L operators is built and which can be fulfilled in distinguished representations only. Further, generalized L operators, obeying the modified RLL relation with the fundamental R matrix replaced by the spinorial or metaplectic one, are considered in the particular case of linear dependence on the spectral parameter. It is shown how by fusion with respect to the spinorial or metaplectic representation these first order spinorial L operators reproduce the ordinary L operators with second order truncation.
Orthogonal and symplectic Yangians and Yang–Baxter R-operators
Energy Technology Data Exchange (ETDEWEB)
Isaev, A.P., E-mail: isaevap@theor.jinr.ru [Bogoliubov Lab., Joint Institute of Nuclear Research, Dubna (Russian Federation); Karakhanyan, D., E-mail: karakhan@yerphi.am [Yerevan Physics Institute, 2 Alikhanyan br., 0036 Yerevan (Armenia); Kirschner, R., E-mail: Roland.Kirschner@itp.uni-leipzig.de [Institut für Theoretische Physik, Universität Leipzig, PF 100 920, D-04009 Leipzig (Germany)
2016-03-15
Yang–Baxter R operators symmetric with respect to the orthogonal and symplectic algebras are considered in an uniform way. Explicit forms for the spinorial and metaplectic R operators are obtained. L operators, obeying the RLL relation with the orthogonal or symplectic fundamental R matrix, are considered in the interesting cases, where their expansion in inverse powers of the spectral parameter is truncated. Unlike the case of special linear algebra symmetry the truncation results in additional conditions on the Lie algebra generators of which the L operators is built and which can be fulfilled in distinguished representations only. Further, generalized L operators, obeying the modified RLL relation with the fundamental R matrix replaced by the spinorial or metaplectic one, are considered in the particular case of linear dependence on the spectral parameter. It is shown how by fusion with respect to the spinorial or metaplectic representation these first order spinorial L operators reproduce the ordinary L operators with second order truncation.
An orthogonality condition model treatment of elastic and inelastic (α, 12C) scattering
International Nuclear Information System (INIS)
Suzuki, Y.; Imanishi, B.
1981-02-01
Elastic and inelastic scattering of α-particles on the deformed nucleus 12 C are investigated in the range of incident α-particle energies of 9 to 11 MeV by using the coupled-channel method with orthogonality condition. A doubly folded potential generated by the shell model wave functions of the α-particle and the deformed nucleus 12 C is employed for the relative motion between the α-particle and 12 C. Good agreement between theory and experiment is obtained for the elastic and inelastic angular distributions and the resonance structures. It is found, from the Born series expansion of the T-matrix, that the orthogonality constraint stresses the effects of the channel-coupling between the elastic and inelastic processes, and it indicates that the DWBA does not work well in this system. (author)
Method of orthogonally splitting imaging pose measurement
Zhao, Na; Sun, Changku; Wang, Peng; Yang, Qian; Liu, Xintong
2018-01-01
In order to meet the aviation's and machinery manufacturing's pose measurement need of high precision, fast speed and wide measurement range, and to resolve the contradiction between measurement range and resolution of vision sensor, this paper proposes an orthogonally splitting imaging pose measurement method. This paper designs and realizes an orthogonally splitting imaging vision sensor and establishes a pose measurement system. The vision sensor consists of one imaging lens, a beam splitter prism, cylindrical lenses and dual linear CCD. Dual linear CCD respectively acquire one dimensional image coordinate data of the target point, and two data can restore the two dimensional image coordinates of the target point. According to the characteristics of imaging system, this paper establishes the nonlinear distortion model to correct distortion. Based on cross ratio invariability, polynomial equation is established and solved by the least square fitting method. After completing distortion correction, this paper establishes the measurement mathematical model of vision sensor, and determines intrinsic parameters to calibrate. An array of feature points for calibration is built by placing a planar target in any different positions for a few times. An terative optimization method is presented to solve the parameters of model. The experimental results show that the field angle is 52 °, the focus distance is 27.40 mm, image resolution is 5185×5117 pixels, displacement measurement error is less than 0.1mm, and rotation angle measurement error is less than 0.15°. The method of orthogonally splitting imaging pose measurement can satisfy the pose measurement requirement of high precision, fast speed and wide measurement range.
Polar plate theory for orthogonal anisotropy
Bailey, Michelle D.
1998-11-01
The following paper discusses the derivation and evaluation of the plate equations for a circular composite disk with orthogonal anisotropy. The work will be on a macromechanical level and include buckling, static and dynamic load applications. Necessary to a complete examination of the circular disk is the conversion of the stiffness matrix to cylindrical coordinates. In the transformed state, these coefficients are no longer constant, adding to the complexity of the proposed differential equations. Laminated fiber-reinforced (or filamentary) composites are used today for their high strength-to weight and stiffness-to-weight ratios. However, because of the typical anisotropic behavior of composites, determining the material properties on a microscopic level and the mechanics on a macroscopic level is much more difficult. This difficulty manifests itself particularly well in the evaluation of material properties and governing differential equations of a circular disk with the fibers of the lamina oriented orthogonally. One could encounter such a situation in space structures that require a circular geometry. For example, determining fastener pull through in a circular composite plate would best be performed in a polar coordinate system. In order to calculate the strain (which is a function of the angle, θ) from the displacements, the stiffness matrix and boundary conditions would need to be expressed in cylindrical coordinates. Naturally the composite would be constructed with fibers in orthogonal directions, then the necessary geometry would be cut out, thus the required lengthy transformation of coordinate systems. To bypass this derivation, numerical methods have been used and finite element models have been attempted. FEM over predicts plate stiffness by 20% and underpredicts failure by 70%. Obviously there is a need to transform classical plate theory to a cylindrical coordinate system.
New discrete orthogonal moments for signal analysis
Czech Academy of Sciences Publication Activity Database
Honarvar Shakibaei Asli, Barmak; Flusser, Jan
2017-01-01
Roč. 141, č. 1 (2017), s. 57-73 ISSN 0165-1684 R&D Projects: GA ČR GA15-16928S Institutional support: RVO:67985556 Keywords : Orthogonal polynomials * Moment functions * Z-transform * Rodrigues formula * Hypergeometric form Subject RIV: JD - Computer Applications, Robotics OBOR OECD: Computer sciences, information science, bioinformathics (hardware development to be 2.2, social aspect to be 5.8) Impact factor: 3.110, year: 2016 http://library.utia.cas.cz/separaty/2017/ZOI/flusser-0475248.pdf
Fourier analysis of the parametric resonance in neutrino oscillations
International Nuclear Information System (INIS)
Koike, Masafumi; Ota, Toshihiko; Saito, Masako; Sato, Joe
2009-01-01
Parametric enhancement of the appearance probability of the neutrino oscillation under the inhomogeneous matter is studied. Fourier expansion of the matter density profile leads to a simple resonance condition and manifests that each Fourier mode modifies the energy spectrum of oscillation probability at around the corresponding energy; below the MSW resonance energy, a large-scale variation modifies the spectrum in high energies while a small-scale one does in low energies. In contrast to the simple parametric resonance, the enhancement of the oscillation probability is itself an slow oscillation as demonstrated by a numerical analysis with a single Fourier mode of the matter density. We derive an analytic solution to the evolution equation on the resonance energy, including the expression of frequency of the slow oscillation.
Fourier phase in Fourier-domain optical coherence tomography
Uttam, Shikhar; Liu, Yang
2015-01-01
Phase of an electromagnetic wave propagating through a sample-of-interest is well understood in the context of quantitative phase imaging in transmission-mode microscopy. In the past decade, Fourier-domain optical coherence tomography has been used to extend quantitative phase imaging to the reflection-mode. Unlike transmission-mode electromagnetic phase, however, the origin and characteristics of reflection-mode Fourier phase are poorly understood, especially in samples with a slowly varying refractive index. In this paper, the general theory of Fourier phase from first principles is presented, and it is shown that Fourier phase is a joint estimate of subresolution offset and mean spatial frequency of the coherence-gated sample refractive index. It is also shown that both spectral-domain phase microscopy and depth-resolved spatial-domain low-coherence quantitative phase microscopy are special cases of this general theory. Analytical expressions are provided for both, and simulations are presented to explain and support the theoretical results. These results are further used to show how Fourier phase allows the estimation of an axial mean spatial frequency profile of the sample, along with depth-resolved characterization of localized optical density change and sample heterogeneity. Finally, a Fourier phase-based explanation of Doppler optical coherence tomography is also provided. PMID:26831383
Fourier phase in Fourier-domain optical coherence tomography.
Uttam, Shikhar; Liu, Yang
2015-12-01
Phase of an electromagnetic wave propagating through a sample-of-interest is well understood in the context of quantitative phase imaging in transmission-mode microscopy. In the past decade, Fourier-domain optical coherence tomography has been used to extend quantitative phase imaging to the reflection-mode. Unlike transmission-mode electromagnetic phase, however, the origin and characteristics of reflection-mode Fourier phase are poorly understood, especially in samples with a slowly varying refractive index. In this paper, the general theory of Fourier phase from first principles is presented, and it is shown that Fourier phase is a joint estimate of subresolution offset and mean spatial frequency of the coherence-gated sample refractive index. It is also shown that both spectral-domain phase microscopy and depth-resolved spatial-domain low-coherence quantitative phase microscopy are special cases of this general theory. Analytical expressions are provided for both, and simulations are presented to explain and support the theoretical results. These results are further used to show how Fourier phase allows the estimation of an axial mean spatial frequency profile of the sample, along with depth-resolved characterization of localized optical density change and sample heterogeneity. Finally, a Fourier phase-based explanation of Doppler optical coherence tomography is also provided.
FOURIER COEFFICIENTS OF CONTINUOUS FUNCTIONS WITH RESPECT TO LOCALIZED HAAR SYSTEM
Directory of Open Access Journals (Sweden)
E. S. Belkina
2017-06-01
Full Text Available We construct a nontrivial example of a continuous function f* on [0, 1]² which is orthogonal to tensor products of Haar functions supported on intervals of the same length. This example clarifies the possible behaviour of Fourier coefficients of continuous functions with respect to a localized Haar system. The function f* has fractal structure. We give lower bounds on its smoothness.
Fourier analysis and stochastic processes
Brémaud, Pierre
2014-01-01
This work is unique as it provides a uniform treatment of the Fourier theories of functions (Fourier transforms and series, z-transforms), finite measures (characteristic functions, convergence in distribution), and stochastic processes (including arma series and point processes). It emphasises the links between these three themes. The chapter on the Fourier theory of point processes and signals structured by point processes is a novel addition to the literature on Fourier analysis of stochastic processes. It also connects the theory with recent lines of research such as biological spike signals and ultrawide-band communications. Although the treatment is mathematically rigorous, the convivial style makes the book accessible to a large audience. In particular, it will be interesting to anyone working in electrical engineering and communications, biology (point process signals) and econometrics (arma models). A careful review of the prerequisites (integration and probability theory in the appendix, Hilbert spa...
Symplectic geometry and Fourier analysis
Wallach, Nolan R
2018-01-01
Suitable for graduate students in mathematics, this monograph covers differential and symplectic geometry, homogeneous symplectic manifolds, Fourier analysis, metaplectic representation, quantization, Kirillov theory. Includes Appendix on Quantum Mechanics by Robert Hermann. 1977 edition.
Fourier transform nuclear magnetic resonance
International Nuclear Information System (INIS)
Geick, R.
1981-01-01
This review starts with the basic principles of resonance phenomena in physical systems. Especially, the connection is shown between the properties of these systems and Fourier transforms. Next, we discuss the principles of nuclear magnetic resonance. Starting from the general properties of physical systems showing resonance phenomena and from the special properties of nuclear spin systems, the main part of this paper reviews pulse and Fourier methods in nuclear magnetic resonance. Among pulse methods, an introduction will be given to spin echoes, and, apart from the principle of Fourier transform nuclear magnetic resonance, an introduction to the technical problems of this method, e.g. resolution in the frequency domain, aliasing, phase and intensity errors, stationary state of the spin systems for repetitive measurements, proton decoupling, and application of Fourier methods to systems in a nonequilibrium state. The last section is devoted to special applications of Fourier methods and recent developments, e.g. measurement of relaxation times, solvent peak suppression, 'rapid scan'-method, methods for suppressing the effects of dipolar coupling in solids, two-dimensional Fourier transform nuclear magnetic resonance, and spin mapping or zeugmatography. (author)
A novel orthogonally linearly polarized Nd:YVO4 laser
International Nuclear Information System (INIS)
Xing-Peng, Yan; Qiang, Liu; Hai-Long, Chen; Xing, Fu; Ma-Li, Gong; Dong-Sheng, Wang
2010-01-01
We presented a novel orthogonally linearly polarized Nd:YVO 4 laser. Two pieces of α-cut grown-together composite YVO 4 /Nd:YVO 4 crystals were placed in the resonant cavity with the c-axis of the two crystals orthogonally. The polarization and power performance of the orthogonally polarized laser were investigated. A 26.2-W orthogonally linearly polarized laser was obtained. The power ratio between the two orthogonally polarized lasers was varied with the pump power caused by the polarized mode coupling. The longitudinal modes competition and the corresponding variable optical beats were also observed from the orthogonally polarized laser. We also adjusted the crystals with their c-axis parallele to each other, and a 40.7-W linearly polarized TEM 00 laser was obtained, and the beam quality factors were M x 2 = 1.37 and M y 2 = 1.25. (classical areas of phenomenology)
Effective Results Analysis for the Similar Software Products’ Orthogonality
Ion Ivan; Daniel Milodin
2009-01-01
It is defined the concept of similar software. There are established conditions of archiving the software components. It is carried out the orthogonality evaluation and the correlation between the orthogonality and the complexity of the homogenous software components is analyzed. Shall proceed to build groups of similar software products, belonging to the orthogonality intervals. There are presented in graphical form the results of the analysis. There are detailed aspects of the functioning o...
Kernel versions of some orthogonal transformations
DEFF Research Database (Denmark)
Nielsen, Allan Aasbjerg
Kernel versions of orthogonal transformations such as principal components are based on a dual formulation also termed Q-mode analysis in which the data enter into the analysis via inner products in the Gram matrix only. In the kernel version the inner products of the original data are replaced...... by inner products between nonlinear mappings into higher dimensional feature space. Via kernel substitution also known as the kernel trick these inner products between the mappings are in turn replaced by a kernel function and all quantities needed in the analysis are expressed in terms of this kernel...... function. This means that we need not know the nonlinear mappings explicitly. Kernel principal component analysis (PCA) and kernel minimum noise fraction (MNF) analyses handle nonlinearities by implicitly transforming data into high (even infinite) dimensional feature space via the kernel function...
Orthogonal cutting of laser beam melted parts
Götze, Elisa; Zanger, Frederik; Schulze, Volker
2018-05-01
The finishing process of parts manufactured by laser beam melting is of high concern due to the lack of surface accuracy. Therefore, the focus of this work lies on the influence of the build-up direction of the parts and their effect on the finishing process. The orthogonal cutting reveals findings in the fields of chip formation, involved forces and temperatures appearing during machining. In the investigations, the cutting depth was varied between 0.05 and 0.15 mm representing a finishing process and the cutting velocity ranges from 30 to 200 m/min depending on the material. The experiments contain the materials stainless steel (AISI 316L), titanium (Ti6Al4V) and nickel-base alloy (IN718). The two materials named latter are of high interest in the aerospace sector and at the same time titanium is used in the medical field due to its biocompatibility. For the materials IN718 and Ti6Al4V a negative rake angle of -7.5° and for stainless steel a rake angle of 12.5° are chosen for the cutting experiments. The results provide the base for processing strategies. Therefore, the specimens were solely laser beam melted without post-processing like heat treatment. The evaluation of the experiments shows that an increase in cutting speed has different effects depending on the material. For stainless steel the measured forces regarding the machining direction to the layers approach the same values. In contrast, the influence of the layers regarding the forces appearing during orthogonal cutting of the materials IN718 and Ti6Al4V differ for lower cutting speeds.
Babaee, Hessam; Choi, Minseok; Sapsis, Themistoklis P.; Karniadakis, George Em
2017-09-01
We develop a new robust methodology for the stochastic Navier-Stokes equations based on the dynamically-orthogonal (DO) and bi-orthogonal (BO) methods [1-3]. Both approaches are variants of a generalized Karhunen-Loève (KL) expansion in which both the stochastic coefficients and the spatial basis evolve according to system dynamics, hence, capturing the low-dimensional structure of the solution. The DO and BO formulations are mathematically equivalent [3], but they exhibit computationally complimentary properties. Specifically, the BO formulation may fail due to crossing of the eigenvalues of the covariance matrix, while both BO and DO become unstable when there is a high condition number of the covariance matrix or zero eigenvalues. To this end, we combine the two methods into a robust hybrid framework and in addition we employ a pseudo-inverse technique to invert the covariance matrix. The robustness of the proposed method stems from addressing the following issues in the DO/BO formulation: (i) eigenvalue crossing: we resolve the issue of eigenvalue crossing in the BO formulation by switching to the DO near eigenvalue crossing using the equivalence theorem and switching back to BO when the distance between eigenvalues is larger than a threshold value; (ii) ill-conditioned covariance matrix: we utilize a pseudo-inverse strategy to invert the covariance matrix; (iii) adaptivity: we utilize an adaptive strategy to add/remove modes to resolve the covariance matrix up to a threshold value. In particular, we introduce a soft-threshold criterion to allow the system to adapt to the newly added/removed mode and therefore avoid repetitive and unnecessary mode addition/removal. When the total variance approaches zero, we show that the DO/BO formulation becomes equivalent to the evolution equation of the Optimally Time-Dependent modes [4]. We demonstrate the capability of the proposed methodology with several numerical examples, namely (i) stochastic Burgers equation: we
On a Convergence of Rational Approximations by the Modified Fourier Basis
Directory of Open Access Journals (Sweden)
Tigran Bakaryan
2017-12-01
Full Text Available We continue investigations of the modified-trigonometric-rational approximations that arise while accelerating the convergence of the modified Fourier expansions by means of rational corrections. Previously, we investigated the pointwise convergence of the rational approximations away from the endpoints and the $L_2$-convergence on the entire interval. Here, we study the convergence at the endpoints and derive the exact constants for the main terms of asymptotic errors. We show that the Fourier-Pade approximations are much more accurate in all frameworks than the modified expansions for sufficiently smooth functions. Moreover, we consider a simplified version of the rational approximations and explore the optimal values of parameters that lead to better accuracy in the framework of the $L_2$-error. Numerical experiments perform comparisons of the rational approximations with the modified Fourier expansions.
General Correlation Theorem for Trinion Fourier Transform
Bahri, Mawardi
2017-01-01
- The trinion Fourier transform is an extension of the Fourier transform in the trinion numbers setting. In this work we derive the correlation theorem for the trinion Fourier transform by using the relation between trinion convolution and correlation definitions in the trinion Fourier transform domains.
Fourier Series, the DFT and Shape Modelling
DEFF Research Database (Denmark)
Skoglund, Karl
2004-01-01
This report provides an introduction to Fourier series, the discrete Fourier transform, complex geometry and Fourier descriptors for shape analysis. The content is aimed at undergraduate and graduate students who wish to learn about Fourier analysis in general, as well as its application to shape...
Fourier series, Fourier transform and their applications to mathematical physics
Serov, Valery
2017-01-01
This text serves as an introduction to the modern theory of analysis and differential equations with applications in mathematical physics and engineering sciences. Having outgrown from a series of half-semester courses given at University of Oulu, this book consists of four self-contained parts. The first part, Fourier Series and the Discrete Fourier Transform, is devoted to the classical one-dimensional trigonometric Fourier series with some applications to PDEs and signal processing. The second part, Fourier Transform and Distributions, is concerned with distribution theory of L. Schwartz and its applications to the Schrödinger and magnetic Schrödinger operations. The third part, Operator Theory and Integral Equations, is devoted mostly to the self-adjoint but unbounded operators in Hilbert spaces and their applications to integral equations in such spaces. The fourth and final part, Introduction to Partial Differential Equations, serves as an introduction to modern methods for classical theory o...
Representations for the extreme zeros of orthogonal polynomials
van Doorn, Erik A.; van Foreest, Nicky D.; Zeifman, Alexander I.
2009-01-01
We establish some representations for the smallest and largest zeros of orthogonal polynomials in terms of the parameters in the three-terms recurrence relation. As a corollary we obtain representations for the endpoints of the true interval of orthogonality. Implications of these results for the
Construction of MDS self-dual codes from orthogonal matrices
Shi, Minjia; Sok, Lin; Solé, Patrick
2016-01-01
In this paper, we give algorithms and methods of construction of self-dual codes over finite fields using orthogonal matrices. Randomization in the orthogonal group, and code extension are the main tools. Some optimal, almost MDS, and MDS self-dual codes over both small and large prime fields are constructed.
Processing of dual-orthogonal cw polarimetric radar signals
Babur, G.
2009-01-01
The thesis consists of two parts. The first part is devoted to the theory of dual-orthogonal polarimetric radar signals with continuous waveforms. The thesis presents a comparison of the signal compression techniques, namely correlation and de-ramping methods, for the dual-orthogonal sophisticated
FOURIER SERIES MODELS THROUGH TRANSFORMATION
African Journals Online (AJOL)
DEPT
monthly temperature data (1996 – 2005) collected from the National Root ... KEY WORDS: Fourier series, square transformation, multiplicative model, ... fluctuations or movements are often periodic(Ekpeyong,2005). .... significant trend or not, if the trend is not significant, the grand mean may be used as an estimate of trend.
Fourier-Based Transmit Beampattern Design Using MIMO Radar
Lipor, John
2014-05-01
In multiple-input multiple-output (MIMO) radar settings, it is often desirable to transmit power only to a given location or set of locations defined by a beampattern. Transmit waveform design is a topic that has received much attention recently, involving synthesis of both the signal covariance matrix,, as well as the actual waveforms. Current methods involve a two-step process of designing via iterative solutions and then using to generate waveforms that fulfill practical constraints such as having a constant-envelope or drawing from a finite alphabet. In this paper, a closed-form method to design for a uniform linear array is proposed that utilizes the discrete Fourier transform (DFT) coefficients and Toeplitz matrices. The resulting covariance matrix fulfills the practical constraints such as positive semidefiniteness and the uniformelemental power constraint and provides performance similar to that of iterative methods, which require a much greater computation time. Next, a transmit architecture is presented that exploits the orthogonality of frequencies at discrete DFT values to transmit a sum of orthogonal signals from each antenna. The resulting waveforms provide a lower mean-square error than current methods at a much lower computational cost, and a simulated detection scenario demonstrates the performance advantages achieved.
Nonambipolarity, orthogonal conductivity, poloidal flow, and torque
International Nuclear Information System (INIS)
Hulbert, G.W.; Perkins, F.W.
1989-02-01
Nonambipolar processes, such as neutral injection onto trapped orbits or ripple-diffusion loss of α-particles, act to charge a plasma. A current j/sub r/ across magnetic surfaces must arise in the bulk plasma to maintain charge neutrality. An axisymmetric, neoclassical model of the bulk plasma shows that these currents are carried by the ions and exert a j/sub r/B/sub θ/R/c torque in the toroidal direction. A driven poloidal flow V/sub θ/ = E/sub r/'c/B must also develop. The average current density is related to the radial electric field E/sub r/' = E/sub r/ + v/sub /phi//B/sub θ//c in a frame moving with the plasma via the orthogonal conductivity = σ/sub /perpendicular//E/sub r/', which has the value σ/sub /perpendicular// = (1.65ε/sup 1/2/)(ne 2 ν/sub ii//MΩ/sub θ/ 2 ) in the banana regime. If an ignited plasma loses an appreciable fraction Δ of its thermonuclear α-particles by banana ripple diffusion, then the torque will spin the plasma to sonic rotation in a time /tau//sub s/ ∼ 2/tau//sub E//Δ, /tau//sub E/ being the energy confinement time. 10 refs., 1 fig
Coherent optical DFT-spread OFDM transmission using orthogonal band multiplexing.
Yang, Qi; He, Zhixue; Yang, Zhu; Yu, Shaohua; Yi, Xingwen; Shieh, William
2012-01-30
Coherent optical OFDM (CO-OFDM) combined with orthogonal band multiplexing provides a scalable and flexible solution for achieving ultra high-speed rate. Among many CO-OFDM implementations, digital Fourier transform spread (DFT-S) CO-OFDM is proposed to mitigate fiber nonlinearity in long-haul transmission. In this paper, we first illustrate the principle of DFT-S OFDM. We then experimentally evaluate the performance of coherent optical DFT-S OFDM in a band-multiplexed transmission system. Compared with conventional clipping methods, DFT-S OFDM can reduce the OFDM peak-to-average power ratio (PAPR) value without suffering from the interference of the neighboring bands. With the benefit of much reduced PAPR, we successfully demonstrate 1.45 Tb/s DFT-S OFDM over 480 km SSMF transmission.
International Nuclear Information System (INIS)
Feit, M.D.; Fleck, J.A. Jr.
1989-01-01
We describe a spectral method for solving the paraxial wave equation in cylindrical geometry that is based on expansion of the exponential evolution operator in a Taylor series and use of fast Fourier transforms to evaluate derivatives. A fourth-order expansion gives excellent agreement with a two-transverse-dimensional split-operator calculation at a fraction of the cost in computation time per z step and at a considerable savings in storage
Moore, R. K.; Fung, A. K.; Dome, G. J.; Birrer, I. J.
1978-01-01
The wind direction properties of radar backscatter from the sea were empirically modelled using a cosine Fourier series through the 4th harmonic in wind direction (referenced to upwind). A comparison with 1975 JONSWAP (Joint North Sea Wave Project) scatterometer data, at incidence angles of 40 and 65, indicates that effects to third and fourth harmonics are negligible. Another important result is that the Fourier coefficients through the second harmonic are related to wind speed by a power law expression. A technique is also proposed to estimate the wind speed and direction over the ocean from two orthogonal scattering measurements. A comparison between two different types of sea scatter theories, one type presented by the work of Wright and the other by that of Chan and Fung, was made with recent scatterometer measurements. It demonstrates that a complete scattering model must include some provisions for the anisotropic characteristics of the sea scatter, and use a sea spectrum which depends upon wind speed.
Ocean Models and Proper Orthogonal Decomposition
Salas-de-Leon, D. A.
2007-05-01
The increasing computational developments and the better understanding of mathematical and physical systems resulted in an increasing number of ocean models. Long time ago, modelers were like a secret organization and recognize each other by using secret codes and languages that only a select group of people was able to recognize and understand. The access to computational systems was reduced, on one hand equipment and the using time of computers were expensive and restricted, and on the other hand, they required an advance computational languages that not everybody wanted to learn. Now a days most college freshman own a personal computer (PC or laptop), and/or have access to more sophisticated computational systems than those available for research in the early 80's. The resource availability resulted in a mayor access to all kind models. Today computer speed and time and the algorithms does not seem to be a problem, even though some models take days to run in small computational systems. Almost every oceanographic institution has their own model, what is more, in the same institution from one office to the next there are different models for the same phenomena, developed by different research member, the results does not differ substantially since the equations are the same, and the solving algorithms are similar. The algorithms and the grids, constructed with algorithms, can be found in text books and/or over the internet. Every year more sophisticated models are constructed. The Proper Orthogonal Decomposition is a technique that allows the reduction of the number of variables to solve keeping the model properties, for which it can be a very useful tool in diminishing the processes that have to be solved using "small" computational systems, making sophisticated models available for a greater community.
Fourier-based magnetic induction tomography for mapping resistivity
International Nuclear Information System (INIS)
Puwal, Steffan; Roth, Bradley J.
2011-01-01
Magnetic induction tomography is used as an experimental tool for mapping the passive electromagnetic properties of conductors, with the potential for imaging biological tissues. Our numerical approach to solving the inverse problem is to obtain a Fourier expansion of the resistivity and the stream functions of the magnetic fields and eddy current density. Thus, we are able to solve the inverse problem of determining the resistivity from the applied and measured magnetic fields for a two-dimensional conducting plane. When we add noise to the measured magnetic field, we find the fidelity of the measured to the true resistivity is quite robust for increasing levels of noise and increasing distances of the applied and measured field coils from the conducting plane, when properly filtered. We conclude that Fourier methods provide a reliable alternative for solving the inverse problem.
Skew-orthogonal polynomials, differential systems and random matrix theory
International Nuclear Information System (INIS)
Ghosh, S.
2007-01-01
We study skew-orthogonal polynomials with respect to the weight function exp[-2V (x)], with V (x) = Σ K=1 2d (u K /K)x K , u 2d > 0, d > 0. A finite subsequence of such skew-orthogonal polynomials arising in the study of Orthogonal and Symplectic ensembles of random matrices, satisfy a system of differential-difference-deformation equation. The vectors formed by such subsequence has the rank equal to the degree of the potential in the quaternion sense. These solutions satisfy certain compatibility condition and hence admit a simultaneous fundamental system of solutions. (author)
Orthogonal polynomials on the unit circle part 2 spectral theory
Simon, Barry
2013-01-01
This two-part book is a comprehensive overview of the theory of probability measures on the unit circle, viewed especially in terms of the orthogonal polynomials defined by those measures. A major theme involves the connections between the Verblunsky coefficients (the coefficients of the recurrence equation for the orthogonal polynomials) and the measures, an analog of the spectral theory of one-dimensional Schrödinger operators. Among the topics discussed along the way are the asymptotics of Toeplitz determinants (Szegő's theorems), limit theorems for the density of the zeros of orthogonal po
Orthogonal polynomials on the unit circle part 1 classical theory
2009-01-01
This two-part book is a comprehensive overview of the theory of probability measures on the unit circle, viewed especially in terms of the orthogonal polynomials defined by those measures. A major theme involves the connections between the Verblunsky coefficients (the coefficients of the recurrence equation for the orthogonal polynomials) and the measures, an analog of the spectral theory of one-dimensional Schrodinger operators. Among the topics discussed along the way are the asymptotics of Toeplitz determinants (SzegÅ‘'s theorems), limit theorems for the density of the zeros of orthogonal po
Orthogonal Algorithm of Logic Probability and Syndrome-Testable Analysis
Institute of Scientific and Technical Information of China (English)
无
1990-01-01
A new method,orthogonal algoritm,is presented to compute the logic probabilities(i.e.signal probabilities)accurately,The transfer properties of logic probabilities are studied first,which are useful for the calculation of logic probability of the circuit with random independent inputs.Then the orthogonal algoritm is described to compute the logic probability of Boolean function realized by a combinational circuit.This algorithm can make Boolean function “ORTHOGONAL”so that the logic probabilities can be easily calculated by summing up the logic probabilities of all orthogonal terms of the Booleam function.
Orthogonally Based Digital Content Management Applicable to Projects-bases
Directory of Open Access Journals (Sweden)
Daniel MILODIN
2009-01-01
Full Text Available There is defined the concept of digital content. The requirements of an efficient management of the digital content are established. There are listed the quality characteristics of digital content. Orthogonality indicators of digital content are built up. They are meant to measure the image, the sound as well as the text orthogonality as well. Projects-base concept is introduced. There is presented the model of structuring the content in order to maximize orthogonality via a convergent iterative process. The model is instantiated for the digital content of a projects-base. It is introduced the application used to test the model. The paper ends with conclusions.
From Fourier analysis to wavelets
Gomes, Jonas
2015-01-01
This text introduces the basic concepts of function spaces and operators, both from the continuous and discrete viewpoints. Fourier and Window Fourier Transforms are introduced and used as a guide to arrive at the concept of Wavelet transform. The fundamental aspects of multiresolution representation, and its importance to function discretization and to the construction of wavelets is also discussed. Emphasis is given on ideas and intuition, avoiding the heavy computations which are usually involved in the study of wavelets. Readers should have a basic knowledge of linear algebra, calculus, and some familiarity with complex analysis. Basic knowledge of signal and image processing is desirable. This text originated from a set of notes in Portuguese that the authors wrote for a wavelet course on the Brazilian Mathematical Colloquium in 1997 at IMPA, Rio de Janeiro.
Compact Microwave Fourier Spectrum Analyzer
Savchenkov, Anatoliy; Matsko, Andrey; Strekalov, Dmitry
2009-01-01
A compact photonic microwave Fourier spectrum analyzer [a Fourier-transform microwave spectrometer, (FTMWS)] with no moving parts has been proposed for use in remote sensing of weak, natural microwave emissions from the surfaces and atmospheres of planets to enable remote analysis and determination of chemical composition and abundances of critical molecular constituents in space. The instrument is based on a Bessel beam (light modes with non-zero angular momenta) fiber-optic elements. It features low power consumption, low mass, and high resolution, without a need for any cryogenics, beyond what is achievable by the current state-of-the-art in space instruments. The instrument can also be used in a wide-band scatterometer mode in active radar systems.
Uncertainty Principles and Fourier Analysis
Indian Academy of Sciences (India)
analysis on the part of the reader. Those who are not fa- miliar with Fourier analysis are encouraged to look up Box. 1 along with [3]. (A) Heisenberg's inequality: Let us measure concentration in terms of standard deviation i.e. for a square integrable func-. 00 tion defined on 1R and normalized so that J If(x)12d,x = 1,. -00. 00.
An introduction to Fourier series and integrals
Seeley, Robert T
2006-01-01
This compact guide emphasizes the relationship between physics and mathematics, introducing Fourier series in the way that Fourier himself used them: as solutions of the heat equation in a disk. 1966 edition.
Systems of Differential Equations with Skew-Symmetric, Orthogonal Matrices
Glaister, P.
2008-01-01
The solution of a system of linear, inhomogeneous differential equations is discussed. The particular class considered is where the coefficient matrix is skew-symmetric and orthogonal, and where the forcing terms are sinusoidal. More general matrices are also considered.
Skew-orthogonal polynomials and random matrix theory
Ghosh, Saugata
2009-01-01
Orthogonal polynomials satisfy a three-term recursion relation irrespective of the weight function with respect to which they are defined. This gives a simple formula for the kernel function, known in the literature as the Christoffel-Darboux sum. The availability of asymptotic results of orthogonal polynomials and the simple structure of the Christoffel-Darboux sum make the study of unitary ensembles of random matrices relatively straightforward. In this book, the author develops the theory of skew-orthogonal polynomials and obtains recursion relations which, unlike orthogonal polynomials, depend on weight functions. After deriving reduced expressions, called the generalized Christoffel-Darboux formulas (GCD), he obtains universal correlation functions and non-universal level densities for a wide class of random matrix ensembles using the GCD. The author also shows that once questions about higher order effects are considered (questions that are relevant in different branches of physics and mathematics) the ...
Using orthogonal design to determine optimal conditions for ...
African Journals Online (AJOL)
African Journal of Biotechnology ... Because of the narrow genetic diversity of common wheat and elite agronomic traits of many wild relatives, it is very ... Key words: Protoplast, fusion, orthogonal design method, Mingxian 169, Y2155a.
Orthogonal Projector Kit (OPK) as a new teaching aids with ...
African Journals Online (AJOL)
... as a new teaching aids with innovation ICT in teaching and learning 21 st century. ... Mathematics education filled with abstract concepts, the use of teaching aids is ... This article aims to introduce and express the importance of Orthogonal ...
Non-Orthogonal Opportunistic Beamforming: Performance Analysis and Implementation
Xia, Minghua
2012-04-01
Aiming to achieve the sum-rate capacity in multi-user multi-antenna systems where $N_t$ antennas are implemented at the transmitter, opportunistic beamforming (OBF) generates~$N_t$ orthonormal beams and serves $N_t$ users during each channel use, which results in high scheduling delay over the users, especially in densely populated networks. Non-orthogonal OBF with more than~$N_t$ transmit beams can be exploited to serve more users simultaneously and further decrease scheduling delay. However, the inter-beam interference will inevitably deteriorate the sum-rate. Therefore, there is a tradeoff between sum-rate and scheduling delay for non-orthogonal OBF. In this context, system performance and implementation of non-orthogonal OBF with $N>N_t$ beams are investigated in this paper. Specifically, it is analytically shown that non-orthogonal OBF is an interference-limited system as the number of users $K \\\\to \\\\infty$. When the inter-beam interference reaches its minimum for fixed $N_t$ and~$N$, the sum-rate scales as $N\\\\ln\\\\left(\\\\frac{N}{N-N_t}\\ ight)$ and it degrades monotonically with the number of beams $N$ for fixed $N_t$. On the contrary, the average scheduling delay is shown to scale as $\\\\frac{1}{N}K\\\\ln{K}$ channel uses and it improves monotonically with $N$. Furthermore, two practical non-orthogonal beamforming schemes are explicitly constructed and they are demonstrated to yield the minimum inter-beam interference for fixed $N_t$ and $N$. This study reveals that, if user traffic is light and one user can be successfully served within a single transmission, non-orthogonal OBF can be applied to obtain lower worst-case delay among the users. On the other hand, if user traffic is heavy, non-orthogonal OBF is inferior to orthogonal OBF in terms of sum-rate and packet delay.
Bounds and asymptotics for orthogonal polynomials for varying weights
Levin, Eli
2018-01-01
This book establishes bounds and asymptotics under almost minimal conditions on the varying weights, and applies them to universality limits and entropy integrals. Orthogonal polynomials associated with varying weights play a key role in analyzing random matrices and other topics. This book will be of use to a wide community of mathematicians, physicists, and statisticians dealing with techniques of potential theory, orthogonal polynomials, approximation theory, as well as random matrices. .
COMPUTER GRAPHICAL REPRESENTATION, IN TREBLE ORTHOGONAL PROJECTION, OF A POINT
Directory of Open Access Journals (Sweden)
SLONOVSCHI Andrei
2017-05-01
Full Text Available In the stages of understanding and study, by students, of descriptive geometry, the treble orthogonal projection of a point, creates problems in the situations in that one or more descriptive coordinates are zero. Starting from these considerations the authors have created an original computer program which offers to the students the possibility to easily understanding of the way in which a point is represented, in draught, in the treble orthogonal projection whatever which are its values of the descriptive coordinates.
Properties of the distributional finite Fourier transform
Carmichael, Richard D.
2016-01-01
The analytic functions in tubes which obtain the distributional finite Fourier transform as boundary value are shown to have a strong boundedness property and to be recoverable as a Fourier-Laplace transform, a distributional finite Fourier transform, and as a Cauchy integral of a distribution associated with the boundary value.
Fourier techniques in X-ray timing
van der Klis, M.
1988-01-01
Basic principles of Fourier techniques often used in X-ray time series analysis are reviewed. The relation between the discrete Fourier transform and the continuous Fourier transform is discussed to introduce the concepts of windowing and aliasing. The relation is derived between the power spectrum
International Nuclear Information System (INIS)
Shestakov, A.I.; Mirin, A.A.
1984-01-01
A numerical method based on Fourier expansions and finite differences is presented. The method is demonstrated by solving a scalar, three-dimensional elliptic equation arising in MFE research, but has applicability to a wider class of problems. The scheme solves equations whose solutions are expected to be periodic in one or more of the independent variables
Nazrul Islam, Mohammed; Karim, Mohammad A.; Vijayan Asari, K.
2013-09-01
Protecting and processing of confidential information, such as personal identification, biometrics, remains a challenging task for further research and development. A new methodology to ensure enhanced security of information in images through the use of encryption and multiplexing is proposed in this paper. We use orthogonal encoding scheme to encode multiple information independently and then combine them together to save storage space and transmission bandwidth. The encoded and multiplexed image is encrypted employing multiple reference-based joint transform correlation. The encryption key is fed into four channels which are relatively phase shifted by different amounts. The input image is introduced to all the channels and then Fourier transformed to obtain joint power spectra (JPS) signals. The resultant JPS signals are again phase-shifted and then combined to form a modified JPS signal which yields the encrypted image after having performed an inverse Fourier transformation. The proposed cryptographic system makes the confidential information absolutely inaccessible to any unauthorized intruder, while allows for the retrieval of the information to the respective authorized recipient without any distortion. The proposed technique is investigated through computer simulations under different practical conditions in order to verify its overall robustness.
Non-Archimedean analogues of orthogonal and symmetric operators
International Nuclear Information System (INIS)
Albeverio, S; Bayod, J M; Perez-Garsia, C; Khrennikov, A Yu; Cianci, R
1999-01-01
We study orthogonal and symmetric operators on non-Archimedean Hilbert spaces in connection with the p-adic quantization. This quantization describes measurements with finite precision. Symmetric (bounded) operators on p-adic Hilbert spaces represent physical observables. We study the spectral properties of one of the most important quantum operators, namely, the position operator (which is represented on p-adic Hilbert L 2 -space with respect to the p-adic Gaussian measure). Orthogonal isometric isomorphisms of p-adic Hilbert spaces preserve the precision of measurements. We study properties of orthogonal operators. It is proved that every orthogonal operator on non-Archimedean Hilbert space is continuous. However, there are discontinuous operators with dense domain of definition that preserve the inner product. There exist non-isometric orthogonal operators. We describe some classes of orthogonal isometric operators on finite-dimensional spaces. We study some general questions in the theory of non-Archimedean Hilbert spaces (in particular, general connections between the topology, norm and inner product)
Directory of Open Access Journals (Sweden)
Lingyang Song
2007-04-01
Full Text Available We report a simple differential modulation scheme for quasi-orthogonal space-time block codes. A new class of quasi-orthogonal coding structures that can provide partial transmit diversity is presented for various numbers of transmit antennas. Differential encoding and decoding can be simplified for differential Alamouti-like codes by grouping the signals in the transmitted matrix and decoupling the detection of data symbols, respectively. The new scheme can achieve constant amplitude of transmitted signals, and avoid signal constellation expansion; in addition it has a linear signal detector with very low complexity. Simulation results show that these partial-diversity codes can provide very useful results at low SNR for current communication systems. Extension to more than four transmit antennas is also considered.
Improved Fourier-transform profilometry
International Nuclear Information System (INIS)
Mao Xianfu; Chen Wenjing; Su Xianyu
2007-01-01
An improved optical geometry of the projected-fringe profilometry technique, in which the exit pupil of the projecting lens and the entrance pupil of the imaging lens are neither at the same height above the reference plane nor coplanar, is discussed and used in Fourier-transform profilometry. Furthermore, an improved fringe-pattern description and phase-height mapping formula based on the improved geometrical generalization is deduced. Employing the new optical geometry, it is easier for us to obtain the full-field fringe by moving either the projector or the imaging device. Therefore the new method offers a flexible way to obtain reliable height distribution of a measured object
Fourier-transform optical microsystems
Collins, S. D.; Smith, R. L.; Gonzalez, C.; Stewart, K. P.; Hagopian, J. G.; Sirota, J. M.
1999-01-01
The design, fabrication, and initial characterization of a miniature single-pass Fourier-transform spectrometer (FTS) that has an optical bench that measures 1 cm x 5 cm x 10 cm is presented. The FTS is predicated on the classic Michelson interferometer design with a moving mirror. Precision translation of the mirror is accomplished by microfabrication of dovetailed bearing surfaces along single-crystal planes in silicon. Although it is miniaturized, the FTS maintains a relatively high spectral resolution, 0.1 cm-1, with adequate optical throughput.
Fourier Transform Methods. Chapter 4
Kaplan, Simon G.; Quijada, Manuel A.
2015-01-01
This chapter describes the use of Fourier transform spectrometers (FTS) for accurate spectrophotometry over a wide spectral range. After a brief exposition of the basic concepts of FTS operation, we discuss instrument designs and their advantages and disadvantages relative to dispersive spectrometers. We then examine how common sources of error in spectrophotometry manifest themselves when using an FTS and ways to reduce the magnitude of these errors. Examples are given of applications to both basic and derived spectrophotometric quantities. Finally, we give recommendations for choosing the right instrument for a specific application, and how to ensure the accuracy of the measurement results..
DEFF Research Database (Denmark)
2017-01-01
, and performing an iterative manipulation of the input sequence. The performing of the iterative manipulation of the input sequence may include, for example: computing frequency domain response of the sequence, normalizing elements of the computed frequency domain sequence to unitary power while maintaining phase...
Negative thermal expansion materials
International Nuclear Information System (INIS)
Evans, J.S.O.
1997-01-01
The recent discovery of negative thermal expansion over an unprecedented temperature range in ZrW 2 O 8 (which contracts continuously on warming from below 2 K to above 1000 K) has stimulated considerable interest in this unusual phenomenon. Negative and low thermal expansion materials have a number of important potential uses in ceramic, optical and electronic applications. We have now found negative thermal expansion in a large new family of materials with the general formula A 2 (MO 4 ) 3 . Chemical substitution dramatically influences the thermal expansion properties of these materials allowing the production of ceramics with negative, positive or zero coefficients of thermal expansion, with the potential to control other important materials properties such as refractive index and dielectric constant. The mechanism of negative thermal expansion and the phase transitions exhibited by this important new class of low-expansion materials will be discussed. (orig.)
Fourier Spectroscopy: A Bayesian Way
Directory of Open Access Journals (Sweden)
Stefan Schmuck
2017-01-01
Full Text Available The concepts of standard analysis techniques applied in the field of Fourier spectroscopy treat fundamental aspects insufficiently. For example, the spectra to be inferred are influenced by the noise contribution to the interferometric data, by nonprobed spatial domains which are linked to Fourier coefficients above a certain order, by the spectral limits which are in general not given by the Nyquist assumptions, and by additional parameters of the problem at hand like the zero-path difference. To consider these fundamentals, a probabilistic approach based on Bayes’ theorem is introduced which exploits multivariate normal distributions. For the example application, we model the spectra by the Gaussian process of a Brownian bridge stated by a prior covariance. The spectra themselves are represented by a number of parameters which map linearly to the data domain. The posterior for these linear parameters is analytically obtained, and the marginalisation over these parameters is trivial. This allows the straightforward investigation of the posterior for the involved nonlinear parameters, like the zero-path difference location and the spectral limits, and hyperparameters, like the scaling of the Gaussian process. With respect to the linear problem, this can be interpreted as an implementation of Ockham’s razor principle.
Pointwise convergence of Fourier series
Arias de Reyna, Juan
2002-01-01
This book contains a detailed exposition of Carleson-Hunt theorem following the proof of Carleson: to this day this is the only one giving better bounds. It points out the motivation of every step in the proof. Thus the Carleson-Hunt theorem becomes accessible to any analyst.The book also contains the first detailed exposition of the fine results of Hunt, Sjölin, Soria, etc on the convergence of Fourier Series. Its final chapters present original material. With both Fefferman's proof and the recent one of Lacey and Thiele in print, it becomes more important than ever to understand and compare these two related proofs with that of Carleson and Hunt. These alternative proofs do not yield all the results of the Carleson-Hunt proof. The intention of this monograph is to make Carleson's proof accessible to a wider audience, and to explain its consequences for the pointwise convergence of Fourier series for functions in spaces near $äcal Lü^1$, filling a well-known gap in the literature.
Orthogonal and symplectic Yangians and Yang–Baxter R-operators
Directory of Open Access Journals (Sweden)
A.P. Isaev
2016-03-01
Full Text Available Yang–Baxter R operators symmetric with respect to the orthogonal and symplectic algebras are considered in an uniform way. Explicit forms for the spinorial and metaplectic R operators are obtained. L operators, obeying the RLL relation with the orthogonal or symplectic fundamental R matrix, are considered in the interesting cases, where their expansion in inverse powers of the spectral parameter is truncated. Unlike the case of special linear algebra symmetry the truncation results in additional conditions on the Lie algebra generators of which the L operators is built and which can be fulfilled in distinguished representations only. Further, generalized L operators, obeying the modified RLL relation with the fundamental R matrix replaced by the spinorial or metaplectic one, are considered in the particular case of linear dependence on the spectral parameter. It is shown how by fusion with respect to the spinorial or metaplectic representation these first order spinorial L operators reproduce the ordinary L operators with second order truncation.
Fourier analysis of conductive heat transfer for glazed roofing materials
Energy Technology Data Exchange (ETDEWEB)
Roslan, Nurhana Lyana; Bahaman, Nurfaradila; Almanan, Raja Noorliyana Raja; Ismail, Razidah [Faculty of Computer and Mathematical Sciences, Universiti Teknologi MARA, 40450 Shah Alam, Selangor (Malaysia); Zakaria, Nor Zaini [Faculty of Applied Sciences, Universiti Teknologi MARA, 40450 Shah Alam, Selangor (Malaysia)
2014-07-10
For low-rise buildings, roof is the most exposed surface to solar radiation. The main mode of heat transfer from outdoor via the roof is conduction. The rate of heat transfer and the thermal impact is dependent on the thermophysical properties of roofing materials. Thus, it is important to analyze the heat distribution for the various types of roofing materials. The objectives of this paper are to obtain the Fourier series for the conductive heat transfer for two types of glazed roofing materials, namely polycarbonate and polyfilled, and also to determine the relationship between the ambient temperature and the conductive heat transfer for these materials. Ambient and surface temperature data were collected from an empirical field investigation in the campus of Universiti Teknologi MARA Shah Alam. The roofing materials were installed on free-standing structures in natural ventilation. Since the temperature data are generally periodic, Fourier series and numerical harmonic analysis are applied. Based on the 24-point harmonic analysis, the eleventh order harmonics is found to generate an adequate Fourier series expansion for both glazed roofing materials. In addition, there exists a linear relationship between the ambient temperature and the conductive heat transfer for both glazed roofing materials. Based on the gradient of the graphs, lower heat transfer is indicated through polyfilled. Thus polyfilled would have a lower thermal impact compared to polycarbonate.
Hall, Steven R.; Walker, Bruce K.
1990-01-01
A new failure detection and isolation algorithm for linear dynamic systems is presented. This algorithm, the Orthogonal Series Generalized Likelihood Ratio (OSGLR) test, is based on the assumption that the failure modes of interest can be represented by truncated series expansions. This assumption leads to a failure detection algorithm with several desirable properties. Computer simulation results are presented for the detection of the failures of actuators and sensors of a C-130 aircraft. The results show that the OSGLR test generally performs as well as the GLR test in terms of time to detect a failure and is more robust to failure mode uncertainty. However, the OSGLR test is also somewhat more sensitive to modeling errors than the GLR test.
Orthogonality relations and supercharacter formulas of U(m|n) representations
International Nuclear Information System (INIS)
Alfaro, J.; Medina, R.; Urrutia, L.F.
1997-01-01
In this paper we obtain the orthogonality relations for the supergroup U(m|n), which are remarkably different from the ones for the U(N) case. We extend our results for ordinary representations, obtained some time ago, to the case of complex conjugated and mixed representations. Our results are expressed in terms of the Young tableaux notation for irreducible representations. We use the supersymmetric Harish - Chandra - Itzykson endash Zuber integral and the character expansion technique as mathematical tools for deriving these relations. As a byproduct we also obtain closed expressions for the supercharacters and dimensions of some particular irreducible U(m|n) representations. A new way of labeling the U(m|n) irreducible representations in terms of m+n numbers is proposed. Finally, as a corollary of our results, new identities among the dimensions of the irreducible representations of the unitary group U(N) are presented. copyright 1997 American Institute of Physics
Consequences of wave function orthogonality for medium energy nuclear reactions
International Nuclear Information System (INIS)
Noble, J.V.
1978-01-01
In the usual models of high-energy bound-state to continuum transitions no account is taken of the orthogonality of the bound and continuum wave functions. This orthogonality induces considerable cancellations in the overlap integrals expressing the transition amplitudes for reactions such as (e,e'p), (γ,p), and (π,N), which are simply not included in the distorted-wave Born-approximation calculations which to date remain the only computationally feasible heirarchy of approximations. The object of this paper is to present a new formulation of the bound-state to continuum transition problem, based upon flux conservation, in which the orthogonality of wave functions is taken into account ab initio. The new formulation, while exact if exact wave functions are used, offers the possibility of using approximate wave functions for the continuum states without doing violence to the cancellations induced by orthogonality. The method is applied to single-particle states obeying the Schroedinger and Dirac equations, as well as to a coupled-channel model in which absorptive processes can be described in a fully consistent manner. Several types of absorption vertex are considered, and in the (π,N) case the equivalence of pseudoscalar and pseudovector πNN coupling is seen to follow directly from wave function orthogonality
Generalized Pseudospectral Method and Zeros of Orthogonal Polynomials
Directory of Open Access Journals (Sweden)
Oksana Bihun
2018-01-01
Full Text Available Via a generalization of the pseudospectral method for numerical solution of differential equations, a family of nonlinear algebraic identities satisfied by the zeros of a wide class of orthogonal polynomials is derived. The generalization is based on a modification of pseudospectral matrix representations of linear differential operators proposed in the paper, which allows these representations to depend on two, rather than one, sets of interpolation nodes. The identities hold for every polynomial family pνxν=0∞ orthogonal with respect to a measure supported on the real line that satisfies some standard assumptions, as long as the polynomials in the family satisfy differential equations Apν(x=qν(xpν(x, where A is a linear differential operator and each qν(x is a polynomial of degree at most n0∈N; n0 does not depend on ν. The proposed identities generalize known identities for classical and Krall orthogonal polynomials, to the case of the nonclassical orthogonal polynomials that belong to the class described above. The generalized pseudospectral representations of the differential operator A for the case of the Sonin-Markov orthogonal polynomials, also known as generalized Hermite polynomials, are presented. The general result is illustrated by new algebraic relations satisfied by the zeros of the Sonin-Markov polynomials.
Orthogonal polynomials derived from the tridiagonal representation approach
Alhaidari, A. D.
2018-01-01
The tridiagonal representation approach is an algebraic method for solving second order differential wave equations. Using this approach in the solution of quantum mechanical problems, we encounter two new classes of orthogonal polynomials whose properties give the structure and dynamics of the corresponding physical system. For a certain range of parameters, one of these polynomials has a mix of continuous and discrete spectra making it suitable for describing physical systems with both scattering and bound states. In this work, we define these polynomials by their recursion relations and highlight some of their properties using numerical means. Due to the prime significance of these polynomials in physics, we hope that our short expose will encourage experts in the field of orthogonal polynomials to study them and derive their properties (weight functions, generating functions, asymptotics, orthogonality relations, zeros, etc.) analytically.
Applications of Fourier transforms to generalized functions
Rahman, M
2011-01-01
This book explains how Fourier transforms can be applied to generalized functions. The generalized function is one of the important branches of mathematics and is applicable in many practical fields. Its applications to the theory of distribution and signal processing are especially important. The Fourier transform is a mathematical procedure that can be thought of as transforming a function from its time domain to the frequency domain.The book contains six chapters and three appendices. Chapter 1 deals with preliminary remarks on Fourier series from a general point of view and also contains an introduction to the first generalized function. Chapter 2 is concerned with the generalized functions and their Fourier transforms. Chapter 3 contains the Fourier transforms of particular generalized functions. The author has stated and proved 18 formulas dealing with the Fourier transforms of generalized functions, and demonstrated some important problems of practical interest. Chapter 4 deals with the asymptotic esti...
Energy Technology Data Exchange (ETDEWEB)
Dzenus, M.; Hundhausen, W.; Jansing, W.
1979-10-15
This discourse recounts efforts put into the SNR-2 project; specifically the development of compensation devices. The various prototypes of these compensation devices are described and the state of development reviewed. The expansion joints were developed on the basis of specific design criteria whereby differentiation is made between expansion joints of small and large nominal diameter. Expansion joints for installation in the sodium-filled primary piping are equipped with safety bellows in addition to the actual working bellows.
Handbook of Fourier analysis & its applications
Marks, Robert J
2009-01-01
Fourier analysis has many scientific applications - in physics, number theory, combinatorics, signal processing, probability theory, statistics, option pricing, cryptography, acoustics, oceanography, optics and diffraction, geometry, and other areas. In signal processing and related fields, Fourier analysis is typically thought of as decomposing a signal into its component frequencies and their amplitudes. This practical, applications-based professional handbook comprehensively covers the theory and applications of Fourier Analysis, spanning topics from engineering mathematics, signal process
Fourier transform n.m.r. spectroscopy
International Nuclear Information System (INIS)
Shaw, D.
1976-01-01
This book is orientated to techniques rather than applications. The basic theory of n.m.r. is dealt with in a unified approach to the Fourier theory. The middle section of the book concentrates on the practical aspects of Fourier n.m.r., both instrumental and experimental. The final chapters briefly cover general application of n.m.r., but concentrate strongly on those areas where Fourier n.m.r. can give information which is not available by conventional techniques
A simple approach to Fourier aliasing
International Nuclear Information System (INIS)
Foadi, James
2007-01-01
In the context of discrete Fourier transforms the idea of aliasing as due to approximation errors in the integral defining Fourier coefficients is introduced and explained. This has the positive pedagogical effect of getting to the heart of sampling and the discrete Fourier transform without having to delve into effective, but otherwise long and structured, introductions to the topic, commonly met in advanced, specialized books
Fourier transform n. m. r. spectroscopy
Energy Technology Data Exchange (ETDEWEB)
Shaw, D [Varian Ltd., Walton (UK)
1976-01-01
This book is orientated to techniques rather than applications. The basic theory of n.m.r. is dealt with in a unified approach to the Fourier theory. The middle section of the book concentrates on the practical aspects of Fourier n.m.r., both instrumental and experimental. The final chapters briefly cover general application of n.m.r., but concentrate strongly on those areas where Fourier n.m.r. can give information which is not available by conventional techniques.
Quantitative Boltzmann-Gibbs Principles via Orthogonal Polynomial Duality
Ayala, Mario; Carinci, Gioia; Redig, Frank
2018-06-01
We study fluctuation fields of orthogonal polynomials in the context of particle systems with duality. We thereby obtain a systematic orthogonal decomposition of the fluctuation fields of local functions, where the order of every term can be quantified. This implies a quantitative generalization of the Boltzmann-Gibbs principle. In the context of independent random walkers, we complete this program, including also fluctuation fields in non-stationary context (local equilibrium). For other interacting particle systems with duality such as the symmetric exclusion process, similar results can be obtained, under precise conditions on the n particle dynamics.
Automorphisms of Algebras and Bochner's Property for Vector Orthogonal Polynomials
Horozov, Emil
2016-05-01
We construct new families of vector orthogonal polynomials that have the property to be eigenfunctions of some differential operator. They are extensions of the Hermite and Laguerre polynomial systems. A third family, whose first member has been found by Y. Ben Cheikh and K. Douak is also constructed. The ideas behind our approach lie in the studies of bispectral operators. We exploit automorphisms of associative algebras which transform elementary vector orthogonal polynomial systems which are eigenfunctions of a differential operator into other systems of this type.
Problems of the orthogonalized plane wave method. 1
International Nuclear Information System (INIS)
Farberovich, O.V.; Kurganskii, S.I.; Domashevskaya, E.P.
1979-01-01
The main problems of the orthogonalized plane wave method are discussed including (a) consideration of core states; (b) effect of overlap of wave functions of external core states upon the band structure; (c) calculation of d-type states. The modified orthogonal plane wave method (MOPW method) of Deegan and Twose is applied in a general form to solve the problems of the usual OPW method. For the first time the influence on the spectrum of the main parameters of the MOPW method is studied systematically by calculating the electronic energy spectrum in the transition metals Nb and V. (author)
International Nuclear Information System (INIS)
Du, Qiang; Yang, Jiang
2017-01-01
This work is concerned with the Fourier spectral approximation of various integral differential equations associated with some linear nonlocal diffusion and peridynamic operators under periodic boundary conditions. For radially symmetric kernels, the nonlocal operators under consideration are diagonalizable in the Fourier space so that the main computational challenge is on the accurate and fast evaluation of their eigenvalues or Fourier symbols consisting of possibly singular and highly oscillatory integrals. For a large class of fractional power-like kernels, we propose a new approach based on reformulating the Fourier symbols both as coefficients of a series expansion and solutions of some simple ODE models. We then propose a hybrid algorithm that utilizes both truncated series expansions and high order Runge–Kutta ODE solvers to provide fast evaluation of Fourier symbols in both one and higher dimensional spaces. It is shown that this hybrid algorithm is robust, efficient and accurate. As applications, we combine this hybrid spectral discretization in the spatial variables and the fourth-order exponential time differencing Runge–Kutta for temporal discretization to offer high order approximations of some nonlocal gradient dynamics including nonlocal Allen–Cahn equations, nonlocal Cahn–Hilliard equations, and nonlocal phase-field crystal models. Numerical results show the accuracy and effectiveness of the fully discrete scheme and illustrate some interesting phenomena associated with the nonlocal models.
Metasurface Enabled Wide-Angle Fourier Lens.
Liu, Wenwei; Li, Zhancheng; Cheng, Hua; Tang, Chengchun; Li, Junjie; Zhang, Shuang; Chen, Shuqi; Tian, Jianguo
2018-06-01
Fourier optics, the principle of using Fourier transformation to understand the functionalities of optical elements, lies at the heart of modern optics, and it has been widely applied to optical information processing, imaging, holography, etc. While a simple thin lens is capable of resolving Fourier components of an arbitrary optical wavefront, its operation is limited to near normal light incidence, i.e., the paraxial approximation, which puts a severe constraint on the resolvable Fourier domain. As a result, high-order Fourier components are lost, resulting in extinction of high-resolution information of an image. Other high numerical aperture Fourier lenses usually suffer from the bulky size and costly designs. Here, a dielectric metasurface consisting of high-aspect-ratio silicon waveguide array is demonstrated experimentally, which is capable of performing 1D Fourier transform for a large incident angle range and a broad operating bandwidth. Thus, the device significantly expands the operational Fourier space, benefitting from the large numerical aperture and negligible angular dispersion at large incident angles. The Fourier metasurface will not only facilitate efficient manipulation of spatial spectrum of free-space optical wavefront, but also be readily integrated into micro-optical platforms due to its compact size. © 2018 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.
Convergence of mayer expansions
International Nuclear Information System (INIS)
Brydges, D.C.
1986-01-01
The tree graph bound of Battle and Federbush is extended and used to provide a simple criterion for the convergence of (iterated) Mayer expansions. As an application estimates on the radius of convergence of the Mayer expansion for the two-dimensional Yukawa gas (nonstable interaction) are obtained
Hung, Yu-Han; Tseng, Chin-Hao; Hwang, Sheng-Kwang
2018-06-01
This Letter investigates an optically injected semiconductor laser for conversion from non-orthogonally to orthogonally polarized optical single-sideband modulation. The underlying mechanism relies solely on nonlinear laser characteristics and, thus, only a typical semiconductor laser is required as the key conversion unit. This conversion can be achieved for a broadly tunable frequency range up to at least 65 GHz. After conversion, the microwave phase quality, including linewidth and phase noise, is mostly preserved, and simultaneous microwave amplification up to 23 dB is feasible.
Adaptive integrand decomposition in parallel and orthogonal space
International Nuclear Information System (INIS)
Mastrolia, Pierpaolo; Peraro, Tiziano; Primo, Amedeo
2016-01-01
We present the integrand decomposition of multiloop scattering amplitudes in parallel and orthogonal space-time dimensions, d=d ∥ +d ⊥ , being d ∥ the dimension of the parallel space spanned by the legs of the diagrams. When the number n of external legs is n≤4, the corresponding representation of multiloop integrals exposes a subset of integration variables which can be easily integrated away by means of Gegenbauer polynomials orthogonality condition. By decomposing the integration momenta along parallel and orthogonal directions, the polynomial division algorithm is drastically simplified. Moreover, the orthogonality conditions of Gegenbauer polynomials can be suitably applied to integrate the decomposed integrand, yielding the systematic annihilation of spurious terms. Consequently, multiloop amplitudes are expressed in terms of integrals corresponding to irreducible scalar products of loop momenta and external ones. We revisit the one-loop decomposition, which turns out to be controlled by the maximum-cut theorem in different dimensions, and we discuss the integrand reduction of two-loop planar and non-planar integrals up to n=8 legs, for arbitrary external and internal kinematics. The proposed algorithm extends to all orders in perturbation theory.
Crossover ensembles of random matrices and skew-orthogonal polynomials
International Nuclear Information System (INIS)
Kumar, Santosh; Pandey, Akhilesh
2011-01-01
Highlights: → We study crossover ensembles of Jacobi family of random matrices. → We consider correlations for orthogonal-unitary and symplectic-unitary crossovers. → We use the method of skew-orthogonal polynomials and quaternion determinants. → We prove universality of spectral correlations in crossover ensembles. → We discuss applications to quantum conductance and communication theory problems. - Abstract: In a recent paper (S. Kumar, A. Pandey, Phys. Rev. E, 79, 2009, p. 026211) we considered Jacobi family (including Laguerre and Gaussian cases) of random matrix ensembles and reported exact solutions of crossover problems involving time-reversal symmetry breaking. In the present paper we give details of the work. We start with Dyson's Brownian motion description of random matrix ensembles and obtain universal hierarchic relations among the unfolded correlation functions. For arbitrary dimensions we derive the joint probability density (jpd) of eigenvalues for all transitions leading to unitary ensembles as equilibrium ensembles. We focus on the orthogonal-unitary and symplectic-unitary crossovers and give generic expressions for jpd of eigenvalues, two-point kernels and n-level correlation functions. This involves generalization of the theory of skew-orthogonal polynomials to crossover ensembles. We also consider crossovers in the circular ensembles to show the generality of our method. In the large dimensionality limit, correlations in spectra with arbitrary initial density are shown to be universal when expressed in terms of a rescaled symmetry breaking parameter. Applications of our crossover results to communication theory and quantum conductance problems are also briefly discussed.
Orthogonal experimental study on high frequency cascade thermoacoustic engine
International Nuclear Information System (INIS)
Hu Zhongjun; Li Qing; Li Zhengyu; Li Qiang
2008-01-01
Orthogonal experiment design and variance analysis were adopted to investigate a miniature cascade thermoacoustic engine, which consisted of one standing wave stage and one traveling wave stage in series, operating at about 470 Hz, using helium as the working gas. Optimum matching of the heater powers between stages was very important for the performance of a cascade thermoacoustic engine, which was obtained from the orthogonal experiments. The orthogonal experiment design considered three experimental factors, i.e. the charging pressure and the heater powers in the two stages, which varied on five different levels, respectively. According to the range analysis and variance analysis from the orthogonal experiments, the charging pressure was the most sensitive factor influencing the dynamic pressure amplitude and onset temperature. The total efficiency and the dynamic pressure amplitude increased when the traveling wave stage heater power increased. The optimum ratio of the heater powers between the traveling wave stage and the standing wave stage was about 1.25, compromising the total efficiency with the dynamic pressure amplitude
Synthesis of an Orthogonal Topological Analogue of Helicene
DEFF Research Database (Denmark)
Wixe, Torbjörn; Wallentin, Carl‐Johan; Johnson, Magnus T.
2013-01-01
The synthesis of an orthogonal topological pentamer analogue of helicene is presented. This analogue forms a tubular structure with its aromatic systems directed parallel to the axis of propagation, which creates a cavity with the potential to function as a host molecule. The synthetic strategy r...
Secrecy Capacity of a Class of Orthogonal Relay Eavesdropper Channels
Directory of Open Access Journals (Sweden)
Aggarwal Vaneet
2009-01-01
Full Text Available The secrecy capacity of relay channels with orthogonal components is studied in the presence of an additional passive eavesdropper node. The relay and destination receive signals from the source on two orthogonal channels such that the destination also receives transmissions from the relay on its channel. The eavesdropper can overhear either one or both of the orthogonal channels. Inner and outer bounds on the secrecy capacity are developed for both the discrete memoryless and the Gaussian channel models. For the discrete memoryless case, the secrecy capacity is shown to be achieved by a partial decode-and-forward (PDF scheme when the eavesdropper can overhear only one of the two orthogonal channels. Two new outer bounds are presented for the Gaussian model using recent capacity results for a Gaussian multiantenna point-to-point channel with a multiantenna eavesdropper. The outer bounds are shown to be tight for two subclasses of channels. The first subclass is one in which the source and relay are clustered, and the eavesdropper receives signals only on the channel from the source and the relay to the destination, for which the PDF strategy is optimal. The second is a subclass in which the source does not transmit to the relay, for which a noise-forwarding strategy is optimal.
Interactive 3D segmentation using connected orthogonal contours
de Bruin, P. W.; Dercksen, V. J.; Post, F. H.; Vossepoel, A. M.; Streekstra, G. J.; Vos, F. M.
2005-01-01
This paper describes a new method for interactive segmentation that is based on cross-sectional design and 3D modelling. The method represents a 3D model by a set of connected contours that are planar and orthogonal. Planar contours overlayed on image data are easily manipulated and linked contours
Adaptive integrand decomposition in parallel and orthogonal space
Energy Technology Data Exchange (ETDEWEB)
Mastrolia, Pierpaolo [Dipartimento di Fisica ed Astronomia, Università di Padova,Via Marzolo 8, 35131 Padova (Italy); INFN, Sezione di Padova,Via Marzolo 8, 35131 Padova (Italy); Peraro, Tiziano [Higgs Centre for Theoretical Physics, School of Physics and Astronomy,The University of Edinburgh,James Clerk Maxwell Building,Peter Guthrie Tait Road, Edinburgh EH9 3FD, Scotland (United Kingdom); Primo, Amedeo [Dipartimento di Fisica ed Astronomia, Università di Padova,Via Marzolo 8, 35131 Padova (Italy); INFN, Sezione di Padova,Via Marzolo 8, 35131 Padova (Italy)
2016-08-29
We present the integrand decomposition of multiloop scattering amplitudes in parallel and orthogonal space-time dimensions, d=d{sub ∥}+d{sub ⊥}, being d{sub ∥} the dimension of the parallel space spanned by the legs of the diagrams. When the number n of external legs is n≤4, the corresponding representation of multiloop integrals exposes a subset of integration variables which can be easily integrated away by means of Gegenbauer polynomials orthogonality condition. By decomposing the integration momenta along parallel and orthogonal directions, the polynomial division algorithm is drastically simplified. Moreover, the orthogonality conditions of Gegenbauer polynomials can be suitably applied to integrate the decomposed integrand, yielding the systematic annihilation of spurious terms. Consequently, multiloop amplitudes are expressed in terms of integrals corresponding to irreducible scalar products of loop momenta and external ones. We revisit the one-loop decomposition, which turns out to be controlled by the maximum-cut theorem in different dimensions, and we discuss the integrand reduction of two-loop planar and non-planar integrals up to n=8 legs, for arbitrary external and internal kinematics. The proposed algorithm extends to all orders in perturbation theory.
Dynamic imaging of skeletal muscle contraction in three orthogonal directions
Lopata, R.G.; van Dijk, J.P; Pillen, S.; Nillisen, M.M.; Maas, H.; Thijssen, J.M.; Stegeman, D.F.; Korte, C.L.
2010-01-01
In this study, a multidimensional strain estimation method using biplane ultrasound is presented to assess local relative deformation (i.e., local strain) in three orthogonal directions in skeletal muscles during induced and voluntary contractions. The method was tested in the musculus biceps
Dynamic imaging of skeletal muscle contraction in three orthogonal directions.
Lopata, R.G.P.; Dijk, J.P. van; Pillen, S.; Nillesen, M.M.; Maas, H.; Thijssen, J.M.; Stegeman, D.F.; Korte, C.L. de
2010-01-01
In this study, a multidimensional strain estimation method using biplane ultrasound is presented to assess local relative deformation (i.e., local strain) in three orthogonal directions in skeletal muscles during induced and voluntary contractions. The method was tested in the musculus biceps
Some p-ranks related to orthogonal spaces
Blokhuis, A.; Moorhouse, G.E.
1995-01-01
We determine the p-rank of the incidence matrix of hyperplanes of PG(n, p e) and points of a nondegenerate quadric. This yields new bounds for ovoids and the size of caps in finite orthogonal spaces. In particular, we show the nonexistence of ovoids in O10+ (2e ),O10+ (3e ),O9 (5e ),O12+ (5e
Short-Term Memory in Orthogonal Neural Networks
White, Olivia L.; Lee, Daniel D.; Sompolinsky, Haim
2004-04-01
We study the ability of linear recurrent networks obeying discrete time dynamics to store long temporal sequences that are retrievable from the instantaneous state of the network. We calculate this temporal memory capacity for both distributed shift register and random orthogonal connectivity matrices. We show that the memory capacity of these networks scales with system size.
Cospectral Graphs and Regular Orthogonal Matrices of Level 2
Abiad Monge, A.; Haemers, W.H.
2012-01-01
Abstract: For a graph Γ with adjacency matrix A, we consider a switching operation that takes Γ into a graph Γ' with adjacency matrix A', defined by A' = QtAQ, where Q is a regular orthogonal matrix of level 2 (that is, QtQ = I, Q1 = 1, 2Q is integral, and Q is not a permutation matrix). If such an
Application of Orthogonal Design to Optimize Extraction of ...
African Journals Online (AJOL)
Purpose: To optimize the extraction technology of polysaccharides from Cynomorium songaricum Rupr by ultrasonic-assisted extraction (UAE). Methods: Four parameters including ultrasonic power, ratio of raw material to water, extraction temperature, and extraction time were optimized by orthogonal design. The effects of ...
Non-orthogonally transitive G2 spike solution
International Nuclear Information System (INIS)
Lim, Woei Chet
2015-01-01
We generalize the orthogonally transitive (OT) G 2 spike solution to the non-OT G 2 case. This is achieved by applying Geroch’s transformation on a Kasner seed. The new solution contains two more parameters than the OT G 2 spike solution. Unlike the OT G 2 spike solution, the new solution always resolves its spike. (fast track communication)
Constructing General Orthogonal Fractional Factorial Split-Plot Designs
Sartono, B.; Goos, P.; Schoen, E.
2015-01-01
While the orthogonal design of split-plot fractional factorial experiments has received much attention already, there are still major voids in the literature. First, designs with one or more factors acting at more than two levels have not yet been considered. Second, published work on nonregular
Orthogonal designs Hadamard matrices, quadratic forms and algebras
Seberry, Jennifer
2017-01-01
Orthogonal designs have proved fundamental to constructing code division multiple antenna systems for more efficient mobile communications. Starting with basic theory, this book develops the algebra and combinatorics to create new communications modes. Intended primarily for researchers, it is also useful for graduate students wanting to understand some of the current communications coding theories.
Orthogonal feature selection method. [For preprocessing of man spectral data
Energy Technology Data Exchange (ETDEWEB)
Kowalski, B R [Univ. of Washington, Seattle; Bender, C F
1976-01-01
A new method of preprocessing spectral data for extraction of molecular structural information is desired. This SELECT method generates orthogonal features that are important for classification purposes and that also retain their identity to the original measurements. A brief introduction to chemical pattern recognition is presented. A brief description of the method and an application to mass spectral data analysis follow. (BLM)
A turbulent jet in crossflow analysed with proper orthogonal decomposition
DEFF Research Database (Denmark)
Meyer, Knud Erik; Pedersen, Jakob Martin; Özcan, Oktay
2007-01-01
and pipe diameter was 2400 and the jet to crossflow velocity ratios were R = 3.3 and R = 1.3. The experimental data have been analysed by proper orthogonal decomposition (POD). For R = 3.3, the results in several different planes indicate that the wake vortices are the dominant dynamic flow structures...
Differentiation by integration using orthogonal polynomials, a survey
Diekema, E.; Koornwinder, T.H.
2012-01-01
This survey paper discusses the history of approximation formulas for n-th order derivatives by integrals involving orthogonal polynomials. There is a large but rather disconnected corpus of literature on such formulas. We give some results in greater generality than in the literature. Notably we
Sparsely-Packetized Predictive Control by Orthogonal Matching Pursuit
DEFF Research Database (Denmark)
Nagahara, Masaaki; Quevedo, Daniel; Østergaard, Jan
2012-01-01
We study packetized predictive control, known to be robust against packet dropouts in networked systems. To obtain sparse packets for rate-limited networks, we design control packets via an ℓ0 optimization, which can be eectively solved by orthogonal matching pursuit. Our formulation ensures...
Short-term memory in orthogonal neural networks
International Nuclear Information System (INIS)
White, Olivia L.; Lee, Daniel D.; Sompolinsky, Haim
2004-01-01
We study the ability of linear recurrent networks obeying discrete time dynamics to store long temporal sequences that are retrievable from the instantaneous state of the network. We calculate this temporal memory capacity for both distributed shift register and random orthogonal connectivity matrices. We show that the memory capacity of these networks scales with system size
Velocity field calculation for non-orthogonal numerical grids
Energy Technology Data Exchange (ETDEWEB)
Flach, G. P. [Savannah River Site (SRS), Aiken, SC (United States). Savannah River National Lab. (SRNL)
2015-03-01
Computational grids containing cell faces that do not align with an orthogonal (e.g. Cartesian, cylindrical) coordinate system are routinely encountered in porous-medium numerical simulations. Such grids are referred to in this study as non-orthogonal grids because some cell faces are not orthogonal to a coordinate system plane (e.g. xy, yz or xz plane in Cartesian coordinates). Non-orthogonal grids are routinely encountered at the Savannah River Site in porous-medium flow simulations for Performance Assessments and groundwater flow modeling. Examples include grid lines that conform to the sloping roof of a waste tank or disposal unit in a 2D Performance Assessment simulation, and grid surfaces that conform to undulating stratigraphic surfaces in a 3D groundwater flow model. Particle tracking is routinely performed after a porous-medium numerical flow simulation to better understand the dynamics of the flow field and/or as an approximate indication of the trajectory and timing of advective solute transport. Particle tracks are computed by integrating the velocity field from cell to cell starting from designated seed (starting) positions. An accurate velocity field is required to attain accurate particle tracks. However, many numerical simulation codes report only the volumetric flowrate (e.g. PORFLOW) and/or flux (flowrate divided by area) crossing cell faces. For an orthogonal grid, the normal flux at a cell face is a component of the Darcy velocity vector in the coordinate system, and the pore velocity for particle tracking is attained by dividing by water content. For a non-orthogonal grid, the flux normal to a cell face that lies outside a coordinate plane is not a true component of velocity with respect to the coordinate system. Nonetheless, normal fluxes are often taken as Darcy velocity components, either naively or with accepted approximation. To enable accurate particle tracking or otherwise present an accurate depiction of the velocity field for a non-orthogonal
Quantum arithmetic with the Quantum Fourier Transform
Ruiz-Perez, Lidia; Garcia-Escartin, Juan Carlos
2014-01-01
The Quantum Fourier Transform offers an interesting way to perform arithmetic operations on a quantum computer. We review existing Quantum Fourier Transform adders and multipliers and propose some modifications that extend their capabilities. Among the new circuits, we propose a quantum method to compute the weighted average of a series of inputs in the transform domain.
On the inverse windowed Fourier transform
Rebollo Neira, Laura; Fernández Rubio, Juan Antonio
1999-01-01
The inversion problem concerning the windowed Fourier transform is considered. It is shown that, out of the infinite solutions that the problem admits, the windowed Fourier transform is the "optimal" solution according to a maximum-entropy selection criterion. Peer Reviewed
Wigner distribution and fractional Fourier transform
Alieva, T.; Bastiaans, M.J.; Boashash, B.
2003-01-01
We have described the relationship between the fractional Fourier transform and the Wigner distribution by using the Radon-Wigner transform, which is a set of projections of the Wigner distribution as well as a set of squared moduli of the fractional Fourier transform. We have introduced the concept
The Fourier decomposition method for nonlinear and non-stationary time series analysis.
Singh, Pushpendra; Joshi, Shiv Dutt; Patney, Rakesh Kumar; Saha, Kaushik
2017-03-01
for many decades, there has been a general perception in the literature that Fourier methods are not suitable for the analysis of nonlinear and non-stationary data. In this paper, we propose a novel and adaptive Fourier decomposition method (FDM), based on the Fourier theory, and demonstrate its efficacy for the analysis of nonlinear and non-stationary time series. The proposed FDM decomposes any data into a small number of 'Fourier intrinsic band functions' (FIBFs). The FDM presents a generalized Fourier expansion with variable amplitudes and variable frequencies of a time series by the Fourier method itself. We propose an idea of zero-phase filter bank-based multivariate FDM (MFDM), for the analysis of multivariate nonlinear and non-stationary time series, using the FDM. We also present an algorithm to obtain cut-off frequencies for MFDM. The proposed MFDM generates a finite number of band-limited multivariate FIBFs (MFIBFs). The MFDM preserves some intrinsic physical properties of the multivariate data, such as scale alignment, trend and instantaneous frequency. The proposed methods provide a time-frequency-energy (TFE) distribution that reveals the intrinsic structure of a data. Numerical computations and simulations have been carried out and comparison is made with the empirical mode decomposition algorithms.
The fractional Fourier transform and applications
Bailey, David H.; Swarztrauber, Paul N.
1991-01-01
This paper describes the 'fractional Fourier transform', which admits computation by an algorithm that has complexity proportional to the fast Fourier transform algorithm. Whereas the discrete Fourier transform (DFT) is based on integral roots of unity e exp -2(pi)i/n, the fractional Fourier transform is based on fractional roots of unity e exp -2(pi)i(alpha), where alpha is arbitrary. The fractional Fourier transform and the corresponding fast algorithm are useful for such applications as computing DFTs of sequences with prime lengths, computing DFTs of sparse sequences, analyzing sequences with noninteger periodicities, performing high-resolution trigonometric interpolation, detecting lines in noisy images, and detecting signals with linearly drifting frequencies. In many cases, the resulting algorithms are faster by arbitrarily large factors than conventional techniques.
Teaching Fourier optics through ray matrices
International Nuclear Information System (INIS)
Moreno, I; Sanchez-Lopez, M M; Ferreira, C; Davis, J A; Mateos, F
2005-01-01
In this work we examine the use of ray-transfer matrices for teaching and for deriving some topics in a Fourier optics course, exploiting the mathematical simplicity of ray matrices compared to diffraction integrals. A simple analysis of the physical meaning of the elements of the ray matrix provides a fast derivation of the conditions to obtain the optical Fourier transform. We extend this derivation to fractional Fourier transform optical systems, and derive the order of the transform from the ray matrix. Some examples are provided to stress this point of view, both with classical and with graded index lenses. This formulation cannot replace the complete explanation of Fourier optics provided by the wave theory, but it is a complementary tool useful to simplify many aspects of Fourier optics and to relate them to geometrical optics
Zhao, Zhanshan; An, Le; Zhang, Yijing; Yuan, Jie
2017-03-01
Recycled lightweight aggregate concrete was made with construction waste and ceramsite brick mainly including brick. Using the orthogonal test method, the mix proportion of recycled lightweight aggregate concrete was studied, and the Influence regularity and significance of water binder ratio, fly ash, sand ratio, the amount of recycled aggregate proportion on the compressive strength of concrete, the strong influence of mass ratio, slump expansion degree was studied. Through the mean and range analysis of the test results, the results show that the water binder ratio has the greatest influence on the 28d intensity of recycled lightweight aggregate concrete. Secondly, the fly ash content, the recycled aggregate replacement rate and the sand ratio have little influence. For the factors of expansion: the proportion of fly ash = water binder ratio sand >sand rate> recycled aggregate replacement rate. When the content of fly ash is about 30%, the expanded degree of recycled lightweight aggregate concrete is the highest, and the workability of that is better and the strength of concrete with 28d and 56d are the highest. When the content of brickbat is about 40% brick particles, the strength of concrete reaches the highest.
Modeling laser beam diffraction and propagation by the mode-expansion method.
Snyder, James J
2007-08-01
In the mode-expansion method for modeling propagation of a diffracted beam, the beam at the aperture can be expanded as a weighted set of orthogonal modes. The parameters of the expansion modes are chosen to maximize the weighting coefficient of the lowest-order mode. As the beam propagates, its field distribution can be reconstructed from the set of weighting coefficients and the Gouy phase of the lowest-order mode. We have developed a simple procedure to implement the mode-expansion method for propagation through an arbitrary ABCD matrix, and we have demonstrated that it is accurate in comparison with direct calculations of diffraction integrals and much faster.
Universal discrete Fourier optics RF photonic integrated circuit architecture.
Hall, Trevor J; Hasan, Mehedi
2016-04-04
This paper describes a coherent electro-optic circuit architecture that generates a frequency comb consisting of N spatially separated orders using a generalised Mach-Zenhder interferometer (MZI) with its N × 1 combiner replaced by an optical N × N Discrete Fourier Transform (DFT). Advantage may be taken of the tight optical path-length control, component and circuit symmetries and emerging trimming algorithms offered by photonic integration in any platform that offers linear electro-optic phase modulation such as LiNbO3, silicon, III-V or hybrid technology. The circuit architecture subsumes all MZI-based RF photonic circuit architectures in the prior art given an appropriate choice of output port(s) and dimension N although the principal application envisaged is phase correlated subcarrier generation for all optical orthogonal frequency division multiplexing. A transfer matrix approach is used to model the operation of the architecture. The predictions of the model are validated by simulations performed using an industry standard software tool. Implementation is found to be practical.
The Geostationary Fourier Transform Spectrometer
Key, Richard; Sander, Stanley; Eldering, Annmarie; Blavier, Jean-Francois; Bekker, Dmitriy; Manatt, Ken; Rider, David; Wu, Yen-Hung
2012-01-01
The Geostationary Fourier Transform Spectrometer (GeoFTS) is an imaging spectrometer designed for a geostationary orbit (GEO) earth science mission to measure key atmospheric trace gases and process tracers related to climate change and human activity. GEO allows GeoFTS to continuously stare at a region of the earth for frequent sampling to capture the variability of biogenic fluxes and anthropogenic emissions from city to continental spatial scales and temporal scales from diurnal, synoptic, seasonal to interannual. The measurement strategy provides a process based understanding of the carbon cycle from contiguous maps of carbon dioxide (CO2), methane (CH4), carbon monoxide (CO), and chlorophyll fluorescence (CF) collected many times per day at high spatial resolution (2.7kmx2.7km at nadir). The CO2/CH4/CO/CF measurement suite in the near infrared spectral region provides the information needed to disentangle natural and anthropogenic contributions to atmospheric carbon concentrations and to minimize uncertainties in the flow of carbon between the atmosphere and surface. The half meter cube size GeoFTS instrument is based on a Michelson interferometer design that uses all high TRL components in a modular configuration to reduce complexity and cost. It is self-contained and as independent of the spacecraft as possible with simple spacecraft interfaces, making it ideal to be a "hosted" payload on a commercial communications satellite mission. The hosted payload approach for measuring the major carbon-containing gases in the atmosphere from the geostationary vantage point will affordably advance the scientific understating of carbon cycle processes and climate change.
Controlled Thermal Expansion Alloys
National Aeronautics and Space Administration — There has always been a need for controlled thermal expansion alloys suitable for mounting optics and detectors in spacecraft applications. These alloys help...
Fuel Thermal Expansion (FTHEXP)
International Nuclear Information System (INIS)
Reymann, G.A.
1978-07-01
A model is presented which deals with dimensional changes in LWR fuel pellets caused by changes in temperature. It is capable of dealing with any combination of UO 2 and PuO 2 in solid, liquid or mixed phase states, and includes expansion due to the solid-liquid phase change. The function FTHEXP models fuel thermal expansion as a function of temperature, fraction of PuO 2 , and the fraction of fuel which is molten
Multipurpose RTOF Fourier diffractometer at the ET-RR-1 reactor
International Nuclear Information System (INIS)
Maayouf, R.M.A.; Tiitta, A.T.
1993-09-01
The present work represents a further study of the basic RTOF Fourier multipurpose diffractometer, to start with, at the ET-RR-1 reactor. The functions of the suggested arrangement are thoroughly discussed and the possibilities if its expansion are also assessed. The flexibility of the arrangement allows its further expansion both for stress measurement at 90 deg. scattering angle with two detector banks at opposite sides of the incident beam and for operation in the transmission diffraction mode. (orig.). (19 refs., 10 figs., 1 tab.)
International Nuclear Information System (INIS)
Caldwell, J.
1984-01-01
Martinelli and Morini have used an analytical method for calculating values and distribution of the magnetic field in superconducting magnets. Using Fourier series the magnetic field is determined by carrying out a series expansion of the current density distribution of the system of coils. This Fourier method can be modified to include axial iron to a far greater accuracy (for finite permeability) by incorporating the image series approach of Caldwell and Zisserman. Also an exact solution can be obtained for the case of infinite permeability. A comparison of the results derived from the expansion of Martinelli and Morini with the exact solution of Caldwell and Zisserman shows excellent agreement for the iron-free case but the accuracy deteriorates as the permeability μ/sub z/ increases. The exact solution should be used for infinite permeability and also gives satisfactory results for permeability μ/sub z/ >100. A symmetric geometry is used throughout the communication for simplicity of presentation
Application of the Proper Orthogonal Decomposition to Turbulent Czochralski Convective Flows
International Nuclear Information System (INIS)
Rahal, S; Cerisier, P; Azuma, H
2007-01-01
The aim of this work is to study the general aspects of the convective flow instabilities in a simulated Czochralski system. We considered the influence of the buoyancy and crystal rotation. Velocity fields, obtained by an ultrasonic technique, the corresponding 2D Fourier spectra and a correlation function, have been used. Steady, quasi-periodic and turbulent flows, are successively recognized, as the Reynolds number was increased, for a fixed Rayleigh number. The orthogonal decomposition method was applied and the numbers of modes, involved in the dynamics of turbulent flows, calculated. As far as we know, this method has been used for the first time to study the Czochralski convective flows. This method provides also information on the most important modes and allows simple theoretical models to be established. The large rotation rates of the crystal were found to stabilize the flow, and conversely the temperature gradients destabilize the flow. Indeed, the increase of the rotation effects reduces the number of involved modes and oscillations, and conversely, as expected, the increase of the buoyancy effects induces more modes to be involved in the dynamics. Thus, the flow oscillations can be reduced either by increasing the crystal rotation rate to the adequate value, as shown in this study or by imposing a magnetic field
Replica Fourier Transform: Properties and applications
International Nuclear Information System (INIS)
Crisanti, A.; De Dominicis, C.
2015-01-01
The Replica Fourier Transform is the generalization of the discrete Fourier Transform to quantities defined on an ultrametric tree. It finds use in conjunction of the replica method used to study thermodynamics properties of disordered systems such as spin glasses. Its definition is presented in a systematic and simple form and its use illustrated with some representative examples. In particular we give a detailed discussion of the diagonalization in the Replica Fourier Space of the Hessian matrix of the Gaussian fluctuations about the mean field saddle point of spin glass theory. The general results are finally discussed for a generic spherical spin glass model, where the Hessian can be computed analytically
Fourier transforms in radar and signal processing
Brandwood, David
2011-01-01
Fourier transforms are used widely, and are of particular value in the analysis of single functions and combinations of functions found in radar and signal processing. Still, many problems that could have been tackled by using Fourier transforms may have gone unsolved because they require integration that is difficult and tedious. This newly revised and expanded edition of a classic Artech House book provides you with an up-to-date, coordinated system for performing Fourier transforms on a wide variety of functions. Along numerous updates throughout the book, the Second Edition includes a crit
The Convergence Problems of Eigenfunction Expansions of Elliptic Differential Operators
Ahmedov, Anvarjon
2018-03-01
In the present research we investigate the problems concerning the almost everywhere convergence of multiple Fourier series summed over the elliptic levels in the classes of Liouville. The sufficient conditions for the almost everywhere convergence problems, which are most difficult problems in Harmonic analysis, are obtained. The methods of approximation by multiple Fourier series summed over elliptic curves are applied to obtain suitable estimations for the maximal operator of the spectral decompositions. Obtaining of such estimations involves very complicated calculations which depends on the functional structure of the classes of functions. The main idea on the proving the almost everywhere convergence of the eigenfunction expansions in the interpolation spaces is estimation of the maximal operator of the partial sums in the boundary classes and application of the interpolation Theorem of the family of linear operators. In the present work the maximal operator of the elliptic partial sums are estimated in the interpolation classes of Liouville and the almost everywhere convergence of the multiple Fourier series by elliptic summation methods are established. The considering multiple Fourier series as an eigenfunction expansions of the differential operators helps to translate the functional properties (for example smoothness) of the Liouville classes into Fourier coefficients of the functions which being expanded into such expansions. The sufficient conditions for convergence of the multiple Fourier series of functions from Liouville classes are obtained in terms of the smoothness and dimensions. Such results are highly effective in solving the boundary problems with periodic boundary conditions occurring in the spectral theory of differential operators. The investigations of multiple Fourier series in modern methods of harmonic analysis incorporates the wide use of methods from functional analysis, mathematical physics, modern operator theory and spectral
Directory of Open Access Journals (Sweden)
Yael Yaniv
Full Text Available The cardiomyocyte cytoskeleton, composed of rigid and elastic elements, maintains the isolated cell in an elongated cylindrical shape with an elliptical cross-section, even during contraction-relaxation cycles. Cardiomyocyte mitochondria are micron-sized, fluid-filled passive spheres distributed throughout the cell in a crystal-like lattice, arranged in pairs sandwiched between the sarcomere contractile machinery, both longitudinally and radially. Their shape represents the extant 3-dimensional (3D force-balance. We developed a novel method to examine mitochondrial 3D-deformation in response to contraction and relaxation to understand how dynamic forces are balanced inside cardiomyocytes. The variation in transmitted light intensity induced by the periodic lattice of myofilaments alternating with mitochondrial rows can be analyzed by Fourier transformation along a given cardiomyocyte axis to measure mitochondrial deformation along that axis. This technique enables precise detection of changes in dimension of ∼1% in ∼1 µm (long-axis structures with 8 ms time-resolution. During active contraction (1 Hz stimulation, mitochondria deform along the length- and width-axes of the cell with similar deformation kinetics in both sarcomere and mitochondrial structures. However, significant deformation anisotropy (without hysteresis was observed between the orthogonal short-axes (i.e., width and depth of mitochondria during electrical stimulation. The same degree of deformation anisotropy was also found between the myocyte orthogonal short-axes during electrical stimulation. Therefore, the deformation of the mitochondria reflects the overall deformation of the cell, and the apparent stiffness and stress/strain characteristics of the cytoskeleton differ appreciably between the two cardiomyocyte orthogonal short-axes. This method may be applied to obtaining a better understanding of the dynamic force-balance inside cardiomyocytes and of changes in the
Orthogonal Analysis Based Performance Optimization for Vertical Axis Wind Turbine
Directory of Open Access Journals (Sweden)
Lei Song
2016-01-01
Full Text Available Geometrical shape of a vertical axis wind turbine (VAWT is composed of multiple structural parameters. Since there are interactions among the structural parameters, traditional research approaches, which usually focus on one parameter at a time, cannot obtain performance of the wind turbine accurately. In order to exploit overall effect of a novel VAWT, we firstly use a single parameter optimization method to obtain optimal values of the structural parameters, respectively, by Computational Fluid Dynamics (CFD method; based on the results, we then use an orthogonal analysis method to investigate the influence of interactions of the structural parameters on performance of the wind turbine and to obtain optimization combination of the structural parameters considering the interactions. Results of analysis of variance indicate that interactions among the structural parameters have influence on performance of the wind turbine, and optimization results based on orthogonal analysis have higher wind energy utilization than that of traditional research approaches.
Tomographic Approach in Three-Orthogonal-Basis Quantum Key Distribution
International Nuclear Information System (INIS)
Liang Wen-Ye; Yin Zhen-Qiang; Chen Hua; Li Hong-Wei; Chen Wei; Han Zheng-Fu; Wen Hao
2015-01-01
At present, there is an increasing awareness of some three-orthogonal-basis quantum key distribution protocols, such as, the reference-frame-independent (RFI) protocol and the six-state protocol. For secure key rate estimations of these protocols, there are two methods: one is the conventional approach, and another is the tomographic approach. However, a comparison between these two methods has not been given yet. In this work, with the general model of rotation channel, we estimate the key rate using conventional and tomographic methods respectively. Results show that conventional estimation approach in RFI protocol is equivalent to tomographic approach only in the case of that one of three orthogonal bases is always aligned. In other cases, tomographic approach performs much better than the respective conventional approaches of the RFI protocol and the six-state protocol. Furthermore, based on the experimental data, we illustrate the deep connections between tomography and conventional RFI approach representations. (paper)
Quantum secret sharing using orthogonal multiqudit entangled states
Bai, Chen-Ming; Li, Zhi-Hui; Liu, Cheng-Ji; Li, Yong-Ming
2017-12-01
In this work, we investigate the distinguishability of orthogonal multiqudit entangled states under restricted local operations and classical communication. According to these properties, we propose a quantum secret sharing scheme to realize three types of access structures, i.e., the ( n, n)-threshold, the restricted (3, n)-threshold and restricted (4, n)-threshold schemes (called LOCC-QSS scheme). All cooperating players in the restricted threshold schemes are from two disjoint groups. In the proposed protocol, the participants use the computational basis measurement and classical communication to distinguish between those orthogonal states and reconstruct the original secret. Furthermore, we also analyze the security of our scheme in four primary quantum attacks and give a simple encoding method in order to better prevent the participant conspiracy attack.
Force Modelling in Orthogonal Cutting Considering Flank Wear Effect
Rathod, Kanti Bhikhubhai; Lalwani, Devdas I.
2017-05-01
In the present work, an attempt has been made to provide a predictive cutting force model during orthogonal cutting by combining two different force models, that is, a force model for a perfectly sharp tool plus considering the effect of edge radius and a force model for a worn tool. The first force model is for a perfectly sharp tool that is based on Oxley's predictive machining theory for orthogonal cutting as the Oxley's model is for perfectly sharp tool, the effect of cutting edge radius (hone radius) is added and improve model is presented. The second force model is based on worn tool (flank wear) that was proposed by Waldorf. Further, the developed combined force model is also used to predict flank wear width using inverse approach. The performance of the developed combined total force model is compared with the previously published results for AISI 1045 and AISI 4142 materials and found reasonably good agreement.
A General Approach for Orthogonal 4-Tap Integer Multiwavelet Transforms
Directory of Open Access Journals (Sweden)
Mingli Jing
2010-01-01
Full Text Available An algorithm for orthogonal 4-tap integer multiwavelet transforms is proposed. We compute the singular value decomposition (SVD of block recursive matrices of transform matrix, and then transform matrix can be rewritten in a product of two block diagonal matrices and a permutation matrix. Furthermore, we factorize the block matrix of block diagonal matrices into triangular elementary reversible matrices (TERMs, which map integers to integers by rounding arithmetic. The cost of factorizing block matrix into TERMs does not increase with the increase of the dimension of transform matrix, and the proposed algorithm is in-place calculation and without allocating auxiliary memory. Examples of integer multiwavelet transform using DGHM and CL are given, which verify that the proposed algorithm is an executable algorithm and outperforms the existing algorithm for orthogonal 4-tap integer multiwavelet transform.
Least squares orthogonal polynomial approximation in several independent variables
International Nuclear Information System (INIS)
Caprari, R.S.
1992-06-01
This paper begins with an exposition of a systematic technique for generating orthonormal polynomials in two independent variables by application of the Gram-Schmidt orthogonalization procedure of linear algebra. It is then demonstrated how a linear least squares approximation for experimental data or an arbitrary function can be generated from these polynomials. The least squares coefficients are computed without recourse to matrix arithmetic, which ensures both numerical stability and simplicity of implementation as a self contained numerical algorithm. The Gram-Schmidt procedure is then utilised to generate a complete set of orthogonal polynomials of fourth degree. A theory for the transformation of the polynomial representation from an arbitrary basis into the familiar sum of products form is presented, together with a specific implementation for fourth degree polynomials. Finally, the computational integrity of this algorithm is verified by reconstructing arbitrary fourth degree polynomials from their values at randomly chosen points in their domain. 13 refs., 1 tab
Analytical calculation of the average scattering cross sections using fourier series
International Nuclear Information System (INIS)
Palma, Daniel A.P.; Goncalves, Alessandro C.; Martinez, Aquilino S.; Silva, Fernando C. da
2009-01-01
The precise determination of the Doppler broadening functions is very important in different applications of reactors physics, mainly in the processing of nuclear data. Analytical approximations are obtained in this paper for average scattering cross section using expansions in Fourier series, generating an approximation that is simple and precise. The results have shown to be satisfactory from the point-of-view of accuracy and do not depend on the type of resonance considered. (author)
Analytical calculation of the average scattering cross sections using fourier series
Energy Technology Data Exchange (ETDEWEB)
Palma, Daniel A.P. [Instituto Federal do Rio de Janeiro, Nilopolis, RJ (Brazil)], e-mail: dpalmaster@gmail.com; Goncalves, Alessandro C.; Martinez, Aquilino S.; Silva, Fernando C. da [Coordenacao dos Programas de Pos-graduacao de Engenharia (COPPE/UFRJ), Rio de Janeiro, RJ (Brazil). Programa de Engenharia Nuclear], e-mail: asilva@con.ufrj.br, e-mail: agoncalves@con.ufrj.br, e-mail: aquilino@lmp.ufrj.br, e-mail: fernando@con.ufrj.br
2009-07-01
The precise determination of the Doppler broadening functions is very important in different applications of reactors physics, mainly in the processing of nuclear data. Analytical approximations are obtained in this paper for average scattering cross section using expansions in Fourier series, generating an approximation that is simple and precise. The results have shown to be satisfactory from the point-of-view of accuracy and do not depend on the type of resonance considered. (author)
Series de Fourier aplicadas a problemas de cálculo de variaciones con retardo
Lorena Salazar Solórzano
2012-01-01
In this article we present an approximation of the minimizing function of the functional J[x]=\\int_0^T F(t,X(t),X(t-\\tau),\\dot{X}(t))dt by approximating X(t) with Cosine Fourier series expansions X_n(t). We give conditions under which J[X_n(t)]\\longrightarrow J[X(t)] cuando n\\rightarrow \\infty
International Nuclear Information System (INIS)
Eaker, C.W.; Schatz, G.C.; De Leon, N.; Heller, E.J.
1984-01-01
Two methods for calculating the good action variables and semiclassical eigenvalues for coupled oscillator systems are presented, both of which relate the actions to the coefficients appearing in the Fourier representation of the normal coordinates and momenta. The two methods differ in that one is based on the exact expression for the actions together with the EBK semiclassical quantization condition while the other is derived from the Sorbie--Handy (SH) approximation to the actions. However, they are also very similar in that the actions in both methods are related to the same set of Fourier coefficients and both require determining the perturbed frequencies in calculating actions. These frequencies are also determined from the Fourier representations, which means that the actions in both methods are determined from information entirely contained in the Fourier expansion of the coordinates and momenta. We show how these expansions can very conveniently be obtained from fast Fourier transform (FFT) methods and that numerical filtering methods can be used to remove spurious Fourier components associated with the finite trajectory integration duration. In the case of the SH based method, we find that the use of filtering enables us to relax the usual periodicity requirement on the calculated trajectory. Application to two standard Henon--Heiles models is considered and both are shown to give semiclassical eigenvalues in good agreement with previous calculations for nondegenerate and 1:1 resonant systems. In comparing the two methods, we find that although the exact method is quite general in its ability to be used for systems exhibiting complex resonant behavior, it converges more slowly with increasing trajectory integration duration and is more sensitive to the algorithm for choosing perturbed frequencies than the SH based method
Discriminants and functional equations for polynomials orthogonal on the unit circle
International Nuclear Information System (INIS)
Ismail, M.E.H.; Witte, N.S.
2000-01-01
We derive raising and lowering operators for orthogonal polynomials on the unit circle and find second order differential and q-difference equations for these polynomials. A general functional equation is found which allows one to relate the zeros of the orthogonal polynomials to the stationary values of an explicit quasi-energy and implies recurrences on the orthogonal polynomial coefficients. We also evaluate the discriminants and quantized discriminants of polynomials orthogonal on the unit circle
Scheibler, Robin; Hurley, Paul
2012-03-01
We present a novel, accurate and fast algorithm to obtain Fourier series coefficients from an IC layer whose description consists of rectilinear polygons on a plane, and how to implement it using off-the-shelf hardware components. Based on properties of Fourier calculus, we derive a relationship between the Discrete Fourier Transforms of the sampled mask transmission function and its continuous Fourier series coefficients. The relationship leads to a straightforward algorithm for computing the continuous Fourier series coefficients where one samples the mask transmission function, compute its discrete Fourier transform and applies a frequency-dependent multiplicative factor. The algorithm is guaranteed to yield the exact continuous Fourier series coefficients for any sampling representing the mask function exactly. Computationally, this leads to significant saving by allowing to choose the maximal such pixel size and reducing the fast Fourier transform size by as much, without compromising accuracy. In addition, the continuous Fourier series is free from aliasing and follows closely the physical model of Fourier optics. We show that in some cases this can make a significant difference, especially in modern very low pitch technology nodes.
Radar Measurements of Ocean Surface Waves using Proper Orthogonal Decomposition
2017-03-30
Golinval, 2002, Physical interpretation of the proper orthogonal modes using the singular value decomposition, Journal of Sound and Vibration, 249...complex and contain contributions from the environment (e.g., wind, waves, currents) as well as artifacts associated with electromagnetic (EM) (wave...Although there is no physical basis/ interpretation inherent to the method because it is purely a mathematical tool, there has been an increasing
TEACHING BASIC ELEMENTS IN TECHNICAL DRAWING – ORTHOGONAL PROJECTIONS
Directory of Open Access Journals (Sweden)
CLINCIU Ramona
2017-05-01
Full Text Available The paper presents applications developed using AutoCAD and 3D Studio MAX programs. These applications are constructed such as to enable, gradually, the development of the spatial abilities of the students and, at the same time, to enable the understanding of the principles for the representation of the orthogonal projections of the parts, as well as for the construction of their axonometric projections.
Orthogonal frequency division multiple access fundamentals and applications
Jiang, Tao; Zhang, Yan
2010-01-01
Supported by the expert-level advice of pioneering researchers, Orthogonal Frequency Division Multiple Access Fundamentals and Applications provides a comprehensive and accessible introduction to the foundations and applications of one of the most promising access technologies for current and future wireless networks. It includes authoritative coverage of the history, fundamental principles, key techniques, and critical design issues of OFDM systems. Covering various techniques of effective resource management for OFDM/OFDMA-based wireless communication systems, this cutting-edge reference:Add
Cospectral graphs and regular orthogonal matrices of level 2
Abiad Monge, A.; Haemers, W.H.
2012-01-01
For a graph Γ with adjacency matrix A , we consider a switching operation that takes Γ into a graph Γ′ with adjacency matrix A′ , defined by A′ = Q⊤AQ , where Q is a regular orthogonal matrix of level 2 (that is, Q⊤Q=I , Q1 = 1, 2Q is integral, and Q is not a permutation matrix). If such an
Discrete Orthogonal Transforms and Neural Networks for Image Interpolation
Directory of Open Access Journals (Sweden)
J. Polec
1999-09-01
Full Text Available In this contribution we present transform and neural network approaches to the interpolation of images. From transform point of view, the principles from [1] are modified for 1st and 2nd order interpolation. We present several new interpolation discrete orthogonal transforms. From neural network point of view, we present interpolation possibilities of multilayer perceptrons. We use various configurations of neural networks for 1st and 2nd order interpolation. The results are compared by means of tables.
A general boundary capability embedded in an orthogonal mesh
International Nuclear Information System (INIS)
Hewett, D.W.; Yu-Jiuan Chen
1995-01-01
The authors describe how they hold onto orthogonal mesh discretization when dealing with curved boundaries. Special difference operators were constructed to approximate numerical zones split by the domain boundary; the operators are particularly simple for this rectangular mesh. The authors demonstrated that this simple numerical approach, termed Dynamic Alternating Direction Implicit, turned out to be considerably more efficient than more complex grid-adaptive algorithms that were tried previously
International Nuclear Information System (INIS)
Ahmedov, Anvarjon A; Nurullah bin Rasedee, Ahmad Fadly; Rakhimov, Abdumalik
2013-01-01
In this work we investigate the localization principle of the Fourier-Laplace series of the distribution. Here we prove the sufficient conditions of the localization of the Riesz means of the spectral expansions of the Laplace-Beltrami operator on the unit sphere.
Nurbekyan, Levon
2017-03-11
Here, we study a one-dimensional, non-local mean-field game model with congestion. When the kernel in the non-local coupling is a trigonometric polynomial we reduce the problem to a finite dimensional system. Furthermore, we treat the general case by approximating the kernel with trigonometric polynomials. Our technique is based on Fourier expansion methods.
Nurbekyan, Levon
2017-01-01
Here, we study a one-dimensional, non-local mean-field game model with congestion. When the kernel in the non-local coupling is a trigonometric polynomial we reduce the problem to a finite dimensional system. Furthermore, we treat the general case by approximating the kernel with trigonometric polynomials. Our technique is based on Fourier expansion methods.
Partial Fourier techniques in single-shot cross-term spatiotemporal encoded MRI.
Zhang, Zhiyong; Frydman, Lucio
2018-03-01
Cross-term spatiotemporal encoding (xSPEN) is a single-shot approach with exceptional immunity to field heterogeneities, the images of which faithfully deliver 2D spatial distributions without requiring a priori information or using postacquisition corrections. xSPEN, however, suffers from signal-to-noise ratio penalties due to its non-Fourier nature and due to diffusion losses-especially when seeking high resolution. This study explores partial Fourier transform approaches that, acting along either the readout or the spatiotemporally encoded dimensions, reduce these penalties. xSPEN uses an orthogonal (e.g., z) gradient to read, in direct space, the low-bandwidth (e.g., y) dimension. This substantially changes the nature of partial Fourier acquisitions vis-à-vis conventional imaging counterparts. A suitable theoretical analysis is derived to implement these procedures, along either the spatiotemporally or readout axes. Partial Fourier single-shot xSPEN images were recorded on preclinical and human scanners. Owing to their reduction in the experiments' acquisition times, this approach provided substantial sensitivity gains vis-à-vis previous implementations for a given targeted in-plane resolution. The physical origins of these gains are explained. Partial Fourier approaches, particularly when implemented along the low-bandwidth spatiotemporal dimension, provide several-fold sensitivity advantages at minimal costs to the execution and processing of the single-shot experiments. Magn Reson Med 79:1506-1514, 2018. © 2017 International Society for Magnetic Resonance in Medicine. © 2017 International Society for Magnetic Resonance in Medicine.
Minimal parameter solution of the orthogonal matrix differential equation
Bar-Itzhack, Itzhack Y.; Markley, F. Landis
1990-01-01
As demonstrated in this work, all orthogonal matrices solve a first order differential equation. The straightforward solution of this equation requires n sup 2 integrations to obtain the element of the nth order matrix. There are, however, only n(n-1)/2 independent parameters which determine an orthogonal matrix. The questions of choosing them, finding their differential equation and expressing the orthogonal matrix in terms of these parameters are considered. Several possibilities which are based on attitude determination in three dimensions are examined. It is shown that not all 3-D methods have useful extensions to higher dimensions. It is also shown why the rate of change of the matrix elements, which are the elements of the angular rate vector in 3-D, are the elements of a tensor of the second rank (dyadic) in spaces other than three dimensional. It is proven that the 3-D Gibbs vector (or Cayley Parameters) are extendable to other dimensions. An algorithm is developed emplying the resulting parameters, which are termed Extended Rodrigues Parameters, and numerical results are presented of the application of the algorithm to a fourth order matrix.
Efficiency Improvements of Antenna Optimization Using Orthogonal Fractional Experiments
Directory of Open Access Journals (Sweden)
Yen-Sheng Chen
2015-01-01
Full Text Available This paper presents an extremely efficient method for antenna design and optimization. Traditionally, antenna optimization relies on nature-inspired heuristic algorithms, which are time-consuming due to their blind-search nature. In contrast, design of experiments (DOE uses a completely different framework from heuristic algorithms, reducing the design cycle by formulating the surrogates of a design problem. However, the number of required simulations grows exponentially if a full factorial design is used. In this paper, a much more efficient technique is presented to achieve substantial time savings. By using orthogonal fractional experiments, only a small subset of the full factorial design is required, yet the resultant response surface models are still effective. The capability of orthogonal fractional experiments is demonstrated through three examples, including two tag antennas for radio-frequency identification (RFID applications and one internal antenna for long-term-evolution (LTE handheld devices. In these examples, orthogonal fractional experiments greatly improve the efficiency of DOE, thereby facilitating the antenna design with less simulation runs.
Limited-memory adaptive snapshot selection for proper orthogonal decomposition
Energy Technology Data Exchange (ETDEWEB)
Oxberry, Geoffrey M. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States); Kostova-Vassilevska, Tanya [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States); Arrighi, Bill [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States); Chand, Kyle [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
2015-04-02
Reduced order models are useful for accelerating simulations in many-query contexts, such as optimization, uncertainty quantification, and sensitivity analysis. However, offline training of reduced order models can have prohibitively expensive memory and floating-point operation costs in high-performance computing applications, where memory per core is limited. To overcome this limitation for proper orthogonal decomposition, we propose a novel adaptive selection method for snapshots in time that limits offline training costs by selecting snapshots according an error control mechanism similar to that found in adaptive time-stepping ordinary differential equation solvers. The error estimator used in this work is related to theory bounding the approximation error in time of proper orthogonal decomposition-based reduced order models, and memory usage is minimized by computing the singular value decomposition using a single-pass incremental algorithm. Results for a viscous Burgers’ test problem demonstrate convergence in the limit as the algorithm error tolerances go to zero; in this limit, the full order model is recovered to within discretization error. The resulting method can be used on supercomputers to generate proper orthogonal decomposition-based reduced order models, or as a subroutine within hyperreduction algorithms that require taking snapshots in time, or within greedy algorithms for sampling parameter space.
MRI isotropic resolution reconstruction from two orthogonal scans
Tamez-Pena, Jose G.; Totterman, Saara; Parker, Kevin J.
2001-07-01
An algorithm for the reconstructions of ISO-resolution volumetric MR data sets from two standard orthogonal MR scans having anisotropic resolution has been developed. The reconstruction algorithm starts by registering a pair of orthogonal volumetric MR data sets. The registration is done by maximizing the correlation between the gradient magnitude using a simple translation-rotation model in a multi-resolution approach. Then algorithm assumes that the individual voxels on the MR data are an average of the magnetic resonance properties of an elongated imaging volume. Then, the process is modeled as the projection of MR properties into a single sensor. This model allows the derivation of a set of linear equations that can be used to recover the MR properties of every single voxel in the SO-resolution volume given only two orthogonal MR scans. Projections on convex sets (POCS) was used to solve the set of linear equations. Experimental results show the advantage of having a ISO-resolution reconstructions for the visualization and analysis of small and thin muscular structures.
Parallel and orthogonal stimulus in ultradiluted neural networks
International Nuclear Information System (INIS)
Sobral, G. A. Jr.; Vieira, V. M.; Lyra, M. L.; Silva, C. R. da
2006-01-01
Extending a model due to Derrida, Gardner, and Zippelius, we have studied the recognition ability of an extreme and asymmetrically diluted version of the Hopfield model for associative memory by including the effect of a stimulus in the dynamics of the system. We obtain exact results for the dynamic evolution of the average network superposition. The stimulus field was considered as proportional to the overlapping of the state of the system with a particular stimulated pattern. Two situations were analyzed, namely, the external stimulus acting on the initialization pattern (parallel stimulus) and the external stimulus acting on a pattern orthogonal to the initialization one (orthogonal stimulus). In both cases, we obtained the complete phase diagram in the parameter space composed of the stimulus field, thermal noise, and network capacity. Our results show that the system improves its recognition ability for parallel stimulus. For orthogonal stimulus two recognition phases emerge with the system locking at the initialization or stimulated pattern. We confront our analytical results with numerical simulations for the noiseless case T=0
International Nuclear Information System (INIS)
Lind, P.
1993-02-01
The completeness properties of the discrete set of bound state, virtual states and resonances characterizing the system of a single nonrelativistic particle moving in a central cutoff potential is investigated. From a completeness relation in terms of these discrete states and complex scattering states one can derive several Resonant State Expansions (RSE). It is interesting to obtain purely discrete expansion which, if valid, would significantly simplify the treatment of the continuum. Such expansions can be derived using Mittag-Leffler (ML) theory for a cutoff potential and it would be nice to see if one can obtain the same expansions starting from an eigenfunction theory that is not restricted to a finite sphere. The RSE of Greens functions is especially important, e.g. in the continuum RPA (CRPA) method of treating giant resonances in nuclear physics. The convergence of RSE is studied in simple cases using square well wavefunctions in order to achieve high numerical accuracy. Several expansions can be derived from each other by using the theory of analytic functions and one can the see how to obtain a natural discretization of the continuum. Since the resonance wavefunctions are oscillating with an exponentially increasing amplitude, and therefore have to be interpreted through some regularization procedure, every statement made about quantities involving such states is checked by numerical calculations.Realistic nuclear wavefunctions, generated by a Wood-Saxon potential, are used to test also the usefulness of RSE in a realistic nuclear calculation. There are some fundamental differences between different symmetries of the integral contour that defines the continuum in RSE. One kind of symmetry is necessary to have an expansion of the unity operator that is idempotent. Another symmetry must be used if we want purely discrete expansions. These are found to be of the same form as given by ML. (29 refs.)
Content adaptive illumination for Fourier ptychography.
Bian, Liheng; Suo, Jinli; Situ, Guohai; Zheng, Guoan; Chen, Feng; Dai, Qionghai
2014-12-01
Fourier ptychography (FP) is a recently reported technique, for large field-of-view and high-resolution imaging. Specifically, FP captures a set of low-resolution images, under angularly varying illuminations, and stitches them together in the Fourier domain. One of FP's main disadvantages is its long capturing process, due to the requisite large number of incident illumination angles. In this Letter, utilizing the sparsity of natural images in the Fourier domain, we propose a highly efficient method, termed adaptive Fourier ptychography (AFP), which applies content adaptive illumination for FP, to capture the most informative parts of the scene's spatial spectrum. We validate the effectiveness and efficiency of the reported framework, with both simulated and real experiments. Results show that the proposed AFP could shorten the acquisition time of conventional FP, by around 30%-60%.
X-ray interferometric Fourier holography
International Nuclear Information System (INIS)
Balyan, M.K.
2016-01-01
The X-ray interferometric Fourier holography is proposed and theoretically investigated. Fourier The X-ray interferometric Young fringes and object image reconstruction are investigated. It is shown that the interference pattern of two slits formed on the exit surface of the crystal-analyzer (the third plate of the interferometer) is the X-ray interferometric Young fringes. An expression for X-ray interferometric Young fringes period is obtained. The subsequent reconstruction of the slit image as an object is performed by means of Fourier transform of the intensity distribution on the hologram. Three methods of reconstruction of the amplitude transmission complex function of the object are presented: analytical - approximate method, method of iteration and step by step method. As an example the X-ray Fourier interferometric hologram recording and the complex amplitude transmission function reconstruction for a beryllium circular wire are considered
New focus on Fourier optics techniques
Calvo, M.L.; Alieva, T.; Bastiaans, M.J.; Rodrigo Martín-Romo, J.A.; Rodríguez Merlo, D.; Vlad, V.I.
2004-01-01
We present a short overview on the application of fractional cyclic and linear canonical transformations to optical signal processing and dedicate some of the discussions to the particular features found in the fractional Fourier transform domain.
On the Scaled Fractional Fourier Transformation Operator
International Nuclear Information System (INIS)
Hong-Yi, Fan; Li-Yun, Hu
2008-01-01
Based on our previous study [Chin. Phys. Lett. 24 (2007) 2238] in which the Fresnel operator corresponding to classical Fresnel transform was introduced, we derive the fractional Fourier transformation operator, and the optical operator method is then enriched
Mountain Wave Analysis Using Fourier Methods
National Research Council Canada - National Science Library
Roadcap, John R
2007-01-01
...) their requirements for only a coarse horizontal background state. Common traits of Fourier mountain wave models include use of the Boussinesq approximation and neglect of moisture and Coriolis terms...
A new twist to fourier transforms
Meikle, Hamish D
2004-01-01
Making use of the inherent helix in the Fourier transform expression, this book illustrates both Fourier transforms and their properties in the round. The author draws on elementary complex algebra to manipulate the transforms, presenting the ideas in such a way as to avoid pages of complicated mathematics. Similarly, abbreviations are not used throughout and the language is kept deliberately clear so that the result is a text that is accessible to a much wider readership.The treatment is extended with the use of sampled data to finite and discrete transforms, the fast Fourier transform, or FFT, being a special case of a discrete transform. The application of Fourier transforms in statistics is illustrated for the first time using the examples operational research and later radar detection. In addition, a whole chapter on tapering or weighting functions is added for reference. The whole is rounded off by a glossary and examples of diagrams in three dimensions made possible by today's mathematics programs
International Nuclear Information System (INIS)
Bulut, S.; Guelecyuez, M.C.; Kaskas, A.; Tezcan, C.
2007-01-01
H N and singular eigenfunction methods are used to determine the neutron distribution everywhere in a source-free half space with zero incident flux for a linearly anisotropic scattering kernel. The singular eigenfunction expansion of the method of elementary solutions is used. The orthogonality relations of the discrete and continuous eigenfunctions for linearly anisotropic scattering provides the determination of the expansion coefficients. Different expansions of the exit distribution are used: the expansion in powers of μ, the expansion in terms of Legendre polynomials and the expansion in powers of 1/(1+μ). The results are compared to each other. In the second part of our work, the transport equation and the infinite medium Green function are used. The numerical results of the extrapolation length obtained for the different expansions is discussed. (orig.)
Mapped Fourier Methods for stiff problems in toroidal geometry
Guillard , Herve
2014-01-01
Fourier spectral or pseudo-spectral methods are usually extremely efficient for periodic problems. However this efficiency is lost if the solutions have zones of rapid variations or internal layers. For these cases, a large number of Fourier modes are required and this makes the Fourier method unpractical in many cases. This work investigates the use of mapped Fourier method as a way to circumvent this problem. Mapped Fourier method uses instead of the usual Fourier interpolant the compositio...
International Nuclear Information System (INIS)
Dzenus, M.; Hundhausen, W.; Jansing, W.
1980-01-01
This discourse recounts efforts put into the SNR-2 project; specifically the development of compensation devices. The various prototypes of these compensation devices are described and the state of the development reviewed. Large Na (sodium)-heat transfer systems require a lot of valuable space if the component lay-out does not include compensation devices. So, in order to condense the spatial requirement as much as possible, expansion joints must be integrated into the pipe system. There are two basic types to suit the purpose: axial expansion joints and angular expansion joints. The expansion joints were developed on the basis of specific design criteria whereby differentiation is made between expansion joints of small and large nominal diameter. Expansion joints for installation in the sodium-filled primary piping are equipped with safety bellows in addition to the actual working bellows. Expansion joints must be designed and mounted in a manner to completely withstand seismic forces. The design must exclude any damage to the bellows during intermittent operations, that is, when sodium is drained the bellows' folds must be completely empty; otherwise residual solidified sodium could destroy the bellows when restarting. The expansion joints must be engineered on the basis of the following design data for the secondary system of the SNR project: working pressure: 16 bar; failure mode pressure: 5 events; failure mode: 5 sec., 28.5 bar, 520 deg. C; working temperature: 520 deg. C; temperature transients: 30 deg. C/sec.; service life: 200,000 h; number of load cycles: 10 4 ; material: 1.4948 or 1.4919; layer thickness of folds: 0.5 mm; angular deflection (DN 800): +3 deg. C or; axial expansion absorption (DN 600): ±80 mm; calculation: ASME class. The bellows' development work is not handled within this scope. The bellows are supplied by leading manufacturers, and warrant highest quality. Multiple bellows were selected on the basis of maximum elasticity - a property
Accelerating the loop expansion
International Nuclear Information System (INIS)
Ingermanson, R.
1986-01-01
This thesis introduces a new non-perturbative technique into quantum field theory. To illustrate the method, I analyze the much-studied phi 4 theory in two dimensions. As a prelude, I first show that the Hartree approximation is easy to obtain from the calculation of the one-loop effective potential by a simple modification of the propagator that does not affect the perturbative renormalization procedure. A further modification then susggests itself, which has the same nice property, and which automatically yields a convex effective potential. I then show that both of these modifications extend naturally to higher orders in the derivative expansion of the effective action and to higher orders in the loop-expansion. The net effect is to re-sum the perturbation series for the effective action as a systematic ''accelerated'' non-perturbative expansion. Each term in the accelerated expansion corresponds to an infinite number of terms in the original series. Each term can be computed explicitly, albeit numerically. Many numerical graphs of the various approximations to the first two terms in the derivative expansion are given. I discuss the reliability of the results and the problem of spontaneous symmetry-breaking, as well as some potential applications to more interesting field theories. 40 refs
Tate, Stephen James
2013-10-01
In the 1960s, the technique of using cluster expansion bounds in order to achieve bounds on the virial expansion was developed by Lebowitz and Penrose (J. Math. Phys. 5:841, 1964) and Ruelle (Statistical Mechanics: Rigorous Results. Benjamin, Elmsford, 1969). This technique is generalised to more recent cluster expansion bounds by Poghosyan and Ueltschi (J. Math. Phys. 50:053509, 2009), which are related to the work of Procacci (J. Stat. Phys. 129:171, 2007) and the tree-graph identity, detailed by Brydges (Phénomènes Critiques, Systèmes Aléatoires, Théories de Jauge. Les Houches 1984, pp. 129-183, 1986). The bounds achieved by Lebowitz and Penrose can also be sharpened by doing the actual optimisation and achieving expressions in terms of the Lambert W-function. The different bound from the cluster expansion shows some improvements for bounds on the convergence of the virial expansion in the case of positive potentials, which are allowed to have a hard core.
Conformal expansions and renormalons
Energy Technology Data Exchange (ETDEWEB)
Rathsman, J.
2000-02-07
The coefficients in perturbative expansions in gauge theories are factorially increasing, predominantly due to renormalons. This type of factorial increase is not expected in conformal theories. In QCD conformal relations between observables can be defined in the presence of a perturbative infrared fixed-point. Using the Banks-Zaks expansion the authors study the effect of the large-order behavior of the perturbative series on the conformal coefficients. The authors find that in general these coefficients become factorially increasing. However, when the factorial behavior genuinely originates in a renormalon integral, as implied by a postulated skeleton expansion, it does not affect the conformal coefficients. As a consequence, the conformal coefficients will indeed be free of renormalon divergence, in accordance with previous observations concerning the smallness of these coefficients for specific observables. The authors further show that the correspondence of the BLM method with the skeleton expansion implies a unique scale-setting procedure. The BLM coefficients can be interpreted as the conformal coefficients in the series relating the fixed-point value of the observable with that of the skeleton effective charge. Through the skeleton expansion the relevance of renormalon-free conformal coefficients extends to real-world QCD.
International Nuclear Information System (INIS)
Taylor, D.
1984-01-01
This paper gives regression data for a modified second order polynomial fitted to the expansion data of, and percentage expansions for dioxides with (a) the fluorite and antifluorite structure: AmO 2 , BkO 2 , CeO 2 , CmO 2 , HfO 2 , Li 2 O, NpO 2 , PrO 2 , PuO 2 , ThO 2 , UO 2 , ZrO 2 , and (b) the rutile structure: CrO 2 , GeO 2 , IrO 2 , MnO 2 , NbO 2 , PbO 2 , SiO 2 , SnO 2 , TeO 2 , TiO 2 and VO 2 . Reduced expansion curves for the dioxides showed only partial grouping into iso-electronic series for the fluorite structures and showed that the 'law of corresponding states' did not apply to the rutile structures. (author)
Giovannini, Massimo
2015-01-01
Cosmological singularities are often discussed by means of a gradient expansion that can also describe, during a quasi-de Sitter phase, the progressive suppression of curvature inhomogeneities. While the inflationary event horizon is being formed the two mentioned regimes coexist and a uniform expansion can be conceived and applied to the evolution of spatial gradients across the protoinflationary boundary. It is argued that conventional arguments addressing the preinflationary initial conditions are necessary but generally not sufficient to guarantee a homogeneous onset of the conventional inflationary stage.
Low-temperature thermal expansion
International Nuclear Information System (INIS)
Collings, E.W.
1986-01-01
This chapter discusses the thermal expansion of insulators and metals. Harmonicity and anharmonicity in thermal expansion are examined. The electronic, magnetic, an other contributions to low temperature thermal expansion are analyzed. The thermodynamics of the Debye isotropic continuum, the lattice-dynamical approach, and the thermal expansion of metals are discussed. Relative linear expansion at low temperatures is reviewed and further calculations of the electronic thermal expansion coefficient are given. Thermal expansions are given for Cu, Al and Ti. Phenomenologic thermodynamic relationships are also discussed
A planar waveguide optical discrete Fourier transformer design for 160 Gb/s all-optical OFDM systems
Li, Wei; Liang, Xiaojun; Ma, Weidong; Zhou, Tianhong; Huang, Benxiong; Liu, Deming
2010-01-01
A cost-effective all-optical discrete Fourier transformer (ODFT) is designed based on a silicon planar lightwave circuit (PLC), which can be applied to all-optical orthogonal frequency division multiplexing (OFDM) transmission systems and can be achieved by current techniques. It consists of 2 × 2 directional couplers, phase shifters and optical delay lines. Metal-film heaters are used as phase shifters, according to the thermooptic effect of SiO 2. Based on the ODFT, a 160 Gb/s OFDM system is set up. Simulation results show excellent bit error rate (BER) and optical signal-to-noise ratio (OSNR) performances after 400 km transmission.
OPEC future capacity expansions
International Nuclear Information System (INIS)
Sandrea, I.
2005-01-01
This conference presentation examined OPEC future capacity expansions including highlights from 2000-2004 from the supply perspective and actions by OPEC; OPEC spare capacity in 2005/2006; medium-term capacity expansion and investments; long-term scenarios, challenges and opportunities; and upstream policies in member countries. Highlights from the supply perspective included worst than expected non-OPEC supply response; non-OPEC supply affected by a number of accidents and strikes; geopolitical tensions; and higher than expected demand for OPEC crude. OPEC's actions included closer relationship with other producers and consumers; capacity expansions in 2004 and 2005/2006; and OPEC kept the market well supplied with crude in 2004. The presentation also provided data using graphical charts on OPEC net capacity additions until 2005/2006; OPEC production versus spare capacity from 2003 to 2005; OPEC production and capacity to 2010; and change in required OPEC production from 2005-2020. Medium term expansion to 2010 includes over 60 projects. Medium-term risks such as project execution, financing, costs, demand, reserves, depletion, integration of Iraq, and geopolitical tensions were also discussed. The presentation concluded that in the long term, large uncertainties remain; the peak of world supply is not imminent; and continued and enhanced cooperation is essential to market stability. tabs., figs
Physics suggests that the interplay of momentum, continuity, and geometry in outward radial flow must produce density and concomitant pressure reductions. In other words, this flow is intrinsically auto-expansive. It has been proposed that this process is the key to understanding...
Integrated, Dual Orthogonal Antennas for Polarimetric Ground Penetrating Radar
Pauli, Mario; Wiesbeck, Werner
2015-04-01
Ground penetrating radar systems are mostly equipped with single polarized antennas, for example with single linear polarization or with circular polarization. The radiated waves are partly reflected at the ground surface and very often the penetrating waves are distorted in their polarization. The distortion depends on the ground homogeneity and the orientation of the antennas relative to the ground structure. The received signals from the reflecting objects may most times only be classified according to their coverage and intensity. This makes the recognition of the objects difficult or impossible. In airborne and spaceborne Remote Sensing the systems are meanwhile mostly equipped with front ends with dual orthogonal polarized antennas for a full polarimetric operation. The received signals, registered in 2x2 scattering matrices according to co- and cross polarization, are processed for the evaluation of all features of the targets. Ground penetrating radars could also profit from the scientific results of Remote Sensing. The classification of detected objects for their structure and orientation requires more information in the reflected signal than can be measured with a single polarization [1, 2]. In this paper dual linear, orthogonal polarized antennas with a common single, frequency independent phase center, are presented [3]. The relative bandwidth of these antennas can be 1:3, up to 1:4. The antenna is designed to work in the frequency range between 3 GHz and 11 GHz, but can be easily adapted to the GPR frequency range by scaling. The size of the antenna scaled for operation in typical GPR frequencies would approximately be 20 by 20 cm2. By the implementation in a dielectric carrier it could be reduced in size if required. The major problem for ultra wide band, dual polarized antennas is the frequency independent feed network, realizing the required phase shifts. For these antennas a network, which is frequency independent over a wide range, has been
Fourier phasing with phase-uncertain mask
International Nuclear Information System (INIS)
Fannjiang, Albert; Liao, Wenjing
2013-01-01
Fourier phasing is the problem of retrieving Fourier phase information from Fourier intensity data. The standard Fourier phase retrieval (without a mask) is known to have many solutions which cause the standard phasing algorithms to stagnate and produce wrong or inaccurate solutions. In this paper Fourier phase retrieval is carried out with the introduction of a randomly fabricated mask in measurement and reconstruction. Highly probable uniqueness of solution, up to a global phase, was previously proved with exact knowledge of the mask. Here the uniqueness result is extended to the case where only rough information about the mask’s phases is assumed. The exponential probability bound for uniqueness is given in terms of the uncertainty-to-diversity ratio of the unknown mask. New phasing algorithms alternating between the object update and the mask update are systematically tested and demonstrated to have the capability of recovering both the object and the mask (within the object support) simultaneously, consistent with the uniqueness result. Phasing with a phase-uncertain mask is shown to be robust with respect to the correlation in the mask as well as the Gaussian and Poisson noises. (paper)
Adaptive PID control based on orthogonal endocrine neural networks.
Milovanović, Miroslav B; Antić, Dragan S; Milojković, Marko T; Nikolić, Saša S; Perić, Staniša Lj; Spasić, Miodrag D
2016-12-01
A new intelligent hybrid structure used for online tuning of a PID controller is proposed in this paper. The structure is based on two adaptive neural networks, both with built-in Chebyshev orthogonal polynomials. First substructure network is a regular orthogonal neural network with implemented artificial endocrine factor (OENN), in the form of environmental stimuli, to its weights. It is used for approximation of control signals and for processing system deviation/disturbance signals which are introduced in the form of environmental stimuli. The output values of OENN are used to calculate artificial environmental stimuli (AES), which represent required adaptation measure of a second network-orthogonal endocrine adaptive neuro-fuzzy inference system (OEANFIS). OEANFIS is used to process control, output and error signals of a system and to generate adjustable values of proportional, derivative, and integral parameters, used for online tuning of a PID controller. The developed structure is experimentally tested on a laboratory model of the 3D crane system in terms of analysing tracking performances and deviation signals (error signals) of a payload. OENN-OEANFIS performances are compared with traditional PID and 6 intelligent PID type controllers. Tracking performance comparisons (in transient and steady-state period) showed that the proposed adaptive controller possesses performances within the range of other tested controllers. The main contribution of OENN-OEANFIS structure is significant minimization of deviation signals (17%-79%) compared to other controllers. It is recommended to exploit it when dealing with a highly nonlinear system which operates in the presence of undesirable disturbances. Copyright © 2016 Elsevier Ltd. All rights reserved.
The endoscopic classification of representations orthogonal and symplectic groups
Arthur, James
2013-01-01
Within the Langlands program, endoscopy is a fundamental process for relating automorphic representations of one group with those of another. In this book, Arthur establishes an endoscopic classification of automorphic representations of orthogonal and symplectic groups G. The representations are shown to occur in families (known as global L-packets and A-packets), which are parametrized by certain self-dual automorphic representations of an associated general linear group GL(N). The central result is a simple and explicit formula for the multiplicity in the automorphic discrete spectrum of G
Cavity enhanced interference of orthogonal modes in a birefringent medium
Kolluru, Kiran; Saha, Sudipta; Gupta, S. Dutta
2018-03-01
Interference of orthogonal modes in a birefringent crystal mediated by a rotator is known to lead to interesting physical effects (Solli et al., 2003). In this paper we show that additional feedback offered by a Fabry-Perot cavity (containing the birefringent crystal and the rotator) can lead to a novel strong interaction regime. Usual signatures of the strong interaction regime like the normal mode splitting and avoided crossings, sensitive to the rotator orientation, are reported. A high finesse cavity is shown to offer an optical setup for measuring small angles. The results are based on direct calculations of the cavity transmissions along with an analysis of its dispersion relation.
ORIENTATION FIELD RECONSTRUCTION OF ALTERED FINGERPRINT USING ORTHOGONAL WAVELETS
Directory of Open Access Journals (Sweden)
Mini M.G.
2016-11-01
Full Text Available Ridge orientation field is an important feature for fingerprint matching and fingerprint reconstruction. Matching of the altered fingerprint against its unaltered mates can be done by extracting the available features in the altered fingerprint and using it along with approximated ridge orientation. This paper presents a method for approximating ridge orientation field of altered fingerprints. In the proposed method, sine and cosine of doubled orientation of the fingerprint is decomposed using orthogonal wavelets and reconstructed back using only the approximation coefficients. No prior information about the singular points is needed for orientation approximation. The method is found suitable for orientation estimation of low quality fingerprint images also.
Introduction to orthogonal, symplectic and unitary representations of finite groups
Riehm, Carl R
2011-01-01
Orthogonal, symplectic and unitary representations of finite groups lie at the crossroads of two more traditional subjects of mathematics-linear representations of finite groups, and the theory of quadratic, skew symmetric and Hermitian forms-and thus inherit some of the characteristics of both. This book is written as an introduction to the subject and not as an encyclopaedic reference text. The principal goal is an exposition of the known results on the equivalence theory, and related matters such as the Witt and Witt-Grothendieck groups, over the "classical" fields-algebraically closed, rea
Orthogonal polarization in lasers physical phenomena and engineering applications
Zhang, Shulian
2013-01-01
This practical book summarizes the latest research results of orthogonally polarized lasers, birefringence laser cavities, and their applications. Coverage ranges from basic principles and technologies to the characteristics of different cavities and lasers to various measurement techniques. A number of figures, experimental designs, and measurement curves are included, helping readers gain a thorough understanding of the many applications in modern engineering and start their own projects. Many types of relevant lasers (Helium/Neon lasers, Nd:YAG lasers, laser diodes, etc.) are also discussed
Neural Based Orthogonal Data Fitting The EXIN Neural Networks
Cirrincione, Giansalvo
2008-01-01
Written by three leaders in the field of neural based algorithms, Neural Based Orthogonal Data Fitting proposes several neural networks, all endowed with a complete theory which not only explains their behavior, but also compares them with the existing neural and traditional algorithms. The algorithms are studied from different points of view, including: as a differential geometry problem, as a dynamic problem, as a stochastic problem, and as a numerical problem. All algorithms have also been analyzed on real time problems (large dimensional data matrices) and have shown accurate solutions. Wh
Directed Formation of DNA Nanoarrays through Orthogonal Self-Assembly
Directory of Open Access Journals (Sweden)
Eugen Stulz
2011-06-01
Full Text Available We describe the synthesis of terpyridine modified DNA strands which selectively form DNA nanotubes through orthogonal hydrogen bonding and metal complexation interactions. The short DNA strands are designed to self-assemble into long duplexes through a sticky-end approach. Addition of weakly binding metals such as Zn(II and Ni(II induces the formation of tubular arrays consisting of DNA bundles which are 50-200 nm wide and 2-50 nm high. TEM shows additional long distance ordering of the terpy-DNA complexes into fibers.
Orthogonal functions, discrete variable representation, and generalized gauss quadratures
DEFF Research Database (Denmark)
Schneider, B. I.; Nygaard, Nicolai
2002-01-01
in the original representation. This has been exploited in bound-state, scattering, and time-dependent problems using the so-called, discrete variable representation (DVR). At the core of this approach is the mathematical three-term recursion relationship satisfied by the classical orthogonal functions...... functions, this is not the case. However, they may be computed in a stable numerical fashion, via the recursion. In essence, this is an application of the well-known Lanczos recursion approach. Once the recursion coefficients are known, it is possible to compute the points and weights of quadratures on...
Magnitude conversion to unified moment magnitude using orthogonal regression relation
Das, Ranjit; Wason, H. R.; Sharma, M. L.
2012-05-01
Homogenization of earthquake catalog being a pre-requisite for seismic hazard assessment requires region based magnitude conversion relationships. Linear Standard Regression (SR) relations fail when both the magnitudes have measurement errors. To accomplish homogenization, techniques like Orthogonal Standard Regression (OSR) are thus used. In this paper a technique is proposed for using such OSR for preparation of homogenized earthquake catalog in moment magnitude Mw. For derivation of orthogonal regression relation between mb and Mw, a data set consisting of 171 events with observed body wave magnitudes (mb,obs) and moment magnitude (Mw,obs) values has been taken from ISC and GCMT databases for Northeast India and adjoining region for the period 1978-2006. Firstly, an OSR relation given below has been developed using mb,obs and Mw,obs values corresponding to 150 events from this data set. M=1.3(±0.004)m-1.4(±0.130), where mb,proxy are body wave magnitude values of the points on the OSR line given by the orthogonality criterion, for observed (mb,obs, Mw,obs) points. A linear relation is then developed between these 150 mb,obs values and corresponding mb,proxy values given by the OSR line using orthogonality criterion. The relation obtained is m=0.878(±0.03)m+0.653(±0.15). The accuracy of the above procedure has been checked with the rest of the data i.e., 21 events values. The improvement in the correlation coefficient value between mb,obs and Mw estimated using the proposed procedure compared to the correlation coefficient value between mb,obs and Mw,obs shows the advantage of OSR relationship for homogenization. The OSR procedure developed in this study can be used to homogenize any catalog containing various magnitudes (e.g., ML, mb, MS) with measurement errors, by their conversion to unified moment magnitude Mw. The proposed procedure also remains valid in case the magnitudes have measurement errors of different orders, i.e. the error variance ratio is
Orthogonal Bases used for Feed Forward Control of Wind Turbines
DEFF Research Database (Denmark)
Odgaard, Peter Fogh; Stoustrup, Jakob
2011-01-01
In optimizing wind turbines it can be of a large help to use information of wind speeds at upwind turbine for the control of downwind turbines, it is, however, problematic to use these measurements directly since they are highly inﬂuenced by turbulence behind the wind turbine rotor plane. In this....... In this paper an orthogonal basis is use to extract the general trends in the wind signal, which are forward to the down wind turbines. This concept controller is designed and simulated on a generic 4.8 MW wind turbine model, which shows the potential of this proposed scheme....
Magnetic particle detection in unshielded environment using orthogonal fluxgate gradiometer
Energy Technology Data Exchange (ETDEWEB)
Elrefai, Ahmed L., E-mail: a.lotfyelrefai@gmail.com; Sasada, Ichiro [Applied Science for Electronics and Materials, Kyushu University, Kasuga (Japan)
2015-05-07
A new detection system for magnetic particles, which can operate in an unshielded environment, is developed using a fundamental mode orthogonal fluxgate gradiometer. The proposed detection system offers the advantages of cost, size, and weight reduction as compared to contamination detection systems using superconducting quantum interference device sensor. The detection system can be used to detect metallic contamination in foods or lithium ion battery production lines. The system has been investigated numerically to optimize various design parameters of the system. Experimental setup has been developed to evaluate some of the numerically predicted results. Steel balls were successfully detected down to the diameter of 50 μm.
Nucleic acid constructs containing orthogonal site selective recombinases (OSSRs)
Energy Technology Data Exchange (ETDEWEB)
Gilmore, Joshua M.; Anderson, J. Christopher; Dueber, John E.
2017-08-29
The present invention provides for a recombinant nucleic acid comprising a nucleotide sequence comprising a plurality of constructs, wherein each construct independently comprises a nucleotide sequence of interest flanked by a pair of recombinase recognition sequences. Each pair of recombinase recognition sequences is recognized by a distinct recombinase. Optionally, each construct can, independently, further comprise one or more genes encoding a recombinase capable of recognizing the pair of recombinase recognition sequences of the construct. The recombinase can be an orthogonal (non-cross reacting), site-selective recombinase (OSSR).
Direct fourier method reconstruction based on unequally spaced fast fourier transform
International Nuclear Information System (INIS)
Wu Xiaofeng; Zhao Ming; Liu Li
2003-01-01
First, We give an Unequally Spaced Fast Fourier Transform (USFFT) method, which is more exact and theoretically more comprehensible than its former counterpart. Then, with an interesting interpolation scheme, we discusse how to apply USFFT to Direct Fourier Method (DFM) reconstruction of parallel projection data. At last, an emulation experiment result is given. (authors)
DEFF Research Database (Denmark)
Guan, Pengyu; Røge, Kasper Meldgaard; Lillieholm, Mads
2017-01-01
We review recent progress in the use of time lens based optical Fourier transformation for advanced all-optical signal processing. A novel time lens based complete optical Fourier transformation (OFT) technique is introduced. This complete OFT is based on two quadratic phase-modulation stages using...... four-wave mixing (FWM), separated by a dispersive medium, which enables time-to-frequency and frequency-to-time conversions simultaneously, thus performing an exchange between the temporal and spectral profiles of the input signal. Using the proposed complete OFT, several advanced all-optical signal......, such as orthogonal frequency division multiplexing (OFDM), Nyquist wavelength-division multiplexing (Nyquist-WDM) and Nyquist optical time division multiplexing (Nyquist-OTDM) signals....
An efficient pricing algorithm for swing options based on Fourier cosine expansions
Zhang, B.; Oosterlee, C.W.
2013-01-01
Swing options give contract holders the right to modify amounts of future delivery of certain commodities, such as electricity or gas. We assume that these options can be exercised at any time before the end of the contract, and more than once. However, a recovery time between any two consecutive
Two-Dimensional Fourier Cosine Series Expansion Method for Pricing Financial Options
Ruijter, M.J.; Oosterlee, C.W.
2012-01-01
The COS method for pricing European and Bermudan options with one underlying asset was developed in [F. Fang and C. W. Oosterlee, SIAM J. Sci. Comput., 31 (2008), pp. 826--848] and [F. Fang and C. W. Oosterlee, Numer. Math., 114 (2009), pp. 27--62]. In this paper, we extend the method to higher
Efficient Pricing of Early : Exercise and Exotic Options Based on Fourier Cosine Expansions
Zhang, B.
2012-01-01
In the financial world, two tasks are of prime importance: model calibration and portfolio hedging. For both tasks, efficient option pricing is necessary, particularly for the calibration where many options with different strike prices and different maturities need to be priced at the same time.
An efficient pricing algorithm for swing options based on Fourier cosine expansions
B. Zhang (Bo); C.W. Oosterlee (Kees)
2013-01-01
htmlabstractSwing options give contract holders the right to modify amounts of future delivery of certain commodities, such as electricity or gas. We assume that these options can be exercised at any time before the end of the contract, and more than once. However, a recovery time between any two
Fourier optical cryptosystem using complex spatial modulation
International Nuclear Information System (INIS)
Sarkadi, T; Koppa, P
2014-01-01
Our goal is to enhance the security level of a Fourier optical encryption system. Therefore we propose a Mach–Zehnder interferometer based encryption setup. The input data is organized in a binary array, and it is encoded in the two wave fronts propagated in the arms of the interferometer. Both input wave fronts are independently encrypted by Fourier systems, hence the proposed method has two encryption keys. During decryption, the encrypted wave fronts are propagated through the interferometer setup. The interference pattern of the output shows the reconstructed data in cases where the correct decryption Fourier keys are used. We propose a novel input image modulation method with a user defined phase parameter. We show that the security level of the proposed cryptosystem can be enhanced by an optimally chosen phase parameter. (paper)
Harmonic analysis from Fourier to wavelets
Pereyra, Maria Cristina
2012-01-01
In the last 200 years, harmonic analysis has been one of the most influential bodies of mathematical ideas, having been exceptionally significant both in its theoretical implications and in its enormous range of applicability throughout mathematics, science, and engineering. In this book, the authors convey the remarkable beauty and applicability of the ideas that have grown from Fourier theory. They present for an advanced undergraduate and beginning graduate student audience the basics of harmonic analysis, from Fourier's study of the heat equation, and the decomposition of functions into sums of cosines and sines (frequency analysis), to dyadic harmonic analysis, and the decomposition of functions into a Haar basis (time localization). While concentrating on the Fourier and Haar cases, the book touches on aspects of the world that lies between these two different ways of decomposing functions: time-frequency analysis (wavelets). Both finite and continuous perspectives are presented, allowing for the introd...
Projective Fourier duality and Weyl quantization
International Nuclear Information System (INIS)
Aldrovandi, R.; Saeger, L.A.
1996-08-01
The Weyl-Wigner correspondence prescription, which makes large use of Fourier duality, is reexamined from the point of view of Kac algebras, the most general background for non-commutative Fourier analysis allowing for that property. It is shown how the standard Kac structure has to be extended in order to accommodate the physical requirements. An Abelian and a symmetric projective Kac algebras are shown to provide, in close parallel to the standard case, a new dual framework and a well-defined notion of projective Fourier duality for the group of translations on the plane. The Weyl formula arises naturally as an irreducible component of the duality mapping between these projective algebras. (author). 29 refs
Fourier duality as a quantization principle
International Nuclear Information System (INIS)
Aldrovandi, R.; Saeger, L.A.
1996-08-01
The Weyl-Wigner prescription for quantization on Euclidean phase spaces makes essential use of Fourier duality. The extension of this property to more general phase spaces requires the use of Kac algebras, which provide the necessary background for the implementation of Fourier duality on general locally groups. Kac algebras - and the duality they incorporate are consequently examined as candidates for a general quantization framework extending the usual formalism. Using as a test case the simplest non-trivial phase space, the half-plane, it is shown how the structures present in the complete-plane case must be modified. Traces, for example, must be replaced by their noncommutative generalizations - weights - and the correspondence embodied in the Weyl-Wigner formalism is no more complete. Provided the underlying algebraic structure is suitably adapted to each case, Fourier duality is shown to be indeed a very powerful guide to the quantization of general physical systems. (author). 30 refs
Methods of Fourier analysis and approximation theory
Tikhonov, Sergey
2016-01-01
Different facets of interplay between harmonic analysis and approximation theory are covered in this volume. The topics included are Fourier analysis, function spaces, optimization theory, partial differential equations, and their links to modern developments in the approximation theory. The articles of this collection were originated from two events. The first event took place during the 9th ISAAC Congress in Krakow, Poland, 5th-9th August 2013, at the section “Approximation Theory and Fourier Analysis”. The second event was the conference on Fourier Analysis and Approximation Theory in the Centre de Recerca Matemàtica (CRM), Barcelona, during 4th-8th November 2013, organized by the editors of this volume. All articles selected to be part of this collection were carefully reviewed.
Fourier analysis and boundary value problems
Gonzalez-Velasco, Enrique A
1996-01-01
Fourier Analysis and Boundary Value Problems provides a thorough examination of both the theory and applications of partial differential equations and the Fourier and Laplace methods for their solutions. Boundary value problems, including the heat and wave equations, are integrated throughout the book. Written from a historical perspective with extensive biographical coverage of pioneers in the field, the book emphasizes the important role played by partial differential equations in engineering and physics. In addition, the author demonstrates how efforts to deal with these problems have lead to wonderfully significant developments in mathematics.A clear and complete text with more than 500 exercises, Fourier Analysis and Boundary Value Problems is a good introduction and a valuable resource for those in the field.Key Features* Topics are covered from a historical perspective with biographical information on key contributors to the field* The text contains more than 500 exercises* Includes practical applicati...
Group-invariant finite Fourier transforms
International Nuclear Information System (INIS)
Shenefelt, M.H.
1988-01-01
The computation of the finite Fourier transform of functions is one of the most used computations in crystallography. Since the Fourier transform involved in 3-dimensional, the size of the computation becomes very large even for relatively few sample points along each edge. In this thesis, there is a family of algorithms that reduce the computation of Fourier transform of functions respecting the symmetries. Some properties of these algorithms are: (1) The algorithms make full use of the group of symmetries of a crystal. (2) The algorithms can be factored and combined according to the prime factorization of the number of points in the sample space. (3) The algorithms are organized into a family using the group structure of the crystallographic groups to make iterative procedures possible
Implementation of quantum and classical discrete fractional Fourier transforms
Weimann, Steffen; Perez-Leija, Armando; Lebugle, Maxime; Keil, Robert; Tichy, Malte; Gräfe, Markus; Heilmann, René; Nolte, Stefan; Moya-Cessa, Hector; Weihs, Gregor; Christodoulides, Demetrios N.; Szameit, Alexander
2016-01-01
Fourier transforms, integer and fractional, are ubiquitous mathematical tools in basic and applied science. Certainly, since the ordinary Fourier transform is merely a particular case of a continuous set of fractional Fourier domains, every property and application of the ordinary Fourier transform becomes a special case of the fractional Fourier transform. Despite the great practical importance of the discrete Fourier transform, implementation of fractional orders of the corresponding discrete operation has been elusive. Here we report classical and quantum optical realizations of the discrete fractional Fourier transform. In the context of classical optics, we implement discrete fractional Fourier transforms of exemplary wave functions and experimentally demonstrate the shift theorem. Moreover, we apply this approach in the quantum realm to Fourier transform separable and path-entangled biphoton wave functions. The proposed approach is versatile and could find applications in various fields where Fourier transforms are essential tools. PMID:27006089
Implementation of quantum and classical discrete fractional Fourier transforms.
Weimann, Steffen; Perez-Leija, Armando; Lebugle, Maxime; Keil, Robert; Tichy, Malte; Gräfe, Markus; Heilmann, René; Nolte, Stefan; Moya-Cessa, Hector; Weihs, Gregor; Christodoulides, Demetrios N; Szameit, Alexander
2016-03-23
Fourier transforms, integer and fractional, are ubiquitous mathematical tools in basic and applied science. Certainly, since the ordinary Fourier transform is merely a particular case of a continuous set of fractional Fourier domains, every property and application of the ordinary Fourier transform becomes a special case of the fractional Fourier transform. Despite the great practical importance of the discrete Fourier transform, implementation of fractional orders of the corresponding discrete operation has been elusive. Here we report classical and quantum optical realizations of the discrete fractional Fourier transform. In the context of classical optics, we implement discrete fractional Fourier transforms of exemplary wave functions and experimentally demonstrate the shift theorem. Moreover, we apply this approach in the quantum realm to Fourier transform separable and path-entangled biphoton wave functions. The proposed approach is versatile and could find applications in various fields where Fourier transforms are essential tools.
An optical Fourier transform coprocessor with direct phase determination.
Macfaden, Alexander J; Gordon, George S D; Wilkinson, Timothy D
2017-10-20
The Fourier transform is a ubiquitous mathematical operation which arises naturally in optics. We propose and demonstrate a practical method to optically evaluate a complex-to-complex discrete Fourier transform. By implementing the Fourier transform optically we can overcome the limiting O(nlogn) complexity of fast Fourier transform algorithms. Efficiently extracting the phase from the well-known optical Fourier transform is challenging. By appropriately decomposing the input and exploiting symmetries of the Fourier transform we are able to determine the phase directly from straightforward intensity measurements, creating an optical Fourier transform with O(n) apparent complexity. Performing larger optical Fourier transforms requires higher resolution spatial light modulators, but the execution time remains unchanged. This method could unlock the potential of the optical Fourier transform to permit 2D complex-to-complex discrete Fourier transforms with a performance that is currently untenable, with applications across information processing and computational physics.
Fourier analysis in several complex variables
Ehrenpreis, Leon
2006-01-01
Suitable for advanced undergraduates and graduate students, this text develops comparison theorems to establish the fundamentals of Fourier analysis and to illustrate their applications to partial differential equations.The three-part treatment begins by establishing the quotient structure theorem or fundamental principle of Fourier analysis. Topics include the geometric structure of ideals and modules, quantitative estimates, and examples in which the theory can be applied. The second part focuses on applications to partial differential equations and covers the solution of homogeneous and inh
Fourier transforms and convolutions for the experimentalist
Jennison, RC
1961-01-01
Fourier Transforms and Convolutions for the Experimentalist provides the experimentalist with a guide to the principles and practical uses of the Fourier transformation. It aims to bridge the gap between the more abstract account of a purely mathematical approach and the rule of thumb calculation and intuition of the practical worker. The monograph springs from a lecture course which the author has given in recent years and for which he has drawn upon a number of sources, including a set of notes compiled by the late Dr. I. C. Browne from a series of lectures given by Mr. J . A. Ratcliffe of t
Electro-optic imaging Fourier transform spectrometer
Chao, Tien-Hsin (Inventor); Znod, Hanying (Inventor)
2009-01-01
An Electro-Optic Imaging Fourier Transform Spectrometer (EOIFTS) for Hyperspectral Imaging is described. The EOIFTS includes an input polarizer, an output polarizer, and a plurality of birefringent phase elements. The relative orientations of the polarizers and birefringent phase elements can be changed mechanically or via a controller, using ferroelectric liquid crystals, to substantially measure the spectral Fourier components of light propagating through the EIOFTS. When achromatic switches are used as an integral part of the birefringent phase elements, the EIOFTS becomes suitable for broadband applications, with over 1 micron infrared bandwidth.
Bifurcations in two-image photometric stereo for orthogonal illuminations
Kozera, R.; Prokopenya, A.; Noakes, L.; Śluzek, A.
2017-07-01
This paper discusses the ambiguous shape recovery in two-image photometric stereo for a Lambertian surface. The current uniqueness analysis refers to linearly independent light-source directions p = (0, 0, -1) and q arbitrary. For this case necessary and sufficient condition determining ambiguous reconstruction is governed by a second-order linear partial differential equation with constant coefficients. In contrast, a general position of both non-colinear illumination directions p and q leads to a highly non-linear PDE which raises a number of technical difficulties. As recently shown, the latter can also be handled for another family of orthogonal illuminations parallel to the OXZ-plane. For the special case of p = (0, 0, -1) a potential ambiguity stems also from the possible bifurcations of sub-local solutions glued together along a curve defined by an algebraic equation in terms of the data. This paper discusses the occurrence of similar bifurcations for such configurations of orthogonal light-source directions. The discussion to follow is supplemented with examples based on continuous reflectance map model and generated synthetic images.
Statistical benchmarking for orthogonal electrostatic quantum dot qubit devices
Gamble, John; Frees, Adam; Friesen, Mark; Coppersmith, S. N.
2014-03-01
Quantum dots in semiconductor systems have emerged as attractive candidates for the implementation of quantum information processors because of the promise of scalability, manipulability, and integration with existing classical electronics. A limitation in current devices is that the electrostatic gates used for qubit manipulation exhibit strong cross-capacitance, presenting a barrier for practical scale-up. Here, we introduce a statistical framework for making precise the notion of orthogonality. We apply our method to analyze recently implemented designs at the University of Wisconsin-Madison that exhibit much increased orthogonal control than was previously possible. We then use our statistical modeling to future device designs, providing practical guidelines for devices to have robust control properties. Sandia National Laboratories is a multi-program laboratory managed and operated by Sandia Corporation, a wholly owned subsidiary of Lockheed Martin Corporation, for the U.S. Department of Energy Nuclear Security Administration under contract DE-AC04-94AL85000. The views and conclusions contained in this document are those of the authors and should not be interpreted as representing the official policies, either expressly or implied, of the US Government. This work was supported in part by the Laboratory Directed Research and Development program at Sandia National Laboratories, by ARO (W911NF-12-0607), and by the United States Department of Defense.
Downlink Non-Orthogonal Multiple Access (NOMA) in Poisson Networks
Ali, Konpal S.
2018-03-21
A network model is considered where Poisson distributed base stations transmit to $N$ power-domain non-orthogonal multiple access (NOMA) users (UEs) each that employ successive interference cancellation (SIC) for decoding. We propose three models for the clustering of NOMA UEs and consider two different ordering techniques for the NOMA UEs: mean signal power-based and instantaneous signal-to-intercell-interference-and-noise-ratio-based. For each technique, we present a signal-to-interference-and-noise ratio analysis for the coverage of the typical UE. We plot the rate region for the two-user case and show that neither ordering technique is consistently superior to the other. We propose two efficient algorithms for finding a feasible resource allocation that maximize the cell sum rate $\\\\mathcal{R}_{\\ m tot}$, for general $N$, constrained to: 1) a minimum rate $\\\\mathcal{T}$ for each UE, 2) identical rates for all UEs. We show the existence of: 1) an optimum $N$ that maximizes the constrained $\\\\mathcal{R}_{\\ m tot}$ given a set of network parameters, 2) a critical SIC level necessary for NOMA to outperform orthogonal multiple access. The results highlight the importance in choosing the network parameters $N$, the constraints, and the ordering technique to balance the $\\\\mathcal{R}_{\\ m tot}$ and fairness requirements. We also show that interference-aware UE clustering can significantly improve performance.
Cerenkov luminescence tomography based on preconditioning orthogonal matching pursuit
Liu, Haixiao; Hu, Zhenhua; Wang, Kun; Tian, Jie; Yang, Xin
2015-03-01
Cerenkov luminescence imaging (CLI) is a novel optical imaging method and has been proved to be a potential substitute of the traditional radionuclide imaging such as positron emission tomography (PET) and single-photon emission computed tomography (SPECT). This imaging method inherits the high sensitivity of nuclear medicine and low cost of optical molecular imaging. To obtain the depth information of the radioactive isotope, Cerenkov luminescence tomography (CLT) is established and the 3D distribution of the isotope is reconstructed. However, because of the strong absorption and scatter, the reconstruction of the CLT sources is always converted to an ill-posed linear system which is hard to be solved. In this work, the sparse nature of the light source was taken into account and the preconditioning orthogonal matching pursuit (POMP) method was established to effectively reduce the ill-posedness and obtain better reconstruction accuracy. To prove the accuracy and speed of this algorithm, a heterogeneous numerical phantom experiment and an in vivo mouse experiment were conducted. Both the simulation result and the mouse experiment showed that our reconstruction method can provide more accurate reconstruction result compared with the traditional Tikhonov regularization method and the ordinary orthogonal matching pursuit (OMP) method. Our reconstruction method will provide technical support for the biological application for Cerenkov luminescence.
Non-Orthogonal Multiple Access for Ubiquitous Wireless Sensor Networks.
Anwar, Asim; Seet, Boon-Chong; Ding, Zhiguo
2018-02-08
Ubiquitous wireless sensor networks (UWSNs) have become a critical technology for enabling smart cities and other ubiquitous monitoring applications. Their deployment, however, can be seriously hampered by the spectrum available to the sheer number of sensors for communication. To support the communication needs of UWSNs without requiring more spectrum resources, the power-domain non-orthogonal multiple access (NOMA) technique originally proposed for 5th Generation (5G) cellular networks is investigated for UWSNs for the first time in this paper. However, unlike 5G networks that operate in the licensed spectrum, UWSNs mostly operate in unlicensed spectrum where sensors also experience cross-technology interferences from other devices sharing the same spectrum. In this paper, we model the interferences from various sources at the sensors using stochastic geometry framework. To evaluate the performance, we derive a theorem and present new closed form expression for the outage probability of the sensors in a downlink scenario under interference limited environment. In addition, diversity analysis for the ordered NOMA users is performed. Based on the derived outage probability, we evaluate the average link throughput and energy consumption efficiency of NOMA against conventional orthogonal multiple access (OMA) technique in UWSNs. Further, the required computational complexity for the NOMA users is presented.
Downlink Non-Orthogonal Multiple Access (NOMA) in Poisson Networks
Ali, Konpal S.; Haenggi, Martin; Elsawy, Hesham; Chaaban, Anas; Alouini, Mohamed-Slim
2018-01-01
A network model is considered where Poisson distributed base stations transmit to $N$ power-domain non-orthogonal multiple access (NOMA) users (UEs) each that employ successive interference cancellation (SIC) for decoding. We propose three models for the clustering of NOMA UEs and consider two different ordering techniques for the NOMA UEs: mean signal power-based and instantaneous signal-to-intercell-interference-and-noise-ratio-based. For each technique, we present a signal-to-interference-and-noise ratio analysis for the coverage of the typical UE. We plot the rate region for the two-user case and show that neither ordering technique is consistently superior to the other. We propose two efficient algorithms for finding a feasible resource allocation that maximize the cell sum rate $\\mathcal{R}_{\\rm tot}$, for general $N$, constrained to: 1) a minimum rate $\\mathcal{T}$ for each UE, 2) identical rates for all UEs. We show the existence of: 1) an optimum $N$ that maximizes the constrained $\\mathcal{R}_{\\rm tot}$ given a set of network parameters, 2) a critical SIC level necessary for NOMA to outperform orthogonal multiple access. The results highlight the importance in choosing the network parameters $N$, the constraints, and the ordering technique to balance the $\\mathcal{R}_{\\rm tot}$ and fairness requirements. We also show that interference-aware UE clustering can significantly improve performance.
Modeling of Particle Emission During Dry Orthogonal Cutting
Khettabi, Riad; Songmene, Victor; Zaghbani, Imed; Masounave, Jacques
2010-08-01
Because of the risks associated with exposure to metallic particles, efforts are being put into controlling and reducing them during the metal working process. Recent studies by the authors involved in this project have presented the effects of cutting speeds, workpiece material, and tool geometry on particle emission during dry machining; the authors have also proposed a new parameter, named the dust unit ( D u), for use in evaluating the quantity of particle emissions relative to the quantity of chips produced during a machining operation. In this study, a model for predicting the particle emission (dust unit) during orthogonal turning is proposed. This model, which is based on the energy approach combined with the microfriction and the plastic deformation of the material, takes into account the tool geometry, the properties of the worked material, the cutting conditions, and the chip segmentation. The model is validated using experimental results obtained during the orthogonal turning of 6061-T6 aluminum alloy, AISI 1018, AISI 4140 steels, and grey cast iron. A good agreement was found with experimental results. This model can help in designing strategies for reducing particle emission during machining processes, at the source.
State orthogonality, boson bunching parameter and bosonic enhancement factor
Marchewka, Avi; Granot, Er'el
2016-04-01
It is emphasized that the bunching parameter β ≡ p B / p D , i.e. the ratio between the probability to measure two bosons and two distinguishable particles at the same state, is a constant of motion and depends only on the overlap between the initial wavefunctions. This ratio is equal to β = 2 / (1 + I 2), where I is the overlap integral between the initial wavefunctions. That is, only when the initial wavefunctions are orthogonal this ratio is equal to 2, however, this bunching ratio can be reduced to 1, when the two wavefunctions are identical. This simple equation explains the experimental evidences of a beam splitter. A straightforward conclusion is that by measuring the local bunching parameter β (at any point in space and time) it is possible to evaluate a global parameter I (the overlap between the initial wavefunctions). The bunching parameter is then generalized to arbitrary number of particles, and in an analogy to the two-particles scenario, the well-known bosonic enhancement appears only when all states are orthogonal.
State orthogonality, boson bunching parameter and bosonic enhancement factor
International Nuclear Information System (INIS)
Marchewka, A.; Granot, E.
2016-01-01
Bosons bunching is the tendency of bosons to bunch together with respect to distinguishable particles. It is emphasized that the bunching parameter β = p_B/p_D, i.e. the ratio between the probability to measure 2 bosons and 2 distinguishable particles at the same state, is a constant of motion and depends only on the overlap between the initial wavefunctions. This ratio is equal to β = 2/(1 + l"2), where l is the overlap integral between the initial wavefunctions. That is, only when the initial wavefunctions are orthogonal this ratio is equal to 2, however, this bunching ratio can be reduced to 1, when the two wavefunctions are identical. This simple equation explains the experimental evidences of a beam splitter. A straightforward conclusion is that by measuring the local bunching parameter β (at any point in space and time) it is possible to evaluate a global parameter l (the overlap between the initial wavefunctions). The bunching parameter is then generalized to arbitrary number of particles, and in an analogy to the two-particles scenario, the well-known bosonic enhancement appears only when all states are orthogonal
Supervised orthogonal discriminant subspace projects learning for face recognition.
Chen, Yu; Xu, Xiao-Hong
2014-02-01
In this paper, a new linear dimension reduction method called supervised orthogonal discriminant subspace projection (SODSP) is proposed, which addresses high-dimensionality of data and the small sample size problem. More specifically, given a set of data points in the ambient space, a novel weight matrix that describes the relationship between the data points is first built. And in order to model the manifold structure, the class information is incorporated into the weight matrix. Based on the novel weight matrix, the local scatter matrix as well as non-local scatter matrix is defined such that the neighborhood structure can be preserved. In order to enhance the recognition ability, we impose an orthogonal constraint into a graph-based maximum margin analysis, seeking to find a projection that maximizes the difference, rather than the ratio between the non-local scatter and the local scatter. In this way, SODSP naturally avoids the singularity problem. Further, we develop an efficient and stable algorithm for implementing SODSP, especially, on high-dimensional data set. Moreover, the theoretical analysis shows that LPP is a special instance of SODSP by imposing some constraints. Experiments on the ORL, Yale, Extended Yale face database B and FERET face database are performed to test and evaluate the proposed algorithm. The results demonstrate the effectiveness of SODSP. Copyright © 2013 Elsevier Ltd. All rights reserved.
Cache-Oblivious Planar Orthogonal Range Searching and Counting
DEFF Research Database (Denmark)
Arge, Lars; Brodal, Gerth Stølting; Fagerberg, Rolf
2005-01-01
present the first cache-oblivious data structure for planar orthogonal range counting, and improve on previous results for cache-oblivious planar orthogonal range searching. Our range counting structure uses O(Nlog2 N) space and answers queries using O(logB N) memory transfers, where B is the block...... size of any memory level in a multilevel memory hierarchy. Using bit manipulation techniques, the space can be further reduced to O(N). The structure can also be modified to support more general semigroup range sum queries in O(logB N) memory transfers, using O(Nlog2 N) space for three-sided queries...... and O(Nlog22 N/log2log2 N) space for four-sided queries. Based on the O(Nlog N) space range counting structure, we develop a data structure that uses O(Nlog2 N) space and answers three-sided range queries in O(logB N+T/B) memory transfers, where T is the number of reported points. Based...
USC orthogonal multiprocessor for image processing with neural networks
Hwang, Kai; Panda, Dhabaleswar K.; Haddadi, Navid
1990-07-01
This paper presents the architectural features and imaging applications of the Orthogonal MultiProcessor (OMP) system, which is under construction at the University of Southern California with research funding from NSF and assistance from several industrial partners. The prototype OMP is being built with 16 Intel i860 RISC microprocessors and 256 parallel memory modules using custom-designed spanning buses, which are 2-D interleaved and orthogonally accessed without conflicts. The 16-processor OMP prototype is targeted to achieve 430 MIPS and 600 Mflops, which have been verified by simulation experiments based on the design parameters used. The prototype OMP machine will be initially applied for image processing, computer vision, and neural network simulation applications. We summarize important vision and imaging algorithms that can be restructured with neural network models. These algorithms can efficiently run on the OMP hardware with linear speedup. The ultimate goal is to develop a high-performance Visual Computer (Viscom) for integrated low- and high-level image processing and vision tasks.
International Nuclear Information System (INIS)
Lewis, C.
1997-01-01
The Olympic Dam orebody is the 6th largest copper and the single largest uranium orebody in the world. Mine production commenced in June 1988, at an annual production rate of around 45,000 tonnes of copper and 1,000 tonnes of uranium. Western Mining Corporation announced in 1996 a proposed $1.25 billion expansion of the Olympic Dam operation to raise the annual production capacity of the mine to 200,000 tonnes of copper, approximately 3,700 tonnes of uranium, 75,000 ounces of gold and 950,000 ounces of silver by 2001. Further optimisation work has identified a faster track expansion route, with an increase in the capital cost to $1.487 billion but improved investment outcome, a new target completion date of end 1999, and a new uranium output of 4,600 tonnes per annum from that date
Financing electricity expansion
International Nuclear Information System (INIS)
Hyman, L.S.
1994-01-01
Expansion of electricity supply is associated with economic development. The installation and enlargement of power systems in developing countries entails a huge financial burden, however. Energy consumers in such countries must pay not only for supplies but for the cost of raising the capital for expansion on the international markets. Estimates are presented for the capital expenditure for electricity supply over the period 1990 to 2020 for the major world regions, using approximations for the cost of plant and capital and for the returns earned. These data lead to the conclusion that the five regions with the lowest per capita incomes are those which will need the major part of the capital expenditure and the highest percentage of external finance. (6 tables) (UK)
Bigravity from gradient expansion
International Nuclear Information System (INIS)
Yamashita, Yasuho; Tanaka, Takahiro
2016-01-01
We discuss how the ghost-free bigravity coupled with a single scalar field can be derived from a braneworld setup. We consider DGP two-brane model without radion stabilization. The bulk configuration is solved for given boundary metrics, and it is substituted back into the action to obtain the effective four-dimensional action. In order to obtain the ghost-free bigravity, we consider the gradient expansion in which the brane separation is supposed to be sufficiently small so that two boundary metrics are almost identical. The obtained effective theory is shown to be ghost free as expected, however, the interaction between two gravitons takes the Fierz-Pauli form at the leading order of the gradient expansion, even though we do not use the approximation of linear perturbation. We also find that the radion remains as a scalar field in the four-dimensional effective theory, but its coupling to the metrics is non-trivial.
International Nuclear Information System (INIS)
Suess, S.T.
1987-01-01
Magnetic clouds are a carefully defined subclass of all interplanetary signatures of coronal mass ejections whose geometry is thought to be that of a cylinder embedded in a plane. It has been found that the total magnetic pressure inside the clouds is higher than the ion pressure outside, and that the clouds are expanding at 1 AU at about half the local Alfven speed. The geometry of the clouds is such that even though the magnetic pressure inside is larger than the total pressure outside, expansion will not occur because the pressure is balanced by magnetic tension - the pinch effect. The evidence for expansion of clouds at 1 AU is nevertheless quite strong so another reason for its existence must be found. It is demonstrated that the observations can be reproduced by taking into account the effects of geometrical distortion of the low plasma beta clouds as they move away from the Sun
IKEA's International Expansion
Harapiak, Clayton
2013-01-01
This case concerns a global retailing firm that is dealing with strategic management and marketing issues. Applying a scenario of international expansion, this case provides a thorough analysis of the current business environment for IKEA. Utilizing a variety of methods (e.g. SWOT, PESTLE, McKinsey Matrix) the overall objective is to provide students with the opportunity to apply their research skills and knowledge regarding a highly competitive industry to develop strategic marketing strateg...
International Nuclear Information System (INIS)
Matsuki, Takayuki
1976-01-01
Symmetric eikonal expansion for the scattering amplitude is formulated for nonrelativistic and relativistic potential scatterings and also for the quantum field theory. The first approximations coincide with those of Levy and Sucher. The obtained scattering amplitudes are time reversal invariant for all cases and are crossing symmetric for the quantum field theory in each order of approximation. The improved eikonal phase introduced by Levy and Sucher is also derived from the different approximation scheme from the above. (auth.)
Series expansions without diagrams
International Nuclear Information System (INIS)
Bhanot, G.; Creutz, M.; Horvath, I.; Lacki, J.; Weckel, J.
1994-01-01
We discuss the use of recursive enumeration schemes to obtain low- and high-temperature series expansions for discrete statistical systems. Using linear combinations of generalized helical lattices, the method is competitive with diagrammatic approaches and is easily generalizable. We illustrate the approach using Ising and Potts models. We present low-temperature series results in up to five dimensions and high-temperature series in three dimensions. The method is general and can be applied to any discrete model
Machine learning (ML)-guided OPC using basis functions of polar Fourier transform
Choi, Suhyeong; Shim, Seongbo; Shin, Youngsoo
2016-03-01
With shrinking feature size, runtime has become a limitation of model-based OPC (MB-OPC). A few machine learning-guided OPC (ML-OPC) have been studied as candidates for next-generation OPC, but they all employ too many parameters (e.g. local densities), which set their own limitations. We propose to use basis functions of polar Fourier transform (PFT) as parameters of ML-OPC. Since PFT functions are orthogonal each other and well reflect light phenomena, the number of parameters can significantly be reduced without loss of OPC accuracy. Experiments demonstrate that our new ML-OPC achieves 80% reduction in OPC time and 35% reduction in the error of predicted mask bias when compared to conventional ML-OPC.
Kähler, Sven; Olsen, Jeppe
2017-11-01
A computational method is presented for systems that require high-level treatments of static and dynamic electron correlation but cannot be treated using conventional complete active space self-consistent field-based methods due to the required size of the active space. Our method introduces an efficient algorithm for perturbative dynamic correlation corrections for compact non-orthogonal MCSCF calculations. In the algorithm, biorthonormal expansions of orbitals and CI-wave functions are used to reduce the scaling of the performance determining step from quadratic to linear in the number of configurations. We describe a hierarchy of configuration spaces that can be chosen for the active space. Potential curves for the nitrogen molecule and the chromium dimer are compared for different configuration spaces. Already the most compact spaces yield qualitatively correct potentials that with increasing size of configuration spaces systematically approach complete active space results.
Energy Technology Data Exchange (ETDEWEB)
Park, Ju Yeop; In, Wang Kee; Chun, Tae Hyun; Oh, Dong Seok [Korea Atomic Energy Research Institute, Taejeon (Korea)
2000-02-01
The development of orthogonal 2-dimensional numerical code is made. The present code contains 9 kinds of turbulence models that are widely used. They include a standard k-{epsilon} model and 8 kinds of low Reynolds number ones. They also include 6 kinds of numerical schemes including 5 kinds of low order schemes and 1 kind of high order scheme such as QUICK. To verify the present numerical code, pipe flow, channel flow and expansion pipe flow are solved by this code with various options of turbulence models and numerical schemes and the calculated outputs are compared to experimental data. Furthermore, the discretization error that originates from the use of standard k-{epsilon} turbulence model with wall function is much more diminished by introducing a new grid system than a conventional one in the present code. 23 refs., 58 figs., 6 tabs. (Author)
A comparison of orthogonal transformations for digital speech processing.
Campanella, S. J.; Robinson, G. S.
1971-01-01
Discrete forms of the Fourier, Hadamard, and Karhunen-Loeve transforms are examined for their capacity to reduce the bit rate necessary to transmit speech signals. To rate their effectiveness in accomplishing this goal the quantizing error (or noise) resulting for each transformation method at various bit rates is computed and compared with that for conventional companded PCM processing. Based on this comparison, it is found that Karhunen-Loeve provides a reduction in bit rate of 13.5 kbits/s, Fourier 10 kbits/s, and Hadamard 7.5 kbits/s as compared with the bit rate required for companded PCM. These bit-rate reductions are shown to be somewhat independent of the transmission bit rate.
Nikzad-Langerodi, Ramin; Arth, Katharina; Klatte-Asselmeyer, Valerie; Bressler, Sabine; Saukel, Johannes; Reznicek, Gottfried; Dobeš, Christoph
2018-04-01
(Acetoxy-)valerenic acid and total essential oil content are important quality attributes of pharmacy grade valerian root (Valerianae radix). Traditional analysis of these quantities is time-consuming and necessitates (harmful) solvents. Here we investigated an application of attenuated total reflection Fourier transform infrared spectroscopy for extractionless analysis of these quality attributes on a representative sample comprising 260 wild-crafted individuals covering the Central European taxonomic diversity of the Valeriana officinalis L. s. l. species aggregate with its three major ploidy cytotypes (i.e., di-, tetra- and octoploid). Calibration models were built by orthogonal partial least squares regression for quantitative analysis of (acetoxy-)valerenic acid and total essential oil content. For the latter, we propose a simplistic protocol involving apolar extraction followed by gas chromatography as a reference method for multivariate calibration in order to handle the analysis of samples taken from individual plants. We found good predictive ability of chemometric models for quantification of valerenic acid, acetoxyvalerenic acid, total sesquiterpenoid acid, and essential oil content with a root mean squared error of cross-validation of 0.064, 0.043, and 0.09 and root mean squared error of prediction of 0.066, 0.057, and 0.09 (% content), respectively. Orthogonal partial least squares discriminant analysis revealed good discriminability between the most productive phenotype (i.e., the octoploid cytotype) in terms of sesquiterpenoid acids, and the less productive ones (i.e., di- and tetraploid). All in all, our results demonstrate the application of attenuated total reflection Fourier transform infrared spectroscopy for rapid, extractionless estimation of the most important quality attributes of valerian root and minimally invasive identification of the most productive phenotype in terms of sesquiterpenoid acids. Georg Thieme Verlag KG Stuttgart · New
The periodogram at the Fourier frequencies
Kokoszka, P; Mikosch, T
In the time series literature one can often find the claim that the periodogram ordinates of an lid sequence at the Fourier frequencies behave like an lid standard exponential sequence. We review some results about functions of these periodogram ordinates, including the convergence of extremes,
Pi, Fourier Transform and Ludolph van Ceulen
Vajta, Miklos
2000-01-01
The paper describes an interesting (and unexpected) application of the Fast Fourier transform in number theory. Calculating more and more decimals of p (first by hand and then from the mid-20th century, by digital computers) not only fascinated mathematicians from ancient times but kept them busy as
Fourier transform infrared spectrometery: an undergraduate experiment
International Nuclear Information System (INIS)
Lerner, L
2016-01-01
Simple apparatus is developed, providing undergraduate students with a solid understanding of Fourier transform (FT) infrared (IR) spectroscopy in a hands on experiment. Apart from its application to measuring the mid-IR spectra of organic molecules, the experiment introduces several techniques with wide applicability in physics, including interferometry, the FT, digital data analysis, and control theory. (paper)
Wigner distribution and fractional Fourier transform
Alieva, T.; Bastiaans, M.J.
2001-01-01
The connection between the Wigner distribution and the squared modulus of the fractional Fourier transform - which are both well-known time-frequency representations of a signal - is established. In particular the Radon-Wigner transform is used, which relates projections of the Wigner distribution
The Fourier transform of tubular densities
Prior, C B; Goriely, A
2012-01-01
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
Geometric Representations for Discrete Fourier Transforms
Cambell, C. W.
1986-01-01
Simple geometric representations show symmetry and periodicity of discrete Fourier transforms (DFT's). Help in visualizing requirements for storing and manipulating transform value in computations. Representations useful in any number of dimensions, but particularly in one-, two-, and three-dimensional cases often encountered in practice.
Fourier analysis in combinatorial number theory
International Nuclear Information System (INIS)
Shkredov, Il'ya D
2010-01-01
In this survey applications of harmonic analysis to combinatorial number theory are considered. Discussion topics include classical problems of additive combinatorics, colouring problems, higher-order Fourier analysis, theorems about sets of large trigonometric sums, results on estimates for trigonometric sums over subgroups, and the connection between combinatorial and analytic number theory. Bibliography: 162 titles.
Fourier analysis in combinatorial number theory
Energy Technology Data Exchange (ETDEWEB)
Shkredov, Il' ya D [M. V. Lomonosov Moscow State University, Moscow (Russian Federation)
2010-09-16
In this survey applications of harmonic analysis to combinatorial number theory are considered. Discussion topics include classical problems of additive combinatorics, colouring problems, higher-order Fourier analysis, theorems about sets of large trigonometric sums, results on estimates for trigonometric sums over subgroups, and the connection between combinatorial and analytic number theory. Bibliography: 162 titles.
A Fourier analysis of extremal events
DEFF Research Database (Denmark)
Zhao, Yuwei
is the extremal periodogram. The extremal periodogram shares numerous asymptotic properties with the periodogram of a linear process in classical time series analysis: the asymptotic distribution of the periodogram ordinates at the Fourier frequencies have a similar form and smoothed versions of the periodogram...
Bernoulli Polynomials, Fourier Series and Zeta Numbers
DEFF Research Database (Denmark)
Scheufens, Ernst E
2013-01-01
Fourier series for Bernoulli polynomials are used to obtain information about values of the Riemann zeta function for integer arguments greater than one. If the argument is even we recover the well-known exact values, if the argument is odd we find integral representations and rapidly convergent...
The Fourier modal method for aperiodic structures
Pisarenco, M.; Maubach, J.M.L.; Setija, I.D.; Mattheij, R.M.M.
2010-01-01
This paper extends the area of application of the Fourier modal method from periodic structures to non-periodic ones illuminated under arbitrary angles. This is achieved by placing perfectly matched layers at the lateral boundaries and reformulating the problem in terms of a contrast field.
Discrete Fourier analysis of multigrid algorithms
van der Vegt, Jacobus J.W.; Rhebergen, Sander
2011-01-01
The main topic of this report is a detailed discussion of the discrete Fourier multilevel analysis of multigrid algorithms. First, a brief overview of multigrid methods is given for discretizations of both linear and nonlinear partial differential equations. Special attention is given to the
Euler Polynomials, Fourier Series and Zeta Numbers
DEFF Research Database (Denmark)
Scheufens, Ernst E
2012-01-01
Fourier series for Euler polynomials is used to obtain information about values of the Riemann zeta function for integer arguments greater than one. If the argument is even we recover the well-known exact values, if the argument is odd we find integral representations and rapidly convergent series....
Fourier inversion on a reductive symmetric space
Ban, E.P. van den
1999-01-01
Let X be a semisimple symmetric space. In previous papers, [8] and [9], we have dened an explicit Fourier transform for X and shown that this transform is injective on the space C 1 c (X) ofcompactly supported smooth functions on X. In the present paper, which is a continuation of these papers, we
Fractional-Fourier-domain weighted Wigner distribution
Stankovic, L.; Alieva, T.; Bastiaans, M.J.
2001-01-01
A fractional-Fourier-domain realization of the weighted Wigner distribution (or S-method), producing auto-terms close to the ones in the Wigner distribution itself, but with reduced cross-terms, is presented. The computational cost of this fractional-domain realization is the same as the
Clifford Fourier transform on vector fields.
Ebling, Julia; Scheuermann, Gerik
2005-01-01
Image processing and computer vision have robust methods for feature extraction and the computation of derivatives of scalar fields. Furthermore, interpolation and the effects of applying a filter can be analyzed in detail and can be advantages when applying these methods to vector fields to obtain a solid theoretical basis for feature extraction. We recently introduced the Clifford convolution, which is an extension of the classical convolution on scalar fields and provides a unified notation for the convolution of scalar and vector fields. It has attractive geometric properties that allow pattern matching on vector fields. In image processing, the convolution and the Fourier transform operators are closely related by the convolution theorem and, in this paper, we extend the Fourier transform to include general elements of Clifford Algebra, called multivectors, including scalars and vectors. The resulting convolution and derivative theorems are extensions of those for convolution and the Fourier transform on scalar fields. The Clifford Fourier transform allows a frequency analysis of vector fields and the behavior of vector-valued filters. In frequency space, vectors are transformed into general multivectors of the Clifford Algebra. Many basic vector-valued patterns, such as source, sink, saddle points, and potential vortices, can be described by a few multivectors in frequency space.
Fourier transforms on a semisimple symmetric space
Ban, E.P. van den; Schlichtkrull, H.
1994-01-01
Let G=H be a semisimple symmetric space, that is, G is a connected semisimple real Lie group with an involution ?, and H is an open subgroup of the group of xed points for ? in G. The main purpose of this paper is to study an explicit Fourier transform on G=H. In terms of general representation
Fourier transforms on a semisimple symmetric space
Ban, E.P. van den; Carmona, J.; Delorme, P.
1997-01-01
Let G=H be a semisimple symmetric space, that is, G is a connected semisimple real Lie group with an involution ?, and H is an open subgroup of the group of xed points for ? in G. The main purpose of this paper is to study an explicit Fourier transform on G=H. In terms of general representation
International Nuclear Information System (INIS)
Zheng Youqi; Wu Hongchun; Cao Liangzhi
2013-01-01
This paper describes the stability analysis for the coarse mesh finite difference (CMFD) acceleration used in the wavelet expansion method. The nonlinear CMFD acceleration scheme is transformed by linearization and the Fourier ansatz is introduced into the linearized formulae. The spectral radius is defined as the stability criterion, which is the least upper bound (LUB) of the largest eigenvalue of Fourier analysis matrix. The stability analysis considers the effect of mesh size (spectral length), coarse mesh division and scattering ratio. The results show that for the wavelet expansion method, the CMFD acceleration is conditionally stable. The small size of fine mesh brings stability and fast convergent. With the increase of the mesh size, the stability becomes worse. The scattering ratio does not impact the stability obviously. It makes the CMFD acceleration highly efficient in the strong scattering case. The results of Fourier analysis are verified by the numerical tests based on a homogeneous slab problem.
Decomposition of orthogonal polygons in a set of rectanglеs
Shestakov, E.; Voronov, A.
2009-01-01
Algorithm for covering orthogonal integrated circuit layout objects is considered. Objects of the research are special single-connected orthogonal polygons which are generated during decomposition of any multiply connected polygon in a set of single-connected orthogonal polygons. Developed algorithm for covering polygons based on the mathematical techinque of logic matrix transformation. Results described in this paper, can be applied in computer geometry and image analysis.
A high-order q-difference equation for q-Hahn multiple orthogonal polynomials
DEFF Research Database (Denmark)
Arvesú, J.; Esposito, Chiara
2012-01-01
A high-order linear q-difference equation with polynomial coefficients having q-Hahn multiple orthogonal polynomials as eigenfunctions is given. The order of the equation coincides with the number of orthogonality conditions that these polynomials satisfy. Some limiting situations when are studie....... Indeed, the difference equation for Hahn multiple orthogonal polynomials given in Lee [J. Approx. Theory (2007), ), doi: 10.1016/j.jat.2007.06.002] is obtained as a limiting case....
Expansions for Coulomb wave functions
Boersma, J.
1969-01-01
In this paper we derive a number of expansions for Whittaker functions, regular and irregular Coulomb wave functions. The main result consists of a new expansion for the irregular Coulomb wave functions of orders zero and one in terms of regular Coulomb wave functions. The latter expansions are
Virial expansion for almost diagonal random matrices
International Nuclear Information System (INIS)
Yevtushenko, Oleg; Kravtsov, Vladimir E
2003-01-01
Energy level statistics of Hermitian random matrices H-circumflex with Gaussian independent random entries H i≥j is studied for a generic ensemble of almost diagonal random matrices with (vertical bar H ii vertical bar 2 ) ∼ 1 and (vertical bar H i≠j vertical bar 2 ) bF(vertical bar i - j vertical bar) parallel 1. We perform a regular expansion of the spectral form-factor K(τ) = 1 + bK 1 (τ) + b 2 K 2 (τ) + c in powers of b parallel 1 with the coefficients K m (τ) that take into account interaction of (m + 1) energy levels. To calculate K m (τ), we develop a diagrammatic technique which is based on the Trotter formula and on the combinatorial problem of graph edges colouring with (m + 1) colours. Expressions for K 1 (τ) and K 2 (τ) in terms of infinite series are found for a generic function F(vertical bar i - j vertical bar ) in the Gaussian orthogonal ensemble (GOE), the Gaussian unitary ensemble (GUE) and in the crossover between them (the almost unitary Gaussian ensemble). The Rosenzweig-Porter and power-law banded matrix ensembles are considered as examples
Self-assembly of orthogonal three-axis sensors
International Nuclear Information System (INIS)
Cho, J. H.; Hu, S.; Gracias, D. H.
2008-01-01
Conventional planar microfabrication is widely utilized to construct sensors for the measurement of physical or chemical properties. However, in these devices, the information component measured is typically restricted to only one vectorial axis. Here, we describe a self-assembling strategy that can be utilized to construct three dimensional (3D) cubic devices that facilitate measurement along three axes. This 3D measurement is achieved by arranging sensing elements orthogonally; any sensing element that can be lithographically patterned can be utilized. The 3D arrangement of sensors allows for the measurement of angular and orientation parameters. As an example, we describe a three-axis cantilever based sensor and demonstrate measurement of an evaporated analyte using resonant frequency shifts of cantilevers in each of the x, y, and z axes
q-analogue of the Krawtchouk and Meixner orthogonal polynomials
International Nuclear Information System (INIS)
Campigotto, C.; Smirnov, Yu.F.; Enikeev, S.G.
1993-06-01
The comparative analysis of Krawtchouk polynomials on a uniform grid with Wigner D-functions for the SU(2) group is presented. As a result the partnership between corresponding properties of the polynomials and D-functions is established giving the group-theoretical interpretation of the Krawtchouk polynomials properties. In order to extend such an analysis on the quantum groups SU q (2) and SU q (1,1), q-analogues of Krawtchouk and Meixner polynomials of a discrete variable are studied. The total set of characteristics of these polynomials is calculated, including the orthogonality condition, normalization factor, recurrent relation, the explicit analytic expression, the Rodrigues formula, the difference derivative formula and various particular cases and values. (R.P.) 22 refs.; 2 tabs
Orthogonal functions, discrete variable representation, and generalized gauss quadratures
DEFF Research Database (Denmark)
Schneider, B. I.; Nygaard, Nicolai
2002-01-01
in the original representation. This has been exploited in bound-state, scattering, and time-dependent problems using the so-called, discrete variable representation (DVR). At the core of this approach is the mathematical three-term recursion relationship satisfied by the classical orthogonal functions......, the distinction between spectral and grid approaches becomes blurred. In fact, the two approaches can be related by a similarity transformation. By the exploitation of this idea, calculations can be considerably simplified by removing the need to compute difficult matrix elements of the Hamiltonian...... functions, this is not the case. However, they may be computed in a stable numerical fashion, via the recursion. In essence, this is an application of the well-known Lanczos recursion approach. Once the recursion coefficients are known, it is possible to compute the points and weights of quadratures on...
Study of α-16O scattering by orthogonality condition models
International Nuclear Information System (INIS)
Breitschaft, A.M.; Canto, L.F.; Schechter, H.
1983-01-01
The use of approximate microscopic theories in α- 16 O scattering is investigated. The Orthogonality Condition Model (OCM) with both the direct potential of the Resonating Group Method (RMG) and with an effective local potential, V sub(eff), derived from Kernels of Generator Coordinate Method (GCM) is employed to study collisions at CM energies up to 30 MeV, for all relevant partial waves. Although the predictions of the OCM are consistent with 'exact' RGM results in both cases, the nuclear phase-shifts obtained with the effective potential are better. The presence of ambiguities in the derivation of V sub(eff) is noticed. The nature of such ambiguities is discussed. (Author) [pt
Study of α-16O scattering by orthogonality condition models
International Nuclear Information System (INIS)
Breitschaft, A.M.; Canto, L.F.; Schechter, H.
1982-01-01
The use of approximate microscopic theories in α- 16 O scattering is investigated. The Orthogonality Condition Model (OCM) with the direct potential of the Resonating Group Method (RGM) and with an effective local potential V sub(eff') derived from Kernels of the Generator Coordinate Method (GCM) is employed to study collisions at CM energies up to 30 MeV, for all relevant partial waves. Although the predictions of the OCM are consistent with 'exact' RGM results in both cases, the nuclear phase-shifts obtained with the effective potential are better. It is noticed the presence of ambiguities in the derivation of V sub(eff'). The nature of such ambiguities is discussed. (Author) [pt
Landmine detection using two-tapped joint orthogonal matching pursuits
Goldberg, Sean; Glenn, Taylor; Wilson, Joseph N.; Gader, Paul D.
2012-06-01
Joint Orthogonal Matching Pursuits (JOMP) is used here in the context of landmine detection using data obtained from an electromagnetic induction (EMI) sensor. The response from an object containing metal can be decomposed into a discrete spectrum of relaxation frequencies (DSRF) from which we construct a dictionary. A greedy iterative algorithm is proposed for computing successive residuals of a signal by subtracting away the highest matching dictionary element at each step. The nal condence of a particular signal is a combination of the reciprocal of this residual and the mean of the complex component. A two-tap approach comparing signals on opposite sides of the geometric location of the sensor is examined and found to produce better classication. It is found that using only a single pursuit does a comparable job, reducing complexity and allowing for real-time implementation in automated target recognition systems. JOMP is particularly highlighted in comparison with a previous EMI detection algorithm known as String Match.
Downlink scheduling using non-orthogonal uplink beams
Eltayeb, Mohammed E.
2014-04-01
Opportunistic schedulers rely on the feedback of the channel state information of users in order to perform user selection and downlink scheduling. This feedback increases with the number of users, and can lead to inefficient use of network resources and scheduling delays. We tackle the problem of feedback design, and propose a novel class of nonorthogonal codes to feed back channel state information. Users with favorable channel conditions simultaneously transmit their channel state information via non-orthogonal beams to the base station. The proposed formulation allows the base station to identify the strong users via a simple correlation process. After deriving the minimum required code length and closed-form expressions for the feedback load and downlink capacity, we show that i) the proposed algorithm reduces the feedback load while matching the achievable rate of full feedback algorithms operating over a noiseless feedback channel, and ii) the proposed codes are superior to the Gaussian codes.
Relativistic resonances as non-orthogonal states in Hilbert space
Blum, W
2003-01-01
We analyze the energy-momentum properties of relativistic short-lived particles with the result that they are characterized by two 4-vectors: in addition to the familiar energy-momentum vector (timelike) there is an energy-momentum 'spread vector' (spacelike). The wave functions in space and time for unstable particles are constructed. For the relativistic properties of unstable states we refer to Wigner's method of Poincare group representations that are induced by representations of the space-time translation and rotation groups. If stable particles, unstable particles and resonances are treated as elementary objects that are not fundamentally different one has to take into account that they will not generally be orthogonal to each other in their state space. The scalar product between a stable and an unstable state with otherwise identical properties is calculated in a particular Lorentz frame. The spin of an unstable particle is not infinitely sharp but has a 'spin spread' giving rise to 'spin neighbors'....
Orthogonally Evolved AI to Improve Difficulty Adjustment in Video Games
DEFF Research Database (Denmark)
Hintze, Arend; Olson, Randal; Lehman, Joel Anthony
2016-01-01
Computer games are most engaging when their difficulty is well matched to the player's ability, thereby providing an experience in which the player is neither overwhelmed nor bored. In games where the player interacts with computer-controlled opponents, the difficulty of the game can be adjusted...... not only by changing the distribution of opponents or game resources, but also through modifying the skill of the opponents. Applying evolutionary algorithms to evolve the artificial intelligence that controls opponent agents is one established method for adjusting opponent difficulty. Less-evolved agents...... (i.e. agents subject to fewer generations of evolution) make for easier opponents, while highly-evolved agents are more challenging to overcome. In this publication we test a new approach for difficulty adjustment in games: orthogonally evolved AI, where the player receives support from collaborating...
Downlink scheduling using non-orthogonal uplink beams
Eltayeb, Mohammed E.; Al-Naffouri, Tareq Y.; Bahrami, Hamid Reza Talesh
2014-01-01
Opportunistic schedulers rely on the feedback of the channel state information of users in order to perform user selection and downlink scheduling. This feedback increases with the number of users, and can lead to inefficient use of network resources and scheduling delays. We tackle the problem of feedback design, and propose a novel class of nonorthogonal codes to feed back channel state information. Users with favorable channel conditions simultaneously transmit their channel state information via non-orthogonal beams to the base station. The proposed formulation allows the base station to identify the strong users via a simple correlation process. After deriving the minimum required code length and closed-form expressions for the feedback load and downlink capacity, we show that i) the proposed algorithm reduces the feedback load while matching the achievable rate of full feedback algorithms operating over a noiseless feedback channel, and ii) the proposed codes are superior to the Gaussian codes.
International Nuclear Information System (INIS)
Nkemzi, B.
2005-10-01
Three-dimensional time-harmonic Maxwell's problems in axisymmetric domains Ω-circumflex with edges and conical points on the boundary are treated by means of the Fourier-finite-element method. The Fourier-fem combines the approximating Fourier series expansion of the solution with respect to the rotational angle using trigonometric polynomials of degree N (N → ∞), with the finite element approximation of the Fourier coefficients on the plane meridian domain Ω a is a subset of R + 2 of Ω-circumflex with mesh size h (h → 0). The singular behaviors of the Fourier coefficients near angular points of the domain Ω a are fully described by suitable singular functions and treated numerically by means of the singular function method with the finite element method on graded meshes. It is proved that the rate of convergence of the mixed approximations in H 1 (Ω-circumflex) 3 is of the order O (h+N -1 ) as known for the classical Fourier-finite-element approximation of problems with regular solutions. (author)
Radial expansion and multifragmentation
International Nuclear Information System (INIS)
Angelique, J.C.; Bizard, G.; Bougault, R.; Brou, R.; Buta, A.; Colin, J.; Cussol, D.; Durand, D.; Kerambrun, A.; Le Brun, C.; Lecolley, J.F.; Lopez, O.; Louvel, M.; Meslin, C.; Nakagawa, T.; Patry, J.P.; Peter, J.; Popescu, R.; Regimbart, R.; Steckmeyer, J.C.; Tamain, B.; Vient, E.; Yuasa-Nakagawa, K.; Wieloch, A.
1998-01-01
The light systems 36 Ar + 27 Al and 64 Zn + nat Ti were measured at several bombarding energies between ∼ 35 and 95 MeV/nucleon. It was found that the predominant part of the cross section is due to binary collisions. In this paper the focus is placed on the properties of the quasi-projectile nuclei. In the central collisions the excitation energies of the quasi-projectile reach values exceeding largely 10 MeV/nucleon. The slope of the high energy part of the distribution can give only an upper limit of the apparent temperature (the average temperature along the decay chain). The highly excited quasi-projectile may get rapidly fragmented rather than sequentially. The heavy fragments are excited and can emit light particles (n, p, d, t, 3 He, α,...) what perturbs additionally the spectrum of these particles. Concerning the expansion energy, one can determine the average kinetic energies of the product (in the quasi-projectile-framework) and compare with simulation values. To fit the experimental data an additional radial expansion energy is to be considered. The average expansion energy depends slightly on the impact parameter but it increases with E * / A, ranging from 0.4 to 1,2 MeV/nucleon for an excitation energy increasing from 7 to 10.5 MeV/nucleon. This collective radial energy seems to be independent of the fragment mass, what is possibly valid for the case of larger quasi-projectile masses. The origin of the expansion is to be determined. It may be due to a compression in the interaction zone at the initial stage of the collision, which propagates in the quasi-projectile and quasi-target, or else, may be due, simply, to the increase of thermal energy leading to a rapid fragment emission. The sequential de-excitation calculation overestimates light particle emission and consequently heavy residues, particularly, at higher excitation energies. This disagreement indicates that a sequential process can not account for the di-excitation of very hot nuclei
DEFF Research Database (Denmark)
Kolbæk, Ditte; Lundh Snis, Ulrika
Abstract: This paper analyses an online community of master’s students taking a course in ICT and organisational learning. The students initiated and facilitated an educational design for organisational learning called Proactive Review in the organisation where they are employed. By using an online...... discussion forum on Google groups, they created new ways of reflecting and learning. We used netnography to select qualitative postings from the online community and expansive learning concepts for data analysis. The findings show how students changed practices of organisational learning...
Load regulating expansion fixture
International Nuclear Information System (INIS)
Wagner, L.M.; Strum, M.J.
1998-01-01
A free standing self contained device for bonding ultra thin metallic films, such as 0.001 inch beryllium foils is disclosed. The device will regulate to a predetermined load for solid state bonding when heated to a bonding temperature. The device includes a load regulating feature, whereby the expansion stresses generated for bonding are regulated and self adjusting. The load regulator comprises a pair of friction isolators with a plurality of annealed copper members located there between. The device, with the load regulator, will adjust to and maintain a stress level needed to successfully and economically complete a leak tight bond without damaging thin foils or other delicate components. 1 fig
Orthogonal views improves localisation in bone scans of wrist
International Nuclear Information System (INIS)
Roth, A.L.
1997-01-01
Full text: Of all nuclear medicine studies, bone scans are the most fundamental. However, straightforward these may seem, there are always mechanisms that can be implemented which assist in a more precise diagnosis, particularly in areas with an intricate bone structure. An 18-year-old right-handed student presented to her doctor with a one month history of pain over the right distal radio-ulna joint area. Clinically, she had prominence of the right ulna, which suggested that there may have been a previous injury to the wrist. Also, pronation/supination were painful where there was swelling of the extensor carpi ulnaris tendon, as well as some discomfort with clicking in ulna deviation/rotation. The X-rays demonstrated some premature radial epiphysial closure. A bone scan was requested to attempt to localise the main inflammatory focus. The dynamic study was performed in the planar projection with an immediate blood pool for 300k being taken. These demonstrated a vascular blush medially. A medial blood pool image was acquired and it localised the abnormal vascularity as being dorsal. A separate focal area of less intense blood pooling was also noted in the line of the distal ulna. Delayed images showed increased uptake localised to the ulna styloid. Anatomically, the superficial vascular blush correlated with tenosynovitis. Hence, the orthogonal initial and delayed images were definitive in the diagnoses of tenosynovitis of the extensor carpi ulnaris tendon. This clearly complements the information provided by the palmar view. However, it is important to remember that an increased radiation dose to the technologist is incurred as a result of the extra orthogonal view, hence attention to technique is imperative
Orthogonal views improves localisation in bone scans of wrist
Energy Technology Data Exchange (ETDEWEB)
Roth, A.L.
1997-09-01
Full text: Of all nuclear medicine studies, bone scans are the most fundamental. However, straightforward these may seem, there are always mechanisms that can be implemented which assist in a more precise diagnosis, particularly in areas with an intricate bone structure. An 18-year-old right-handed student presented to her doctor with a one month history of pain over the right distal radio-ulna joint area. Clinically, she had prominence of the right ulna, which suggested that there may have been a previous injury to the wrist. Also, pronation/supination were painful where there was swelling of the extensor carpi ulnaris tendon, as well as some discomfort with clicking in ulna deviation/rotation. The X-rays demonstrated some premature radial epiphysial closure. A bone scan was requested to attempt to localise the main inflammatory focus. The dynamic study was performed in the planar projection with an immediate blood pool for 300k being taken. These demonstrated a vascular blush medially. A medial blood pool image was acquired and it localised the abnormal vascularity as being dorsal. A separate focal area of less intense blood pooling was also noted in the line of the distal ulna. Delayed images showed increased uptake localised to the ulna styloid. Anatomically, the superficial vascular blush correlated with tenosynovitis. Hence, the orthogonal initial and delayed images were definitive in the diagnoses of tenosynovitis of the extensor carpi ulnaris tendon. This clearly complements the information provided by the palmar view. However, it is important to remember that an increased radiation dose to the technologist is incurred as a result of the extra orthogonal view, hence attention to technique is imperative.
Automatic Fourier transform and self-Fourier beams due to parabolic potential
Energy Technology Data Exchange (ETDEWEB)
Zhang, Yiqi, E-mail: zhangyiqi@mail.xjtu.edu.cn [Key Laboratory for Physical Electronics and Devices of the Ministry of Education & Shaanxi Key Lab of Information Photonic Technique, Xi’an Jiaotong University, Xi’an 710049 (China); Liu, Xing [Key Laboratory for Physical Electronics and Devices of the Ministry of Education & Shaanxi Key Lab of Information Photonic Technique, Xi’an Jiaotong University, Xi’an 710049 (China); Belić, Milivoj R., E-mail: milivoj.belic@qatar.tamu.edu [Science Program, Texas A& M University at Qatar, P.O. Box 23874 Doha (Qatar); Zhong, Weiping [Department of Electronic and Information Engineering, Shunde Polytechnic, Shunde 528300 (China); Petrović, Milan S. [Institute of Physics, P.O. Box 68, 11001 Belgrade (Serbia); Zhang, Yanpeng, E-mail: ypzhang@mail.xjtu.edu.cn [Key Laboratory for Physical Electronics and Devices of the Ministry of Education & Shaanxi Key Lab of Information Photonic Technique, Xi’an Jiaotong University, Xi’an 710049 (China)
2015-12-15
We investigate the propagation of light beams including Hermite–Gauss, Bessel–Gauss and finite energy Airy beams in a linear medium with parabolic potential. Expectedly, the beams undergo oscillation during propagation, but quite unexpectedly they also perform automatic Fourier transform, that is, periodic change from the beam to its Fourier transform and back. In addition to oscillation, the finite-energy Airy beams exhibit periodic inversion during propagation. The oscillating period of parity-asymmetric beams is twice that of the parity-symmetric beams. Based on the propagation in parabolic potential, we introduce a class of optically-interesting beams that are self-Fourier beams—that is, the beams whose Fourier transforms are the beams themselves.
Energy Technology Data Exchange (ETDEWEB)
Sanginés, R., E-mail: roberto.sangines@ccadet.unam.mx; Sobral, H.
2013-10-01
The evolution of laser induced ablation plume on aluminum targets has been investigated in orthogonal pre-ablation double pulse scheme at atmospheric pressure from the earliest stages of plasma evolution. Time-resolved emission spectra from neutrals, singly- and doubly-ionized species obtained with the double pulse experiment have been compared with those from the single pulse configuration. Signal-to-noise enhancement reaches values of up to 15 depending on the analyzed species; and the lower the charge state the later its maximum signal-to-noise ratio is reached. Ablation plume dynamics was monitored from 10 ns after the plasma onset via shadowgraphy and fast-photography with narrow interference filters to follow the evolution of individual species. Results show that ionic species from the target are located at the plasma core while nitrogen from the background air is found at the plume peripheral. Initially both configurations exhibit similar ablation plume sizes and their expansions were successfully fitted with the strong explosion model for the first 500 ns. At later times a good agreement was obtained by using the drag model, which predicts that the plume expansion eventually stops due to interaction with the background gas particles. The emission enhancement measured in the double pulse scheme is discussed in terms of the models describing the plume dynamics. - Highlights: • Production of 2 + ions at the earliest stages of plasma evolution • The higher the charge state the inner the location within the ablation plume. • The expansion rate of the second (ablation) plume was measured. • Shock and drag models successfully fit the ablation shock front expansion.
Tutorial on Fourier space coverage for scattering experiments, with application to SAR
Deming, Ross W.
2010-04-01
The Fourier Diffraction Theorem relates the data measured during electromagnetic, optical, or acoustic scattering experiments to the spatial Fourier transform of the object under test. The theorem is well-known, but since it is based on integral equations and complicated mathematical expansions, the typical derivation may be difficult for the non-specialist. In this paper, the theorem is derived and presented using simple geometry, plus undergraduatelevel physics and mathematics. For practitioners of synthetic aperture radar (SAR) imaging, the theorem is important to understand because it leads to a simple geometric and graphical understanding of image resolution and sampling requirements, and how they are affected by radar system parameters and experimental geometry. Also, the theorem can be used as a starting point for imaging algorithms and motion compensation methods. Several examples are given in this paper for realistic scenarios.
Thermal expansion of granite rocks
International Nuclear Information System (INIS)
Stephansson, O.
1978-04-01
The thermal expansion of rocks is strongly controlled by the thermal expansion of the minerals. The theoretical thermal expansion of the Stripa Granite is gound to be 21 . 10 -6 [deg C] -1 at 25 deg C and 38 . 10 -6 [deg C] -1 at 400 deg C. The difference in expansion for the rock forming minerals causes micro cracking at heating. The expansion due to micro cracks is found to be of the same order as the mineral expansion. Most of the micro cracks will close at pressures of the order of 10 - 20 MPa. The thermal expansion of a rock mass including the effect of joints is determined in the pilot heater test in the Stripa Mine
Energy Technology Data Exchange (ETDEWEB)
Froschauer, K J
1993-01-01
A study of the development of five provincial hydroelectric utilities in Canada indicates that power companies and the state invited manufacturers to use hydroelectricity and natural resources in order to diversify provincial economies. These hydro expansions also show that utilities and government designed hydro projects to serve continental requirements; serving both objectives became problematic. It is argued that when the Canadian state and firms such as utilities use hydro expansions to serve both continentalism and industrialization, then at best they foster dependent industrialization and staple processing. At worst, they overbuild the infrastructure to generate provincial surplus energy for continental, rather than national, integration. Hydro developments became subject to state intervention in Canada mainly through the failures of private utilities to provide power for the less-lucrative industrial markets within provincial subregions. Although the state and utilities invited foreign firms to manufacture hydro equipment within the provinces and others to use electricity to diversify production beyond resource processing, such a diversification did not occur. Since 1962, ca 80% of industrial energy was used to semi-process wood-derived products, chemicals, and metals. The idea for a national power network became undermined by interprovincial political-economic factors and since 1963, the federal national/continential power policy prevailed. 187 refs., 6 figs., 52 tabs.
International Nuclear Information System (INIS)
Vogeleer, J. P.
1985-01-01
The expansion of the primary tubes or sleeves of the steam generator of a nuclear reactor plant are measured while the tubes or sleeves are being expanded. A primary tube or sleeve is expanded by high pressure of water which flows through a channel in an expander body. The water is supplied through an elongated conductor and is introduced through a connector on the shank connected to the conductor at its outer end. A wire extends through the mandrel and through the conductor to the end of the connector. At its inner end the wire is connected to a tapered pin which is subject to counteracting forces produced by the pressure of the water. The force on the side where the wire is connected to the conductor is smaller than on the opposite side. The tapered pin is moved in the direction of the higher force and extrudes the wire outwardly of the conductor. The tapered surface of the tapered pin engages transverse captive plungers which are maintained in engagement with the expanding tube or sleeve as they are moved outwardly by the tapered pin. The wire and the connector extend out of the generator and, at its outer end, the wire is connected to an indicator which measures the extent to which the wire is moved by the tapered pin, thus measuring the expansion of the tube or sleeve as it progresses
Fourier analysis: from cloaking to imaging
Wu, Kedi; Cheng, Qiluan; Wang, Guo Ping
2016-04-01
Regarding invisibility cloaks as an optical imaging system, we present a Fourier approach to analytically unify both Pendry cloaks and complementary media-based invisibility cloaks into one kind of cloak. By synthesizing different transfer functions, we can construct different devices to realize a series of interesting functions such as hiding objects (events), creating illusions, and performing perfect imaging. In this article, we give a brief review on recent works of applying Fourier approach to analysis invisibility cloaks and optical imaging through scattering layers. We show that, to construct devices to conceal an object, no constructive materials with extreme properties are required, making most, if not all, of the above functions realizable by using naturally occurring materials. As instances, we experimentally verify a method of directionally hiding distant objects and create illusions by using all-dielectric materials, and further demonstrate a non-invasive method of imaging objects completely hidden by scattering layers.
Fourier analysis: from cloaking to imaging
International Nuclear Information System (INIS)
Wu, Kedi; Ping Wang, Guo; Cheng, Qiluan
2016-01-01
Regarding invisibility cloaks as an optical imaging system, we present a Fourier approach to analytically unify both Pendry cloaks and complementary media-based invisibility cloaks into one kind of cloak. By synthesizing different transfer functions, we can construct different devices to realize a series of interesting functions such as hiding objects (events), creating illusions, and performing perfect imaging. In this article, we give a brief review on recent works of applying Fourier approach to analysis invisibility cloaks and optical imaging through scattering layers. We show that, to construct devices to conceal an object, no constructive materials with extreme properties are required, making most, if not all, of the above functions realizable by using naturally occurring materials. As instances, we experimentally verify a method of directionally hiding distant objects and create illusions by using all-dielectric materials, and further demonstrate a non-invasive method of imaging objects completely hidden by scattering layers. (review)
Multichannel Dynamic Fourier-Transform IR Spectrometer
Balashov, A. A.; Vaguine, V. A.; Golyak, Il. S.; Morozov, A. N.; Khorokhorin, A. I.
2017-09-01
A design of a multichannel continuous scan Fourier-transform IR spectrometer for simultaneous recording and analysis of the spectral characteristics of several objects is proposed. For implementing the design, a multi-probe fiber is used, constructed from several optical fibers connected into a single optical connector and attached at the output of the interferometer. The Fourier-transform spectrometer is used as a signal modulator. Each fiber is individually mated with an investigated sample and a dedicated radiation detector. For the developed system, the radiation intensity of the spectrometer is calculated from the condition of the minimum spectral resolution and parameters of the optical fibers. Using the proposed design, emission spectra of a gas-discharge neon lamp have been recorded using a single fiber 1 mm in diameter with a numerical aperture NA = 0.22.
Discrete Fourier transform in nanostructures using scattering
International Nuclear Information System (INIS)
Leuenberger, Michael N.; Flatte, Michael E.; Loss, Daniel; Awschalom, D.D.
2004-01-01
In this article, we show that the discrete Fourier transform (DFT) can be performed by scattering a coherent particle or laser beam off an electrically controllable two-dimensional (2D) potential that has the shape of rings or peaks. After encoding the initial vector into the two-dimensional potential by means of electric gates, the Fourier-transformed vector can be read out by detectors surrounding the potential. The wavelength of the laser beam determines the necessary accuracy of the 2D potential, which makes our method very fault-tolerant. Since the time to perform the DFT is much smaller than the clock cycle of today's computers, our proposed device performs DFTs at the frequency of the computer clock speed
The PROSAIC Laplace and Fourier Transform
International Nuclear Information System (INIS)
Smith, G.A.
1994-01-01
Integral Transform methods play an extremely important role in many branches of science and engineering. The ease with which many problems may be solved using these techniques is well known. In Electrical Engineering especially, Laplace and Fourier Transforms have been used for a long time as a way to change the solution of differential equations into trivial algebraic manipulations or to provide alternate representations of signals and data. These techniques, while seemingly overshadowed by today's emphasis on digital analysis, still form an invaluable basis in the understanding of systems and circuits. A firm grasp of the practical aspects of these subjects provides valuable conceptual tools. This tutorial paper is a review of Laplace and Fourier Transforms from an applied perspective with an emphasis on engineering applications. The interrelationship of the time and frequency domains will be stressed, in an attempt to comfort those who, after living so much of their lives in the time domain, find thinking in the frequency domain disquieting
Fourier transform of momentum distribution in vanadium
International Nuclear Information System (INIS)
Singh, A.K.; Manuel, A.A.; Peter, M.; Singru, R.M.
1985-01-01
Experimental Compton profile and 2D-angular correlation of positron annihilation radiation data from vanadium are analyzed by the mean of their Fourier transform. They are compared with the functions calculated with the help of both the linear muffin-tin orbital and the Hubbard-Mijnarends band structure methods. The results show that the functions are influenced by the positron wave function, by the e + -e - many-body correlations and by the differences in the electron wave functions used for the band structure calculations. It is concluded that Fourier analysis is a sensitive approach to investigate the momentum distributions in transition metals and to understnad the effects of the positron. (Auth.)
Correcting sample drift using Fourier harmonics.
Bárcena-González, G; Guerrero-Lebrero, M P; Guerrero, E; Reyes, D F; Braza, V; Yañez, A; Nuñez-Moraleda, B; González, D; Galindo, P L
2018-07-01
During image acquisition of crystalline materials by high-resolution scanning transmission electron microscopy, the sample drift could lead to distortions and shears that hinder their quantitative analysis and characterization. In order to measure and correct this effect, several authors have proposed different methodologies making use of series of images. In this work, we introduce a methodology to determine the drift angle via Fourier analysis by using a single image based on the measurements between the angles of the second Fourier harmonics in different quadrants. Two different approaches, that are independent of the angle of acquisition of the image, are evaluated. In addition, our results demonstrate that the determination of the drift angle is more accurate by using the measurements of non-consecutive quadrants when the angle of acquisition is an odd multiple of 45°. Copyright © 2018 Elsevier Ltd. All rights reserved.
FPGA Implementation of Real-Time Compressive Sensing with Partial Fourier Dictionary
Directory of Open Access Journals (Sweden)
Yinghui Quan
2016-01-01
Full Text Available This paper presents a novel real-time compressive sensing (CS reconstruction which employs high density field-programmable gate array (FPGA for hardware acceleration. Traditionally, CS can be implemented using a high-level computer language in a personal computer (PC or multicore platforms, such as graphics processing units (GPUs and Digital Signal Processors (DSPs. However, reconstruction algorithms are computing demanding and software implementation of these algorithms is extremely slow and power consuming. In this paper, the orthogonal matching pursuit (OMP algorithm is refined to solve the sparse decomposition optimization for partial Fourier dictionary, which is always adopted in radar imaging and detection application. OMP reconstruction can be divided into two main stages: optimization which finds the closely correlated vectors and least square problem. For large scale dictionary, the implementation of correlation is time consuming since it often requires a large number of matrix multiplications. Also solving the least square problem always needs a scalable matrix decomposition operation. To solve these problems efficiently, the correlation optimization is implemented by fast Fourier transform (FFT and the large scale least square problem is implemented by Conjugate Gradient (CG technique, respectively. The proposed method is verified by FPGA (Xilinx Virtex-7 XC7VX690T realization, revealing its effectiveness in real-time applications.
Fourier evaluation of broad Moessbauer spectra
International Nuclear Information System (INIS)
Vincze, I.
1981-01-01
It is shown by the Fourier analysis of broad Moessbauer spectra that the even part of the distribution of the dominant hyperfine interaction (hyperfine field or quadrupole splitting) can be obtained directly without using least-square fitting procedures. Also the odd part of this distribution correlated with other hyperfine parameters (e.g. isomer shift) can be directly determined. Examples for amorphous magnetic and paramagnetic iron-based alloys are presented. (author)
Fourier evaluation of broad Moessbauer spectra
International Nuclear Information System (INIS)
Vincze, I.
1981-09-01
It is shown by the Fourier analysis of broad Moessbauer spectra that the even part of the distribution of the dominant hyperfine interaction (hyperfine field or quadrupole splitting) can be obtained directly without using least-square fitting procedures. Also the odd part of this distribution correlated with other hyperfine parameters (e.g. isomer shift) can be directly determined. Examples covering the case of amorphous magnetic and paramagnetic iron-based alloys are presented. (author)
Quantum Fourier Transform Over Galois Rings
Zhang, Yong
2009-01-01
Galois rings are regarded as "building blocks" of a finite commutative ring with identity. There have been many papers on classical error correction codes over Galois rings published. As an important warm-up before exploring quantum algorithms and quantum error correction codes over Galois rings, we study the quantum Fourier transform (QFT) over Galois rings and prove it can be efficiently preformed on a quantum computer. The properties of the QFT over Galois rings lead to the quantum algorit...
Fourier Transform Spectrometer Controller for Partitioned Architectures
DEFF Research Database (Denmark)
Tamas-Selicean, Domitian; Keymeulen, D.; Berisford, D.
2013-01-01
The current trend in spacecraft computing is to integrate applications of different criticality levels on the same platform using no separation. This approach increases the complexity of the development, verification and integration processes, with an impact on the whole system life cycle. Resear......, such as avionics and automotive. In this paper we investigate the challenges of developing and the benefits of integrating a scientific instrument, namely a Fourier Transform Spectrometer, in such a partitioned architecture....
A Fourier analysis of extreme events
DEFF Research Database (Denmark)
Mikosch, Thomas Valentin; Zhao, Yuwei
2014-01-01
The extremogram is an asymptotic correlogram for extreme events constructed from a regularly varying stationary sequence. In this paper, we define a frequency domain analog of the correlogram: a periodogram generated from a suitable sequence of indicator functions of rare events. We derive basic ...... properties of the periodogram such as the asymptotic independence at the Fourier frequencies and use this property to show that weighted versions of the periodogram are consistent estimators of a spectral density derived from the extremogram....
Fourier transform resampling: Theory and application
International Nuclear Information System (INIS)
Hawkins, W.G.
1996-01-01
One of the most challenging problems in medical imaging is the development of reconstruction algorithms for nonstandard geometries. This work focuses on the application of Fourier analysis to the problem of resampling or rebinning. Conventional resampling methods utilizing some form of interpolation almost always result in a loss of resolution in the tomographic image. Fourier Transform Resampling (FTRS) offers potential improvement because the Modulation Transfer Function (MTF) of the process behaves like an ideal low pass filter. The MTF, however, is nonstationary if the coordinate transformation is nonlinear. FTRS may be viewed as a generalization of the linear coordinate transformations of standard Fourier analysis. Simulated MTF's were obtained by projecting point sources at different transverse positions in the flat fan beam detector geometry. These MTF's were compared to the closed form expression for FIRS. Excellent agreement was obtained for frequencies at or below the estimated cutoff frequency. The resulting FTRS algorithm is applied to simulations with symmetric fan beam geometry, an elliptical orbit and uniform attenuation, with a normalized root mean square error (NRME) of 0.036. Also, a Tc-99m point source study (1 cm dia., placed in air 10 cm from the COR) for a circular fan beam acquisition was reconstructed with a hybrid resampling method. The FWHM of the hybrid resampling method was 11.28 mm and compares favorably with a direct reconstruction (FWHM: 11.03 mm)
Sets of Fourier coefficients using numerical quadrature
International Nuclear Information System (INIS)
Lyness, J. N.
2001-01-01
One approach to the calculation of Fourier trigonometric coefficients f(r) of a given function f(x) is to apply the trapezoidal quadrature rule to the integral representation f(r)=(line i ntegral)(sub 0)(sup 1) f(x)e(sup -2(pi)irx)dx. Some of the difficulties in this approach are discussed. A possible way of overcoming many of these is by means of a subtraction function. Thus, one sets f(x)= h(sub p-1)(x)+ g(sub p)(x), where h(sub -1)(x) is an algebraic polynomial of degree p-1, specified in such a way that the Fourier series of g(sub p)(x) converges more rapidly than that of f(x). To obtain the Fourier coefficients of f(x), one uses an analytic expression for those of h(sub p-1)(x) and numerical quadrature to approximately those of g(sub p)(x)
The derivative-free Fourier shell identity for photoacoustics.
Baddour, Natalie
2016-01-01
In X-ray tomography, the Fourier slice theorem provides a relationship between the Fourier components of the object being imaged and the measured projection data. The Fourier slice theorem is the basis for X-ray Fourier-based tomographic inversion techniques. A similar relationship, referred to as the 'Fourier shell identity' has been previously derived for photoacoustic applications. However, this identity relates the pressure wavefield data function and its normal derivative measured on an arbitrary enclosing aperture to the three-dimensional Fourier transform of the enclosed object evaluated on a sphere. Since the normal derivative of pressure is not normally measured, the applicability of the formulation is limited in this form. In this paper, alternative derivations of the Fourier shell identity in 1D, 2D polar and 3D spherical polar coordinates are presented. The presented formulations do not require the normal derivative of pressure, thereby lending the formulas directly adaptable for Fourier based absorber reconstructions.
Thermal expansion of coking coals
Energy Technology Data Exchange (ETDEWEB)
Orlik, M.; Klimek, J. (Vyzkumny a Zkusebni Ustav Nova Hut, Ostrava (Czechoslovakia))
1992-12-01
Analyzes expansion of coal mixtures in coke ovens during coking. Methods for measuring coal expansion on both a laboratory and pilot plant scale are comparatively evaluated. The method, developed, tested and patented in Poland by the Institute for Chemical Coal Processing in Zabrze (Polish standard PN-73/G-04522), is discussed. A laboratory device developed by the Institute for measuring coal expansion is characterized. Expansion of black coal from 10 underground mines in the Ostrava-Karvina coal district and from 9 coal mines in the Upper Silesia basin in Poland is comparatively evaluated. Investigations show that coal expansion reaches a maximum for coal types with a volatile matter ranging from 20 to 25%. With increasing volatile matter in coal, its expansion decreases. Coal expansion increases with increasing swelling index. Coal expansion corresponds with coal dilatation. With increasing coal density its expansion increases. Coal mixtures should be selected in such a way that their expansion does not cause a pressure exceeding 40 MPa. 11 refs.
On sets of convergence and divergence of multiple orthogonal series
International Nuclear Information System (INIS)
D'yachenko, M I; Kazaryan, K S
2002-01-01
Multiple Fourier series with respect to uniformly bounded orthonormal systems (ONSs) are studied. The following results are obtained. Theorem 1. Let Φ={φ n (x)} n=1 ∞ be a complete orthonormal system on [0,1] that is uniformly bounded by M on this interval, assume that m≥2, and let Φ(m)={φ n (x)} nelement ofN m , where φ n (n)=φ n 1 (x 1 )...φ n m (x m ). Then there exists a function f(x) element of L([0,1] m ) cubically diverges on some measurable subset H of [0,1] m with μ m (H)≥1-(1-1/M 2 ) m . Theorem 3. For M>1 and an integer m≥2 let E be an arbitrary measurable subset of [0,1] such that μ(E)=1-1/M 2 . Then there exists a complete orthonormal system Φ on [0,1] uniformly bounded by M there such that the multiple Fourier series of each function f(x) element of L([0,1] m ) with respect to the product system Φ(m) cubically converges to f(x) a.e. on E m . Definitive results in this direction are established also for incomplete uniformly bounded ONSs
Identity Expansion and Transcendence
Directory of Open Access Journals (Sweden)
William Sims Bainbridge
2014-05-01
Full Text Available Emerging developments in communications and computing technology may transform the nature of human identity, in the process rendering obsolete the traditional philosophical and scientific frameworks for understanding the nature of individuals and groups. Progress toward an evaluation of this possibility and an appropriate conceptual basis for analyzing it may be derived from two very different but ultimately connected social movements that promote this radical change. One is the governmentally supported exploration of Converging Technologies, based in the unification of nanoscience, biology, information science and cognitive science (NBIC. The other is the Transhumanist movement, which has been criticized as excessively radical yet is primarily conducted as a dignified intellectual discussion within a new school of philosophy about human enhancement. Together, NBIC and Transhumanism suggest the immense transformative power of today’s technologies, through which individuals may explore multiple identities by means of online avatars, semi-autonomous intelligent agents, and other identity expansions.
Representations for the extreme zeros of orthogonal polynomials (vol 233, pg 847, 2009)
van Doorn, Erik A.; van Foreest, Nicky D.; Zeifman, Alexander I.
2013-01-01
We correct representations for the endpoints of the true interval of orthogonality of a sequence of orthogonal polynomials that were stated by us in the Journal of Computational and Applied Mathematics 233 (2009) 847-851. (c) 2013 Elsevier B.V. All rights reserved.
A note on the zeros of Freud-Sobolev orthogonal polynomials
Moreno-Balcazar, Juan J.
2007-10-01
We prove that the zeros of a certain family of Sobolev orthogonal polynomials involving the Freud weight function e-x4 on are real, simple, and interlace with the zeros of the Freud polynomials, i.e., those polynomials orthogonal with respect to the weight function e-x4. Some numerical examples are shown.
Bio-inspired supramolecular materials by orthogonal self-assembly of hydrogelators and phospholipids
Boekhoven, J.; Brizard, AMA; Stuart, M. C A; Florusse, L.J.; Raffy, G.; Del Guerzo, A.; van Esch, J.H.
2016-01-01
The orthogonal self-assembly of multiple components is a powerful strategy towards the formation of complex biomimetic architectures, but so far the rules for designing such systems are unclear. Here we show how to identify orthogonal self-assembly at the supramolecular level and describe
Aspects of Orthogonality in the Development of the National Digital Wealth (NDW
Directory of Open Access Journals (Sweden)
Ion IVAN
2014-01-01
Full Text Available There are presented aspects of orthogonality in the development of the national digital wealth. There is presented the concept of NDW. Are identified quality characteristics. Are built orthogonality metrics for software development applications which are parts of NDW.
2017-10-01
AWARD NUMBER: W81XWH-16-1-0595 TITLE: Prostate-Specific Membrane Antigen (PSMA) Targeted Bio -orthogonal Therapy for Metastatic Prostate Cancer...Sep 2016 - 14 Sep 2017 4. TITLE AND SUBTITLE Prostate-Specific Membrane Antigen (PSMA) Targeted Bio -orthogonal Therapy for Metastatic Prostate
Fourier spectral simulations for wake fields in conducting cavities
International Nuclear Information System (INIS)
Min, M.; Chin, Y.-H.; Fischer, P.F.; Chae, Y.-Chul; Kim, K.-J.
2007-01-01
We investigate Fourier spectral time-domain simulations applied to wake field calculations in two-dimensional cylindrical structures. The scheme involves second-order explicit leap-frogging in time and Fourier spectral approximation in space, which is obtained from simply replacing the spatial differentiation operator of the YEE scheme by the Fourier differentiation operator on nonstaggered grids. This is a first step toward investigating high-order computational techniques with the Fourier spectral method, which is relatively simple to implement.
A Note on Fourier and the Greenhouse Effect
Postma, Joseph E.
2015-01-01
Joseph Fourier's discovery of the greenhouse effect is discussed and is compared to the modern conception of the greenhouse effect. It is confirmed that what Fourier discovered is analogous to the modern concept of the greenhouse effect. However, the modern concept of the greenhouse effect is found to be based on a paradoxical analogy to Fourier's greenhouse work and so either Fourier's greenhouse work, the modern conception of the greenhouse effect, or the modern definition of heat is incorr...
International Nuclear Information System (INIS)
Cristoforetti, G.; Legnaioli, S.; Pardini, L.; Palleschi, V.; Salvetti, A.; Tognoni, E.
2006-01-01
This work focuses on the study of the plumes obtained in the double pulse orthogonal Laser Induced Breakdown Spectroscopy (LIBS) in the pre-ablation configuration using both spectroscopic and shadowgraphic approaches. Single and double pulse LIBS experiments were carried out on a brass sample in air. Both the distance of the air plasma from the target surface and the interpulse delay were varied (respectively in the range 0.1-4.2 mm and up to 50 μs) revealing a significant variation of the plasma emission and of the plume-shock wave dynamical expansion in different cases. The intensity of both atomic and ionized zinc lines was measured in all the cases, allowing the calculation of the spatially averaged temperature and electron density and an estimation of the ablated mass. The line intensities and the thermodynamic parameters obtained by the spectroscopic measurements were discussed bearing in mind the dynamical expansion characteristics obtained from the shadowgraphic approach. All the data seem to be consistent with the model previously proposed for the double pulse collinear configuration where the line enhancement is mainly attributed to the ambient gas rarefaction produced by the first laser pulse, which causes a less effective shielding of the second laser pulse
DEFF Research Database (Denmark)
Taghizadeh, Alireza; Mørk, Jesper; Chung, Il-Sug
2016-01-01
We explore the use of a modal expansion technique, Fourier modal method (FMM), for investigating the optical properties of vertical cavities employing high-contrast gratings (HCGs). Three techniques for determining the resonance frequency and quality factor (Q-factor) of a cavity mode are compared......, the scattering losses of several HCG-based vertical cavities with inplane heterostructures which have promising prospects for fundamental physics studies and on-chip laser applications, are investigated. This type of parametric study of 3D structures would be numerically very demanding using spatial...
A time-dependent semiclassical wavepacket method using a fast Fourier transform (FFT) algorithm
International Nuclear Information System (INIS)
Gauss, J.; Heller, E.J.
1991-01-01
A new semiclassical propagator based on a local expansion of the potential up to second order around the moving center of the wavepackt is proposed. Formulas for the propagator are derived and the implementation using grid and fast Fourier transform (FFT) methods is discussed. The semiclassical propagator can be improved up to the exact quantum mechanical limit by including anharmonic corrections using a split operator approach. Preliminary applications to the CH 3 I photodissociation problem show the applicability and accuracy of the proposed method. (orig.)D
Modeling cavities exhibiting strong lateral confinement using open geometry Fourier modal method
DEFF Research Database (Denmark)
Häyrynen, Teppo; Gregersen, Niels
2016-01-01
We have developed a computationally eﬃcient Fourier-Bessel expansion based open geometry formalism for modeling the optical properties of rotationally symmetric photonic nanostructures. The lateral computation domain is assumed inﬁnite so that no artiﬁcial boundary conditions are needed. Instead,...... around a geometry speciﬁc dominant transverse wavenumber region. We will use the developed approach to investigate the Q factor and mode conﬁnement in cavities where top DBR mirror has small rectangular defect conﬁning the modes laterally on the defect region....
Response of multiferroic composites inferred from a fast-Fourier-transform-based numerical scheme
International Nuclear Information System (INIS)
Brenner, Renald; Bravo-Castillero, Julián
2010-01-01
The effective response and the local fields within periodic magneto-electric multiferroic composites are investigated by means of a numerical scheme based on fast Fourier transforms. This computational framework relies on the iterative resolution of coupled series expansions for the magnetic, electric and strain fields. By using an augmented Lagrangian formulation, a simple and robust procedure which makes use of the uncoupled Green operators for the elastic, electrostatics and magnetostatics problems is proposed. Its accuracy is assessed in the cases of laminated and fibrous two-phase composites for which analytical solutions exist
PCT Uncertainty Analysis Using Unscented Transform with Random Orthogonal Matrix
Energy Technology Data Exchange (ETDEWEB)
Fynana, Douglas A.; Ahn, Kwang-Il [KAERI, Daejeon (Korea, Republic of); Lee, John C. [Univ. of Michigan, Michigan (United States)
2015-05-15
Most Best Estimate Plus Uncertainty (BEPU) methods employ nonparametric order statistics through Wilks' formula to quantify uncertainties of best estimate simulations of nuclear power plant (NPP) transients. 95%/95% limits, the 95''t{sup h} percentile at a 95% confidence level, are obtained by randomly sampling all uncertainty contributors through conventional Monte Carlo (MC). Advantages are simple implementation of MC sampling of input probability density functions (pdfs) and limited computational expense of 1''s{sup t}, 2''n{sup d}, and 3''r{sup d} order Wilks' formula requiring only 59, 93, or 124 simulations, respectively. A disadvantage of small sample size is large sample to sample variation of statistical estimators. This paper presents a new efficient sampling based algorithm for accurate estimation of mean and variance of the output parameter pdf. The algorithm combines a deterministic sampling method, the unscented transform (UT), with random sampling through the generation of a random orthogonal matrix (ROM). The UT guarantees the mean, covariance, and 3''r{sup d} order moments of the multivariate input parameter distributions are exactly preserved by the sampled input points and the orthogonal transformation of the points by a ROM guarantees the sample error of all 4''t{sup h} order and higher moments are unbiased. The UT with ROM algorithm is applied to the uncertainty quantification of the peak clad temperature (PCT) during a large break loss-of-coolant accident (LBLOCA) in an OPR1000 NPP to demonstrate the applicability of the new algorithm to BEPU. This paper presented a new algorithm combining the UT with ROM for efficient multivariate parameter sampling that ensures sample input covariance and 3''r{sup d} order moments are exactly preserved and 4''th moment errors are small and unbiased. The advantageous sample properties guarantee higher order accuracy and
Some Applications of Fourier's Great Discovery for Beginners
Kraftmakher, Yaakov
2012-01-01
Nearly two centuries ago, Fourier discovered that any periodic function of period T can be presented as a sum of sine waveforms of frequencies equal to an integer times the fundamental frequency [omega] = 2[pi]/T (Fourier's series). It is impossible to overestimate the importance of Fourier's discovery, and all physics or engineering students…
Fourier Transforms Simplified: Computing an Infrared Spectrum from an Interferogram
Hanley, Quentin S.
2012-01-01
Fourier transforms are used widely in chemistry and allied sciences. Examples include infrared, nuclear magnetic resonance, and mass spectroscopies. A thorough understanding of Fourier methods assists the understanding of microscopy, X-ray diffraction, and diffraction gratings. The theory of Fourier transforms has been presented in this "Journal",…
Orthogonal optimization of a water hydraulic pilot-operated pressure-reducing valve
Mao, Xuyao; Wu, Chao; Li, Bin; Wu, Di
2017-12-01
In order to optimize the comprehensive characteristics of a water hydraulic pilot-operated pressure-reducing valve, numerical orthogonal experimental design was adopted. Six parameters of the valve, containing diameters of damping plugs, volume of spring chamber, half cone angle of main spool, half cone angle of pilot spool, mass of main spool and diameter of main spool, were selected as the orthogonal factors, and each factor has five different levels. An index of flowrate stability, pressure stability and pressure overstrike stability (iFPOS) was used to judge the merit of each orthogonal attempt. Embedded orthogonal process turned up and a final optimal combination of these parameters was obtained after totally 50 numerical orthogonal experiments. iFPOS could be low to a fairly low value which meant that the valve could have much better stabilities. During the optimization, it was also found the diameters of damping plugs and main spool played important roles in stability characteristics of the valve.
Compressive sampling of polynomial chaos expansions: Convergence analysis and sampling strategies
International Nuclear Information System (INIS)
Hampton, Jerrad; Doostan, Alireza
2015-01-01
Sampling orthogonal polynomial bases via Monte Carlo is of interest for uncertainty quantification of models with random inputs, using Polynomial Chaos (PC) expansions. It is known that bounding a probabilistic parameter, referred to as coherence, yields a bound on the number of samples necessary to identify coefficients in a sparse PC expansion via solution to an ℓ 1 -minimization problem. Utilizing results for orthogonal polynomials, we bound the coherence parameter for polynomials of Hermite and Legendre type under their respective natural sampling distribution. In both polynomial bases we identify an importance sampling distribution which yields a bound with weaker dependence on the order of the approximation. For more general orthonormal bases, we propose the coherence-optimal sampling: a Markov Chain Monte Carlo sampling, which directly uses the basis functions under consideration to achieve a statistical optimality among all sampling schemes with identical support. We demonstrate these different sampling strategies numerically in both high-order and high-dimensional, manufactured PC expansions. In addition, the quality of each sampling method is compared in the identification of solutions to two differential equations, one with a high-dimensional random input and the other with a high-order PC expansion. In both cases, the coherence-optimal sampling scheme leads to similar or considerably improved accuracy
Compressive sampling of polynomial chaos expansions: Convergence analysis and sampling strategies
Hampton, Jerrad; Doostan, Alireza
2015-01-01
Sampling orthogonal polynomial bases via Monte Carlo is of interest for uncertainty quantification of models with random inputs, using Polynomial Chaos (PC) expansions. It is known that bounding a probabilistic parameter, referred to as coherence, yields a bound on the number of samples necessary to identify coefficients in a sparse PC expansion via solution to an ℓ1-minimization problem. Utilizing results for orthogonal polynomials, we bound the coherence parameter for polynomials of Hermite and Legendre type under their respective natural sampling distribution. In both polynomial bases we identify an importance sampling distribution which yields a bound with weaker dependence on the order of the approximation. For more general orthonormal bases, we propose the coherence-optimal sampling: a Markov Chain Monte Carlo sampling, which directly uses the basis functions under consideration to achieve a statistical optimality among all sampling schemes with identical support. We demonstrate these different sampling strategies numerically in both high-order and high-dimensional, manufactured PC expansions. In addition, the quality of each sampling method is compared in the identification of solutions to two differential equations, one with a high-dimensional random input and the other with a high-order PC expansion. In both cases, the coherence-optimal sampling scheme leads to similar or considerably improved accuracy.
Analysis of the physical simulation on Fourier transform infrared spectrometer
Yue, Peng-yuan; Wan, Yu-xi; Zhao, Zhen
2017-10-01
A kind of oscillating arm type Fourier Transform Infrared Spectrometer (FTS) which based on the corner cube retroreflector is presented, and its principle and properties are studied. It consists of a pair of corner cube retroreflector, beam splitter and compensator. The optical path difference(OPD) is created by oscillating reciprocating motion of the moving corner cube pair, and the OPD value is four times the physical shift value of the moving corner cube pair. Due to the basic property of corner cube retroreflector, the oscillating arm type FTS has no tilt problems. It is almost ideal for very high resolution infrared spectrometer. However, there are some factors to reduce the FTS capability. First, wavefront aberration due to the figures of these surfaces will reduce modulation of FTS system; second, corner cube retroreflector consist of three plane mirror, and orthogonal to each other. When there is a deviation from right angle, it will reduced the modulation of system; third, the apexes of corner cube retroreflector are symmetric about the surface of beam splitter, if one or both of the corner cube retroreflector is displaced laterally from its nominal position, phase of off-axis rays returning from the two arms were difference, this also contributes to loss of modulation of system. In order to solve these problems, this paper sets up a non-sequential interference model, and a small amount of oscillating arm rotation is set to realize the dynamic simulation process, the dynamic interference energy data were acquired at different times, and calculated the modulation of the FTS system. In the simulation, the influence of wedge error of beam splitter, compensator or between them were discussed; effects of oscillating arm shaft deviation from the coplanar of beam splitter was analyzed; and compensation effect of corner cube retroreflector alignment on beam splitter, oscillating arm rotary shaft alignment error is analyzed. In addition, the adjustment procedure
Thermal expansion of beryllium oxide
International Nuclear Information System (INIS)
Solodukhin, A.V.; Kruzhalov, A.V.; Mazurenko, V.G.; Maslov, V.A.; Medvedev, V.A.; Polupanova, T.I.
1987-01-01
Precise measurements of temperature dependence of the coefficient of linear expansion in the 22-320 K temperature range on beryllium oxide monocrystals are conducted. A model of thermal expansion is suggested; the range of temperature dependence minimum of the coefficient of thermal expansion is well described within the frames of this model. The results of the experiment may be used for investigation of thermal stresses in crystals
Modeling cavities exhibiting strong lateral confinement using open geometry Fourier modal method
Häyrynen, Teppo; Gregersen, Niels
2016-04-01
We have developed a computationally efficient Fourier-Bessel expansion based open geometry formalism for modeling the optical properties of rotationally symmetric photonic nanostructures. The lateral computation domain is assumed infinite so that no artificial boundary conditions are needed. Instead, the leakage of the modes due to an imperfect field confinement is taken into account by using a basis functions that expand the whole infinite space. The computational efficiency is obtained by using a non-uniform discretization in the frequency space in which the lateral expansion modes are more densely sampled around a geometry specific dominant transverse wavenumber region. We will use the developed approach to investigate the Q factor and mode confinement in cavities where top DBR mirror has small rectangular defect confining the modes laterally on the defect region.
Matching-pursuit/split-operator Fourier-transform simulations of nonadiabatic quantum dynamics
Wu, Yinghua; Herman, Michael F.; Batista, Victor S.
2005-03-01
A rigorous and practical approach for simulations of nonadiabatic quantum dynamics is introduced. The algorithm involves a natural extension of the matching-pursuit/split-operator Fourier-transform (MP/SOFT) method [Y. Wu and V. S. Batista, J. Chem. Phys. 121, 1676 (2004)] recently developed for simulations of adiabatic quantum dynamics in multidimensional systems. The MP/SOFT propagation scheme, extended to nonadiabatic dynamics, recursively applies the time-evolution operator as defined by the standard perturbation expansion to first-, or second-order, accuracy. The expansion is implemented in dynamically adaptive coherent-state representations, generated by an approach that combines the matching-pursuit algorithm with a gradient-based optimization method. The accuracy and efficiency of the resulting propagation method are demonstrated as applied to the canonical model systems introduced by Tully for testing simulations of dual curve-crossing nonadiabatic dynamics.
Stochastic Ocean Predictions with Dynamically-Orthogonal Primitive Equations
Subramani, D. N.; Haley, P., Jr.; Lermusiaux, P. F. J.
2017-12-01
The coastal ocean is a prime example of multiscale nonlinear fluid dynamics. Ocean fields in such regions are complex and intermittent with unstationary heterogeneous statistics. Due to the limited measurements, there are multiple sources of uncertainties, including the initial conditions, boundary conditions, forcing, parameters, and even the model parameterizations and equations themselves. For efficient and rigorous quantification and prediction of these uncertainities, the stochastic Dynamically Orthogonal (DO) PDEs for a primitive equation ocean modeling system with a nonlinear free-surface are derived and numerical schemes for their space-time integration are obtained. Detailed numerical studies with idealized-to-realistic regional ocean dynamics are completed. These include consistency checks for the numerical schemes and comparisons with ensemble realizations. As an illustrative example, we simulate the 4-d multiscale uncertainty in the Middle Atlantic/New York Bight region during the months of Jan to Mar 2017. To provide intitial conditions for the uncertainty subspace, uncertainties in the region were objectively analyzed using historical data. The DO primitive equations were subsequently integrated in space and time. The probability distribution function (pdf) of the ocean fields is compared to in-situ, remote sensing, and opportunity data collected during the coincident POSYDON experiment. Results show that our probabilistic predictions had skill and are 3- to 4- orders of magnitude faster than classic ensemble schemes.
Large Covariance Estimation by Thresholding Principal Orthogonal Complements
Fan, Jianqing; Liao, Yuan; Mincheva, Martina
2012-01-01
This paper deals with the estimation of a high-dimensional covariance with a conditional sparsity structure and fast-diverging eigenvalues. By assuming sparse error covariance matrix in an approximate factor model, we allow for the presence of some cross-sectional correlation even after taking out common but unobservable factors. We introduce the Principal Orthogonal complEment Thresholding (POET) method to explore such an approximate factor structure with sparsity. The POET estimator includes the sample covariance matrix, the factor-based covariance matrix (Fan, Fan, and Lv, 2008), the thresholding estimator (Bickel and Levina, 2008) and the adaptive thresholding estimator (Cai and Liu, 2011) as specific examples. We provide mathematical insights when the factor analysis is approximately the same as the principal component analysis for high-dimensional data. The rates of convergence of the sparse residual covariance matrix and the conditional sparse covariance matrix are studied under various norms. It is shown that the impact of estimating the unknown factors vanishes as the dimensionality increases. The uniform rates of convergence for the unobserved factors and their factor loadings are derived. The asymptotic results are also verified by extensive simulation studies. Finally, a real data application on portfolio allocation is presented. PMID:24348088
Aeroelastic System Development Using Proper Orthogonal Decomposition and Volterra Theory
Lucia, David J.; Beran, Philip S.; Silva, Walter A.
2003-01-01
This research combines Volterra theory and proper orthogonal decomposition (POD) into a hybrid methodology for reduced-order modeling of aeroelastic systems. The out-come of the method is a set of linear ordinary differential equations (ODEs) describing the modal amplitudes associated with both the structural modes and the POD basis functions for the uid. For this research, the structural modes are sine waves of varying frequency, and the Volterra-POD approach is applied to the fluid dynamics equations. The structural modes are treated as forcing terms which are impulsed as part of the uid model realization. Using this approach, structural and uid operators are coupled into a single aeroelastic operator. This coupling converts a free boundary uid problem into an initial value problem, while preserving the parameter (or parameters) of interest for sensitivity analysis. The approach is applied to an elastic panel in supersonic cross ow. The hybrid Volterra-POD approach provides a low-order uid model in state-space form. The linear uid model is tightly coupled with a nonlinear panel model using an implicit integration scheme. The resulting aeroelastic model provides correct limit-cycle oscillation prediction over a wide range of panel dynamic pressure values. Time integration of the reduced-order aeroelastic model is four orders of magnitude faster than the high-order solution procedure developed for this research using traditional uid and structural solvers.
Combining orthogonal polarization for elongated target detection with GPR
International Nuclear Information System (INIS)
Lualdi, Maurizio; Lombardi, Federico
2014-01-01
For an accurate imaging of ground penetrating radar data the polarization characteristics of the propagating electromagnetic (EM) wavefield and wave amplitude variations with antenna pattern orientation must be taken into account. For objects that show some directionality feature and cylindrical shape any misalignment between transmitter and target can strongly modify the polarization state of the backscattered wavefield, thus conditioning the detection capability of the system. Hints on the depolarization can be used to design the optimal GPR antenna survey to avoid omissions and pitfalls during data processing. This research addresses the issue of elongated target detection through a multi azimuth (or multi polarization) approach based on the combination of mutually orthogonal GPR data. Results from the analysis of the formal scattering problem demonstrate how this strategy can reach a scalar formulation of the scattering matrix and achieve a rotational invariant quantity. The effectiveness of the algorithm is then evaluated with a detailed field example showing results closely proximal to those obtained under the optimal alignment condition: detection is significantly improved and the risk of target missing is reduced. (paper)
Systematic Identification of MCU Modulators by Orthogonal Interspecies Chemical Screening.
Arduino, Daniela M; Wettmarshausen, Jennifer; Vais, Horia; Navas-Navarro, Paloma; Cheng, Yiming; Leimpek, Anja; Ma, Zhongming; Delrio-Lorenzo, Alba; Giordano, Andrea; Garcia-Perez, Cecilia; Médard, Guillaume; Kuster, Bernhard; García-Sancho, Javier; Mokranjac, Dejana; Foskett, J Kevin; Alonso, M Teresa; Perocchi, Fabiana
2017-08-17
The mitochondrial calcium uniporter complex is essential for calcium (Ca 2+ ) uptake into mitochondria of all mammalian tissues, where it regulates bioenergetics, cell death, and Ca 2+ signal transduction. Despite its involvement in several human diseases, we currently lack pharmacological agents for targeting uniporter activity. Here we introduce a high-throughput assay that selects for human MCU-specific small-molecule modulators in primary drug screens. Using isolated yeast mitochondria, reconstituted with human MCU, its essential regulator EMRE, and aequorin, and exploiting a D-lactate- and mannitol/sucrose-based bioenergetic shunt that greatly minimizes false-positive hits, we identify mitoxantrone out of more than 600 clinically approved drugs as a direct selective inhibitor of human MCU. We validate mitoxantrone in orthogonal mammalian cell-based assays, demonstrating that our screening approach is an effective and robust tool for MCU-specific drug discovery and, more generally, for the identification of compounds that target mitochondrial functions. Copyright © 2017 Elsevier Inc. All rights reserved.
Predicting coastal morphological changes with empirical orthogonal functionmethod
Directory of Open Access Journals (Sweden)
Fernando Alvarez
2016-01-01
Full Text Available In order to improve the accuracy of prediction when using the empirical orthogonal function (EOF method, this paper describes a novel approach for two-dimensional (2D EOF analysis based on extrapolating both the spatial and temporal EOF components for long-term prediction of coastal morphological changes. The approach was investigated with data obtained from a process-based numerical model, COAST2D, which was applied to an idealized study site with a group of shore-parallel breakwaters. The progressive behavior of the spatial and temporal EOF components, related to bathymetric changes over a training period, was demonstrated, and EOF components were extrapolated with combined linear and exponential functions for long-term prediction. The extrapolated EOF components were then used to reconstruct bathymetric changes. The comparison of the reconstructed bathymetric changes with the modeled results from the COAST2D model illustrates that the presented approach can be effective for long-term prediction of coastal morphological changes, and extrapolating both the spatial and temporal EOF components yields better results than extrapolating only the temporal EOF component.
Statistical mechanics of learning orthogonal signals for general covariance models
International Nuclear Information System (INIS)
Hoyle, David C
2010-01-01
Statistical mechanics techniques have proved to be useful tools in quantifying the accuracy with which signal vectors are extracted from experimental data. However, analysis has previously been limited to specific model forms for the population covariance C, which may be inappropriate for real world data sets. In this paper we obtain new statistical mechanical results for a general population covariance matrix C. For data sets consisting of p sample points in R N we use the replica method to study the accuracy of orthogonal signal vectors estimated from the sample data. In the asymptotic limit of N,p→∞ at fixed α = p/N, we derive analytical results for the signal direction learning curves. In the asymptotic limit the learning curves follow a single universal form, each displaying a retarded learning transition. An explicit formula for the location of the retarded learning transition is obtained and we find marked variation in the location of the retarded learning transition dependent on the distribution of population covariance eigenvalues. The results of the replica analysis are confirmed against simulation
Large Covariance Estimation by Thresholding Principal Orthogonal Complements.
Fan, Jianqing; Liao, Yuan; Mincheva, Martina
2013-09-01
This paper deals with the estimation of a high-dimensional covariance with a conditional sparsity structure and fast-diverging eigenvalues. By assuming sparse error covariance matrix in an approximate factor model, we allow for the presence of some cross-sectional correlation even after taking out common but unobservable factors. We introduce the Principal Orthogonal complEment Thresholding (POET) method to explore such an approximate factor structure with sparsity. The POET estimator includes the sample covariance matrix, the factor-based covariance matrix (Fan, Fan, and Lv, 2008), the thresholding estimator (Bickel and Levina, 2008) and the adaptive thresholding estimator (Cai and Liu, 2011) as specific examples. We provide mathematical insights when the factor analysis is approximately the same as the principal component analysis for high-dimensional data. The rates of convergence of the sparse residual covariance matrix and the conditional sparse covariance matrix are studied under various norms. It is shown that the impact of estimating the unknown factors vanishes as the dimensionality increases. The uniform rates of convergence for the unobserved factors and their factor loadings are derived. The asymptotic results are also verified by extensive simulation studies. Finally, a real data application on portfolio allocation is presented.
Theory of direct sunlight transmission through orthogonal screen cells
International Nuclear Information System (INIS)
Aljofi, E.K.
2006-01-01
The Purpose of this paper is to investigate the feasibility of using the Rawshan screens to control high light intensity and to avoid excessive solar radiation penetrating inside the building interior. The exploration of the environmental characteristics of this device indicates an ideal solution to utilize available daylight in the arid atmosphere, reduces energy consumption due to the us of artificial light and ensures the continuity of the traditional architecture and the country heritage. A systematic analysis of direct sunlight transmission has been explored using a mathematical approach. The study intends to construct a predictive tool for the architects through which different specifications of the Rawshan screens were identified as far as direct beam of light concerned. The predictive tool was set-up to investigate various parameters of the screen such as the screen configurations, the aperture configurations, the change in orientation and the effect of the sky condition. The analysis of light transmission through the screen were set-up for orthogonal shapes
Validation of Fourier analysis of videokeratographic data.
Sideroudi, Haris; Labiris, Georgios; Ditzel, Fienke; Tsaragli, Efi; Georgatzoglou, Kimonas; Siganos, Haralampos; Kozobolis, Vassilios
2017-06-15
The aim was to assess the repeatability of Fourier transfom analysis of videokeratographic data using Pentacam in normal (CG), keratoconic (KC) and post-CXL (CXL) corneas. This was a prospective, clinic-based, observational study. One randomly selected eye from all study participants was included in the analysis: 62 normal eyes (CG group), 33 keratoconus eyes (KC group), while 34 eyes, which had already received CXL treatment, formed the CXL group. Fourier analysis of keratometric data were obtained using Pentacam, by two different operators within each of two sessions. Precision, repeatability and Intraclass Correlation Coefficient (ICC), were calculated for evaluating intrassesion and intersession repeatability for the following parameters: Spherical Component (SphRmin, SphEcc), Maximum Decentration (Max Dec), Regular Astigmatism, and Irregularitiy (Irr). Bland-Altman analysis was used for assessing interobserver repeatability. All parameters were presented to be repeatable, reliable and reproductible in all groups. Best intrasession and intersession repeatability and reliability were detected for parameters SphRmin, SphEcc and Max Dec parameters for both operators using ICC (intrasession: ICC > 98%, intersession: ICC > 94.7%) and within subject standard deviation. Best precision and lowest range of agreement was found for the SphRmin parameter (CG: 0.05, KC: 0.16, and CXL: 0.2) in all groups, while the lowest repeatability, reliability and reproducibility was detected for the Irr parameter. The Pentacam system provides accurate measurements of Fourier tranform keratometric data. A single Pentacam scan will be sufficient for most clinical applications.
Fourier optics treatment of classical relativistic electrodynamics
Energy Technology Data Exchange (ETDEWEB)
Geloni, G.; Saldin, E.; Schneidmiller, E.; Yurkov, M.
2006-08-15
In this paper we couple Synchrotron Radiation (SR) theory with a branch of physical optics, namely laser beam optics. We show that the theory of laser beams is successful in characterizing radiation fields associated with any SR source. Both radiation beam generated by an ultra-relativistic electron in a magnetic device and laser beam are solutions of the wave equation based on paraxial approximation. It follows that they are similar in all aspects. In the space-frequency domain SR beams appear as laser beams whose transverse extents are large compared with the wavelength. In practical solutions (e.g. undulator, bending magnet sources), radiation beams exhibit a virtual ''waist'' where the wavefront is often plane. Remarkably, the field distribution of a SR beam across the waist turns out to be strictly related with the inverse Fourier transform of the far-field angle distribution. Then, we take advantage of standard Fourier Optics techniques and apply the Fresnel propagation formula to characterize the SR beam. Altogether, we show that it is possible to reconstruct the near-field distribution of the SR beam outside the magnetic setup from the knowledge of the far-field pattern. The general theory of SR in the near-zone developed in this paper is illustrated for the special cases of undulator radiation, edge radiation and transition undulator radiation. Using known analytical formulas for the far-field pattern and its inverse Fourier transform we find analytical expressions for near-field distributions in terms of far-field distributions. Finally, we compare these expressions with incorrect or incomplete literature. (orig.)
Fourier transforms in the complex domain
Wiener, N
1934-01-01
With the aid of Fourier-Mellin transforms as a tool in analysis, the authors were able to attack such diverse analytic questions as those of quasi-analytic functions, Mercer's theorem on summability, Milne's integral equation of radiative equilibrium, the theorems of MÃ¼nz and SzÃ¡sz concerning the closure of sets of powers of an argument, Titchmarsh's theory of entire functions of semi-exponential type with real negative zeros, trigonometric interpolation and developments in polynomials of the form \\sum^N_1A_ne^{i\\lambda_nx}, lacunary series, generalized harmonic analysis in the complex domain,
Analog fourier transform channelizer and OFDM receiver
2007-01-01
An OFDM receiver having an analog multiplier based I-Q channelizing filter, samples and holds consecutive analog I-Q samples of an I-Q baseband, the I-Q basebands having OFDM sub-channels. A lattice of analog I-Q multipliers and analog I-Q summers concurrently receives the held analog I-Q samples, performs analog I-Q multiplications and analog I-Q additions to concurrently generate a plurality of analog I-Q output signals, representing an N-point discrete Fourier transform of the held analog ...
Bruzzo, Ugo; Maciocia, Antony
2017-12-01
This special issue celebrates the 34 years since the discovery of the Fourier-Mukai Transform by Shigeru Mukai. It mostly contains papers presented at the conference held in the Mathematics Research Centre of the University of Warwick, 15th to 19th June 2015 as part of a year long Warwick symposium on Derived categories and applications. The conference was also the annual conference of the Vector Bundles on Algebraic Curves series led by Peter Newstead. The symposium was principally supported by the Engineering and Physical Sciences Research Council of the UK and there was further funding from the London Mathematical Society and the Foundation Compositio.
Noise figure of amplified dispersive Fourier transformation
International Nuclear Information System (INIS)
Goda, Keisuke; Jalali, Bahram
2010-01-01
Amplified dispersive Fourier transformation (ADFT) is a powerful tool for fast real-time spectroscopy as it overcomes the limitations of traditional optical spectrometers. ADFT maps the spectrum of an optical pulse into a temporal waveform using group-velocity dispersion and simultaneously amplifies it in the optical domain. It greatly simplifies spectroscopy by replacing the diffraction grating and detector array in the conventional spectrometer with a dispersive fiber and single-pixel photodetector, enabling ultrafast real-time spectroscopic measurements. Following our earlier work on the theory of ADFT, here we study the effect of noise on ADFT. We derive the noise figure of ADFT and discuss its dependence on various parameters.
Fourier transform infrared spectroscopy of peptides.
Bakshi, Kunal; Liyanage, Mangala R; Volkin, David B; Middaugh, C Russell
2014-01-01
Fourier transform infrared (FTIR) spectroscopy provides data that are widely used for secondary structure characterization of peptides. A wide array of available sampling methods permits structural analysis of peptides in diverse environments such as aqueous solution (including optically turbid media), powders, detergent micelles, and lipid bilayers. In some cases, side chain vibrations can also be resolved and used for tertiary structure and chemical analysis. Data from several low-resolution spectroscopic techniques, including FTIR, can be combined to generate an empirical phase diagram, an overall picture of peptide structure as a function of environmental conditions that can aid in the global interpretation of large amounts of spectroscopic data.
Complex nonlinear Fourier transform and its inverse
International Nuclear Information System (INIS)
Saksida, Pavle
2015-01-01
We study the nonlinear Fourier transform associated to the integrable systems of AKNS-ZS type. Two versions of this transform appear in connection with the AKNS-ZS systems. These two versions can be considered as two real forms of a single complex transform F c . We construct an explicit algorithm for the calculation of the inverse transform (F c ) -1 (h) for an arbitrary argument h. The result is given in the form of a convergent series of functions in the domain space and the terms of this series can be computed explicitly by means of finitely many integrations. (paper)
Functional Fourier transforms and the loop equation
International Nuclear Information System (INIS)
Bershadskii, M.A.; Vaisburd, I.D.; Migdal, A.A.
1986-01-01
The Migdal-Makeenko momentum-space loop equation is investigated. This equation is derived from the ordinary loop equation by taking the Fourier transform of the Wilson functional. A perturbation theory is constructed for the new equation and it is proved that the action of the loop operator is determined by vertex functions which coincide with those of the previous equation. It is shown how the ghost loop arises in direct iterations of the momentum-space equation with respect to the coupling constant. A simple example is used to illustrate the mechanism of appearance of an integration in the interior loops in transition to observables
Fourier transform spectroscopy of six stars
Energy Technology Data Exchange (ETDEWEB)
Mendoza V, E E [Universidad Nacional Autonoma de Mexico, Mexico City. Inst. de Astronomia
1981-01-01
This paper outlines results from a digital analysis of the Fourier transform spectroscopy of six stars: ..sigma.. Aur, rho Ori, ..cap alpha.. Lyr, zeta Aql and ..cap alpha.. Cyg. Nearly 1200 different spectral lines have been identified in the spectra of these six stars in the wavelength interval 4800-10200 A where the spectra are of very high quality, less than the one per cent level of noise versus signal. ..cap alpha.. Lyr and ..cap alpha.. Cyg show spectral line and profile variations easily seen in their spectra.
Generalized Fourier transforms Fk,a
DEFF Research Database (Denmark)
Salem, Ben Said; Kobayashi, Toshiyuki; Ørsted, Bent
2009-01-01
We construct a two-parameter family of actions ωk,a of the Lie algebra by differential-difference operators on . Here, k is a multiplicity-function for the Dunkl operators, and a>0 arises from the interpolation of the Weil representation and the minimal unitary representation of the conformal gro...... of our semigroup Ωk,a provides us with (k,a) -generalized Fourier transforms , which includes the Dunkl transform ( a=2 ) and a new unitary operator ( a=1 ) as a Dunkl-type generalization of the classical Hankel transform....
Fourier-transforming with quantum annealers
Directory of Open Access Journals (Sweden)
Itay eHen
2014-07-01
Full Text Available We introduce a set of quantum adiabatic evolutions that we argue may be used as `building blocks', or subroutines, in the onstruction of an adiabatic algorithm that executes Quantum Fourier Transform (QFT with the same complexity and resources as its gate-model counterpart. One implication of the above construction is the theoretical feasibility of implementing Shor's algorithm for integer factorization in an optimal manner, and any other algorithm that makes use of QFT, on quantum annealing devices. We discuss the possible advantages, as well as the limitations, of the proposed approach as well as its relation to traditional adiabatic quantum computation.