The Experts below are selected from a list of 2196 Experts worldwide ranked by ideXlab platform
Richard Easther - One of the best experts on this subject based on the ideXlab platform.
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fermions gauge theories and the Sinc Function representation for feynman diagrams
Physical Review D, 2001Co-Authors: D Petrov, Richard Easther, G S Guralnik, Stephen C Hahn, Weimun WangAbstract:We extend our new approach for numeric evaluation of Feynman diagrams to integrals that include fermionic and vector propagators. In this initial discussion we begin by deriving the Sinc Function representation for the propagators of spin-1/2 and spin-1 fields and exploring their properties. We show that the attributes of the spin-0 propagator which allowed us to derive the Sinc Function representation for scalar field Feynman integrals are shared by fields with nonzero spin. We then investigate the application of the Sinc Function representation to simple QED diagrams, including first order corrections to the propagators and the vertex.
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Sinc Function representation and three loop master diagrams
Physical Review D, 2001Co-Authors: Richard Easther, G S Guralnik, Stephen C HahnAbstract:We test the Sinc Function representation, a novel method for numerically evaluating Feynman diagrams, by using it to evaluate the three-loop master diagrams. Analytical results have been obtained for all these diagrams, and we find excellent agreement between our calculations and the exact values. The Sinc Function representation converges rapidly, and it is straightforward to obtain accuracies of 1 part in 10{sup 6} for these diagrams and with longer runs we found results better than 1 part in 10{sup 12}. Finally, this paper extends the Sinc Function representation to diagrams containing massless propagators.
Stephen C Hahn - One of the best experts on this subject based on the ideXlab platform.
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fermions gauge theories and the Sinc Function representation for feynman diagrams
Physical Review D, 2001Co-Authors: D Petrov, Richard Easther, G S Guralnik, Stephen C Hahn, Weimun WangAbstract:We extend our new approach for numeric evaluation of Feynman diagrams to integrals that include fermionic and vector propagators. In this initial discussion we begin by deriving the Sinc Function representation for the propagators of spin-1/2 and spin-1 fields and exploring their properties. We show that the attributes of the spin-0 propagator which allowed us to derive the Sinc Function representation for scalar field Feynman integrals are shared by fields with nonzero spin. We then investigate the application of the Sinc Function representation to simple QED diagrams, including first order corrections to the propagators and the vertex.
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Sinc Function representation and three loop master diagrams
Physical Review D, 2001Co-Authors: Richard Easther, G S Guralnik, Stephen C HahnAbstract:We test the Sinc Function representation, a novel method for numerically evaluating Feynman diagrams, by using it to evaluate the three-loop master diagrams. Analytical results have been obtained for all these diagrams, and we find excellent agreement between our calculations and the exact values. The Sinc Function representation converges rapidly, and it is straightforward to obtain accuracies of 1 part in 10{sup 6} for these diagrams and with longer runs we found results better than 1 part in 10{sup 12}. Finally, this paper extends the Sinc Function representation to diagrams containing massless propagators.
Tao Qian - One of the best experts on this subject based on the ideXlab platform.
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Co-dimension- p Shannon sampling theorems
Complex Variables and Elliptic Equations, 2020Co-Authors: Yan Yang, Tao QianAbstract:In this article, by defining the generalized co-dimension-p Sinc Function, the corresponding Sinc interpolations (Shannon sampling theorems) are obtained.
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Sampling theorem and multi-scale spectrum based on non-linear Fourier atoms
Applicable Analysis, 2009Co-Authors: Qiuhui Chen, Tao QianAbstract:This study concerns some new developments of unit analytic signals with non-linear phase. It includes ladder-shaped filter, generalized Sinc Function based on non-linear Fourier atoms, generalized sampling theorem for non-bandlimited signals and the notion of multi-scale spectrum for discrete sequences. We first introduce the ladder-shaped filter and show that the impulse response of its corresponding linear time-shift invariant system is the generalized Sinc Function as a product of periodic Poisson kernel and Sinc Function. Secondly, we establish a Shannon-type sampling theorem based on generalized Sinc Function for this type of non-bandlimited signal. We further prove that this type of signal may be holomorphically extended to strips in the complex plane containing the real axis. Finally, we introduce the notion of multi-scale spectrums for discrete sequences and develop the related fast algorithm.
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Shannon Sampling in the Clifford Analysis Setting
Zeitschrift Fur Analysis Und Ihre Anwendungen, 2005Co-Authors: Tao QianAbstract:The paper concerns the generalization of the one-dimensional Sinc Function to (n+ 1)-real variables within the Clifford analysis setting. The exact interpolation with Shannon sampling is proved.
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SHANNON SAMPLING AND ESTIMATION OF BAND-LIMITED FunctionS IN THE SEVERAL COMPLEX VARIABLES SETTING
Acta Mathematica Scientia, 2005Co-Authors: Tao QianAbstract:Abstract In this work the authors develop the n-dimensional Sinc Function theory in the several complex variables setting. In terms of the corresponding Paley-Wiener theorem the exact Sinc interpolation and quadrature are established. Exponential convergence rate of the error estimates for band-limited Functions in n-dimensional strips are obtained.
G S Guralnik - One of the best experts on this subject based on the ideXlab platform.
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fermions gauge theories and the Sinc Function representation for feynman diagrams
Physical Review D, 2001Co-Authors: D Petrov, Richard Easther, G S Guralnik, Stephen C Hahn, Weimun WangAbstract:We extend our new approach for numeric evaluation of Feynman diagrams to integrals that include fermionic and vector propagators. In this initial discussion we begin by deriving the Sinc Function representation for the propagators of spin-1/2 and spin-1 fields and exploring their properties. We show that the attributes of the spin-0 propagator which allowed us to derive the Sinc Function representation for scalar field Feynman integrals are shared by fields with nonzero spin. We then investigate the application of the Sinc Function representation to simple QED diagrams, including first order corrections to the propagators and the vertex.
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Sinc Function representation and three loop master diagrams
Physical Review D, 2001Co-Authors: Richard Easther, G S Guralnik, Stephen C HahnAbstract:We test the Sinc Function representation, a novel method for numerically evaluating Feynman diagrams, by using it to evaluate the three-loop master diagrams. Analytical results have been obtained for all these diagrams, and we find excellent agreement between our calculations and the exact values. The Sinc Function representation converges rapidly, and it is straightforward to obtain accuracies of 1 part in 10{sup 6} for these diagrams and with longer runs we found results better than 1 part in 10{sup 12}. Finally, this paper extends the Sinc Function representation to diagrams containing massless propagators.
K.c. Ho - One of the best experts on this subject based on the ideXlab platform.
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Optimum discrete wavelet scaling and its application to delay and Doppler estimation
IEEE Transactions on Signal Processing, 1998Co-Authors: K.c. Ho, Y.t. ChanAbstract:This paper studies the scaling of an arbitrary waveform from its samples. The scaling problem is formulated as a mean-square minimization, and the resulting estimator consists of two parts: noise filtering and Sinc Function scaling. Sinc Function scaling is a time-dependent process and requires O(N/sup 2/) operations, where N is the data length. A fast algorithm based on the FFT is proposed to reduce the complexity to O(Nlog/sub 2/N). This new algorithm is applied to wideband time delay and Doppler estimation, where the optimum wavelet is one of the received signal samples that has no analytic form. The scaling method is found to be very effective in that the estimation accuracy achieves the Cramer-Rao lower bound (CRLB).
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A new constrained least mean square time-delay estimation system
IEEE Transactions on Circuits and Systems, 1990Co-Authors: K.c. Ho, P.c. ChingAbstract:An adaptive filter for determining the time difference in a signal between two split-array outputs is described. A least-mean-square (LMS) algorithm is used to adapt the constrained filter coefficients to samples of a Sinc Function. The newly configured LMS time-delay estimation model has a faster convergence speed and a superior ability to track time-varying delays. In addition, the same filter length can be used to measure a longer delay without resulting in a larger truncation error.