Donsker's delta function as a generalized Brownian functional and its application

2006 ◽  
pp. 167-178 ◽  
Author(s):  
Hui-Hsiung Kuo
Keyword(s):  
Delta Function

Dirac delta regularization

2020 ◽  
Author(s):  
Matheus Pereira Lobo
Keyword(s):  
Delta Function ◽  
Dirac Delta Function ◽  
Dirac Delta ◽  
Finite Result

I present a finite result for the Dirac delta "function."

scholarly journals Motion blur invariant for estimating motion parameters of medical ultrasound images

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Barmak Honarvar Shakibaei Asli ◽  
Yifan Zhao ◽  
John Ahmet Erkoyuncu
Keyword(s):  
Image Quality Assessment ◽  
Medical Image Analysis ◽  
Main Idea ◽  
Delta Function ◽  
Motion Blur ◽  
Ultrasound Images ◽  
Medical Ultrasound ◽  
Fetal Ultrasound ◽  
Dirac Delta ◽  
Motion Parameters

AbstractHigh-quality medical ultrasound imaging is definitely concerning motion blur, while medical image analysis requires motionless and accurate data acquired by sonographers. The main idea of this paper is to establish some motion blur invariant in both frequency and moment domain to estimate the motion parameters of ultrasound images. We propose a discrete model of point spread function of motion blur convolution based on the Dirac delta function to simplify the analysis of motion invariant in frequency and moment domain. This model paves the way for estimating the motion angle and length in terms of the proposed invariant features. In this research, the performance of the proposed schemes is compared with other state-of-the-art existing methods of image deblurring. The experimental study performs using fetal phantom images and clinical fetal ultrasound images as well as breast scans. Moreover, to validate the accuracy of the proposed experimental framework, we apply two image quality assessment methods as no-reference and full-reference to show the robustness of the proposed algorithms compared to the well-known approaches.

scholarly journals From sources to initial data and back again: on bulk singularities in Euclidean AdS/CFT

2020 ◽  
Vol 2020 (12) ◽  
Author(s):  
Alexandre Belin ◽  
Benjamin Withers
Keyword(s):  
Quantum Theory ◽  
Initial Data ◽  
Path Integral ◽  
Coherent States ◽  
Microscopic Theory ◽  
Delta Function ◽  
Common Method ◽  
Single Trace

Abstract A common method to prepare states in AdS/CFT is to perform the Euclidean path integral with sources turned on for single-trace operators. These states can be interpreted as coherent states of the bulk quantum theory associated to Lorentzian initial data on a Cauchy slice. In this paper, we discuss the extent to which arbitrary initial data can be obtained in this way. We show that the initial data must be analytic and define the subset of it that can be prepared by imposing bulk regularity. Turning this around, we show that for generic analytic initial data the corresponding Euclidean section contains singularities coming from delta function sources in the bulk. We propose an interpretation of these singularities as non-perturbative objects in the microscopic theory.

scholarly journals Reconciling Lagrangian Diffusivity and Effective Diffusivity in Contour-Based Coordinates

2019 ◽  
Vol 49 (6) ◽  
pp. 1521-1539
Author(s):  
Yu-Kun Qian ◽  
Shiqiu Peng ◽  
Chang-Xia Liang
Keyword(s):  
Time Lag ◽  
Effective Diffusivity ◽  
Delta Function ◽  
Spreading Rate ◽  
Particle Dispersion ◽  
Small Scale ◽  
Time Lags ◽  
Conservative Tracer ◽  
Stirring Effect ◽  
Short Time

AbstractThe present study reconciles theoretical differences between the Lagrangian diffusivity and effective diffusivity in a transformed spatial coordinate based on the contours of a quasi-conservative tracer. In the transformed coordinate, any adiabatic stirring effect, such as shear-induced dispersion, is naturally isolated from diabatic cross-contour motions. Therefore, Lagrangian particle motions in the transformed coordinate obey a transformed zeroth-order stochastic (i.e., random walk) model with the diffusivity replaced by the effective diffusivity. Such a stochastic model becomes the theoretical foundation on which both diffusivities are exactly unified. In the absence of small-scale diffusion, particles do not disperse at all in the transformed contour coordinate. Besides, the corresponding Lagrangian autocorrelation becomes a delta function and is thus free from pronounced overshoot and negative lobe at short time lags that may be induced by either Rossby waves or mesoscale eddies; that is, particles decorrelate immediately and Lagrangian diffusivity is already asymptotic no matter how small the time lag is. The resulting instantaneous Lagrangian spreading rate is thus conceptually identical to the effective diffusivity that only measures the instantaneous irreversible mixing. In these regards, the present study provides a new look at particle dispersion in contour-based coordinates.

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