• Structural Engineering and Mechanics
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• v.28 no.4
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• pp.373-386
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• 2008

In this study stochastic analysis of non-linear dynamical systems under ${\alpha}$-stable, multiplicative white noise has been conducted. The analysis has dealt with a special class of ${\alpha}$-stable stochastic processes namely sub-Gaussian white noises. In this setting the governing equation either of the probability density function or of the characteristic function of the dynamical response may be obtained considering the dynamical system forced by a Gaussian white noise with an uncertain factor with ${\alpha}/2$- stable distribution. This consideration yields the probability density function or the characteristic function of the response by means of a simple integral involving the probability density function of the system under Gaussian white noise and the probability density function of the ${\alpha}/2$-stable random parameter. Some numerical applications have been reported assessing the reliability of the proposed formulation. Moreover a proper way to perform digital simulation of the sub-Gaussian ${\alpha}$-stable random process preventing dynamical systems from numerical overflows has been reported and discussed in detail.

• Journal of the Korean Mathematical Society
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• v.38 no.2
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• pp.297-309
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• 2001

White noise distribution theory over the complex Gaussian space is established on the basis of the recently developed white noise operator theory. Unitarity condition for a white noise operator is discussed by means of the operator symbol and complex Gaussian integration. Concerning the overcompleteness of the exponential vectors, a coherent sate representation of a white noise function is uniquely specified from the diagonal coherent state representation of the associated multiplication operator.

• Journal of applied mathematics & informatics
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• v.15 no.1_2
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• pp.363-375
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• 2004

In this paper, We show that the bandpass random signals of the form ∑$_{\alpha}$$\alpha$$_{\alpha}$ a Sin(2$\pi$f$_{\alpha}$t + b$_{\alpha}$) where a$_{\alpha}$ being a random number in [0,1], f$_{\alpha}$ a random integer in a given frequency band, and b$_{\alpha}$ a random number in [0, 2$\pi$], generate Gaussian white noise signals and hence they are adequate for simulating Continuous Markov processes. We apply the result to the fluctuation-dissipation formula for the Johnson noise and show that the probability distribution for the long term average of the power of the Johnson noise is a X$^2$ distribution and that the relative error of the long term average is (equation omitted) where N is the number of blocks used in the average.error of the long term average is (equation omitted) where N is the number of blocks used in the average.

• Journal of the Korean Mathematical Society
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• v.33 no.4
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• pp.993-1008
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• 1996

The white noise analysis, initiated by Hida [3] in 1975, has been developed to an infinite dimensional distribution theory on Gaussian space $(E^*, \mu)$ as an infinite dimensional analogue of Schwartz distribution theory on Euclidean space with Legesgue measure. The mathematical framework of white noise analysis is the Gel'fand triple $(E) \subset (L^2) \subset (E)^*$ over $(E^*, \mu)$ where $\mu$ is the standard Gaussian measure associated with a Gel'fand triple $E \subset H \subset E^*$.

• Journal of applied mathematics & informatics
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• v.20 no.1_2
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• pp.445-454
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• 2006

We describe a solution to the Ornstein-Uhlenbeck equation $\frac{dI}{dt}-\frac{1}{\tau}$I(t)=cV(t) where V(t) is a constant multiple of a Gaussian white noise. Our solution is based on a discrete set of Gaussian white noise obtained by taking sample points from a sum of single frequency harmonics that have random amplitudes, random frequencies, and random phases. Hence, it is different from the solution by the standard random walk using random numbers generated by the Box-Mueller algorithm. We prove that the power of the signal has the additive property, from which we derive that the Lyapunov characteristic exponent for our solution is positive. This compares with the solution by other methods where the noise is kept to be in an error range so that its Lyapunov exponent is negative.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.9 no.1
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• pp.9-16
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• 2005

The random signals defined as sums of the single frequency sinusoidal signals with random amplitudes and random phases or equivalently sums of functions obtained by adding a Sine and a Cosine function with random amplitudes, are used in the double randomization method for the Monte Carlo solution of the turbulent systems. We show that these random signals can be used for studying the properties of the Johnson noise by proving that constant multiples of these signals with uniformly distributed frequencies in a fixed frequency band satisfy the properties of the Gaussian white noise.

• Nuclear Engineering and Technology
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• v.56 no.2
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• pp.715-727
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• 2024

During fast neutron imaging, besides the dark current noise and readout noise of the CCD camera, the main noise in fast neutron imaging comes from high-energy gamma rays generated by neutron nuclear reactions in and around the experimental setup. These high-energy gamma rays result in the presence of high-density gamma white spots (GWS) in the fast neutron image. Due to the microscopic quantum characteristics of the neutron beam itself and environmental scattering effects, fast neutron images typically exhibit a mixture of Gaussian noise. Existing denoising methods in neutron images are difficult to handle when dealing with a mixture of GWS and Gaussian noise. Herein we put forward a deep learning approach based on the Swin Transformer UNet (SUNet) model to remove high-density GWS-Gaussian mixture noise from fast neutron images. The improved denoising model utilizes a customized loss function for training, which combines perceptual loss and mean squared error loss to avoid grid-like artifacts caused by using a single perceptual loss. To address the high cost of acquiring real fast neutron images, this study introduces Monte Carlo method to simulate noise data with GWS characteristics by computing the interaction between gamma rays and sensors based on the principle of GWS generation. Ultimately, the experimental scenarios involving simulated neutron noise images and real fast neutron images demonstrate that the proposed method not only improves the quality and signal-to-noise ratio of fast neutron images but also preserves the details of the original images during denoising.

• Journal of the Korean Institute of Telematics and Electronics A
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• v.32A no.7
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• pp.1-7
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• 1995

In this paper, we generalize the method to calculate the outage probability in the presence of multiple rayleigh faded cochannel interferences and additive white Gaussian noise. Our result is a computational formula that can be applied with or without Gaussian noise in Rayleigh faded cochannel interferences. Without Gaussian noise, the situation degenerates to usual case of the cochannel interferences. The result can be appiled also in the presence of Gaussian noise with or without cochannel interferences.

• Advances in nano research
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• v.5 no.1
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• pp.13-25
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• 2017

We examine the total optical dielectric function (TODF) of impurity doped GaAs quantum dot (QD) from the viewpoint of anisotropy, position-dependent effective mass (PDEM) and position dependent dielectric screening function (PDDSF), both in presence and absence of noise. The dopant impurity potential is Gaussian in nature and noise employed is Gaussian white noise that has been applied to the doped system via two different modes; additive and multiplicative. A change from fixed effective mass and fixed dielectric constant to those which depend on the dopant coordinate manifestly affects TODF. Presence of noise and also its mode of application bring about more rich subtlety in the observed TODF profiles. The findings indicate promising scope of harnessing the TODF of doped QD systems through expedient control of site of dopant incorporation and application of noise in desired mode.

• Journal of information and communication convergence engineering
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• v.9 no.6
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• pp.758-762
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• 2011

In this paper an efficient algorithm is proposed to remove additive white Gaussian noise(AWGN) with edge preservation. A function is used to separate the filtering mask to two sets according to the direction information. Then, we calculate the mean and standard deviation of the pixels in each set. In order to preserve the details, we also compare standard deviations between the two sets to find out smaller one. Corrupted pixel is replaced by the mean of the filtering window's median value and the smaller set's mean value that the rate of change is faster than the other one. Experiment results show that the proposed algorithm outperforms with significant improvement in image quality than the conventional algorithms. The proposed method removes the Gaussian noise very effectively.