• East Asian mathematical journal
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• v.39 no.5
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• pp.537-547
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• 2023

In this paper, we introduce the optimal approximation by a Gaussian function for a probability density function. We show that the approximation can be obtained by solving a non-linear system of parameters of Gaussian function. Then, to understand the non-normality of the empirical distributions observed in financial markets, we consider the nearly Gaussian function that consists of an optimally approximated Gaussian function and a small periodically oscillating density function. We show that, depending on the parameters of the oscillation, the nearly Gaussian functions can have fairly thick heavy tails.

• Journal of the Optical Society of Korea
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• v.19 no.4
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• pp.363-370
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• 2015

The current waveform model of a laser altimeter is based on a Gaussian laser beam of fundamental mode, while the flattened Gaussian beam has many advantages such as nearly constant energy distribution on the center of the cross-section. Following the theory of the flattened Gaussian beam and the waveform theory of the laser altimeter, some of the primary parameters of the received waveform were derived, and a laser altimetry waveform simulator and waveform processing software were programmed and improved under the circumstance of a flattened Gaussian beam. The result showed that the bias between theoretical and simulated waveforms was less than 3% for every order mode, the waveform width and range error would increase as target slope or order number rose. Under higher order mode, the shapes of the received waveforms were no longer Gaussian, and could be fitted more precisely as a generalized Gaussian function with power bigger than 2. The flattened beam got much better performance for a multi-surface target, especially when the small surface is far from the center of the laser footprint. This article provides the waveform theoretical basis for the use of a flattened Gaussian beam in a laser altimeter.

• Journal of KIEE
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• v.11 no.1
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• pp.14-20
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• 2001

To design a controller based on the pole placement method, it is necessary to obtain either a target transfer function or a desired characteristic equation which results in the closed-loop response. Specially, a step response in which no overshoot occurs in highly desirable in many applications. In this paper, we present two new present two new prototypes of Type I target transfer functions whose step responses have an overshoot of less than 0.1%. One prototype is obtained by Taylor's approximation of a Gaussian function. It is, however, observed that the response delays increase with increasing order, while the rise times are nearly constant. The other prototype is a modification of the first prototype, so that their transfer function coefficients have particular values in terms of specific parameters ${\gamma}$i and $\tau$ (see section 2). The second prototype gives very useful properties in which step responses are almost the same shape, irrespective of the order. It, also, has no overshoot. Some other properties of the prototypes and an application example are given.

• ETRI Journal
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• v.7 no.4
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• pp.3-10
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• 1985

After the light from an incoherent LED was transmitted through the multimode fibers which were linked over 10 km, the nearfield power distribution reached the steady-state independent of launching conditions. It has been also found that the steady-state output power distribution showed the pattern of Gaussian function. In this steady-state Gaussian function pattern, the measured losses of fibers were very repeatable values. In case of using LD source, the speckle phenomena in near -field power distribution appeared until the distance of 10 km. And the output power distribution did not reach the steady-state shown in LED even over 20km on account of the coherence and the nonuniform lasing modes of LD. But the measured losses of fibers were nearly stable in this long distance.

• Journal of applied mathematics & informatics
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• v.27 no.5_6
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• pp.1087-1095
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• 2009

In this paper, we study approximation method from scattered data to the derivatives of a function f by a radial basis function $\phi$. For a given function f, we define a nearly interpolating function and discuss its accuracy. In particular, we are interested in using smooth functions $\phi$ which are (conditionally) positive definite. We estimate accuracy of approximation for the Sobolev space while the classical radial basis function interpolation applies to the so-called native space. We observe that our approximant provides spectral convergence order, as the density of the given data is getting smaller.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.15 no.10
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• pp.797-810
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• 1990

The error rate equations of digitally modulated signals transmitted through the Gaussian noise and tone multiple interference channel have been derived. Using the derived equations of error probabilities in the environments of Gaussian noise tone interferer and Gaussian noise multiple interferer, the error rate performances of various digitally modulated signals have been evaluated, and compared in graphs as a function of average carrier to tone interferer power ratio(CIR), average carrier to multiple interferer power ratio(CIT) and the average carrer-to-Gaussian noise powr ratio(CIR). In this paper, the modulation schemes such as amplitude shift keying (ASK), phase shift keying(PSK), frequency shift keying(FSK), minimum shift keying(MSK), quadrature amplitud modulation(QAM) and amplitude phase shift keying(APK) have been selected for the study of performance comparison. The results of comparison show us that, in low bits/sec/Hz, PSK is superior to the other schemes, but in high bits/sec/Hz, mixed multi ary type is better than single multi ary type. And in strong noise evironment, the multiple interferer has much influence than tone interferer, however, in low noise environment. the mojor error factor is tone interferer. But tone interference effect nearly disappears over specified CIR level about 20[dB]. And the modulation schemes using amplitude are heavily influenced by multiple interference.

• Proceedings of the Korean Society of Broadcast Engineers Conference
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• 1996.06a
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• pp.9-15
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• 1996

In this paper, we propose a new detector based on the median-shift sign. We call it the median-shift sign (MSS) detector, which is an extension of the classical sign detector. We first analyze the problem of detecting a dc signal in noise of known probability density function (pdf). The MSS detector with the optimum median-shift value, the optimum MSS detector, performs better than the sign detector in Gaussian noise: it has the best performance among the detectors compared in Laplacian and Cauchy noise. It is shown that the MSS detectors with constant median-shift values are nearly equal to the optimum MSS detector. We also analyze the problem of detecting a dc signal when only partial information is available on the noise. The MSS detectors with constant median-shift values are almost equal to the sign detector in Gaussian noise: they perform better than the sign and Wilcoxon detectors for most signal ranges in Laplacian and Cauchy noise.

• Transactions of the Korean Society of Mechanical Engineers
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• v.12 no.3
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• pp.599-606
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• 1988

Structures of interfacial waves in nearly-horizontal countercurrent stratified air-water flow have been measured by means of a needle contact method. Based upon a statistical analysis for the liquid film distribution, statistical properties of the waves such as mean film thickness, mean wave amplitude and rms value of the wave fluctuation have been calculated. The results show that the film distribution can be described by a Gaussian probability density function for the three-dimensional wave regime. It is also indicated that the mean film thick ness and the rms value of the wave fluctuation increase as gas and liquid flow rates are increased in countercurrent two-phase flow. The dimensionless intensity of the wave fluctuation may be regarded as a function of the Froude number and the dimensionless mean film thickness.

• Journal of the Korea Institute of Information and Communication Engineering
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• v.15 no.6
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• pp.1338-1342
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• 2011

In this paper, threshold voltage characteristics have been analyzed as one of short channel effects occurred in double gate(DG)MOSFET to be next-generation devices. The Gaussian function to be nearly experimental distribution has been used as carrier distribution to solve Poisson's equation, and threshold voltage has been investigated according to projected range and standard projected deviation, variables of Gaussian function. The analytical potential distribution model has been derived from Poisson's equation, and threshold voltage has been obtained from this model. Since threshold voltage has been defined as gate voltage when surface potential is twice of Fermi potential, threshold voltage has been derived from analytical model of surface potential. Those results of this potential model are compared with those of numerical simulation to verify this model. As a result, since potential model presented in this paper is good agreement with numerical model, the threshold voltage characteristics have been considered according to the doping profile of DGMOSFET.

• The Journal of Engineering Geology
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• v.3 no.1
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• pp.51-61
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• 1993

Restricted maximum likelihood(RML) method was used to determine the parameters of generalized covariance, and universal krigig with RML was applied to estimate a groundwater level distribution of nonstationarv random function. Universal kriging with RML was compared to IRF-k with weighted least squares method for the comparison of their accuracies. Cross validation shows that two methods have nearly the same ability for the estimation of groundwater levels. Scattergram of estimates versus true values and contour maps of groundwater levels have nearly the same results. The reason why two methods produced the same results is thought to be the non-Gaussian distribution and the snaall number of sample data.