• Journal of the Korean Mathematical Society
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• v.59 no.6
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• pp.1185-1201
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• 2022

Feller introduced an unfair-fair-game in his famous book [3]. In this game, at each trial, player will win 2^k yuan with probability p_k = 1/2^kk(k + 1), k ∈ ℕ, and zero yuan with probability p₀ = 1 - Σ^∞_k=1 p_k. Because the expected gain is 1, player must pay one yuan as the entrance fee for each trial. Although this game seemed "fair", Feller [2] proved that when the total trial number n is large enough, player will loss n yuan with its probability approximate 1. So it's an "unfair" game. In this paper, we study in depth its convergence in probability, almost sure convergence and convergence in distribution. Furthermore, we try to take 2^k = m to reduce the values of random variables and their corresponding probabilities at the same time, thus a new probability model is introduced, which is called as the related model of Feller's unfair-fair-game. We find out that this new model follows a long-tailed distribution. We obtain its weak law of large numbers, strong law of large numbers and central limit theorem. These results show that their probability limit behaviours of these two models are quite different.

• ETRI Journal
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• v.28 no.3
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• pp.301-310
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• 2006

In mobile communications, a class of variable-complexity algorithms for convolutional decoding known as sequential decoding algorithms is of interest since they have a computational time that could vary with changing channel conditions. The Fano algorithm is one well-known version of a sequential decoding algorithm. Since the decoding time of a Fano decoder follows the Pareto distribution, which is a heavy-tailed distribution parameterized by the channel signal-to-noise ratio (SNR), buffers are required to absorb the variable decoding delays of Fano decoders. Furthermore, since the decoding time drawn by a certain Pareto distribution can become unbounded, a maximum limit is often employed by a practical decoder to limit the worst-case decoding time. In this paper, we investigate the relations between buffer occupancy, decoding time, and channel conditions in a system where the Fano decoder is not allowed to run with unbounded decoding time. A timeout limit is thus imposed so that the decoding will be terminated if the decoding time reaches the limit. We use discrete-time semi-Markov models to describe such a Fano decoding system with timeout limits. Our queuing analysis provides expressions characterizing the average buffer occupancy as a function of channel conditions and timeout limits. Both numerical and simulation results are provided to validate the analytical results.

• Communications of the Korean Mathematical Society
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• v.14 no.3
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• pp.627-633
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• 1999

Let the given distribution $\pi$ have a log-concave density which is proportional to exp(-V(x)) on $R^d$. We consider a Markov chain induced by the method Gibbs sampling having $\pi$ as its in-variant distribution and prove geometric ergodicity and the functional central limit theorem for the process.

• Transactions of Materials Processing
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• v.27 no.2
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• pp.115-122
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• 2018

Most domestic and international standards on the forming limit diagram (FLD) including ISO 12004-2, use a 'position-dependent method,' which determines the forming limit from a strain distribution measured on the specimen after necking or fracture. However, the position-dependent method has inherent problems such as the incidence of asymmetry of a strain distribution, the estimation of missing data near fracture, the termination time of test, and the deformation due to the new stress equilibrium after a fracture, which is blamed for causing sometimes a significant lab-to-lab variation. The 'time-dependent method,' which is anticipated to be a new international standard for evaluating the forming limit, is expected to greatly improve these intrinsic disadvantages of the position-dependent method. It is because the time-dependent method makes it possible to identify and accurately determine the forming limit, just before the necking point from the strain data as continuously measured in a short time interval. In this study, we propose a new time-dependent method based on a Gaussian fitting of strain acceleration with the introduction of 'normalized correlation coefficient.' It has been shown in this study that this method can determine the forming limit very stably and gives a higher value, which is in comparison with the results of the previously studied position-dependent and time-dependent methods.

• The Korean Journal of Ecology
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• v.6 no.1
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• pp.45-54
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• 1983

A distribution map of black pine, Pinus thunbergii, in south Korea was prepared through field surveys. According to Mirov(1967), the range of black pine is limited in east Asia, Japan and Korea; its northern limit is at about 41。34' north and its southern limit on Takara island, south Kyushu, at 29。 north. According to the present map, its northern limit coincided with the isopath of warmth index 100 by Yim(1977). The density of pine in grid mesh, about 4 km * 4 km, was higher at costal area than that in inland area, and it was also higher at sea side slope than the opposite slope of the same mountain. This suggests that the ecological distribution of black pine is greatly affected by salt content of the soil or the optimal range of summed temperature for the pine growth.

• Communications for Statistical Applications and Methods
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• v.3 no.1
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• pp.243-255
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• 1996

The number of neutron signals from a neutral particle beam(NPB) at the detector, without any errors, obeys Poisson distribution, Under two assumptions that NPB scattering distribution and aiming errors have a circular Gaussian distribution respectively, an exact probability distribution of signals becomes a Poisson-power function distribution. In this paper, we show that the error rate in simple hypothesis testing for the limiting Poisson-power function distribution is not zero. That is, the limit of ${\alpha}+{\beta}$ is zero when Poisson parameter$\kappa\rightarro\infty$, but this limit is not zero (i.e., $\rho\ell$>0)for the Poisson-power function distribution. We also give optimal decision algorithms for a specified error rate.

• Transactions of Materials Processing
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• v.20 no.1
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• pp.36-41
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• 2011

Meso-scale or micro-scale forming of sheet metal parts has been recently considered as one of the important forming technologies with growing demand on meso/micro products for electric or medical devices. Experimental investigation on the cylindrical meso-cup drawing with hemispherical punch is carried out to examine the limit drawing ratio and thickness distribution of drawn cups. The working parameters chosen in this study are blank diameter, die-corner radius and blankholding force. It is found from the experiments that the limit drawing ratio of 2.4 can be achieved in the case of hemispherical cup drawing and uniform thickness distribution in wider region can be obtained compared with the results of conventional cup drawing.

• Journal of the Korean Data and Information Science Society
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• v.17 no.1
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• pp.221-231
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• 2006

A chi-squared test of multivariate normality is suggested which is oriented for detecting deviations from elliptical symmetry. We derive the limiting distribution of the test statistic via a central limit theorem on empirical processes. A simulation study is conducted to study the accuracy of the limiting distribution in finite samples. Finally, we compare the power of our method with those of other popular tests of multivariate normality under a non-normal distribution.

• Geomechanics and Engineering
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• v.24 no.4
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• pp.399-406
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• 2021

It is a key issue in the tunnel design to evaluate the stability of the excavation face. Two efficient analytical models in the context of the limit equilibrium method (LEM) and the limit analysis method (LAM) are used to carry out the deterministic calculations of the safety factor. The safety factor obtained by these two models agrees well with that provided by the numerical modelling by FLAC 3D, but consuming less time. A simple probabilistic approach based on the Mote-Carlo Simulation technique which can quickly calculate the probability distribution of the safety factor was used to perform the probabilistic analysis on the tunnel face stability. Both the cumulative probabilistic distribution and the probability density function in terms of the safety factor were obtained. The obtained results show the effectiveness of this probabilistic approach in the tunnel design.

• Journal of Electrical Engineering and Technology
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• v.12 no.1
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• pp.11-18
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• 2017

In order to maintain customer voltages within the allowable limit($220{\pm}13V$) as much as possible, tap operation strategy of SVR(Step Voltage Regulator) which is located in primary feeder, is widely used for voltage control in the utilities. However, SVR in nature has operation characteristic of the delay time ranging from 30 to 150 sec, and then the compensation of BESS (Battery Energy Storage System) during the delay time is being required because the customer voltages in distribution system may violate the allowable limit during the delay time of SVR. Furthermore, interconnection of PV(Photovoltaic) system could make a difficultly to keep customer voltage within the allowable limit. Therefore, this paper presents an optimal coordination operation algorithm between BESS and SVR based on a conventional LDC (Line Drop Compensation) method which is decided by stochastic approach. Through the modeling of SVR and BESS using the PSCAD/EMTDC, it is confirmed that customer voltages in distribution system can be maintained within the allowable limit.