• Journal of the Chungcheong Mathematical Society
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• v.27 no.1
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• pp.35-37
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• 2014

We examine a question raised in [1] regarding existence and uniqueness of the steady-state solution of certain type of Kolmogorov forward equation in this paper, and prove that the question holds for $S^1$ by giving an explicit solution.

• 한국데이터정보과학회:학술대회논문집
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• 2005.10a
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• pp.171-176
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• 2005

An infinite dam with compound Poisson inputs and a state-dependent release rate is considered. We build the Kolmogorov's backward differential equation and solve it to obtain the Laplace transforms of the first exit times for this dam.

• The Pure and Applied Mathematics
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• v.4 no.2
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• pp.105-110
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• 1997

The distribution of staff in a hierachial organization has been studied in a variety of forms and models. Results here show that the promotion process follows a binomial distribution with parameters n and $\alpha=e^{-pt}$ and the recruitment process follows a poisson distribution with parameter $\lambda$. Futhermore, the mean time to promotion in the grade was estimated.

• Journal of the Korean Institute of Telematics and Electronics
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• v.19 no.3
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• pp.37-45
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• 1982

This paper is a sequel of the Part I paper[1] on the modified digital Costas loop. In this Part II we analyze the performance of the system in the presence of noise. It is shown that, when the input signal is corrupted by additive white Gaussian noise, the noise process in the loop becomes Rician as a result of the tan-1 (.) function of the phase error detector. Steady state probability density functions of phase errors of the first-and second-order loops have been obtained by solving the Chapman-Kolmogorov equation numerically. Also, the mean and variance of phase error in the steady state have been obtained analytically, and are compared with the results obtained by computer simulation.

• Journal of the Korean Institute of Telematics and Electronics
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• v.19 no.2
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• pp.38-50
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• 1982

A new type of digital phase-locked loop (DPLL) called the modified digital Costas loop is proposed and analyzed. The main feature of the proposed loop is that the phase error detector of the loop has linear characteristic. This results from the use of the tan-1 (.) function in the loop. Accordingly, the DPLL can be characterized by a modulo-2$\pi$ linear difference equation. This paper is diveide into two parts. In Part I we describe the proposed system, and analyze the performance of the first-and second-order loops in the absence of noise by the Phase Plane technique. The locking ranges for the DPLL's to achieve exact locking independently of initial conditions have been obtained in closed forms. Also, the false lock and oscillation phenomena occurring under some initial conditions have been considered. These results have been verified by computer simulation. In Part ll we analyze the proposed system in the presence of noise. The steady state probability density function, mean and variance of the phase error have been obtained by solving the Chapman-Kolmogorov equation. These results will be presented in Part ll.

• Proceedings of the Korean Society of Precision Engineering Conference
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• 2002.05a
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• pp.215-218
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• 2002

A control strategy for a dynamic system under irregular disturbance by using stochastic controller is developed. In order to design stochastic controller, system dynamic model in real domain i transformed dynamic moment equation in stochastic domain by F-P-K approach. A study of real time control technique four stochastic controller is performed in this paper.

• Journal of the Korean Geographical Society
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• v.51 no.4
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• pp.525-539
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• 2016

This study attempts to predict the changes in the spatial distribution of occupational employment in Korea by applying Markov Chain Model. For the purpose we analyze the job-related migration pattern and estimate the transition probability with the last six years job-related migration data. By applying the Chapman-Kolmogorov equation based on the transition probability, we predict the changes in the spatial distribution of occupational employment for the next ten years. The result reveals that the employment of professional jobs is predicted to increase at every city and region except Seoul, while the employment of elementary labor jobs is predicted to increase slightly in Seoul. In particular, Gangwon-do and Chuncheongdo are predicted to increase in the employment of all occupational jobs.

• Transactions of the Korean Society of Mechanical Engineers
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• v.9 no.6
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• pp.714-724
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• 1985

Two-phase(air-solid, air-liquid droplet) turbulent round jet has been analyzed numerically using two equation turbulence model. The mean motion of suspending particles in air has been treated as the secondary fluid with virtual density and eddy viscosity. In this paper, the local mean velocity of secondary fluid is not assumed to be the same as that of the primary one. Dissipation rate of turbulent kinetic energy which arises because the particles can not catch up with the turbulent fluctuations of the primary fluid has been modelled by using the concept of Kolmogorov's spectral energy transfer. Numerical computations were performed for flows with different volume fraction of the dispersed phase and the diameter of particle. Results show that the total rate of turbulent energy dissipation, turbulent intensities and spreading rate of jets are reduced by the increase of volume fraction of dispersed phase. However it does not show consistent tendency with increasing the particle diameter. This investigation also shows that presence of particles in the fluid modifies the structure of the primary fluid flow significantly. Predicted velocity profiles and turbulence properties qualitatively agree with available data.

• Journal of Forest and Environmental Science
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• v.36 no.1
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• pp.7-16
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• 2020

Tree size distribution modelling is an integral part of forest management. Most distribution yield systems rely on some flexible probability models. In this study, a simple finite mixture of two components two-parameter Weibull distribution was compared with complex four-parameter distributions in terms of their fitness to predict tree size distribution of teak (Tectona grandis Linn f) plantations. Also, a system of equation was developed using Seemingly Unrelated Regression wherein the size distributions of the stand were predicted. Generalized beta, Johnson's SB, Logit-Logistic and generalized Weibull distributions were the four-parameter distributions considered. The Kolmogorov-Smirnov test and negative log-likelihood value were used to assess the distributions. The results show that the simple finite mixture outperformed the four-parameter distributions especially in stands that are bimodal and heavily skewed. Twelve models were developed in the system of equation-one for predicting mean diameter, seven for predicting percentiles and four for predicting the parameters of the finite mixture distribution. Predictions from the system of equation are reasonable and compare well with observed distributions of the stand. This simplified mixture would allow for wider application in distribution modelling and can also be integrated as component model in stand density management diagram.

• Wind and Structures
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• v.36 no.2
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• pp.133-147
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• 2023

The random vibration of saddle membrane structures under wind load is studied theoretically and experimentally. First, the nonlinear random vibration differential equations of saddle membrane structures under wind loads are established based on von Karman's large deflection theory, thin shell theory and potential flow theory. The probabilistic density function (PDF) and its corresponding statistical parameters of the displacement response of membrane structure are obtained by using the diffusion process theory and the Fokker Planck Kolmogorov equation method (FPK) to solve the equation. Furthermore, a wind tunnel test is carried out to obtain the displacement time history data of the test model under wind load, and the statistical characteristics of the displacement time history of the prototype model are obtained by similarity theory and probability statistics method. Finally, the rationality of the theoretical model is verified by comparing the experimental model with the theoretical model. The results show that the theoretical model agrees with the experimental model, and the random vibration response can be effectively reduced by increasing the initial pretension force and the rise-span ratio within a certain range. The research methods can provide a theoretical reference for the random vibration of the membrane structure, and also be the foundation of structural reliability of membrane structure based on wind-induced response.