• Bulletin of the Korean Mathematical Society
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• v.61 no.3
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• pp.699-715
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• 2024

We study the Riemann problem for the pressureless Euler system with the source term depending on the time. By means of the variable substitution, two kinds of Riemann solutions including deltashock and vacuum are constructed. The generalized Rankine-Hugoniot relation and entropy condition of the delta-shock are clarified. Because of the source term, the Riemann solutions are non-self-similar. Moreover, we propose a time-dependent viscous system to show all of the existence, uniqueness and stability of solutions involving the delta-shock by the vanishing viscosity method.

• The KIPS Transactions:PartD
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• v.8D no.4
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• pp.393-400
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• 2001

This paper presents a stochastic model for the software failure phenomenon based on a nonhomogeneous Poisson process (NHPP). The failure process is analyzed to develop a suitable mean value function for the NHPP ; expressions are given for several performance measure. Actual software failure data are compared with generalized model by Goel dependent on the constant reflecting the quality of testing. The performance measures and parametric inferences of the new models, Rayleigh and Gumbel distributions, are discussed. The results of the new models are applied to real software failure data and compared with Goel-Okumoto and Yamada, Ohba and Osaki models. Tools of parameter inference was used method of the maximun likelihood estimate and the bisection algorithm for the computing nonlinear root. In this paper, using the sum of the squared errors, model selection was employed. The numerical example by NTDS data was illustrated.

• The KIPS Transactions:PartD
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• v.10D no.5
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• pp.805-812
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• 2003

This paper presents a stochastic model for the software failure phenomenon based on a nonhomogeneous Poisson process (NHPP) and performs Bayesian inference using prior information. The failure process is analyzed to develop a suitable mean value function for the NHPP; expressions are given for several performance measure. The parametric inferences of the model using Logarithmic Poisson model, Crow model and Rayleigh model is discussed. Bayesian computation and model selection using the sum of squared errors. The numerical results of this models are applied to real software failure data. Tools of parameter inference was used method of Gibbs sampling and Metropolis algorithm. The numerical example by T1 data (Musa) was illustrated.

• The Journal of Korean Institute of Electromagnetic Engineering and Science
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• v.22 no.1
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• pp.89-97
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• 2011

We analyze the performance of various techniques to overcome degradation of performance of STAP caused by nonhomogeneous clutter. The performance of NHD that used to eliminate outliers from nonhomogeneous clutter is improved by using the projection statistics(PS) that is robust to multiple outliers. The method of clutter covariance matrix estimation using a median value and the conventional method are also investigated and then compared. From the simulation results of STAP, the method of clutter covariance matrix estimation using a median value shows better performance than the conventional method for the calculation of the SINR loss, and MSMI for the single target and the multiple targets regardless of the NHD methods.

• Geotechnical Engineering
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• v.14 no.4
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• pp.5-16
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• 1998

The ground of Taegu area consists mainly of shales with elastic sedimentary rocks. These shales have a nonhomogeneous and anisotropic characteristics. So their physical and mechanical properties are very different due to the angles($\beta$ value) of bedding planes of sedimentary rock. In this study, the physical and mechanical characteristics of shales in Taegu area are studied by performing all kinds of rock test. According to results of test, apparent specific gravity of shale decreases as the $\beta$ value increases. On the contrary, porosity and absorption increase. Elastic wave velocity shorts the highest value at the $90^{\circ}$. And Young's modulus shows the maximum value at the $30^{\circ}$. The uniaxial strength, triaxial strength, cohesion and angle of friction show the minimum value at the $60^{\circ}$respectively.

• Spatial Information Research
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• v.6 no.1
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• pp.77-90
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• 1998

The complex interactions of climate, topography, geology, biota and hwnan activities result in the land cover patterns, which are impacted by natural disturbances such as fire, earthquake and flood. Natural disturbances disrupt ecosystem communities and change the physical environment, thereby generating a new landscape. Community ecologists believe that disturbance is critical in determining how diverse ecological systems function. Fires were once a major agent of disturbance in the North American tall grass prairies, African savannas, and Australian bush. The major focus of this research was to develop stochastic model of spatial process of disturbance or spatial events and simulate the process based on the developed model and it was applied to the fire arrival process in the Great Victoria Desert of Australia, where wildfires generate a mosaic of patches of habitat at various stages of post-fire succession. For this research, Landsat Multi-Spectral Scanner(MSS) data covering the period from 1972 to 1994 were utilized. Fire arrival process is characterized as a spatial point pattern irregularly distributed within a region of space. Here, nonhomogeneous planar Poisson process is proposed as a model for the fire arrival process and rejection sampling thinning the homogeneous Poisson process is used for its simulation.

• Wind and Structures
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• v.25 no.2
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• pp.131-156
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• 2017

This paper deals with the dynamic stability of embedded functionally graded (FG)-carbon nanotubes (CNTs)-reinforced micro cylindrical shells. The structure is subjected to harmonic non-uniform temperature distribution and 2D magnetic field. The CNT reinforcement is either uniformly distributed or FG along the thickness direction where the effective properties of nano-composite structure are estimated through Mixture low. The viscoelastic properties of structure are captured based on the Kelvin-Voigt theory. The surrounding viscoelastic medium is considered nonhomogeneous with the spring, orthotropic shear and damper constants. The material properties of cylindrical shell and the viscoelastic medium constants are assumed temperature-dependent. The first order shear deformation theory (FSDT) or Mindlin theory in conjunction with Hamilton's principle is utilized for deriving the motion equations where the size effects are considered based on Eringen's nonlocal theory. Based on differential quadrature (DQ) and Bolotin methods, the dynamic instability region (DIR) of structure is obtained for different boundary conditions. The effects of different parameters such as volume percent and distribution type of CNTs, mode number, viscoelastic medium type, temperature, boundary conditions, magnetic field, nonlocal parameter and structural damping constant are shown on the DIR of system. Numerical results indicate that the FGX distribution of CNTs is better than other considered cases. In addition, considering structural damping of system reduces the resonance frequency.

• Journal of Korea Water Resources Association
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• v.41 no.3
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• pp.265-276
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• 2008

The observed data of enough period need for design of hydrological works. But, most hydrological data aren't enough. Therefore in this paper, hourly precipitation generated by nonhomogeneous Markov chain model using variable Kernel density function. First, the Kernel estimator is used to estimate the transition probabilities. Second, wet hours are decided by transition probabilities and random numbers. Third, the amount of precipitation of each hours is calculated by the Kernel density function that estimated from observed data. At the results, observed precipitation data and generated precipitation data have similar statistic. Also, rainfall mass curve is derived by calculated transition probabilities for generation of hourly precipitation.

• Journal of Korea Water Resources Association
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• v.41 no.3
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• pp.251-264
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• 2008

In this study, a nonhomogeneous markov model which is able to simulate hourly rainfall series is developed for estimating reliable hydrologic variables. The proposed approach is applied to simulate hourly rainfall series in Korea. The simulated rainfall is used to estimate the design rainfall and flood in the watershed, and compared to observations in terms of reproducing underlying distributions of the data to assure model's validation. The model shows that the simulated rainfall series reproduce a similar statistical attribute with observations, and expecially maximum value is gradually increased as number of simulation increase. Therefore, with the proposed approach, the non-homogeneous markov model can be used to estimate variables for the purpose of design of hydraulic structures and analyze uncertainties associated with rainfall input in the hydrologic models.

• The KIPS Transactions:PartD
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• v.11D no.6
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• pp.1269-1276
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• 2004

The Parameter Estimation for software existing reliability models, Goel-Okumoto, Yamada-Ohba-Osaki model was reviewed and Rayleigh model based on Rayleigh distribution was studied. In this paper, we discusses comparison of parameter estimation using maximum likelihood estimator and Bayesian estimation based on Gibbs sampling to analysis of the estimator' pattern. Model selection based on sum of the squared errors and Braun statistic, for the sake of efficient model, was employed. A numerical example was illustrated using real data. The current areas and models of Superposition, mixture for future development are also employed.