• Communications of the Korean Mathematical Society
• /
• v.33 no.3
• /
• pp.823-831
• /
• 2018

We define progressive tax rate functions, study their properties, and describe some smooth models. The key requirement, defining the progressive nature of the taxation model, is that the progressive tax rate functions should have infinite contact with the zero function at the origin, in order to care the poor. In constructing a wide array of such functions, assisting functions are introduced.

• Journal of the Korean Mathematical Society
• /
• v.57 no.4
• /
• pp.987-1004
• /
• 2020

Motivated by the traffic flow model with Arrhenius looka-head relaxation dynamics introduced in [25], this paper proposes a traffic flow model with look ahead relaxation-behind intensification by inserting look behind intensification dynamics to the flux. Finite time shock formation conditions in the proposed model with various types of interaction potentials are identified. Several numerical experiments are performed in order to demonstrate the performance of the modified model. It is observed that, comparing to other well-known macroscopic traffic flow models, the model equipped with look ahead relaxation-behind intensification has both enhanced dispersive and smoothing effects.

• Korean Journal of Air-Conditioning and Refrigeration Engineering
• /
• v.17 no.8
• /
• pp.780-788
• /
• 2005

Two different types of algorithms were developed and applied to detect the partial faults of a multi-type air conditioning system. Partial faults include the compressor valve leakage, the refrigerant pipe partial blockage, the condenser fouling, and the evaporator fouling. The first algorithm was developed by using mathematical models and parity relations, and the second algorithm was developed by using mathematical models and a RBF neural network. Test results showed that the second algorithm was better than the first algorithm in detecting various partial faults of the system. Therefore, the algorithm developed by using mathematical models and a RBF neural network may be used for the detection of partial faults of an air-conditioning system.

• Journal of the Korean Mathematical Society
• /
• v.52 no.3
• /
• pp.503-522
• /
• 2015

In this paper, we consider the problem of testing for a parameter change in nonlinear time series models with GARCH type errors. We introduce two types of cumulative sum (CUSUM) tests: estimates-based and residual-based tests. It is shown that under regularity conditions, their limiting null distributions are the sup of independent Brownian bridges. A simulation study is conducted for illustration.

• Journal of the Korean Mathematical Society
• /
• v.40 no.5
• /
• pp.869-881
• /
• 2003

In this paper, a nonautonomous predator-prey dispersion delay models with functional response is studied. By using the continuation theorem of coincidence degree theory, the existence of a positive periodic solution for above models is established.

• Bulletin of the Korean Mathematical Society
• /
• v.48 no.4
• /
• pp.839-845
• /
• 2011

In this paper, we consider the cusum of squares test for the dispersion parameter in stochastic differential equation models. It is shown that the test has a limiting distribution of the sup of a Brownian bridge, unaffected by the drift parameter estimation. A simulation result is provided for illustration.

• Communications of the Korean Mathematical Society
• /
• v.22 no.4
• /
• pp.587-596
• /
• 2007

In this paper, we study two-phase flow models. The chunk mix model of the two-phase flow equations is analyzed by a characteristic analysis. The model discussed herein has real characteristic values for all physically acceptable states and except for a set of measure zero has a complete set of characteristic vectors in state space.

• Communications of the Korean Mathematical Society
• /
• v.18 no.4
• /
• pp.703-712
• /
• 2003

This paper deals with the strong consistency of the asymmetric least squares for the nonlinear censored regression models which includes dependent variables cut off midway by any of external conditions, and provide the sufficient conditions which ensure the strong consistency of proposed estimators of the censored regression models. One example is given to illustrate the application of the main result.

• Journal of Korean Society of Transportation
• /
• v.28 no.6
• /
• pp.109-120
• /
• 2010

This study aims to develop mathematical models for estimating saturation flow rates at the stop line of signalized intersection due to Workzones in the vicinity, since the saturation flow rate is the most critical parameter in capacity analysis for signalized intersections. It was found by reference review that saturation flow rates are sensitively influenced by the location of Workzone, the number of lanes, cycle length and effective green time. Extensive microscopic simulation runs were also performed and compared to the those of mathematical models for model verification. Mathematical models were developed based on traffic flow theory and dualizing them by the location of workzones. And then each result produced by changing important parameter values was carefully examined and analyzed. Small but consistent differences in saturation flow rate values between mathematical models and simulations exist. However, the pattern of changes in saturation flow rates depending on each variable was similar.

• The Korean Journal of Applied Statistics
• /
• v.27 no.6
• /
• pp.867-889
• /
• 2014

Nonparametric Bayesian (np Bayes) statistical models are popularly used in a variety of research areas because of their flexibility and computational convenience. This paper reviews the np Bayes models focusing on biomedical research applications. We review key probability models for np Bayes inference while illustrating how each of the models is used to answer different types of research questions using biomedical examples. The examples are chosen to highlight the problems that are challenging for standard parametric inference but can be solved using nonparametric inference. We discuss np Bayes inference in four topics: (1) density estimation, (2) clustering, (3) random effects distribution, and (4) regression.