• The Journal of Korean Medicine
• /
• v.34 no.1
• /
• pp.136-145
• /
• 2013

Objectives: Recently, Korean medicine has been explored by employing mathematical methods, which is an effort to raise Korean medicine to a higher level of scientific research. In that vein, we propose a mathematical model, analyzing the effects of seasonal cycle as an external factor in addition to the internal interactions of five-states, the engendering and the restraining. Methods: Some modified differential equations with 5-state variables were given to describe the interactions of the engendering and the restraining, and effect of seasonal cycle, and are numerically analyzed by Runge-Kutta method. We then simulated it along with time and dynamically analyzed it by Moran's I, a spatial autocorrelation. Results: We showed the effects of seasonal cycle on yin-yang five-states and applied it to the human life cycle. Conclusions: Our result is comparable to previous results in the respect that we consider the seasonal cycle and its effect on five-states, unlike others' mainly focusing on internal interaction. Furthermore, we suggest some follow-up study taking into consideration the complexity and diversity of external factors.

• Journal of applied mathematics & informatics
• /
• v.33 no.5_6
• /
• pp.559-578
• /
• 2015

Human Immune Deficiency Virus (or simply HIV) induces a persistent infection that leads to AIDS causing death in almost every infected individual. As HIV affects the immune system directly by attacking the CD4+ T cells, to exterminate the infection, the natural immune system produces virus-specific cytotoxic T lymphocytes(CTLs) that kills the infected CD4+ T cells. The reduced CD4+ T cell count produce reduced amount of cytokines to stimulate the production of CTLs to fight the invaders that weakens the body immunity succeeding to AIDS. In this paper, we introduce a mathematical model with discrete time-delay to represent this cell dynamics between CD4+ T cells and the CTLs under HIV infection. A modified functional form has been considered to describe the infection mechanism. Characteristics of the system are studied through mathematical analysis. Numerical simulations are carried out to illustrate the analytical findings.

• Journal of the Korean Society of Tobacco Science
• /
• v.26 no.1
• /
• pp.64-72
• /
• 2004

On-going research has recently documented the certain tobacco specific nitrosamines (TSNAs) are formed during the curing process by an interaction of nitrogen oxides (NOx) contained in combustion gases and naturally occurring compounds in the tobacco leaves. Although the role of TSNAs in human health have been extensively investigated, little research has been conducted on the physical and chemical phenomena relating to their formation during curing. In this paper, we developed a mathematical model for describing NOx absorption into green (uncured) tobacco. We found considerable uptake of NOx by green tobacco with variations related to several factors. Specifically, tobacco from the lower stalk positions (bottom one third) absorbs more NOx gas per unit weight than tobacco from upper stalk positions. Additionally, the green tobacco packed with a density of 0.103 g/㎤ absorbs more NOx gas per unit weight than either 0.0443 g/㎤ or 0.0739 g/㎤. Further, the NOx absorption increases proportionally with temperature with the maximum absorption point around 4$0^{\circ}C$.

• Journal of Biomedical Engineering Research
• /
• v.21 no.2
• /
• pp.189-201
• /
• 2000

Mechanical factors in the human body are considered to play a dominant role in low back problems. Various spinal structures. including muscles, act in unison to resist the external load. An estimation of the muscle forces in this structure requires a knowledge of the orientation, location and area of cross-section of the muscles to complete the formulation of a truly three-dimensional mathematical model of the spine. The geometric parameters which are calculated were the line of action, the centroid and physiologic area of cross-section of each muscle as a function of the spinal level. This geometric data were obtained from CT scans of 11 subjects participating in this study.

• Proceedings of the KIEE Conference
• /
• 2000.07d
• /
• pp.2763-2765
• /
• 2000

The interactions between the excavation tool and the excavation environment are dynamic, unstructured and complex. In addition. operating modes of an excavator depend on working conditions, which makes it difficult to derive the exact mathematical model of excavator. Even after the exact mathematical model is established, it is difficult to design of a controller because the system equations are highly nonlinear and the state variable are coupled. The objective of this study is to design a fuzzy logic controller (FLC) which controls the position of excavator's attachment. This approach enables the transfer of human heuristics and expert knowledge to the controller. Expeiments are carried out to check the performance of the FLC.

• Journal of Radiation Protection and Research
• /
• v.16 no.1
• /
• pp.53-72
• /
• 1991

An integrated model is developed in this paper for the performance assessment of high level radioactive waste repository. This integrated model consists of two simple mathematical models. One is a multiple-barrier failure model of the repository system based on constant failure rates which provides source terms to biosphere. The other is a biosphere model which has multiple pathways for radionuclides to reach to human. For the parametric uncertainty and sensitivity analysis for the risk assessment of high level radioactive waste repository, Latin hypercube sampling and rank correlation techniques are applied to this model. The former is cost-effective for large computer programs because it gives smaller error in estimating output distribution even with smaller number of runs compared to crude Monte Carlo technique. The latter is good for generating dependence structure among samples of input parameters. It is also used to find out the most sensitive, or important, parameter groups among given input parameters. The methodology of the mathematical modelling with statistical analysis will provide useful insights to the decision-making of radioactive waste repository selection and future researches related to uncertain and sensitive input parameters.

• Journal of the Korean Mathematical Society
• /
• v.49 no.4
• /
• pp.779-794
• /
• 2012

In this paper, we study the global stability of two mathematical models for human immunodeficiency virus (HIV) infection with intra-cellular delays. The first model is a 5-dimensional nonlinear delay ODEs that describes the interaction of the HIV with two classes of target cells, $CD4^+$ T cells and macrophages taking into account the saturation infection rate. The second model generalizes the first one by assuming that the infection rate is given by Beddington-DeAngelis functional response. Two time delays are used to describe the time periods between viral entry the two classes of target cells and the production of new virus particles. Lyapunov functionals are constructed and LaSalle-type theorem for delay differential equation is used to establish the global asymptotic stability of the uninfected and infected steady states of the HIV infection models. We have proven that if the basic reproduction number $R_0$ is less than unity, then the uninfected steady state is globally asymptotically stable, and if the infected steady state exists, then it is globally asymptotically stable for all time delays.

• Journal of Educational Research in Mathematics
• /
• v.8 no.2
• /
• pp.651-662
• /
• 1998

Mathematics is means for making sense of one's experiential world and products of human activities. A usefulness of mathematics is derived from this features of mathematics. Keeping the meaning of situations during the mathematizing of situations. However, theories about the development of mathematical concepts have turned mainly to an understanding of invariants. The purpose of this study is to show the possibility of computer in representing situation and phenomena. First, we consider situated cognition theory for looking for the relation between various representation and situation in problem. The mathematical concepts or model involves situations, invariants, representations. Thus, we should involve the meaning of situations and translations among various representations in the process of mathematization. Second, we show how the process of computational mathematization can serve as window on relating situations and representations, among various representations. When using computer software such as ALGEBRA ANIMATION in mathematics classrooms, we identified two benifits First, computer software can reduce the cognitive burden for understanding the translation among various mathematical representations. Further, computer softwares is able to connect mathematical representations and concepts to directly situations or phenomena. We propose the case study for the effect of computer software on practical mathematics classrooms.

• The Korean Journal of Ecology
• /
• v.7 no.3
• /
• pp.109-118
• /
• 1983

Near future dynamics of water qualities (nutrient concentration) of the Han River was predicted, based on a mathematical model representing the relationship between the nutrient concentration in th river wagter and environmental factors (population density, land-use types, rock compositions and nutrient accumulation) in the basin. The population density and land-use types were forecasted to change distinctly in the downstream area, especially in Seoul City area in 1985~1990 whereas any environmental factor was not expected to change its level significantly in both upstream and middle reaches areas. It was indicated by the model that the nutrients concentration in the up- and mid-streams would keep its level in future as it was, but it would increase drastially in the downstream area. For the preservation of the water qualities in the downstream at least to keep its level as it was in 1980, practical countermeasures were proposed, based on the assessment of the contribution of each environmental factor to the water qualities.

• The Korean Journal of Physiology and Pharmacology
• /
• v.20 no.4
• /
• pp.367-378
• /
• 2016

Recently, it was reported that the role of mitochondria-reactive oxygen species (ROS) generating pathway in cisplatin-induced apoptosis is remarkable. Since a variety of molecules are involved in the pathway, a comprehensive approach to delineate the biological interactions of the molecules is required. However, quantitative modeling of the mitochondria-ROS generating pathway based on experiment and systemic analysis using the model have not been attempted so far. Thus, we conducted experiments to measure the concentration changes of critical molecules associated with mitochondrial apoptosis in both human mesothelioma H2052 and their ${\rho}^0$ cells lacking mitochondrial DNA (mtDNA). Based on the experiments, a novel mathematical model that can represent the essential dynamics of the mitochondrial apoptotic pathway induced by cisplatin was developed. The kinetic parameter values of the mathematical model were estimated from the experimental data. Then, we have investigated the dynamical properties of this model and predicted the apoptosis levels for various concentrations of cisplatin beyond the range of experiments. From parametric perturbation analysis, we further found that apoptosis will reach its saturation level beyond a certain critical cisplatin concentration.