• Management Science and Financial Engineering
• /
• v.2 no.1
• /
• pp.73-101
• /
• 1996

We show assets can be classified into diversifiable risks and non-diversifiable risks based on aggregate endowment and spanning so that in equilibrium agents eliminate diversifiable risks which must have zero values. Consequently, the benchmark portfolio that represents a pricing operator should have only a non-diversifiable risk, aggregate endowment should earn a positive risk premium over a riskless asset, and, even in incomplete markets, there should be a pricing operator represented by a function of aggregate endowment if any asset mean-independent of aggregate endowment is diversifiable. These results apply to both the CAPM and a representative agent model.

• Bulletin of the Korean Mathematical Society
• /
• v.54 no.2
• /
• pp.383-389
• /
• 2017

This paper devotes to the study of a diffusive model for unstirred membrane reactors with maintenance energy subject to a homogeneous Neumann boundary condition. It shows that the unique constant steady state is globally asymptotically stable when it exists. This result further implies the non-existence of the non-uniform steady state solution.

• Bulletin of the Korean Mathematical Society
• /
• v.54 no.2
• /
• pp.655-666
• /
• 2017

In this paper, we study the pattern formation to a general Degn-Harrison reaction model. We show Turing instability happens by analyzing the stability of the unique positive equilibrium with respect to the PDE model and the corresponding ODE model, which indicate the existence of the non-constant steady state solutions. We also show the existence periodic solutions of the PDE model and the ODE model by using Hopf bifurcation theory. Numerical simulations are presented to verify and illustrate the theoretical results.

• Journal of the Korean Society for Industrial and Applied Mathematics
• /
• v.23 no.2
• /
• pp.139-155
• /
• 2019

In this paper, we study the asymptotic behavior and Hopf bifurcation of the modified Holling-Tanner models for the predator-prey interactions in the absence of diffusion. Further the direction of Hopf bifurcation and stability of bifurcating periodic solutions are investigated. Diffusion driven instability of the positive equilibrium solutions and Turing instability region regarding the parameters are established. Finally we illustrate the theoretical results with some numerical examples.

• Journal of the Chungcheong Mathematical Society
• /
• v.36 no.1
• /
• pp.39-53
• /
• 2023

In this paper, we consider a delayed ratio-dependent predator-prey reaction-diffusion system with homogenous Neumann boundary conditions. We study the existence of nonnegative solutions and the stability of the nonnegative equilibria to the system. In particular, we provide a sufficient condition for the positive equilibrium to be globally asymptotically stable.

• Journal of Ecology and Environment
• /
• v.38 no.1
• /
• pp.1-14
• /
• 2015

Whilst it is clear that increasing temperatures from global environmental change will impact the positions of alpine treelines, it is likely that a range of regional and local scaled factors will mediate the overall impact of global scale climate drivers. We summarized 12 categories of abiotic and biotic factors as 4 groups determining treeline positions. First, there are global factors related to climate-induced growth limitation and carbon limitation. Second, there are seven regional and local factors related to treeline dynamics including frost stress, topography, water stress, snow, wind, fire and non-fire disturbance. Third, species-specific factors can control treeline dynamics through their influence on reproduction and life history traits. Fourth, there are positive feedbacks in structuring the dynamics of treelines. Globally, the commonly accepted growth limitation hypothesis is that growth at a treeline is limited by temperature. Meanwhile, positive feedbacks between canopy cover and tree establishment are likely to control the spatial pattern and temporal dynamics of many treelines. The presence of non-linear dynamics at treelines has implications for the use of treelines as barometers of climate change because the lagged responses and abrupt shifts inherent in non-equilibrium systems may combine to mask the overall climate trend.

• The Journal of Information Systems
• /
• v.16 no.1
• /
• pp.47-64
• /
• 2007

The telecommunication service industry plays a major role in the realization of the perfect information society in the 21st century and, has a great influence in society and culture. Using the Calculable General Equilibrium Model, we analyze the telecommunication service's economic effects on other industries as well as on the national economy. In 2001, the 8 percent increase in the telecom sales caused the 5 billion dollar increase in the GDP, which seems to continue to bring about no less than 5 billion dollar GDP increase each year until 2030. The telecom sales increase has been evaluated to have disproportionately positive effect on transmission device and audio equipment industries. In summary, the telecom sales have a positive net enぉ on the GDP and on most of the industries with a few exceptions.

• Environmental Engineering Research
• /
• v.16 no.1
• /
• pp.29-34
• /
• 2011

The electric charge on a membrane was investigated by analyzing the experimental rejection of various monovalent and divalent ionic solutes. The characteristics of the separation of ionic solutes using various nanofiltration membranes were obtained from an experimental nanofiltration set-up, with a surface area of $40cm^2$ under the operational pressures between 0.25-0.3 MPa. The state of the membrane electric charge was observed using separation coefficients, i.e., the permeation ratio of monovalent to divalent ions. To confirm the state of the membrane charge observed via the separation coefficient, a calculation using the extended Nernst-Planck equation, coupled with the Donnan equilibrium, assuming different electric charge states of the membrane, was compared with the experimental rejection of ionic solutes. The examination of the characteristics of separation using three types of nanofiltration membranes showed that one of the membranes carried a negative/positive double charge density inside, while other two membranes carried either a positive or negative charge density.

• East Asian Economic Review
• /
• v.17 no.1
• /
• pp.3-25
• /
• 2013

This paper evaluates whether the proposed FTAAP is a desirable policy option for APEC member economies and the world economy. More specifically, this paper qualitatively investigates whether the FTAAP satisfies conditions for a trade bloc to generate positive and sufficient net trade creation effect. In addition, this paper estimates the likely impact of the FTAAP by using a CGE model analysis. From the qualitative analysis based on statistical data, this paper strongly argues that the FTAAP can be a desirable regional trade bloc able to generate positive gains from freer trade. From the ex-ante scenario analysis using both static and capital accumulation CGE Models, this paper concludes that the FTAAP has great potential for improving welfare of participating APEC economies and will boost economic growth in the region. In particular, the FTAAP would be even better if it can be linked with liberalization of trade in services and enhanced trade facilitation.

• 제어로봇시스템학회:학술대회논문집
• /
• 1990.10b
• /
• pp.1060-1065
• /
• 1990

In general it is difficult to determine a Liapunov function for a given asymptotically stable, nonlinear differential equations system. But, in the system with control inputs, it is feasible to make a given positive function, except for a small area, globally satisfy the conditions of the Liapunov function for the system. We call such a positive function a Liapunov-like function, and propose a method of nonlinear optimal regulator using this Liapunov-like function. We also use the periodic Liapuitov-like friction that suits the system whose equilibrium points exist periodically. The relationship between the Liapunov function and cost function which this nonlinear regulator minimizes is considered using inverse optimal method.