• Journal of Korean Institute of Industrial Engineers
• /
• v.34 no.2
• /
• pp.181-189
• /
• 2008

Survivability of a network is one of the most important issues in designing present-day communication networks. For the past few decades, a lot of researches have proposed the mathematical models to evaluate the survivability of networks. In this paper, we attempt to survey such researches and classify them based on how these researches measure the survivability of a network.

• Bulletin of the Korean Mathematical Society
• /
• v.41 no.2
• /
• pp.371-385
• /
• 2004

In this paper, we investigate the uniqueness of positive solutions to weak competition models with self-cross diffusion rates under homogeneous Dirichlet boundary conditions. The methods employed are upper-lower solution technique and the variational characterization of eigenvalues.

• Communications of the Korean Mathematical Society
• /
• v.32 no.3
• /
• pp.745-763
• /
• 2017

The Borel-Serre partial compactification gives cofinite models for the proper classifying space for arithmetic lattices. Non-arithmetic lattices arise only in semisimple Lie groups of ${\mathbb{R}}$-rank one. The author generalizes the Borel-Serre partial compactification to construct cofinite models for the proper classifying space for lattices in semisimple Lie groups of ${\mathbb{R}}$-rank one by using the reduction theory of Garland and Raghunathan.

• Journal of the Korean Mathematical Society
• /
• v.42 no.4
• /
• pp.827-845
• /
• 2005

In this paper, we present a general method for the stability analysis of some bursting models. Our method is geometric in the sense that we consider a flow-defined return map defined on a section and determine when the map is a contraction. We find that there are three different stability types in the codimension-1 planar bursters.

• Archives of design research
• /
• v.20
• /
• pp.61-72
• /
• 1997

This study aims to promote understanding level for mathematical model, to improve methods and necessity of application in the process of product design and also to promote approaching and applying methods as a guideline for beginners. For the procedure and method of study first, it was emphasized by linking method and necessity of scientific analysis and a quality of product design and design process. Next, the corresponding relations between mathematical model and design probelem was desciebed, the mathematical model was examinated appeying process of product design. Lastly, approaching and applying methods for beginners was presented based on the discribed studied contents. As the result of the study, some points are by a result or problem : frist, the point that mathematical model is useful to grasp the design problems which various elements are complicately involved quantitatively and structurally, and its necessity can be especially utilized as a tool to justify and convince the convince the conclusion of the designer himself to the persons concerned. Second, the point that in order to apply mathematical model to the design process skillfully, first of all, the substance of all mathematical models which can be applid, and it is not easy to command in perfect method without using computer. Third, the point that since there are many kindsof mathematical models used is mathematical modeland the models which can be applidied to solve design problems differ in accordance with the design types and design process, its applying method can be presented as one kind of standardization or concretely. Fourth the point that in case of approaching mathematical model for the first time, it can start to select model corresponding with design type by stage of design process bassed on understanding for some mathematical knowledge and computer program.

• Education of Primary School Mathematics
• /
• v.26 no.4
• /
• pp.317-332
• /
• 2023

Mathematical modeling activities hold the potential for diverse applications, involving the transformation of real-life situations into mathematical models to facilitate problem-solving. In order to assess the cognitive, affective, and social dimensions of students' engagement in mathematical modeling activities, this study conducted sessions with ten groups of fifth-grade elementary school students. The ensuing processes and outcomes were thoroughly analyzed. As a result, each group effectively applied mathematical concepts and principles in creating mathematical models and gathering essential information to address real-world tasks. This led to notable shifts in interest, enhanced mathematical proficiency, and altered attitudes towards mathematics, all while promoting increased collaboration and communication among group members. Based on these analytical findings, the study offers valuable pedagogical insights and practical guidance for effectively implementing mathematical modeling activities.

• Journal of the Korean Society for Aeronautical & Space Sciences
• /
• v.45 no.11
• /
• pp.939-950
• /
• 2017

In this work, mathematical models are newly presented for three types of double-acting oleo-pneumatic shock absorbers as the first part of a comparative study on the several types of double-acting oleo-pneumatic shock absorbers. After a typical single-acting shock absorber model is presented for the sake of completeness, mathematical models of three types of double-acting shock absorbers are proposed. To derive the models, Bernoulli equation and orifice discharge coefficient are utilized along with the assumptions of incompressibility and poly-tropic process. The proposed models are expected to be used for investigation of the salient features of several types of double-acting oleo-pneumatic shock absorbers.

• Research in Mathematical Education
• /
• v.19 no.4
• /
• pp.195-209
• /
• 2015

The current study investigated meaning of Jigsaw model application in teaching and learning mathematics based on the literature research and analysis of Jigsaw models. Through related literature, properties of the tasks of the expert sheets in mathematics are examined. Then the advantages of the application of Jigsaw in mathematics are discussed in terms of the realizing mathematical connections and promoting positive affective outcomes of Korean students in mathematics.

• Bulletin of the Korean Mathematical Society
• /
• v.53 no.1
• /
• pp.83-90
• /
• 2016

We show that any orthogonal almost complex structure on a warped product Riemannian manifold of an oriented closed surface with nonnegative Gaussian curvature and a round 4-sphere is never integrable. This provides a partial answer to a question raised by E. Calabi.

• Communications of the Korean Mathematical Society
• /
• v.33 no.3
• /
• pp.1039-1048
• /
• 2018

In this paper we study the dynamics of a general ${\omega}-periodic$ model. Necessary and sufficient conditions for the global stability of zero steady state of the model are given. The conditions under which there exists a unique periodic solutions to the model are determined. We also show that the unique periodic solution is the global attractor of all other positive solutions. Some applications to mathematical models for cancer and tumor growth are given.