• Communications of the Korean Mathematical Society
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• v.32 no.1
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• pp.147-163
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• 2017

We define de Sitter focal surfaces and hyperbolic focal surfaces of hyperbolic space curves. As an application of the theory of unfoldings of function germs, we investigate the singularities of these surfaces. For characterizing the singularities of these surfaces, we discover a new hyperbolic invariants and investigate the geometric meanings.

• Kyungpook Mathematical Journal
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• v.58 no.1
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• pp.117-135
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• 2018

The orthogonal trajectories of the first tangents of the curve are called the involutes of x. The hyperspheres which have higher order contact with a curve x are known osculating hyperspheres of x. The centers of osculating hyperspheres form a curve which is called generalized evolute of the given curve x in n-dimensional Euclidean space ${\mathbb{E}}^n$. In the present study, we give a characterization of involute curves of order k (resp. evolute curves) of the given curve x in n-dimensional Euclidean space ${\mathbb{E}}^n$. Further, we obtain some results on these type of curves in ${\mathbb{E}}^3$ and ${\mathbb{E}}^4$, respectively.

• International Journal of Concrete Structures and Materials
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• v.9 no.4
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• pp.453-462
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• 2015

A critical review on existing creep theories in calcium-silicate-hydrate (C-S-H) is presented with an emphasis on several fundamental questions (e.g. the roles of water, relative humidity, temperature, atomic ordering of C-S-H). A consensus on the rearrangement of nanostructures of C-S-H as a main consequence of creep, has almost been achieved. However, main disagreement still exists on two basic aspects regarding creep mechanisms: (1) at which site the creep occurs, like at interlayer, intergranular, or regions where C-S-H has a relatively higher solubility; (2) how the structural rearrangement evolutes, like in a manner of interlayer sliding, intra-transfer of water at various scales, recrystallization of gelled-like particles, or dissolution-diffusion-reprecipitation at inter-particle boundary. The further understanding of creep behavior of C-S-H relies heavily on the appropriate characterization of its nanostructure.

• The KIPS Transactions:PartD
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• v.10D no.5
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• pp.845-858
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• 2003

The various software engineering techniques have been come out in order to cope with the software crisis since 1980's. These days the software Engineering has focused on the process of software development which is the guide for a qualify and productive improvement of software. But, most of the methodologies assume that a new system will be constructed and reused in the future. these do not support how we reuse legacy system's resources and construct a new system efficiently. In this paper, we present an efficient Reengineering Process for legacy system evolutions, RUP+re, which extends and customizes RUP. RUP+re consists of Reverse Engineering Workflow, Transformation Workflow and Evolution Workflow based on Small-h model. We describe RUP+re's workflows with their own detail steps and verify the process through the case study practivally. So, we provide efficient guidelines to the software Reengineering process construction which evolutes the resources of a legacy system.