• Bulletin of the Korean Mathematical Society
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• v.38 no.2
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• pp.347-355
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• 2001

Let ($X, \omega$) be a closed symplectic 4-manifold. Let a finite cyclic group G act semifreely, holomorphically on X as isometries with fixed point set $\Sigma$(may be empty) which is a 2-dimension submanifold. Then there is a smooth structure on the quotient X'=X/G such that the projection $\pi$:X$\rightarrow$X' is a Lipschitz map. Let L$\rightarrow$X be the Spin$^c$ -structure on X pulled back from a Spin$^c$-structure L'$\rightarrow$X' and b_2^$+(X')>1. If the Seiberg-Witten invariant SW(L')$\neq$0 of L' is non-zero and $L=E\bigotimesK^-1\bigotimesE$ then there is a G-invariant pseudo-holomorphic curve u:$C\rightarrowX$,/TEX> such that the image u(C) represents the fundamental class of the Poincare dual $c_1$(E). This is an equivariant version of the Taubes' Theorem.

• Communications of the Korean Mathematical Society
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• v.17 no.2
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• pp.349-361
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• 2002

The ill-posed elliptic wave propagation problems can be transformed into well-posed initial value problems of the reflection and transmission operators characterizing the material structure of the given model by the combination of wave field splitting and invariant imbedding methods. In general, the derived scattering operator equations are of first-order in range, nonlinear, nonlocal, and stiff and oscillatory with a subtle fixed and movable singularity structure. The phase space and path integral analysis reveals that construction and reconstruction algorithms depend crucially on a detailed symbol analysis of the scattering operators. Some information about the singularity structure of the scattering operator symbols is presented and analyzed in the transversely homogeneous limit.

• Communications for Statistical Applications and Methods
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• v.18 no.6
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• pp.751-759
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• 2011

The method of generalized estimating equations(GEE) is widely used in the analysis of a correlated dataset that consists of repeatedly observed responses within subjects. The GEE uses a quasi-likelihood equations to find the parameter estimates without assuming a specific distribution for the correlated responses. In this paper we study the importance of specifying the working correlation structure appropriately in fitting GEE for correlated counts data. We investigate the empirical coverages of confidence intervals for the regression coefficients according to four kinds of working correlations where one structure should be specified by the users. The confidence intervals are computed based on the asymptotic normality and the sandwich variance estimator.

• Lingua Humanitatis
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• v.1 no.1
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• pp.195-217
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• 2001

According to John Crowe Ransom, "the poem is a loose logical structure with an irrelevant local texture." As is implied in the opposition between "structure" and "texture," Ransom′s is a dualistic, that is, non-organic, theory of poetry, in which the poem′s sound does not have any expressive function while its figurative language always goes beyond the realm of abstract meaning and celebrates the ontological density of the world. His theory relies heavily upon a series of oppositions-poetry and prose, art and science, concrete and universal, artistic and utilitarian, to name only a few-in order to uphold the humanistic value of poetry ("poetry as knowledge"). There is, however, a sense that his theoretical consistency derives from a determined refusal to see the blurry borderline between the oppositions. It is more or less easy to point out where Ransom′s theory falters, but more critical efforts should be made to probe into the personal and cultural significance of his persistent dualistic viewpoint. For Ransom the southerner, life demands the precarious balance between the oppositions as the very precondition for its existence and his dualism represents a way to understand man′s fallen state at the realistic level.

• Journal of IKEEE
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• v.18 no.2
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• pp.206-213
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• 2014

In this note, a new robust nonlinear output feedback variable structure controller is first systematically and generally designed for the output control of more affine uncertain nonlinear systems with mismatched uncertainties and matched disturbance. A transformed integral output feedback sliding surface with a most simple form is applied in order to remove the reaching phase problems. The closed loop exponential stability and the existence condition of the sliding mode on the integral output feedback sliding surface is investigated with a corresponding output feedback control input in Theorem 1. For practical application the continuous implementation of the control input is made by the modified saturation function. The effectiveness of the proposed controller is verified through a design example and simulation study.

• The Bulletin of The Korean Astronomical Society
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• v.46 no.2
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• pp.58.1-59
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• 2021

Exploration of asteroids' internal structure is essential for understanding their evolutional history. It also provides a fundamental information about the history of coalescence and collision of the solar system. Among several models of the internal structures, the rubble-pile model, confirmed by the near-Earth asteroid (25143) Itokawa by Hayabusa mission [1], is now widely regarded as the most common to asteroids with size ranging from 200 m to 10 km [2]. On the contrary, monolithic and core-mantle structures are also possible for small asteroids [3]. It is, however, still challenging to look through the interior of a target object using remote-sensing devices. In this presentation, we introduce our ongoing research conducted at Seoul National and propose an idea to infer the internal structure of Apophis using available instruments. Itokawa's research provides an important benchmark for Apophis exploration because both asteroids have similar size and composition [4][5]. We have conducted research on Itokawa's evolution in terms of collision and space weathering. Space weathering is the surface alteration process caused by solar wind implantation and micrometeorite bombardment [6]. Meanwhile, resurfacing via a collision acts as a counter-process of space weathering by exposing fresh materials under the matured layer and lower the overall degree of space weathering. Therefore, the balance of these two processes determine the space weathering degrees of the asteroid. We focus on the impact evidence on the boulder surface and found that space weathering progresses in only 100-10,000 years and modifies the surface optical properties (Jin & Ishiguro, KAS 2020 Fall Meeting). It is important to note that the timescale is significantly shorter than the Itokawa's age, suggesting that the asteroid can be totally processed by space weathering. Accordingly, our result triggers a further discussion about why Itokawa indicates a moderately fresh spectrum (Sq-type denotes less matured than S-type). For example, Itokawa's smooth terrains show a weaker degree of space weathering than other S-type asteroids [7]. We conjecture that the global seismic shaking caused by collisions with >1 mm-sized interplanetary dust particles induces granular convection, which hinders the progression of space weathering [8]. Note that the efficiency of seismic wave propagation is strongly dependent on the internal structure of the asteroid. Finally, we consider possible approaches to investigate Apophis's internal structure. The first idea is studying the space weathering age, as conducted for Itokawa. If Apophis indicates a younger age, the internal structure would have more voids [9]. In addition, the 2029 close encounter with Earth provides a rare natural opportunity to witness the contrast between before and after the event. If the asteroid exhibits a slight change in shape and space weathering degree, one can determine the physical structure of the internal materials (e.g., rubble-pile monolithic, thick or thin regolith layer, the cohesion of the materials). We will also consider a possible science using a seismometer.

• International Journal of Control, Automation, and Systems
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• v.4 no.6
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• pp.714-724
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• 2006

In this note a method of designing optimal vibration control based on Haar functions to control of bounce and pitch vibrations in engine-body vibration structure is presented. Utilizing properties of Haar functions, a computational method to find optimal vibration control for the engine-body system is developed. It is shown that the optimal state trajectories and optimal vibration control are calculated approximately by solving only algebraic equations instead of solving the Riccati differential equation. Simulation results are included to demonstrate the validity and applicability of the technique.

• Honam Mathematical Journal
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• v.37 no.4
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• pp.377-386
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• 2015

The symmetric ring property was due to Lambek and provided many useful results in relation with noncommutative ring theory. In this note we consider this property over centers, introducing symmetric-over-center. It is shown that symmetric and symmetric-over-center are independent of each other. The structure of symmetric-over-center ring is studied in relation to various radicals of polynomial rings.

• Mycobiology
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• v.32 no.1
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• pp.54-56
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• 2004

During the study of mushroom flora in Hongneung Arboretum, Ileodictyon gracile was confirmed as new to Korea and described based on morphological and microscopic characteristics in here. This species has subhypogeous, clathrate structure, and obovoid spores. The clathrate structures have $4{\sim}12$ polygonal meshes.

• Journal of the Korean Mathematical Society
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• v.52 no.2
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• pp.403-416
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• 2015

An operator T on a complex Hilbert space $\mathcal{H}$ is called skew symmetric if T can be represented as a skew symmetric matrix relative to some orthonormal basis for $\mathcal{H}$. In this note, we explore the structure of skew symmetric operators with disconnected spectra. Using the classical Riesz decomposition theorem, we give a decomposition of certain skew symmetric operators with disconnected spectra. Several corollaries and illustrating examples are provided.