• 한국전산유체공학회:학술대회논문집
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• 한국전산유체공학회 1999년도 춘계 학술대회논문집
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• pp.79-84
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• 1999

The shock wave diffracted behind a finite wedge is partially scattered after interacting with a starting vortex originated from the sharp vertex of the wedge. The shock is divided into the accelerated and decelerated shocks. The decelerated shock then interacts with the small vortexlets brought about by the vortex instability, producing weak compression waves. The shock-shock interaction produces Mach stems. Through this successive process, the shock attenuated. In this study, these complicated shock phenomena are computed using Euler equations and compared with experimental results obtained by the authors.

• 대한수학회지
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• 제48권3호
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• pp.551-563
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• 2011

Let ${\kappa}$ be a positive integer and let G be a simple graph with vertex set V(G). A function f : V (G) ${\rightarrow}$ {-1, 1} is called a signed total ${\kappa}$-dominating function if ${\sum}_{u{\in}N({\upsilon})}f(u){\geq}{\kappa}$ for each vertex ${\upsilon}{\in}V(G)$. A set ${f_1,f_2,{\ldots},f_d}$ of signed total ${\kappa}$-dominating functions of G with the property that ${\sum}^d_{i=1}f_i({\upsilon}){\leq}1$ for each ${\upsilon}{\in}V(G)$, is called a signed total ${\kappa}$-dominating family (of functions) of G. The maximum number of functions in a signed total ${\kappa}$-dominating family of G is the signed total k-domatic number of G, denoted by $d^t_{kS}$(G). In this note we initiate the study of the signed total k-domatic numbers of graphs and present some sharp upper bounds for this parameter. We also determine the signed total signed total ${\kappa}$-domatic numbers of complete graphs and complete bipartite graphs.

• Journal of applied mathematics & informatics
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• 제31권3_4호
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• pp.533-544
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• 2013

The multiplicative version of Wiener index (${\pi}$-index), proposed by Gutman et al. in 2000, is equal to the product of the distances between all pairs of vertices of a (molecular) graph G. In this paper, we first present some sharp bounds in terms of the order and other graph parameters including the diameter, degree sequence, Zagreb indices, Zagreb coindices, eccentric connectivity index and Merrifield-Simmons index for ${\pi}$-index of general connected graphs and trees, as well as a Nordhaus-Gaddum-type bound for ${\pi}$-index of connected triangle-free graphs. Then we study the behavior of ${\pi}$-index upon the case when removing a vertex or an edge from the underlying graph. Finally, we investigate the extremal properties of ${\pi}$-index within the set of trees and unicyclic graphs.

• 대한수학회논문집
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• 제33권2호
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• pp.631-638
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• 2018

Chellai et al. [3] gave an upper bound on the [1, 2]-domination number of tree and posed an open question "how to classify trees satisfying the sharp bound?". Yang and Wu [5] gave a partial solution for tree of order n with ${\ell}$-leaves such that every non-leaf vertex has degree at least 4. In this paper, we give a new upper bound on the [1, 2]-domination number of tree which extends the result of Yang and Wu. In addition, we design a polynomial time algorithm for solving the open question. By using this algorithm, we give a characterization on the [1, 2]-domination number for trees of order n with ${\ell}$ leaves satisfying $n-{\ell}$. Thereby, the open question posed by Chellai et al. is solved.

• 한국전산유체공학회지
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• 제11권4호
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• pp.39-47
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• 2006

In this paper, the authors developed a multidimensional interpolation method inside a finite volume cell in the computation of high-order accurate numerical flux such as the fifth order WEND (weighted essentially non-oscillatory) scheme. This numerical method starts from a simple Taylor series expansion in a proper spatial order of accuracy, and the WEND filter is used for the reconstruction of sharp nonlinear waves like shocks in the compressible flow. Two kinds of interpolations are developed: one is for the cell-averaged values of conservative variables divided in one mother cell (Type 1), and the other is for the vertex values in the individual cells (Type 2). The result of the present study can be directly used to the cell refinement as well as the convective flux between finer and coarser cells in the Cartesian adaptive grid system (Type 1) and to the post-processing as well as the viscous flux in the Navier-Stokes equations on any types of structured and unstructured grids (Type 2).

• Journal of applied mathematics & informatics
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• 제33권3_4호
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• pp.365-377
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• 2015

For a (molecular) graph, the first and second Zagreb indices (M₁ and M₂) are two well-known topological indices, first introduced in 1972 by Gutman and Trinajstić. The first Zagreb index M₁ is equal to the sum of the squares of the degrees of the vertices, and the second Zagreb index M₂ is equal to the sum of the products of the degrees of pairs of adjacent vertices. Let $K_{n_1,n_2}^{P}$ with n₁ $\leq$ n₂, n₁ + n₂ = n and p < n₁ be the set of bipartite graphs obtained by deleting p edges from complete bipartite graph K_n1,n2. In this paper, we determine sharp upper and lower bounds on Zagreb indices of graphs from $K_{n_1,n_2}^{P}$ and characterize the corresponding extremal graphs at which the upper and lower bounds on Zagreb indices are attained. As a corollary, we determine the extremal graph from $K_{n_1,n_2}^{P}$ with respect to Zagreb coindices. Moreover a problem has been proposed on the first and second Zagreb indices.

• International Journal of Aeronautical and Space Sciences
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• 제3권1호
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• pp.74-85
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• 2002

The numerical experiment has been conducted to investigate the unsteady shock wave reflecting phenomena. The cell-vertex finite-volume, Roe's upwind flux difference splitting method with unstructured grid is implemented to solve unsteady Euler equations. The $4^{th}$-order Runge-Kutta method is applied for time integration. A linear reconstruction of the flux vector using the least-square method is applied to obtain the $2^{nd}$-order accuracy for the spatial derivatives. For a better resolution of the shock wave and slipline, the dynamic grid adaptation technique is adopted. The new concept of grid adaptation technique, which is much simpler than that of conventional techniques, is introduced for the current study. Three error indicators (divergence and curl of velocity, and gradient of density) are used for the grid adaptation procedure. Considering the quality of the solution and the numerical efficiency, the grid adaptation procedure was updated up to $2^{nd}$ level at every 20 time steps. For the convenience of comparison with other experimental and analytical results, the case of interaction between the straight incoming shock wave and a sharp wedge is simulated for various flow conditions. The numerical results show good agreement with other experimental and analytical results, in the shock wave reflecting structure, slipline, and the trajectory of the triple points. Some critical cases show disagreement with the analytical results, but these cases also have been proven to show hysteresis phenomena.

• Clinical and Experimental Pediatrics
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• 제48권7호
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• pp.753-759
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• 2005

목 적 : 소아에서 위장관염에 동반된 경련의 발생은 오래 전부터 알려져 왔으나 국내에서는 이에 관한 임상보고가 최근에 추가적으로 발표되고 있다. 저자들은 위장관염과 함께 무열성 경련을 보였던 환아들을 대상으로 하여 이의 임상적 특징 고찰과 발작간기 뇌파를 통해 이 질환의 전기 생리학적인 특징을 규명함으로서 향후 이 질환의 간질 증후군 분류와 진단, 치료 및 예후 예측에 도움이 되고자 하였다. 방 법 : 2001년 1월 1일부터 2004년 6월 30일까지 3년 6개월 동안 급성 위장관염으로 분당차병원 소아과에 입원하여 치료받은 환아 중 과거 신경질환이나 발달 이상의 병력이 없으면서 전해질 이상 및 저혈당에 의하지 않는 무열성 경련이 관찰되었던 67례를 연구대상으로 하였다. 결 과 : 급성 위장관염 입원 환아 2,887례 중 67례(2.3%)에서 무열성 경련이 관찰되었고 대상 환아의 연령은 1개월에서 42개월 사이($18.5{\pm}6.1$)이며 남아가 32례, 여아가 35례이었다. 경련 양상은 전신 강직-간대 발작은 51례(76.1%), 전신 강직 발작은 16례(23.9%) 형태였고 평균 경련시간은 2.8분(20초-40분), 입원 기간동안 평균 경련 횟수는 3.1회(1-13회)이었으나 경련 전후의 신경학적 이상 소견은 관찰되지 않았다. 항경련제는 42례(62.7%)에서 사용되었으며 이 중 23례에서는 2가지 이상의 항경련제 사용 후에 경련이 조절되었다. 뇌척수액 검사는 54례에서 시행되었으며 모두 정상이었고, 15례에서 시행된 뇌영상 검사는 모두 정상이었다. 49례에서 시행한 대변 배양 검사 상 세균은 자라지 않았으며, 로타바이러스는 62례 중 51례(82.3%), 노로바이러스는 18례 중 2례, 아스트로바이러스는 18례 중 1례에서 양성반응을 보였다. 대상 환아에서 시행한 총 73례의 발작간기 뇌파에서 49례(67.1%)는 정상 소견을 보였으나 24례(32.9%)에서는 두정위 일과성 예파(vertex sharp transient)와 구분되는 극파 또는 예파가 수면 I-II기에 중심부에서 관찰되었고 이 중 추적뇌파가 가능했던 6례에서 3례는 정상화가 되었으나 3례에서는 저진폭의 비정형적인 극파나 예파가 지속되었다. 퇴원 후 추적조사는 58례(86.6%)에서 시행되었고 최대 36개월까지 모두 신경학적 후유증없이 정상적인 발달을 보였다. 결 론 : 급성 위장관염과 동반된 양성 무열성 경련은 정상발달을 보이며 건강하던 영유아에서 일회성 또는 다발성으로 발생하며 전해질, 혈당, 뇌척수액 등의 검사가 정상이고, 일부에서는 일시적으로 중심부에서 극파 또는 예파를 보이지만 추적 검사 시에는 정상 또는 호전되는 소견을 나타내며 양성 경과를 취한다. 따라서 이 질환군은 간질 증후군 중 특별 증후군으로 분류될 것으로 예상된다. 또한 정상 발달을 보이는 영유아에서 급성 위장관염과 함께 무열성 경련이 발생하는 경우 반드시 이 질환군을 고려하여야 하며 보호자를 안심시키고, 장기간의 과다한 항경련제 투여와 불필요한 방사선 검사를 피하는 등 그 진단과 치료가 선택적으로 이루어져야 한다.

• 한국컴퓨터그래픽스학회논문지
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• 제17권2호
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• pp.27-36
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• 2011

본 논문에서는 일반적으로 직교 좌표계에서 구현되는 듀얼 컨투어링을 구면 좌표계에서 구현하고 그 특성들을 살펴 본다. 듀얼 컨투어링을 구면 좌표계에서 구현하기 위해서 먼저 팔진 트리(octree)를 구면 좌표계에서 정의한다. 이렇게 정의된 구면 팔진 트리(spherical octree)를 기반으로 하는 듀얼 컨투어링 방식은 SDF(signed distance field) 등의 점진적 폴리곤화에서 직교 좌표계에서의 팔진 트리에 비해 동일한 트리 레벨에서 생성되는 버텍스(vertex) 갯수가 줄어드는 특징을 가진다. 특히 구면에 가까운 모델의 경우 압축 등 이용 가능한 정보가 제한적인 애플리케이션에서 직교 좌표계 보다 세밀하고 부드러운 곡면을 얻을 수 있는 장점이 있다.

• 수면정신생리
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• 제17권2호
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• pp.75-84
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• 2010

The cyclic alternating pattern (CAP) is a periodic EEG activity in NREM sleep, characterized by sequences of transient electrocortical events that are distinct from background EEG activities. A CAP cycle consists of two periodic EEG features, phase A and subsequent phase B whose durations are 2-60 s. At least two consecutive CAP cycles are required to define a CAP sequence. The CAP phase A is a phasic EEG event, such as delta bursts, vertex sharp transients, K-complex sequences, polyphasic bursts, K-alpha, intermittent alpha, and arousals. Phase B is repetitive periods of background EEG activity. The absence of CAP more than 60 seconds or an isolated phase A is classified as non-CAP. Phase A activities can be classified into three subtypes (A1, A2, and A3), based on the amounts of high-voltage slow waves (EEG synchrony) and low-amplitude fast rhythms (EEG desynchrony). CAP rate, the percentage of CAP durations in NREM sleep is considered to be a physiologic marker of the NREM sleep instability. In insomnia, the frequent discrepancy between self-reports and polysomnographic findings could be attributed to subtle abnormalities in the sleep tracing, which are overlooked by the conventional scoring methods. The conventional scoring scheme has superiority in analysis of macrostructure of sleep but shows limited power in finding arousals and transient EEG events that are major component of microstructure of sleep. But, it has recently been found that a significant correlation exists between CAP rate and the subjective estimates of the sleep quality in insomniacs and sleep-improving treatments often reduce the amount of CAP. Thus, the extension of conventional sleep measures with the new CAP variables, which appear to be the more sensitive to sleep disturbance, may improve our knowledge on the diagnosis and management of insomnia.